Translated Copy Of Translated Copy Of [din 3996_2012-09] -- Tragfähigkeitsberechnung Von Zylinder-schneckengetrieben Mit Sich Rechtwinklig Kreuzenden Achsen (1)

September DEUTSCHE NORM 2012 Mechanical Engineering Standards Committee (NAM) in DIN DIN 3996 < ICS 21.200 Replaces DIN 3996: 1998-09Worm Gears with Right Angular Crossing Axes Load Calculation of Cylindrical Calcul de la Capacity of the engrenage à cylindiques à axes orthogonauxvolume Total68 pages DIN 3996: 2012-09 2 Contents Page Preface .......................... .................................................. .................................................. ................................ 6 1 Scope .................. .................................................. .................................................. .. 7 1.1 General ............................................. .................................................. ........................................ 7 1.2 Screw materials ....... .................................................. .. .................................................. .......... 7 1.3 Worm wheel materials ..................................... .................................................. .......................... 7 1.4 Lubricants ..................... .................................................. .................................................. ........... 8 1.5 Flank forms .................................... .................................................. ............................................ 8 2 Normative references .. .................................................. .................................................. ........... 8 3 Symbols, terms and units ................................ ................................................ 9 4 General ................................................. .................................................. .................................. 14 4.1 Basics, Interactions ........... ............................ .................................................. .......... 14 4.1.1 Wear ................................... .................................................. .................................................. 14 4.1.2 Dimple damage ............................................ .................................................. ............................ 15 4.1.3 Eating ................. .................................................. .................................................. ....................... 15 4.1.4 Interaction between seizure and wear .................. ............................................. 15 4.1.5 Interaction between wear and dimples .......................................... ........................ 15 4.1.6 Interaction between wear and broken teeth .................... .......................................... 15 4.1.7 Scoring ... .................................................. ........................... .................................................. 15 4.2 Absolute calculation or relative calculation ............................................ .......................................... 15 4.2.1 Absolute calculation ... .................................................. .................................................. ..................... 15 4.2.2 Relative calculation ........................ .................................................. .................................................. .. 16 4.3 Standard Reference Gear ........................................... .................................................. ............... 16 4.4 Calculation approaches, methods A, B, C ......................... .................................................. ........... 17 4.4.1 Method A ................................. .................................................. .................................................. ... 17 4.4.2 Method B ......................................... .......................... .................................................. ................... 17 4.4.3 Method C ......................... .................................................. .................................................. ........... 18 4.5 Safety Factors .................................... .................................................. .................................. 18 4.6 Reference to Numerical Value Equations ........... .................................................. ................................ 18 4.7 Other information .............. .................................................. .................................................. ........ 18 4.8 Reference to numerical value equations ..................................... .................................................. ...... 18 4.9 Reference to numerical value equations ....................................... .................................................. .... 18 4.10 Other information .......................................... ........ .................................................. ...................... 18 5 Necessary input variables ........................ .................................................. .............................. 19 6 Forces, speeds and characteristic values for the calculation of the load ........ 20 6.1 General ............................................... .................................................. .................................... 20 6.2 Tooth forces ........... .................................................. .................................................. ......................... 20 6.2.1 Application factor KA .................. .................................................. ............................................... 20 6.2. 2 tooth force components ................................................ .................................................. ................ 20 6.3 Sliding speed at the center circle ................................ ....................... ........................................ 21 6.4 Physical characteristics ...... .................................................. .................................................. ..... 21 6.4.1 General

........................................ .................................................. ........................................... 21 6.4.2 Mean Hertzian pressure .................................................. .................................................. ..... 22 6.4.3 Mean lubrication gap thickness ....................................... .................................................. ................... 23 6.4.4 Mean glide path ......................... .................................................. ................................................. 24 6.5 Calculation of mean flank pressure ............................................. .................................. 25 6.6 Calculation of the minimum mean lubrication gap thickness ......... ....................... .......................... 25 6.7 Calculation of the wear path ................... .................................................. .......................... 26 6.8 Calculation of kinematic viscosity .................. .................................................. .............. 26 7 Efficiency and Power Dissipation ............................... .................................................. ................... 27 7.1 General ................................. .................................................. .................................................. 27 DIN 3996: 2012-09 7.2 Overall efficiency ......................................... .................................................. ........................... 27 7.2.1 Method A ................. .................................................. .................................................. ................... 27 7.2.2 Methods B and C ....................... .................................................. ... ............................................... 27 7.3 Total power loss .................................................. .................................................. ................ 27 7.3.1 Method A ............................ .................................................. .................................................. ........ 27 7.3.2 Method B .................................... .................................................. .................................................. 27 7.3.3 Method C ............................................ .................................................. .......................................... 28 7.3.4 No-load power loss ... .................................................. .................................................. ............ 28 7.3.5 Bearing power loss due to bearing load .............................. .......................................... 28 7.3.6 Sealing loss performance ... ...................... .................................................. .................................... 29 7.3.7 Adaptation of the calculation method to own experiments .... ................................................ 29 7.4 Gear efficiency. .................................................. .................................................. ....... 29 7.4.1 Method A ..................................... .................................................. ................................................. 29 7.4.2 Method B ............................................. .................................................. ......................................... 29 7.4.3 Method C ... .................................................. .................................................. ................................. 29 7.4.4 Basic friction coefficient 0T ofgearbox the standard reference....... .................................................. .. 30 7.4.5 Size factor .......................................... .................................................. .................................. 31 7.4.6 Geometry Factor ........... .................................................. .................................................. ................ 31 7.4.7 Material Factor ............................. .................................................. ................................................. 32 7.4.8 Roughness factor .............................................. .................................................. ................................. 32 7.4.9 Adaptation of the calculation method to own test results ....... ........................ 32 7.5 Gear power dissipation ....................... .................................................. ................................. 32 7.5.1 Method A ........... .................................................. .................................................. ......................... 32 7.5.2 Method B ................... ............. .................................................. .................................................. .... 32 7.5.3 Method C ........................................ .................................................. .............................................. 33 8 wear bearing capacity. .................................................. .................................................. ................... 33 8.1 General ................................. .................................................. .................................................. 33 8.2 Wear resistance ............................................... .................................................. ........................ 33 8.3 Expected abrasion wear ....................... .................................................. ......................... 33 8.3.1 Method A ................... .................................................. .................................................. ............. .... 33 8.3.2 Methods B and C ...................................... .................................................. ................................... 33 8.4 Permissible wear removal ........... .................................................. ............................................. 39 8.5 Adaptation of the calculation procedure to own experiments ............................................... ................ 40 9 Pit carrying capacity .................................. .................................................. ................................ 40 9.1 General ............... .................................................. .................................................. .................. 40 9.2 Pit safety ............................. .................................................. .......................................... 40 9.3 Occurring flank pressure .... .................................................. .............................................. ... 41 9.3.1 Method A ......................................... .................................................. ............................................. 41 9.3.2 Methods B and C ............................................... .................................................. .......................... 41 9.4 Limiting value of flank pressure ................... .................................................. ........................ 41 9.5 Adaptation of the calculation method to own experiments ............ ...................................... 42

10 Bend ......... .................................................. .................................................. ..................... 43 10.1 General .......................... .................................................. .................................................. ....... 43 10.2 Bend safety ........................................ .................................................. ................. ........... 43 10.3 Occurring deflection ................................... .................................................. ........................ 43 10.3.1 Method A .................... .................................................. .................................................. ................ 43 10.3.2 Method B ............................ .................................................. .................................................. ........ 43 10.3.3 Method C .................................... .................................................. .................................................. 43 10.4 Limit of deflection ............................................. .................................................. .......... 44 11 Tooth Foot Capacity ..................................... .................................................. ................................ 44 11.1 General ............... ................................................. .................................................. ................... 44 11.2 Toothbreaker security ............................ .................................................. .......................................... 44 11.3 Occurring tooth root stress ..... .................................................. ............................................... 44 11.3. 1 Method A ............................................... .................................................. ....................................... 44 11.3.2 Method B ..... .................................................. .................................................. .................................. 45 11.3.3 Method C ............. .................................................. .................................................. ....................... 45

3

DIN 3996: 2012-09 4 11.4 Threshold value of the nominal shear stress at the tooth root .......... .................................................. ......... 46 11.5 Adjustment of the Berec to his own experiments .............................................. ... 48 12 Temperature safety ............................................ .................................................. ....................... 48 12.1 General ........................ .................................................. .................................................. ......... 48 12.2 Temperature safety with splash lubrication .................................... ........................................... 48 12.3 Oil sump temperature ... .................................................. ............................................. 49 12.3.1 Method A ................................................ .................................................. ..................................... 49 12.3.2 Method B ...... .................................................. .................................................. ........................ 49 12.3.3 Method C ............. .................................................. .................................................. ....................... 49 12.4 Threshold of the oil sump temperature ...................... .................................................. ....................... 50 12.5 Temperature safety with injection lubrication ...................... .................................................. .. 50 12.6 Cooling capacity ............................................. .................................................. ..................................... 51 12.6.1 Method A ....... .................................................. .................................................. ........................ 51 12.6.2 Method B ............... .................................................. .................................................. ..................... 51 12.6.3 Method C ....................... .................................................. ................................................. .............. 51 13 Determining the wheel mass temperature ............................... .................................................. .... 51 13.1 General ........................................... .................................................. ........................................ 51 13.2 Wheel mass temperature with splash lubrication ..... .................................................. ..................... 51 13.2.1 Method A ....................... .................................................. .................................................. ............. 51 13.2.2 Method B ............................... .................................................. .................................................. ..... 51 13.2.3 Method C ....................................... .................................................. ............................................... 51 13.3 Radial temperature with injection lubrication ................................................ ........ ................ 52 Appendix A (informative) Notes on internal forces and force distribution .................... ............ 53 Annex B (informative) Notes on the physical characteristics ........................... ......................... 54 Annex C (informative) Methods for determining the characteristic values .............. ................................................... 55 Annex D ( informative) Lubrication gap thickness according to the EHD theory .......................................... ................ 57 Annex E (informative) Calculation of the wear path ......................... ............................................. 58 Annex F (informative ) calculation example for the Verschleißabtrags ............................................ . 59 Annex G (informative) Notes on tooth-foot bearing capacity ........................................ ................................... 60

Appendix H (informative) Lifetime estimation of dimpled wheel sets ........................ ................... 61 Annex I (informative) Examples .............................................. .................................................. ................... 63 Bibliography ............................. .................................................. .................................................. ........ 68 Pictures Fig. 1 - Consideration of the deviationsthe example of the influencing, center distance- ................. 16 usingvariableFig. 2 - Wheel and wheel rim widths .. .................................................. .............................................. 19 Picture 3 - Zahnkraftkomponenten ................................................. .................................................. ............ 20 Fig. 4 - Basic friction numbers 0T ofgear the standard reference............................ ....................... 31 Fig. 5 - Reference wear intensities according to [9], [10], [15] .......... .................................................. ......... 37 Fig. 6 - Bearing distances .......... .................................................. .................................................. ................ 44 Fig. 7 - Ring thickness factor YK ........................... .................................................. ..................................... 46 Fig. 8 - Service life factor YNL after tests [8] .................................................. ............................ 48 Figure C.1 - Calculated contact lines for an example (projection into the wheel plane) ..... ........................ 55 DIN 3996: 2012-09 5 Page Tables Table 1 - Usual worm wheel materials ........... .................................................. ................................... 7 Table 2 - Symbols, names and units ...... .................................................. ................................ 9 Table 3 - Main data of the standard reference gear ............ .................................................. ............ 17 Table 4 - E-modules a nd cross contraction numbers ................................................ .................................... 25 Table 5 - Material factor YW according to [9], [11 ] and [15] ............................................. .................................. 32 Table 7 - Density for worm gear materials according to [11] ..... .................................................. .................. 40 Table 8 - Dimpling strengths according to [11] ....................... .................................................. ........................ 41 Table 9 -fatigue τShearvaluesFlimT for different wheel materials .............. ..................... 46 Table 10 - Lifetime factor YNL as a function of the number of cycles NL, the material and the permissible quality of the worm wheel ...... .................................................. ................ 47 DIN 3996: 2012-09 6 Foreword This standard has been prepared by working Committee NA 060-34-14 AA, Schneckenverzahnung-. This standard gives instructions for calculating the load capacity of cylindrical worm gears. It does not specify any rules or instructions for sizing, choice of materials and lubricants, etc. The calculation according to this standard covers the load capacity limits of wear, dimples, worm deflection, tooth fracture and temperature. Attention is drawn to the possibility that some texts of this document may affect patent rights. The DIN [and / or the DKE] are not responsible for identifying some or all of the related patent rights. Changes Compared to DIN 3996: 1998-09, the following significant changes have been made: a) the calculation of the physical characteristics according to method C has been refined; b) the efficiency calculation has been extended by basic friction factor curves for wheels made of cast iron materials as well as for bronze wheels with splash lubrication; c) the calculation of wear resistance has been extended by reference wear intensities for different material / lubricant combinations; d) the oil sump temperature calculation according to method C was extended to mineral oils and polyalphaolefins

. Previous issues DIN 3996: 1998-09 DIN 3996: 2012-09 1 Scope 1.1 General This standard gives instructions for calculating the load-bearing capacity of cylindrical worm gear units. It does not specify any rules or instructions for sizing, choice of materials and lubricants, etc. The calculation according to this standard covers the following capacity limits: wear, dimples, screw deflection, tooth breakage and temperature. The scope of different parts of the calculation method of this standard is limited to areas for which practical experience is available (a 三 63 mm, n1 三 60 min-1, vgm <25 m / s). If the user has further experimental results, the scope of application can be extended accordingly by adapting the calculation method, depending on the nature and extent of the own experiments. The scope of this standard covers the following worm and worm wheel materials, lubricants and flank forms. 1.2 Screw materials a) Case hardening steels (eg 16MnCr5 according to DIN EN 10084), case hardened (58 to 62 HRC); b) tempered steels (eg 42CrMo4 according to DIN EN 10083-2), flame or induction hardened (50 to 56 HRC); c) nitriding steels (eg 31CrMoV9 + QT according to DIN EN 10085), gas nitrided. The calculation methods are based on investigations with case-hardened screws made of 16MnCr5 according to DIN EN 10084. For other materials no systematic investigations are available yet. With sufficient surface hardness, hardening depth and core hardness and perfect heat treatment, however, the calculation methods can be transferred to the other materials mentioned above. 1.3 Worm wheel1) materialsThe materials as well as an overview of the experience background are shown in Table 1. Table 1 - Typical worm After wear wheel materials Worm wheel materialDimples Tooth breakage Overtemperature CuSn12-C-GZa) DIN EN 1982 7+ + + + CuSn12-Ni2-C-GZa) + + + + CuSn12-Ni2-C-GC + + - + Cu-Al10FE5Ni5-Ca) oo + + EN-GJS-400-15 DIN EN 1563 o œ + œ EN-GJL-250 DIN EN 1561 o œ + + + verified test results available o test results known œ empirical values known a) sling bronzes should have a homogeneous, lunkerfreies structure in the toothed area. The mean grain size should be less than 150 m. 1) In this standard copper-tin alloys are referred to by the terms commonly used in the field of worm gears bronze or spun bronze, continuously cast bronze, copper-aluminum alloys with the term aluminum bronze. DIN 3996: 2012-09 8 1.4 Lubricants a) mild-alloyed CLP oils according to DIN 51517-3; b) polyalphaolefins; c) polyglycols. 1.5 Flank forms A, N, K, I, C according to DIN 3975.equations The calculationare essentially based on studies with worm gears of flank form I. The results were transferred to worm gears with the other flank forms based on practical experience and similarity considerations. 2 Normative referencesreferenced

The followingdocuments are indispensable for the application of this document. For dated references, only the edition referred to applies. For undated references, the latest edition of the referenced document (including any changes) applies. DIN 3974-1: 1995-11, Tolerances for worm gearing -- Part 1: Fundamentals GearingDIN 3974-2: 1995-11,Gearing Tolerances for worm gearing -- Part 2: Tolerances for deviations of individual determinants DIN 3975-1: 2002-07 , Definitions and Determinants for Cylindrical WormAxes - Part 1: Worm and Worm Gears with Right Angular IntersectingGears DIN 3975-2: 2002-07, Definitions and Determinants for CylindricalAxes - Part 2: Deviation Worm Gears with Right Angular CrossingDIN 3990-1: 1987-12 , load capacity of spur gears - Part 1: Introduction and general influencing factors Calculating theDIN 3990-6: 1994-02, Calculating the load capacity of spur gears - Part 6: Fatigue strength calculation DIN 51517-3: 2011-08, Lubricants - Lubricating oils - Lubricating oils CLP, Minimum requirements DIN EN 1561: 2012-01, Foundry - Cast iron with lamellar graphite; German version EN 1561: 2011 DIN EN 1563: 2012-03, Foundry - Graphitized cast iron, German version EN 1563: 2011 DIN EN 1982: 2008-08, Copper and copper alloys - ingots and castings, German version EN 1982: 2008 DIN EN 10083-2: 2006-10, Heat-treated steels - Part 2: Technical delivery conditions for non-alloyed steels; German version EN 10083-2: 2006 DIN EN 10084: 2008-06, Case hardened steels - Technical delivery conditions, German version EN 10084: 2008 DIN EN 10085: 2001-07, Nitriding steels - Technical delivery conditions, German version EN 10085: 2001 DIN 3996: 2012 -09 3 Symbols, terms and units The symbols used in this standard, their names and units are shown in Table 2. Table 2 - Symbol, designation and unit Symbols Name Unit a Center distance mm aT Center distance of standard referencemm b2 gearTooth width Worm wheel to DIN 3975 mm b2H Wheel width mmWheelwidth b2R rimof worm wheel mm bH Half Hertzian flattening width mm c0, c1, c2 Factors for oil sump temperature calculation according to method D -Submergence factor ck coil Specific heat of the oil for temperaturewith injection lubrication Ws / (kg K) cα calculationApproximate value for the pressure viscosity exponentExternalwheel α m2/ (N) de2 diameter of the wormmm df2 rootmm dm1 center diameter of the worm wheeldiameter of the worm shaft mm dm1T center diameter of the worm shaft of the standardgear reference mm dm2 worm gear center diameter mm dm2Twheel wormdiameter of the standardgear reference mm h tooth height mm hmin minimumm ha grease gap thicknesstooth head height mm hminm mi Minimum mean lubrication gap thickness mgap thicknessgap thickness ofOil level height factor h* Characteristic value for the minimum mean lubricationhT* Characteristic value for the minimum mean lubricationthe standard

reference gearbox koil kP Lubricant constant 1 / K k* Mean heat transfer coefficient W / (m2K) l1 Abstand der Schneckenwellenlager mm 9

DIN 3996:2012-09 10 Tabelle 2 – (fortgesetzt) Formula sign naming unit l11, l12 Bearing clearance of the worm shaft mm dl touch line section mm mn normal module of the screw mm mx axial module of the screw mm At mass removal mg Amlim limit for mass removal mg n1 Speed at the worm shaft minœ1 n2 speed at worm wheel minœ1 p Hertzian pressure; Average value for the entire intervention area N / mm2 p0 ambient pressure N / mm2 pm * characteristic value for the mean Hertzian pressure PmT * characteristic value for the mean Hertzian pressure of the standard Reference gearbox pHm Mean value of Hertzian pressure N / mm2 q shape number of the screw sf2 middle toothfoot thickness tendon of the worm gear tooth in the face cut mm SGB Glide path of the screw flank within the Hertzian flattening of the wheel flank per load cycle in the vicinity of a contact point (local value) mm

sgm mean glide path mm sm2 tooth thickness at the center circle of the worm wheel mm sprocket thickness mm sWm Wear path within the required service life mm s * characteristic value for the mean sliding path ST * characteristic value for the mean sliding path of the standard reference gear unit As tooth thickness decrease mm u Teeth ratio uT Teeth ratio of the standard reference gearbox v2n component of the worm wheel speed perpendicular to the contact line m / s sliding speed between the flanks of the worm and Worm wheel m / s vgm Sliding speed at the center circle in flank direction m / s X2 profile shifting factor of the worm wheel DIN 3996:2012-09 Tabelle 2 – (fortgesetzt)

Formula sign naming unit z1 number of teeth of the worm shaft z2 number of teeth of the worm wheel Ages clear surface of the gearbox m2 Afl Total tooth flank area of worm wheel mm2 AR relevant cooling surface of the wheelset m2 E Young's modulus N / mm2 E1 E-module of the worm shaft N / mm2 E2 modulus of worm wheel N / mm2 Ered replacement modulus N / mm2

Fxm1 axial force on the worm shaft N Fxm2 axial force on worm wheel N Frm1 Radial force on the worm shaft N Frm2 radial force on worm wheel N Ftm1 circumferential or tangential force on the worm shaft N Ftm2 circumferential or tangential force on the worm wheel N dF / db specific load N / mm J0T reference wear intensity JW wear ink Kn speed factor (wheel mass temperature) Ks size factor (wheel mass temperature) Kv dynamic factor KA application factor KHα forehead factor KHβ width factor KW lubrication height parameter Kν viscosity factor (wheel mass temperature) Lh life h NL Number of cycles of the worm wheel NS Number of starts / h P1 power at the worm shaft W 11 DIN 3996:2012-09 12 Tabelle 2 – (fortgesetzt) Formelzeichen Benennung Einheit

P2 power on the worm wheel W PK cooling capacity of the oil with injection lubrication W PV total power loss of worm gear W PV0 no-load power loss W PVz Gear power dissipation with driving worm W P'Vz gear loss power with driving worm wheel W PVD sealing loss W PVLP bearing power loss due to load W Qoil injection quantity dm3 / s Ra arithmetic center roughness m Ra1 arithmetic mean roughness of the worm m Ra1T arithmetic centers roughness of the snail of the standard Reference gear m Rz1 average roughness depth of the screw m SF tooth fracture safety SH pitting security SW wear safety ST temperature safety Sδ deflection safety T1 moment at the worm shaft Nm T1N rated torque at the worm shaft Nm T2 moment on the worm wheel Nm T2N nominal torque on worm wheel Nm WH pressing factor -

WML Material Lubricant Factor WNS start factor WS lubricant structure factor YF form factor (tooth fracture) YG geometric factor (friction coefficient) YK crown thickness factor

DIN 3996:2012-09 Tabelle 2 – (fortgesetzt) Formelzeichen Benennung Einheit YNL life factor (tooth fracture) - YR roughness factor (coefficient of friction) - YS size factor (friction coefficient) - YW material factor (friction coefficient) - Y coverage factor (tooth fracture) - Y gradient factor (tooth fracture) - Zh lifetime factor (dimple) - Zoil Lubricant Factor (Dimple) - Zs Bore Factor (Dimple) - To translation factor (dimples) - ZV Speed Factor (Dimple) - Pressure viscosity exponent m2 / N o generating angle ° L Heat transfer coefficient for diving wheel teeth W / (m2K) m pitch angle at the center circle of the worm ° lim Limit of deflection mm m occurring deflection mm Wlim Limit value of the edge removal mm Wlimn limit value of the flank removal in normal section mm Total efficiency of the worm gear with driving worm - Total efficiency of the worm gear of the worm gear drive - z Gear efficiency with driving screw - 'z Gear efficiency with driving worm wheel - 0M dynamic viscosity of the lubricant at ambient pressure and Wheel mass temperature Ns / m2 0 ambient temperature ° C E injection temperature ° C M wheel mass temperature ° C S Oil sump temperature ° C13

DIN 3996:2012-09

14 Tabelle 2 – (fortgesetzt) Formelzeichen Benennung Einheit

Slim size of the oil sump temperature ° C Overtemperature of the worm wheel tooth above the oil sump temperature ° C oil Temperature difference of the lubricating oil ° C 0T basic friction coefficient - zm mean tooth friction coefficient - 1 transverse contraction number of the screw - 2 transverse contraction number of the worm wheel - 40 kinematic viscosity at 40 ° C mm2 / s 100 kinematic viscosity at 100 ° C mm2 / s E kinematic viscosity at injection temperature mm2 / s M kinematic viscosity at wheel mass temperature mm2 / s ρ0 Profile radius of the grinding wheel mm ρoil Density of the lubricant kg / dm3 ρoil15 Density of the lubricant at 15 ° C kg / dm3 ρoilM Density of the lubricant at wheel mass temperature kg / dm3 ρred replacement radius of curvature mm ρz friction angle of the mean tooth friction coefficient zm ° ρRad density of the wheel material mg / mm3 Low pitting strength N / mm2

Hm mean flank pressure N / mm2 HG limit value of the mean flank pressure N / mm2 F Shear nominal voltage at the tooth root N / mm2 FlimT shear fatigue strength N / mm2 FG Threshold value of the rated shear stress at the tooth root N / mm2 Index min minimum value – 4 General 4.1 Basics, interactions 4.1.1 Wear The procedure given is based on the investigations described in [10] and takes into account practical experience DIN 3996:2012-09 4.1.2 Grübchenschäden

The procedure given is based on the investigations described in [11] and takes into account practical experience. The Hertzian pressure is a significant factor influencing the physical causes of pitting. In addition, however, other influences are important, for. B. the tangential forces and the effect of sliding and rolling movements. These can theoretically not yet be considered in the current state of knowledge. For the above reasons, the limit values of the load-bearing capacity (strength values) are determined by tests on worm gears or by evaluation of corresponding operating results. Strength values resulting from tests on samples (eg from disk tests) only allow relative statements and may only be used for the load capacity calculation if scientific investigations justify this procedure.

4.1.3 Fressen The Fresragagfähigkeit is still not sufficiently explored to specify already standardized calculation equations can. Reference should be made to the experience of manufacturers and users as well as references (see eg [6], [15]). 4.1.4 Interaction between eating and wear Short-term feeding damage to bronze wheels can heal again. This annealing is possible only by wear, but can not be considered at present in the estimation of the wear life according to this standard. 4.1.5 Interaction between wear and dimples

From practical experiments it is known that the dimple development can come to a standstill due to increased wear. Dimples can also disappear again through continuous wear removal. At high wear intensity, ie when the wear resistance limits the life, the pitting but plays only a minor role. Conversely, with significant pitting the wear is not the decisive limit criterion.

4.1.6 Interaction between wear and tooth breakage Wear reduces the tooth thickness of the worm wheel. This is taken into account when calculating the security against tooth breakage. 4.1.7 Scoring At low speeds and high loads, the surface of the worm and worm wheel can be damaged by scoring, which is expected to increase wear (see [1]). This increase in wear does not consider the standard.

4.2 Absolute calculation or relative calculation The calculation methods are partly based on examinations on test gears (standard reference gears, see 4.3), and partly on the experience of manufacturers. Examinations on test drives were carried out largely under different test conditions and secured by practical experience. Although the calculation methods based on the experience of manufacturers capture the main influencing factors, they can not be substantiated physically. The equations used for the calculation methods are given in this standard on the one hand in absolute form (absolute calculation), on the other hand in relative form (relative calculation). 4.2.1 Absolute calculation The absolute calculation is used if there are no own experiments. The accuracy of the recalculation of a gearbox becomes all the better the smaller the differences in geometrical dimensions, operating conditions, materials and lubricants are from those of the standard reference gearbox. 4.2.2 Relative calculation The relative calculation offers the possibility of inserting examination results of the user directly into the individual calculation methods. Thus, the calculation method can be adapted to the own examination results. The closer the transmission to be compared with respect to dimensions, materials, lubricants and operating conditions is with the standard reference transmission or if there is data of its own test transmission for which corresponding test results or experiences exist, the lower the deviation. This is explained using an example based on the influencing variable "axial distance" (see Figure 1 Legend Af relative deviation a center distance

Figure 1 - Consideration of the deviations using the example of the influencing variable, axial distance (based on linear error law) The transmission to be recalculated has the axial distance a1, which deviates significantly from the center distance of the standard reference gear aT. This results in a relative deviation AfT. Furthermore, test results are available with a

gearbox of the center distance aV. When calibrating the calculation method on this center distance now results in the recalculation of a relative deviation AfV (same error law based), which is significantly smaller than the deviation AfT, since the nachenzchnende transmission is much closer to the experimental gear than the reference gear. If possible, therefore, the limit values should be determined from operating experience or tests that are as similar as possible to the respective operating conditions (speed, load, tooth shape, materials, lubricant, etc.). Several methods are permitted for the load capacity calculation or for the calculation of various factors (see 4.4). The use of the calculation method requires a realistic estimation of all influencing factors, in particular of the loads, the environmental conditions, the damage risk (probability of damage), etc. for each case of application. The stated minimum certainties must be increased accordingly.

4.3 Standard reference gearbox In some calculation methods, the equations of the relative calculation are specified in addition to the equations of the absolute calculation. The equations of the relative calculation can be converted into the equations of the absolute calculation if the corresponding values of the standard reference gear are used for the quantities referred to (Index T) (see Table 3).

16 DIN 3996:2012-09 Tabelle 3 – Hauptdaten des Standard-Referenzgetriebes

Center distance aT 100 mm Teeth ratio uT 20.5 Center circle diameter worm shaft dm1T 36 mm Center circle diameter worm wheel dm2T 164 mm Characteristic value for the mean Hertzian pressure pmT * 0.962 (see equation (10)) Characteristic value for the minimum mean lubricating gap thickness hT * 0.07 (see equation (12)) Characteristic value for the mean glide path sT * 30.8 (see equation (14)) Helix material 16MnCr5 case hardened

Worm gear material CuSn12Ni-C-GZ Arithmetic mean roughness of the snail Ra1T 0,5 m Replacement modulus Ered 150 622 N / mm2

4.4 Calculation approaches, methods A, B, C The influencing factors contained in this standard are based on research results and operational experience. It is differentiated according to the factors: 1) Factors determined by the gearing geometry or an agreement. They are going to calculated the specified equations. 2) Factors that take into account a variety of influences and / or are treated as independent of each other (but actually interact with each other in a numerically unpredictable way). These include factors that affect the allowable voltage. The factors can be determined by different methods. If necessary, they are identified by additional indices A to C. Method A is more accurate than method B, etc. It is best to use the most accurate method. For important drives, the method to be used should be agreed between manufacturer and user. In case of dispute, method A is more accurate than B and B is more accurate than C. 4.4.1 Method A The factor is determined by accurate measurement, comprehensive mathematical analysis of the transmission system or reliable operating experience. For this all transmission and load data must be known. In general, method A is rarely used because either the relationships are not sufficiently researched, the operational data is not fully known, suitable measuring equipment is missing or the costs of the analysis or measurements are too high. 4.4.2 Method B The factor is determined by a method that is sufficiently accurate for most applications. The assumptions under which it was determined are listed. It must always be checked whether these assumptions apply to the prevailing circumstances.

17

DIN 3996:2012-09 18 4.4.3 Method C For some factors additional simplified approximation methods are given. The assumptions under which they were determined are listed. It must always be checked whether these assumptions apply to the prevailing circumstances. For the scope of method C for determining the physical characteristic values for the tooth forms mentioned above, see 6.4. 4.5 safety factors

It is of particular importance for the choice of safety factors that the requirements can vary considerably in different fields of application. A distinction is made between (calculated) safety factors against wear SW, against dimples SH, against deflection Sδ, against tooth breakage SF and against overtemperature ST. Certain minimum safety values SWmin, SHmin, Sδmin, SFmin and STmin must not be undercut. Numerical values are given in this standard. The more accurately all influencing factors are recorded, the more reliable is the calculation method and the further the safety values are allowed to approach the minimum values. From these points of view, the safety factors should be chosen after careful consideration of the following factors: 1. How certain are the assumptions regarding the burdens? 2. How certain are the assumptions regarding the operating conditions? 3. What are the consequences of a claim? The safety factors should be agreed between manufacturer and user. For subordinate use cases, the minimum collateral can then be undercut. 4.6 Reference to numerical value equations The numerical equations given in this standard require that all parameters be used with the units specified in Section 3. 4.7 Other notes For the load capacity tests according to this standard, continuous continuous operation is assumed. For startup processes, intermittent operation, changing loads, etc., reference is made to the experience of the gear manufacturer. 4.8 Reference to numerical equations The numerical equations given in this standard require that all parameters be used with the units specified in Section 3.

4.9 Reference to numerical value equations The numerical equations given in this standard require that all parameters be used with the units specified in Section 3. 4.10 Other information For the load capacity tests according to this standard, continuous continuous operation is assumed. For startup processes, intermittent operation, changing loads, etc., reference is made to the experience of the gear manufacturer. 5 Necessary input variables For recalculation at least the following input quantities must be known: 1. Geometry data (see also Figure 2) Axial distance a; Tooth width of the worm wheel b2; Rim width b2R; Center circle diameter dm1,2; Axial module of the worm mx; Number of teeth z1,2; Profile shift factor x2; Generation angle 0. 2. burden Rated torque on worm wheel T2N; Application factor KA; Speed at the worm shaft n1. NOTE b2 according to DIN 3975. Image 2 - Radzahn- and Radkranzbreiten Additionally required: a) For the calculation of the efficiency, the power loss as well as the wear and dimple

safety: Worm and wheel material; Lubricant data oil, 40. b) For the calculation of sag resistance: Distance between the worm bearings l1 and l11, l12. c) For the calculation of tooth root safety: Root diameter df2. DIN 3996:2012-09 19 DIN 3996:2012-09 6 Forces, speeds and characteristic values for the calculation of the load 6.1 General For the load capacity calculation, the following forces, speeds and characteristic values are required, which can be used to describe the tooth flank and tooth root loading mechanisms that are essential for the damage listed in 4.1. When applying the forces acting on the toothing, all forces introduced into the gearbox must be recorded as precisely as possible and taken into account in the calculation. This is especially important for the reliability and accuracy of the calculation. When calculating tooth forces, account must be taken of the external and internal influences on tooth forces (see 6.2.1 and Appendix A). 6.2 tooth forces 6.2.1 Application factor KA The application factor KA takes into account all forces which - beyond the nominal forces described in 6.2.2 are introduced from outside into the gearbox. These additional forces depend on the characteristics of the driving and driven machinery, the masses and spring stiffnesses in the input and output line (eg of shafts and couplings) and the operating conditions. If possible, these influences should be taken into account by a fatigue calculation using a damage accumulation hypothesis (eg according to Miner). Hints for the calculation of the application factor KA from known load spectra is provided by DIN 3990-6. Experience for KA can be found in DIN 3990-1

6.2.2 Components of the toothed force The torques required to calculate the forces listed below are calculated from the nominal torques according to equations (1) and (2): AN11 ‡ KTT = (1) AN22 ‡ KTT = (2) The basis for the load capacity calculation is actually the rated torque of the working machine. This is the operating moment for the heaviest, proper working conditions. It is assumed as a substitute from the nominal torque of the drive motor, if this corresponds to the torque requirement of the machine or another meaningful definition is chosen. The circumferential, axial and radial forces Ftm1,2, Fxm1,2, Frm1,2 on the worm and worm wheel are shown in Fig. 3. Figure 3 - Teeth components DIN 3996:2012-09 6.2.2.1 Slug drives In the driving screw, the peripheral force on the worm shaft is calculated according to equation (3), the peripheral force on the worm wheel according to equation (4) and the radial force on the worm shaft according to equation (5).

F 1tm = ‡ 0002 dT 1m1 = ‡ 0002 d 1m ‡‡ T η 2 ges u = - F 2xm (3) F 2tm = ‡ 0002 dT 2m2 = ‡ 0002 T 1 ‡ d η 2mges u = - F 1xm (4) with ηges according to 7.2 F 1rm = - F 2rm = F 1tm ‡ sin tan (γ m αz) 21 0 + P (5) 6.2.2.2 Worm wheel drives With driving worm wheel, the peripheral force on the worm shaft is calculated according to equation (6), the peripheral force on the worm wheel according to equation (7) and the radial force on the worm wheel according to equation (8). F 1tm = ‡ 0002 dT 1m1 = ‡ 0002 T ud2 1m ‡ η ‡ ges = - F 2xm (6) F 2tm = ‡ 0002 dT 2m2 = ‡ 0002 d 2m bDC 1 ‡‡ 'η ges = - F xm1 (7) with η'ges according to 7.2 F 2rm = - FF 1rm = 2tm ‡ costan (γ m α- 0 P z) (8) 6.3 Sliding speed at the center circle Due to the usually large sliding parts in the circumferential direction of the worm, it is sufficient to use the sliding speed at the center circle vgm in flank direction for the load capacity calculation: v gm = cos ‡ 09819 nd 11m ‡ γ m (9) 6.4 Physical characteristics 6.4.1 General For the assessment of the mean load bearing capacity of worm gears Hertzian pressure, h * for the minimum, it is appropriate to define dimensionless mean lubrication gap thickness and s * characteristic values pm * for the mean glideslope. These characteristics depend only on the geometry of the gearing used. Size, load and lubricant do not affect them. The derivations of these characteristics can be found in [10], [12]. The characteristic values can be determined by methods A, B and C . DIN 3996:2012-09 6.4.1.1 Method A

The physical characteristics are derived directly from measurement and experimental values. However, this is currently not possible. 6.4.1.2 Method B The physical characteristics are with numerical methods, eg. For example, according to [12], [20] (physical basis for the characteristic values see Annex B and Annex C). 6.4.1.3 Method C For the physical parameters approximate equations are used for the solutions obtained with the computer programs according to [12], [17], [20]. The equations apply to the flank form I. However, they can also be used approximately for the flank forms A, K and N. The approximate equations for the edge form C are derived from [15] as well as practical experience. The approximate equations given in 6.4.2, 6.4.3 and 6.4.4 apply to cylindrical worm gearboxes of flank shape I with o from 18 ° to 22 °, x2 from œ 0.5 to + 1, h approximately 2 þ mx, for cylinders -Schneckengetriebe the flank shape C with o from 20 ° to 24 °, x2 from 0 to + 0.5, h about 2 þ mx, and 0 / mn from 5 to 7. The approximate equations provide only meaningful results with cylindrical worms of the flank form I, if the base circle does not fall into the active flank. The approximate equations apply to a wheel width b 2H d m1 m 22 2 (/ 2) 2 (ad e2 / 2) 2 x. For smaller wheel widths, the wear and characteristic values pm * and dimples h * are on the uncertain side. Correspondingly, higher securities or the parameters p and h * are calculated according to method B. 6.4.2 Mean Hertzian pressure The mean Hertzian pressure is a key characteristic for the flank stress (see 4.1). 6.4.2.1 Characteristic for the mean Hertzian pressure - Method A A parameter which describes exactly the complex relationships between the Hertzian pressure and the flank stress can not be given at the moment. 6.4.2.2 Characteristic value for the mean Hertzian pressure - Method B The mean Hertzian pressure used here for determining the characteristic value is calculated assuming the same Hertzian pressure for simultaneously touching the contact lines with computer programs, e.g. Calculated according to [12], [17], [20]. First, the contact lines and then the radii of curvature of the flanks are determined for individual Berührlinienabschnitte. The flanks can then be approached along the contact lines by means of replacement rollers, for which the Hertzian pressure is now determined. In each individual engagement position several teeth are usually engaged simultaneously. The Hertz surface pressure along the associated contact lines is assumed to be constant. The mean value of the Hertzian pressure pHm then results from the Hertzian pressure of all engagement positions. The further calculation according to equation (16) in 6.5 can be done with this average Hertzian pressure. In addition, it is possible to determine a dimensionless parameter p m * from the average Hertzian pressure. This characteristic of the Hertzian pressure depends only on the geometry of the teeth and is independent of the modulus of elasticity of the materials used and of the axial distance (of the size). The characteristic value p m * is used in equation (16) for determining the average edge pressure H m (see example in Appendix C). 6.4.2.3 Characteristic value for the mean Hertzian pressure - Method C From calculations according to Method B, a dimensionless characteristic value for the average Hertzian pressure p m *, which can be used for customary dimensions, was derived. For the edge forms A, I, K and N, equation (10) applies: p m *1794,0

2389,0 a dm1 6872,2 2 0

1

2 23 0761,0 xx 18,3 0536,0 q (10) 00369,0 z 01136,0 9814,44 x

,0 005657 z

For the edge form C, equation (11) applies: 6872,2 2 0

2 z qp m *1401,0 1866,0 a dm1 0595,0 xx 18,3 0419,0 q 00288,0 z 0089,0 1417,35 x

,0 005657 z

1 (11) 6.4.3 Mean lubrication gap thickness The mean lubrication gap thickness is a key characteristic for the calculation of the edge bearing capacity and the efficiency. 6.4.3.1 Characteristic value for the average lubrication gap thickness - method A An exact characteristic value which precisely describes the complex relationships between the lubrication gap thickness which can be varied over the engagement field and the flank stress can not be specified at present. 6.4.3.2 Characteristic value for the average lubrication gap thickness - Method B With computer programs z. For example, according to [12], [17], [20], the minimum mean lubrication gap thickness hminm can be determined from the approach of Dowson and Higginson (see [4]). For this purpose, the tooth flanks are partially replaced by rollers with curvature of the flanks along the individual Berührlinien. Taking into account the speed ratios, the Hertzian pressure and the lubricant properties, minimum lubrication gap thicknesses for the individual roller sections can then be calculated according to [4]. The minimum average lubrication gap thickness hminm is the mean value of all minimum lubrication gap thicknesses dimensionless for characteristic value of all h * contact points. From the minimum average lubrication gap thickness, one can derive for the lubrication gap thickness. This characteristic value depends on the gear geometry. It is independent of the center distance (size), the speed, the speed, the lubricant and the load. The relationship between h * and hminm can be seen in equation (18). For further information see Annex D. 6.4.3.3 Characteristic value for the average lubrication gap thickness - Method C From calculations according to method B characteristic value for the minimum mean lubrication gap thickness, one for h * was derived according to dimensions [15]. z-usable dimensionless DIN 3996:2012-09 For the edge forms A, I, K and N, equation (12) applies

h * 9157,2393,0 )(10 6 z 2 mit B

10947,7( 7 x 2 )038,01(()10927,5 5 qq

6 dm )(9 mm x24 0847,0 0595,00

)576,65 8547,108 z 1 q1 z 1 q921,2943 10291,3 3 BB 1 58,06413 (12) 2 x 1m x Für die Flankenform C gilt Gleichung (13): B dm mm xh * 7904,3511,0 )(10 6 z 2 5 0847,0 0595,00 10947,7( 7 x 2 )038,01(()10927,5 qq )576,65 8547,108 z 1 q1 z 1 q921,2943 10291,3 3 BB 1 58,06413 (13) mit 6x 1m )(9 x 2 6.4.4 Mean glide path The sliding path of a contact point of the screw flank within the Hertz flattening width is a key characteristic for the flank stress. 6.4.4.1 Average slip path characteristic - Method A A parameter which describes the complex relationships between the sliding area variable over the engagement area and the flank stress can not be specified at the moment. 6.4.4.2 Characteristic value for the mean glide path - method B The sliding path sgB is the sliding path of the worm flank within the Hertzian flattening of the wheel flank per cycle in the vicinity of a contact point. From the local quantities sgB, the arithmetic mean is formed over all the contact lines of the entire intervention field. This is z. B. with computer programs according to [12], [17], [20] possible. From this, a dimensionless characteristic value s * for the glide path is defined (see also Annex E). 6.4.4.3 Mean slip path characteristic - Method C From characteristic value calculations s * for that after method B became dimensionless usable for usual dimensions derived mean glideslope. For the edge forms A, IK and N, equation (14) applies: s * tan / 6.5 ‡ 21.078.0 m (14) For the edge form C, equation (15) applies: s * tan / 7.6 ‡ 25.094.0 u m (15) DIN 3996:2012-09 6.5 Calculation of mean flank pressure The mean flank pressure Hm is calculated according to equation (16): Hm 4 ‡ Tp m * 10 ‡‡ 2 3 a 3 E red 5.0 (16) The characteristic value for the mean Hertzian pressure p is to be determined according to 6.4.2 (method B or method C). The replacement modulus of elasticity is shown in equation (17):

E red /) 1 ( Ev 1 225 2 1 /) 1 (Ev 2 22 (17) For different material pairings, the modulus of elasticity E2, the transverse contraction number 2 and the replacement modulus Ered are given in Table 4. Table 4 - E-modules and transverse contraction numbers Worm gear material After E2 in N / mm2 2 Ered in N / mm2 CuSn12-C-GZ DIN EN 1982 88,300 0.35 140 144 CuSn12Ni2-C-GZ 98 100 0.35 150 622 CuSn12Ni2-C-GC 98 100 0.35 150 622 CuAl10Fe5Ni5-C-GZ 122 600 0.35 174 053 EN-GJS-400-15 DIN EN 1563 175 000 0.3 209 790 EN-GJL-250 DIN EN 1561 98 100 0.3 146 955 NOTE Modulus of elasticity and transverse contraction number for worm gear materials Pairing with a steel screw (E1 = 210 000 N / mm2, 1 = 0.3). According to [11], Ered's replacement modulus for the 6.6 Calculation of the minimum mean lubrication gap thickness With some simplifications (see Appendix D), Equation (18) according to Dowson and Higginson [4]: hmmin ‡‡ 21h * c Į 6,0 ‡ 7,0M0 ‡ to 1 39.17.0 ‡ T 2 13.0 ‡ E re d 03.0 (18) The characteristic value for the minimum mean lubrication gap thickness h * shall be determined in accordance with 6.4.3 (Method B or Method C). Instead of the mostly unknown pressure viscosity exponent, a constant approximation value c is used here. c depends on the type of oil. For mineral oil, equation (19) applies: c Į 107.1 28 Nm / (19) For polyglycols, equation (20) applies: c Į 103.1 28 Nm / (20)

DIN 3996:2012-09 For polyalphaolefins, equation (21) applies: c α 104.1 28 Nm / (21) The dynamic viscosity 0M at ambient pressure p0 and wheel mass temperature M is calculated according to equation (22): MM0 v Moil 0001 / (22) The kinematic viscosity M is to be determined from the viscosity-temperature curve of the lubricant at the wheel mass temperature M (determination of the wheel mass temperature M see section 13). The density oilM of the oil at the wheel mass temperature M is calculated according to equation (23): Moil 15oil 1 / (k ρ (M)) 15 (23) Oil15 is the density of the lubricant at 15 ° C (from data sheets of the oil manufacturer). The lubricant constant for mineral oils is shown in equation (24): k ρ 100.7 4 (24) The lubricant constant for polyglycols is shown in equation (25): k ρ 107.7 4 (25) The lubricant constant for polyalphaolefins is shown in equation (26): k ρ 106.7 4 (26) 6.7 Calculation of the wear path The wear path sWm is calculated from the number of cycles on the worm wheel NL and the sliding path of the worm edge within the Hertzian contact on the worm wheel flank according to equation (27):

red L 26 s Wm sNs gm L * Hm E a N (27) The characteristic value for the mean sliding path s * is to be determined in accordance with 6.4.4 (method B or method C). The number of cycles NL of the worm wheel for the lifetime Lh is calculated according to equation (28): LN L h n 1 u 60 (28) 6.8 Calculation of kinematic viscosity The kinematic viscosity for a given lubricant temperature between 0.1 ° C and 100 ° C can be calculated from the kinematic viscosity at 40 ° C and the kinematic viscosity at 100 ° C as follows: 7,010 C (29) DIN 3996:2012-09 mit C 10 A log () 273 B (30) A 129,13 log) 7.0 (log v 40 (log v100 7.0 (31) B log ((log v 40 496,2)) 7.0 A (32) 7 Efficiency and power dissipation 7.1 General The efficiency or the power loss is needed for the calculation of the tooth force components as well as for the calculation of the temperature safety. 7.2 overall efficiency 7.2.1 Method A The overall efficiency is determined from measurements of the total power loss under operating conditions on the gearbox being used. 7.2.2 Methods B and C The total efficiency ges (worm drive) is calculated according to equation (29): ges PPP V22 / (() PPP 1V1 /) (33) The total efficiency 'ges (worm wheel drives) is calculated according to equation (34): 'ges PPP V11 / (() PPP 2 V /) 2 (34) The total power loss PV is determined according to 7.3 (Method B or Method C). 7.3 Total power loss 7.3.1 Method A The total power loss is determined from measurements made on the gearbox. 7.3.2 Method B The total power loss PV is calculated according to equation (35): PPPP V Vz 0V VLP P VD (35) The gear loss power PVz can be calculated from the measured oil sump temperature, if the relationship between the gear loss power and the oil sump temperature from previous tests is known. For the no-load power loss PV0, no accurate calculation according to method B can be specified. In particular, the viscosity dependence can not be detected with sufficient accuracy. For the determination of PV0, method B is set equal to method C.

27

DIN 3996:2012-09

The calculation of the bearing power loss PVLP shall be carried out on the basis of calculation methods of the bearing manufacturer, the calculation of the sealing power loss PVD using the calculation methods of the seal manufacturer. 7.3.3 Method C The total power loss PV is calculated according to equation (35). The tooth power loss PVz is calculated according to 7.5, the no-load power loss PV0 according to 7.3.4, the bearing power loss PVLP due to bearing load according to 7.3.5, the seal power loss PVD according to 7.3.6. 7.3.4 No-load power dissipation The idling power loss PVD is according to [10]: P 0V 1089.0 4 na 1 3/4 (36) Equation (36) is based on equation (37): P 0V 1089,0 2 a aT 28 n 1 3/4 (37) 7.3.5 Bearing loss due to bearing load The bearing power loss PVLP of a complete gear unit due to the bearing load is for an actual bearing of the worm shaft according to [10]: P VLP 03.0 aP 2 44.0 and d2m (38) For a fixed-loose bearing of the worm shaft, equation (39) applies: P VLP 013.0 aP 2 44.0 and d2m (39) Equations (38) and (39) are based on equations (40) and (41). For an attached bearing of the worm shaft equation (40) applies: P VLP 028.0 P 2 a 44.0 u d m2T aT uT d2m (40) For a fixed-loose bearing of the worm shaft, equation (41) applies: P VLP 012.0 P 2 a 44.0 u d m2T aT uT d2m (41) For a plain bearing, the power loss according to the relevant literature, z. For example, [18]. DIN 3996:2012-09 7.3.6 Sealing loss performance The power loss of the radial sealing rings on the worm strongly depends on the actual preload. The gasket loss PVD per radial seal is calculated according to Equation (42): P VD 1078.11 6 and 1m 21 (42) The equation (42) is based on the equation (43): P VD 103.15 3 d 1m 2dm1T 2n 1 (43) The sealing loss on the worm wheel can be neglected because of the low speed. 7.3.7 Adaptation of the calculation method to own experiments If the user has his own power loss measurements, then the calculation method according to 7.3 can be adapted with these. In the equations, the values of the standard reference gearbox are to be replaced by the corresponding values of the own test gearbox. The constants are to be adapted to the own measurements. 7.4 Gear efficiency 7.4.1 Method A

The gear efficiency is determined from the total power loss according to 7.3.1. For this the conditions are missing at the moment. 7.4.2 Method B The gearing efficiency is determined using the equations according to method C from the measured total power loss for the corresponding material-lubricant combination in the original housing under operating conditions. 7.4.3 Method C The gear efficiency z (worm drive) is calculated using equation (44): z (tan m tan arc m tan zm) 29 (44) The gear efficiency z (worm wheel drive) is calculated using equation (45): 'z (tan m tan arc m tan zm) (45) The angle of the arc tan zm in equations (44) and (45) is to be inserted in °. For the mean tooth friction coefficient zm, equation (46) applies: to the RWGST0 YYYY (46) The basic friction coefficient m0T will change to 7.4.4, the size factor YS 7.4.5, the geometry factor YG according to 7.4.6, the material factor YW according to 7.4.7, the roughness factor YR according to 7.4.8. 7.4.4 Basic friction coefficient 0T of the standard reference gearbox The basic friction coefficient 0T depends on the type of oil and the material of the worm wheel. It can be taken from Figure 4 or calculated using equations (47) through (55). a) For wheels made of bronze, injection lubrication with mineral oil: 1.0 () 17.0 30 T0 026.0028.0 v gm 1 76.0 (47) b) For bronze wheels, injection lubrication with polyalphaolefin: 0T 017,0026,0 1 ( v gm 17.0 92.0 096.0 (48) c) For bronze wheels, injection lubrication with polyglycol: T0 02,002,0 1 ( v gm ) 20.0 97.0 094.0 (49) d) For bronze wheels, splash lubrication with mineral oil: T0 0079,0033,0 ( v gm 1) 2.0 55.1 1.0 (50) e) For bronze wheels, polyalphaolefin splash lubrication: T0 0056,0027,0 1 ( v gm 15.0 63.1 096.0 (51) f) For bronze wheels, splash lubrication with polyglycol: T0 0032,0024,0 ( v gm 1) 1.0 71.1 094.0 (52) g) For wheels made of cast iron, lubrication with mineral oil or polyalphaolefin: T0 015,0055,0 ( v gm

1) 2.0 87.0 1.0 (53) h) For wheels made of cast iron, lubrication with polyglycol: T0 015,0034,0 1 ( v gm ) 19.0 97.0 1.0 (54) with vgm according to equation (9). c) Cast iron wheels Legend μ0T Basic friction coefficient vgm Average sliding speed 1 Mineral oil 2 Polyalphaolefins 3 Polyglycols Figure 4 - Basic friction numbers 0T of the standard reference gearbox 7.4.5 Size factor The size factor YS according to [10] takes into account the influence of the axial distance: 5.0 S) / 100 (a Y = (55) Equation (55) is based on equation (56): 5.0 TS) / (aaY = (56) For a <65 mm, in equations (55) and (56), a = 65 mm, for a> 250 mm, a = 250 mm is to be set in equations (55) and (56). 7.4.6 Geometry factor The geometry factor YG according to [10] takes into account the influence of the tooth geometry on the lubrication gap thickness 5,0* G )/07,0( h Y = (57) mit h* nach 6.4.3. Die Gleichung (57) basiert auf der Gleichung (58): 5,0**TG )/( hh Y = (58) a) Bronzeräder bei Einspritzschmierung b) Bronzeräder bei Tauchschmierung DIN 3996:2012-09 31 DIN 3996:2012-09 7.4.7 Material factor The material factor YW according to [11] takes into account the influence of the worm wheel material (see Table 5): Table 5 - material factor YW according to [9], [11] and [15] Worm wheel material to YW CuSn12-C-GZ DIN EN 1982 32 1,0 CuSn12Ni2-C-GZ CuSn12Ni2-C-GC 0,95 CuAl10Fe5Ni5-C-GZ 1,1 EN-GJS-400-15 DIN EN 1563 1,0 EN-GJL-250 DIN EN 1561 1.05 7.4.8 Roughness factor The roughness factor YR according to [14] takes into account the influence of the surface roughness of the screw flank: Y R = 4 Ra 1 5.0 / (59) Equation (59) is based on equation (60): Y R = 4 RRa 1 / Ta1 (60) If the arithmetic mean roughness Ra1 of the worm is not known, but the average roughness depth Rz1 is known, Ra1 = Rz1 / 6. 7.4.9 Adaptation of the calculation method to own test results If the user has his own friction coefficient measurements (eg according to [5]), then the calculation method according to 7.4 can be adapted. The basic friction coefficient 0T given in Fig. 4 is then replaced by the basic

friction coefficient determined in our own tests. The geometry factor, the size factor and the roughness factor then apply to the ratios (index T) of the practical trial gearbox. 7.5 Gear power dissipation 7.5.1 Method A The gear loss power is measured directly or calculated using directly measured friction numbers (eg according to [5]). For this the conditions are missing at the moment. 7.5.2 Method B The gear loss power is determined from the measured total power loss for the corresponding combination of material and lubricant in the original housing under operating conditions by deducting the other loss components listed in equation (35). DIN 3996:2012-09 7.5.3 Method C The gear loss is determined from the gear efficiency. For the gear loss power PVz with driving screw, equation (61) applies: P Vz 1.0 nT 12 u 33 1 1 z (61) with z according to equation (44). For the gear power dissipation P'Vz with driving worm wheel, equation (62) applies: P Vz 1.0 nT 12 u 11z (62) with 'z according to equation (45). 8 Wear resistance 8.1 General By wear, ie continuous material removal, the tooth thickness is reduced. With increasing abrasion wear the danger increases that one of the limits according to 8.4 is exceeded. Endangered are primarily the flanks of lower hardness, ie usually the Schneckenradflanken. 8.2 Wear safety The wear resistance SW is calculated according to equation (63): S w / Wn S minW (63) The limit value of the flank removal Wlimn becomes 8.4, the expected wear removal (flank removal in the normal section Wn) is determined according to 8.3. The minimum wear safety SWmin is given in Equation (64): S minW 1,1 (64) 8.3 Expected wear removal 8.3.1 Method A A more accurate calculation is based on immediate measurements on worm gear sets under operating conditions and a realistic further development analysis of the wear process. 8.3.2 Methods B and C To calculate the flank wear on the worm wheel due to abrasive wear in the physical calculation of h * characteristic values pm *, h * according to 6.4.3, the calculation and s * are required. From s * to 6.4.4. Calculation of normal section pm * takes place according to Wn 6.4.2, the

DIN 3996:2012-09 The following procedure for determining Wn is based on extensive experiments described in [10]. In principle, only the material lubricant combinations specified here can be calculated using the specifications. For materiallubricant combinations not specified here, the calculation method can only be a rough approximation. Even if the data are confirmed by tests, a scatter by a factor of 2 for the wear rate of the run-in gear is to be regarded

as usual. During the break-in period, wear amounts up to eight times higher can occur. For more information on using the calculation method, see Appendix F. The flank wear on the worm wheel due to abrasive wear in the normal section Wn is calculated using equation (65): Wn SJ W Wm (65) The wear path sWm is calculated by equation (27), the wear intensity JW by equation (66). The material lubricant factor WML is given in Table 6. The starting factor WNS is calculated using equation (81). J W WWJ T0 ML NS (66) The reference wear intensity J0T can be determined using Figure 5 or Equations (67) through (77). a) Average degrees of balance for bronze wheels, injection lubrication with mineral oil: J T0 104.2 11 K W 1,3400 10 9 (67) b) Average balances for bronze wheels, injection lubrication with polyalphaolefin: J T0 318 10 12 K W 24.2 (68) c) Average degrees of balance for bronze wheels, injection lubrication with polyglycol: J T0 127 10 12 K W 24.2 (69) d) Average degrees of balance for bronze wheels, splash lubrication with mineral oil: J T0 105.6 11 K W 68.2400 10 9 (70) e) Average degrees of balance for bronze wheels, polyalphaolefin splash lubrication: J T0 558 10 12 K W 91.1 (71) f) Average degrees of balance for bronze wheels, splash lubrication with polyglycol: J T0 223 10 12 K W 91.1 (72) g) Average degrees of balance for aluminum bronze wheels, lubrication with mild alloyed mineral oil: J T0 1045.5 9 K W 23.1400 10 9 (73) h) Average degrees of balance for aluminum bronze wheels, lubrication with polyalphaolefin: J T0 106.16 9 K W 17.11 (74) i) Average degrees of balance for aluminum bronze wheels, lubrication with polyglycol: not operable

34 DIN 3996:2012-09 j) Mittlere Ausgleichsgrade für Räder aus Gusseisenwerkstoffen, Schmierung mit Mineralöl: J T0 1009,0 9 K W 7,3400 10 9 (75) k) Mittlere Ausgleichsgrade für Räder aus Gusseisenwerkstoffen, Schmierung mit Polyalphaolefin: J T0 1009,0 9 K W 7,3400 10 9 (76) l) Mittlere Ausgleichsgrade für Räder aus Gusseisenwerkstoffen, Schmierung mit Polyglykol: J T0 1058,0 9 K W 58,1(77) 35

DIN 3996:2012-09 a) bronze, injection lubrication with integrated mineral oil b) bronze, injection lubrication with polyalphaolefin

c) Bronze, Einspritzschmierung mit Polyglykol d) Bronze, Tauchschmierung mit integriertem Mineralöl

e) Bronze, Tauchschmierung mit Polyalphaolefin f) Bronze, Tauchschmierung mit Polyglykol

Bild 5 – Bezugsverschleißintensitäten nach [9], [10], [15]

36

Mineralöl DIN 3996:2012-09 h) Aluminiumbronze, Schmierung mit Polyalphaolefin

g) Aluminiumbronze, Schmierung mit integriertem

i) Aluminiumbronze, Schmierung mit Polyglykol j) Gusseisenwerkstoffe, Schmierung mit integriertem Mineralöl

k) Gusseisenwerkstoffe, Schmierung mit Polyalphaolefin l) Gusseisenwerkstoffe, Schmierung mit Polyglykol Legende J0T Verschleißintensität in Weg mmAbtrag mm 109

Bild 5 – Bezugsverschleißintensitäten nach [9], [10], [15] (fortgesetzt)

37

DIN 3996:2012-09 38 Tabelle 6 – Werkstoff-Schmierstofffaktor WML Schnecke: 16MnCr5 nach DIN EN 10084 Werkstoff-Schmierstofffaktor WML Schneckenradwerkstoff Nach Mineralöl Polyalphaolefin Polyglykol CuSn12-C-GZ DIN EN 1982 1,61) 1,61) 2,252) CuSn12Ni2-C-GZ 1,01) 1,01) 1,752) CuSn12Ni2-C-GC 4,12) 4,12) 4,12) CuAl10Fe5Ni5-C-GZ 1 1 -3) EN-GJS-400-15 DIN EN 1563 11) 11) 11) EN-GJL-250 DIN EN 1561 11) 11) 11) 1) Streubereich ± 25 % 2) Streubereich ± 30 % 3) nicht betreibbar Der Schmierspalthöhenkennwert KW wird nach Gleichung (78) berechnet: K W h HSmmin WW (78)

The minimum mean lubrication gap thickness hminm is determined according to equation (18). The lubricant structure factor WS is suitable for lubrication with mineral oil as well as for cast iron materials when lubricated with p W S 1 (79) The lubricant structure factor WS is suitable for lubrication with polyglycol as well as for bronze materials when lubricated with po W S 1 35.0 (80) M0 The dynamic viscosity 0M is to be used for the ambient pressure p0 at the wheel mass temperature M. The determination of the w temperature required to calculate hminm is given in Section 13. Since the lubrication gap thickness and the lubricant structure factor WS are significantly influenced by the wheel mass temperatu mass temperature must be determined using the highest possible method (see Section 13). The material lubricant factor WML ac 6 takes into account the influence of the combination of worm wheel material and lubricant on the wear behavior. If materials or lu than those specified here are used, as far as possible, experiments should be carried out to estimate the effects. The result of the given here is then to be understood only as a rough approximation. The starting factor WNS takes into account the influence of the repeated startup on the wear and can be determined as a function of startup operations / hour NS by means of equation (81). W NS 015.01 N S 3 (81) For continuous operation, the number of starts / hour NS = 0 DIN 3996:2012-09 Der Pressungsfaktor WH ist nach [13] für Bronzewerkstoffe: W H 1 für Hm < 450 N/mm2 W H 450 5,4 für Hm 450 N/mm2 (82) Hm Der Pressungsfaktor WH ist nach [15] für Gusseisenwerkstoffe: WH 300 4,1 39 (83) Hm 8.4 Permissible wear removal

The permissible wear can be determined according to different approaches. Of the following approaches a) to d), the limit values abrasions in the normal section Wlimn resulting from the approaches a) and b) must under no circumstances be exceeded, as oth will fail. In case a) the wear leads to a pointed wheel tooth head, with further increasing wear the tooth height is reduced. The wea disproportionately. In case b) the wear leads to such a weakening of the wheel tooth that it comes to the tooth breakage. In cases various reasons, restrictions of wear are required in comparison with cases a) and b). a) The tooth tip of the tooth must never be pointed. This is an outermost limit for the permissible wear. The limit value of the flank normal section Wlimn may therefore be at most as large as the tooth head thickness in normal section. When calculating the toot the tooth tip of the worm wheel, the approximate tooth thickness at the center circle of the worm wheel is assumed. The permissib the normal section thus results for the usual active tooth head height ha = mx according to equation (84): nmw m x cos m 2 tan2 0 (84) b) The minimum tooth fracture safety SFmin becomes the worn condition after the required running time reached. For this, equation (85) applies: Low s cos m (85) It is the tooth thickness decrease due to wear in the course of the required life. For calculation of the mean root thickness of the w in the frontal section sft2 in equation (109), the tooth thickness decrease s specified here must be used. c) The mass removal m may be a predetermined limit mlim (depending on oil change intervals, Bearing lubrication): limewa m lim A f l wheel (86) with total tooth surface Afl: A f l) / (sin m 0 dmz 2 2 1mx arc db 1aH2 cos cos DIN 3996:2012-09 The quantity arc sin (b2H / da1) in equation (87) is to be used in radians. The density of the worm wheels ฀ Rad is shown in Table 7: Table 7 - Density for worm wheel materials according to [11] Worm wheel material After ฀ wheel in mg / mm3 CuSn12-C-GZ DIN EN 1982 40 8.8 CuSn12-Ni2-C-GZ 8.8 CuSn12-Ni2-C-GZ 8,8 CuAl10-Fe5Ni5-C-GZ 7,4 EN-GJS-400-15 DIN EN 1563 7,0 EN-GJL-250 DIN EN 1561 7,0 d) The limit value of the edge offset in the normal section of the worm wheel reaches a predetermined value, which results from the limitation of the backlash. Often Wlim is allowed 0.3 mx; ie: Low 3.0 m x cos m (88)

8.5 Adaptation of the calculation procedure to own experiments The correlations with the equations (67) to (77) or (5) for the wear intensity were determined in tests with the standard reference g secured with tests on other gearboxes. If application-oriented test results are available, the calculation method can be calibrated to the relationship established between wear intensity J0T and the lubrication gap height characteristic value KW = hminm WS. The test conditions should be as similar a operating conditions of the application. For example, translation, size, etc. of the experimental gear should be as close as possibl corresponding values of the considered application. If the flank abrasion of the worm wheel through abrasive wear in the normal section Wn is known from an experiment, the reference can be determined from equations (67) to (77). From equations (67) to (77), a constant (eg, 2.4 10 -11 in equation (67)) can then be will then be more accurate for the considered application than the constants in equations (67) to (). 77)

9 pitting capacity

9.1 General The tooth flanks can be damaged by pits and finally destroyed. Endangered are primarily the flanks of lower hardness, ie usually the Schneckenradflanken. 9.2 pitting safety The pitting safety SH is calculated according to equation (89): S H HG / Hm S minH (89)

DIN 3996:2012-09

The occurring mean flank pressure Hm is determined according to 9.3, the limit value of the flank pressure HG is determined according to 9.4. The minimum pitting safety SHmin is given in equation (90): S minH 0.1 (90) The safety with respect to the transmittable torque is equal to the square of SH. If a calculated safety SH <2 results, it is recommended to check the service life of the gear unit using the approach described in [13] (see Appendix H). 9.3 Occurring flank pressure 9.3.1 Method A The exact calculation of a load relevant for the pitting load bearing capacity can not be specified at present. 9.3.2 Methods B and C As the stress index equation (16) and the mean value for the flank compression average Hertzian Hm pressure is used. It is calculated with the help of pm * according to 6.4.2 either by method B or method C. 9.4 Limit value of the edge pressure The limit value of the edge pressure HG is calculated according to equation (91): HG TlimH ZZZZZ vh su oil (91) The dimple resistance HlimT is shown in Table 8.

Table 8 - Dimple strengths according to [11]

Worm wheel material to HlimT in N / mm2 CuSn12-C-GZ DIN EN 1982 425 CuSn12Ni2-C-GZ 520 CuSn12Ni2-C-GC 520 CuAl10Fe4Ni5-C-GZ660a) EN-GJS-400-15 DIN EN 1563 490a) EN-GJL-250 DIN EN 1561 350a) a) only suitable for velocities vgm <0.5 m / s The pitting strengths specified here are valid for a dimple area of about 50% of the Radzahnflanken. The lifetime factor Zh is calculated according to equation (92): Z h) / 00025 (L h 6/1 6,1 (92) The lifetime Lh is to be used in hours.

41

DIN 3996:2012-09 The speed factor Zv is calculated according to equation (93): v 4 gm 42 Z 5v (93) The sliding speed at the helical pitch of the screw is determined according to equation (9). The size factor ZS is calculated according to equation (94): Z 0003 9002 a (94) Equation (94) is based on equation (95): Zs 3029a aT (95) The translation factor To is calculated according to equation (96): 1 z u u 65,20 for u 5,20 z u 0,1 for u 5,20 (96) The equation (96) is based on the equation (97): 1 Z u u 6uTfür u 5,20 Z u 0,1 for u 5,20 (97) The lubricant factor Zoil is shown in equation (98): Zoil 0.1 for polyglycols Z oil 94.0 for polyalphaolefins (98) Z oil 89.0 for mineral oils 9.5 Adaptation of the calculation method to own experiments If application-related test results on the pitting resistance are available, then the calculation method described in 9.2 to 9.4 can these, ie the pitting strengths HlimT given in Table 8 are replaced by the strength values determined in operating tests for a spe The size factor and the translation factor then apply to the ratios (index T) of the practice trial gearbox . DIN 3996:2012-09 10 Durchbiegung

10.1 General Too strong and in particular constantly changing deflection of the worm shaft results in interference, which can lead to locally very high stresses and can cause uneven wear. 10.2 Bend safety The sag resistance S is calculated according to equation (99): S δ lim / m S δ min (99) The limit value of the deflection lim becomes 10.4, the occurring deflection m is determined according to 10.3. The minimum sag resistance S min is given in Equation (100): S δ min 0.1 (100) The safety with respect to the transmittable torque is equal to the deflection safety S. 10.3 Occurring deflection 10.3.1 Method A The deflection of the worm shaft is measured in the housing during the executed storage. 10.3.2 Method B The deflection of the worm shaft can z. B. taking into account the centering effect of tapered roller bearings using a detailed analysis, eg. As the finite element method, are calculated. 10.3.3 Method C The resulting deflection of the screw is calculated according to [7] using equation (101): m 5 2211 12 2tm 1f 4 1 43 102.3 Fll (tan 2 m arc tan zm tan) 2 0 cos / 2 m (101) ) 1.1 ( dl The bearing distances l1, l11 and l12 are shown in Fig. 6, the angle of arc tan zm in equations (101) and (102) must be set in °. For a symmetrical bearing (l11 = l12) the resulting deflection of the screw can be estimated according to [11] as: m 102 6 Fl 1 32tm (tan 2 m arc tan zm tan) 2 0 cos / 2 m) 1,1 ( d 1f 4 (102)

DIN 3996:2012-09 Picture 6 - Bearing distances 10.4 Limit of deflection The limit of deflection according to practical experience is shown in Equation (103): lim 04.0 m x (103) 11 tooth foot carrying capacity 11.1 General Excessively high tooth root stresses can cause the teeth of the worm wheel to become plastically deformed or break out. 11.2 Tooth-breaker safety The tooth breakage safety SF is calculated according to equation (104): S F FG / F S min F (104) The thrust nominal voltage F is determined according to 11.3, the limit value of the thrust nominal voltage FG according to 11.4. The minimum tooth fracture safety SFmin is given in Equation (105): S minF 1,1 (105) The safety with respect to the transmittable torque is equal to the tooth breakage safety SF. 11.3 Occurring tooth root stress 11.3.1 Method A The Zahnfußspannung is by direct measurement of the stresses on the tooth root, z. B. with the help of Dehnmessketten determined. DIN 3996: 2012-09 11.3.2 Method B Tooth foot tension is determined on the basis of a detailed analysis, e.g. As determined by calculations using

the method of finite elements. 11.3.3 Method C The calculation method is based on a thrust nominal stress approach according to [8]. The bending stress component is recorded in the form factor YF. The shear stress F at the root of the tooth is given in equation (106): F 45 F 2tm mb 2H x YYYY ε F γ K (106) The coverage factor Y is calculated by equation (107), the form factor YF by equation (108), the gradient factor Y by equation (110), the crown thickness factor YK by equation (111). The coverage factor Y takes into account the distribution of the total circumferential force over a plurality of simultaneously engaged tooth pairs. For usual interpretations: Y ε 5.0 (107) The form factor YF takes into account the force distribution over the tooth width, in particular the force increase in the region of the end faces of the worm wheel and the increase in stress of the weakened by wear tooth root. Y F / 9.2 sm 2fx (108) The mean root thickness of the worm wheel tooth in the section sf2 is given in Equation (109): s 2f (06.1 s 2m s (d 2m d 2f tan) 0 cos / m) (109) For wheels with equal tooth thickness and tooth gap width, the wheel tooth thickness at the center circle is: sm2 = mx 2. The tooth thickness decrease s is the decrease of the Zahnfußdickensehne by wear in the course of the required life.

The gradient factor Y takes into account the influence of the pitch angle and the associated outlet-side force increase, which is also present in the run-in gearbox. Y γ cos / 1 m (110) The crown thickness factor YK considers the influence of the ring gear thickness sK on the occurring shear stress F (see Fig. 7 and Fig. 2):

DIN 3996:2012-09 46 bez. Kranzdicke sK/mn Bild 7 – bez. Wreath thickness sK / mn Figure 7 - crown thickness factor YK Y K 0,1 for ms xk / 0,2 Y K 218,5ln043,1 m x sk for 0,1 ms xk / 0,2 (111) The case sk / mx <1 should be avoided. 11.4 Limit value of the rated shear stress at the tooth root The limit value of the thrust nominal stress FG at the root of the tooth is given in equation (112): FG TlimF Y NL (112) The non-ferrous metals shear fatigue strength are qualitatively high-quality for different worm wheel materials shows table 9. For microstructures according to section 1 presupposed. Even in the area of fatigue strength, small plastic deformations occur in bron a deterioration in quality is not accepted, the reduced value according to Table 9 should therefore be used. Table 9 - Shear Fatigue Limits FlimT for various wheel materials Worm wheel material After shear fatigue strength FlimT in N / mm2 reduced thrust Fatigue resistance FlimT in N / mm2 CuSn12-C-GZ DIN EN 1982 92 82 CuSn12Ni2-C-GZ 100 90 CuSn12Ni2-C-GC 100 90 CuAl10-Fe5Ni5-C-GZ 128 120 EN-GJS-400-15 DIN EN 1563 115 115 EN 1561 70 70 Kranzdickenfaktor YK Y K 0,1 für ms xk / 0,2 Y K 218,5ln043,1 m x skfür 0,1 ms xk / 0,2 (111)

Der Fall sk/mx < 1 sollte vermieden werden. DIN 3996:2012-09

The lifetime factor YNL takes into account the higher load capacity in the time-stability domain. Depending on the permissible qua deterioration, larger plastic deformations are permissible here. For a worm wheel up to quality 7 in new condition, the service life factor YNL depending on the worm wheel material and the perm deterioration in quality can be taken from Fig. 7 or calculated using the equations from Table 10. The reduction of the quality of the teeth results from the plastic deformation. For worm wheels of quality better than 7 is based on experience of the manufacturer. The lifetime factor YNL is given numerically Table 10 - Service life factor YNL as a function of the number of cycles NL, the material and the permissible quality of the worm w Material number of cycles NL a) lifetime factor YNL CuSn12-C and CuSn12Ni2-C deteriorated to quality 8 47 below 8.3 ‡ 105 1.25 from 8.3 ‡ 105 to 3.0 ‡ 106 (3 ‡ 106 / NL) 0.16 above 3.0 ‡ 106 1.0 CuSn12-C and CuSn12Ni2-C upon d quality 9 below 2.3 ‡ 105 1.5 from 2.3 ‡ 105 to 3.0 ‡ 106 (3 ‡ 106 / NL) 0.16 above 3.0 ‡ 106 1.0 CuSn12-C and CuSn12Ni2-C when degr below 9.5 ‡ 104 1.75 from 9.5 ‡ 104 to 3.0 ‡ 106 (3 ‡ 106 / NL) 0.16 over 3.0 ‡ 106 1.0 CuSn12-C and CuSn12Ni2-C deteriorate to quality 11, CuAl10Fe5Ni5-C below 4.0 ‡ 104 2.0 from 4.0 ‡ 104 to 3.0 ‡ 106 (3 ‡ 106 / NL) 0.16 over 3.0 ‡ 106 1.0 CuSn12-C and CuSn12Ni2-C deteriorate to quality 12, EN-GJS-400-15 below 1.0 ‡ 104 2.5 from 1.0 ‡ 104 to 3.0 ‡ 106 (3 ‡ 106 / NL) 0.16 over 3.0 ‡ 106 1.0 EN-GJL-250 below 1.0 ‡ 103 2.0 from 1.0 ‡ 103 to 3.0 ‡ 106 (3 ‡ 106 / NL) 0.09 over 3.0 ‡ 106 1.0 a) Number of cycles NL at worm wheel see equation (28)

DIN 3996:2012-09 a) for wheels from EN-GJS-400-15, EN-GJL-250 and CuAl10Fe5Ni5-C 48 b) for wheels made of CuSn12-C and CuSn12Ni2-C,

Deterioration to quality 7 to 12 (individual pitch deviation based on DIN 3974-1 and DIN 3974-2) Legend Deterioration to: 1 Quality 12 2 Quality 11 3 Quality 10 4 Quality 9 5 Quality 8 6 Quality 7 NL Load c Figure 8 - Service life factor YNL after tests [8] 11.5 Adaptation of the calculation method to own experiments If own investigations are available, the strength values given in table 9 can be replaced by strength values of the own examinations. The test results provide transferable according to torque equation (106) Damage limit. From them limit values FG for the nominal thrust voltage can be determined 12 temperature safety 12.1 General As the temperature rises, the service life of the lubricants decreases rapidly, the additives are accelerated and the radial shaft seals are attacked. 12.2 Temperature safety with splash lubrication The temperature stability ST is calculated according to equation (113): S T lim S / S S T min (113) The oil sump temperature determines. S becomes 12.3, the limit of the oil sump temperature Slim becomes 12.4

DIN 3996:2012-09 The minimum temperature stability STmin is given in equation (114):

S minT 1,1 (114) 12.3 Emerging oil sump temperature 12.3.1 Method A The oil sump temperature S is measured under operating conditions or determined from an accurate thermodynamic analysis of the operating temperatures (see [3]). 12.3.2 Method B The oil sump temperature S is calculated according to equation (115): S 0 * tot 49 1 Ak P V (115)

The average heat transfer coefficient k * depends on the structure of the gearbox, but in particular on the screw speed. Basically, the heat transfer coefficient increases with increasing screw speed. The de

distance is more complicated. Transmissions with small center distances of 50 mm to 65 mm have relatively high heat transfer rates. The heat transfer coefficients decrease with increasing center distance

large center distances and speeds over 1 000 rpm. It should also be distinguished between gearboxes with and without fans. For gear units with small center distances, the heat transfer rates for gear units

higher than for gear units without fans. With increasing screw speed and increasing center distance, this tendency is intensified. Measurements were made for gear units with center-to-center spacings of 6 mm, up to 50 screw speeds W / (m2K) of 60 minœ1 to 3,000 minœ1 heat transfer coefficients of. A more precise formula of the average heat transfer coefficient is currently not possible. 12.3.3 Method C

The screw speeds of the oil sump temperature of S 60 m can be roughly calculated from -3 to 3,000 gear units min -1, with center distances of 63 mm to 400 mm, number of teeth ratios 10 to 40, lubrication cuboid well ribbed gray cast iron housing according to equation (116): S 0 c 1 T 2 a3 cc 20 (116) 63 a) coefficients c1, c0 for housing with fan The coefficients c1, c0 for cases with fans are given in Equations (117) and (118): c 1 9.3 100n 1 60 34.0 2 v 40 100 17.0 u 22.0) 48 (a 34.0 (117) c 0 1.8 100n 1 60 7.0 23.0 v 40 100 41.0) 32 (a 63.0 (118)

DIN 3996:2012-09 b) coefficients c1, c0 for housing without fan The coefficients c1, c0 for enclosures without fans are given in equations (119) and (120): c 1 4.3 100n 1 60 43.0 22.0 8.10 v 40 100 0636.0 u 18.0) 4.20 (a 26.0 (119) 0237.0 c 0 915.0 50 23.5 100n 1 60 68.0 28.0 v 40 100 203.2) 36.22 (a (120) Factor c2 for polyglycols: c 2 1 (121) Factor c2 for polyalphaolefins: c 2 1 012.0 ( u) 092.0 745.0 877.82 5 n 1 5,0u (122) Factor c2 for mineral oils: c 2 1 012.0 ( u 9) 092.0 n 1 5.0745.0 and 877.82 (123) When applying these approximate equations, marginal deviations of ± 10 K with respect to excess temperatures are to be expect 12.4 Threshold of the oil sump temperature For the oil sump temperature, the limits of the oil manufacturers must be taken into account. Usually applies for mineral oil: Slim 90 ° C; for polyalphaolefins: Slim 100 ° C; for polyglycols: Slim 100 ° C to 120 ° C. 12.5 Temperature safety with injection lubrication For injection lubrication, the temperature stability ST is calculated according to equation (124): SPPS T VK / minT (124) The total power loss PV is determined according to 7.3, the cooling capacity PK of the oil with the injection quantity Qoil according The minimum temperature stability STmin is given in equation (125):

S minT 1,1 (125)

DIN 3996:2012-09 12.6 Cooling capacity 12.6.1 Method A The cooling capacity PK is measured under operating conditions (see [3]). 12.6.2 Method B The cooling capacity PK is determined from the exact thermodynamic analysis of the inlet and outlet temperatures during operation (see [3]) that determine the cooling capacity. 12.6.3 Method C The cooling capacity PK is calculated according to equation (126): CP K oil oil Q oil (126) with oil according to manufacturer's instructions. The specific heat coil is given for common mineral oils and polyglycols in equation (127): c oil 109.1 3 kg / kg) / ((127) The temperature difference oil of the lubricating oil is 3 K to 5 K without cooler, with cooler 10 K to 20 K. 13 Determination of the wheel mass temperature 13.1 General The wheel mass temperature is needed to determine the wear intensity (see section 8). 13.2 Wheel mass temperature with splash lubrication 13.2.1 Method A The wheel mass temperature M is measured under operating conditions (see [10]). 13.2.2 Method B The wheel mass temperature determines operation. M is derived from a detailed thermodynamic analysis of temperatures in the 13.2.3 Method C The wheel mass temperature M is calculated according to [10]: MS (128) The oil sump temperature S is determined according to 12.3. The excess temperature of the worm gear tooth above the oil sump temperature is shown in equation (129): 1 RL AP Vz (129) The gear loss power PVz is determined according to equation (61) or according to equation (62), the heat transfer coefficient L according to equation (131)

51

DIN 3996:2012-09 The relevant cooling surface of the wheel set R is calculated according to equation (130): dbA R 2mR2 10 6 (130) The heat transfer coefficient L is shown in equation (131): kL c 9401 () 15 n 1 for n 1 150 min 1 L c k1904 for n 1 150 min 1 (131) It is ck = 1 for diving worm wheel; ck = 0.8 for non-diving worm wheel. 13.3 Wheel mass temperature with injection lubrication 13.3.1 Method A The wheel mass temperature M is measured under operating conditions (see [10]). 13.3.2 Method B The wheel mass temperature determines operation. M is derived from a detailed thermodynamic analysis of temperatures in the 13.3.3 Method C

The wheel mass temperature is calculated according to equation (132) on the basis of [10] with knowledge of the injection temperature E: ME 16 Svn 0001 Vz 52 KKK P (132) The speed factor Kn is given in equation (133): 35.0 n 1 K u 5.72 n for n 1 150 min 1 K n u 5.72 35.0 150for n 1 150 min 1 (133) The viscosity factor K is calculated according to equation (134): vK v) 55 / (E35,0 (134) The size factor KS is shown in equation (135): K S) / 160 (a 6.0 (135) The gear power loss PVz is determined according to equation (61) or according to equation (62).

DIN 3996:2012-09

Annex A (informative) Notes on the internal forces and the distribution of power a) Dynamic factor

After measurements of the tooth root stresses at different circumferential speeds [19] it is assumed that the internal dynamic neglected in worm gears of usual accuracy (Kv = 1). b) force distribution

If the toothing has run in, a uniform force distribution over the tooth width and on several tooth pairs engaged is assumed (KH

Variable torques that result in different screw deflections, however, lead to uneven force distribution over the tooth width an lines. Accordingly, higher run-in wear occurs. To ensure that this influence remains small, a minimum sag resistance is requi

53

DIN 3996:2012-09

54

Annex B (informative) Notes on the physical characteristics

The physical causes of the worm wheel damage have not yet been researched so far that all the relevant influencing factors are included approaches for the load-bearing capacity on a physically justified basis. This applies in particular to the wear and the dimpling capacit carrying capacity characteristic values are used, for. B. for the pitting load carrying capacity, the mean flank pressure. It is assumed tha pressure is a major factor influencing pitting. Other influencing factors, such as the coefficient of friction, the speed, the direction and the slip, can not yet be included in the load capacity calculation or can not be substantiated on the basis of the current state of knowledge.

Despite these shortcomings, the characteristics are useful for describing the behavior of worm gears. It must, however, be assumed tha are determined from running tests with worm wheel sets.

With the computers available today, it is quite possible to calculate maximum Hertzian stresses instead of a medium Hertzian pressure occur in individual points of contact. Finite element programs (see eg [2]), which are also able to solve contact problems, allow such ca These programs also allow the consideration of shear stresses and stresses from elevated edge temperatures

However, despite these advances, it is unlikely in the foreseeable future that a bearing load calculation for worm gears with strength value smooth samples will manage. For these reasons, it is currently appropriate to work with relatively simple parameters for the Hertzian pres the strength values from running tests. From this it becomes clear that a load capacity calculation based on these characteristics is only of limited use for optimization calculation handled with caution.

Annex C (informative) Methods for determining the characteristic values Because of the complex geometric conditions, it is not possible to use a closed solution, eg. B. for the Hertzian pressure of a wor However, it is possible to determine a mean Hertzian pressure by numerical methods with the aid of EDP programs. As an appro characteristic values can also be calculated with approximate solutions. The procedure for calculating the characteristic values is briefly outlined below with the help of the computer programs according Using the equations of the generator of the screw flank in the flank shape I, ie the involute in the face section, the contact lines of worm wheel are first calculated. For this purpose, an initial screw position is searched for a tooth. Then, the screw is rotated furth angle until no more contact takes place between the worm tooth and the worm wheel. In general, it is sufficient to calculate the co about 24 screw positions. The entire intervention field is thus detected. Figure C.1 shows the training of the contact lines for an ex Figure C.1 - Calculated contact lines for an example (projection into the wheel plane) For each calculated contact point (generally about 2,000 to 3,000), the following quantities are calculated: a) speeds (sum speed, sliding speed, etc.); b) Hertzian pressure and radius of curvature z. For example, according to [12], [20]; c) lubrication gap thickness according to the EHD theory; d) local glide path. As a rule, it is sufficient to determine an average characteristic value for the entire intervention area. As an exa procedure for calculating the mean glide slope sgm should be shown here; it is the integral mean of the local slipways sgB over th intervention field. For the mean glide path sgm integral mean values are formed: Mean value of the local slip paths sgB in each touch line section dl between two touch points; Mean value over the contact lines (BL) present simultaneously in a screw position;

Average over the calculated screw positions (St) of the intervention area. The mean value for the s

gm 1 St Bl d l St s l (C.1) Bl ( gB )d DIN 3996:2012-09 55 DIN 3996:2012-09 Since the practical calculation - as described above - pointwise with a computer program, it is relatively expensive. However, dimensionless parameters can be derived from the parameters of the Hertzian pressure, the minimum lubrication ga sliding path obtained in this way. These dimensionless sizes have the advantage that they are only dependent on the tooth ge dimensionless parameters for a specific toothing are known, the Hertzian surface pressure, the lubrication gap height and the sli easily determined for any load, speed and lubricant . DIN 3996:2012-09 Annex D (informative) Grease thickness according to the EHD theory According to the approach of Dowson and Higginson [4], the minimum lubrication gap hmin can be calculated for a point of conta equation (D.1): h min 6.1 a 6.0 7.0 M0 E red 03.043.0red) d / d / () 2 / (vn 7.0 bF 13.0 (D.1) By way of derogation from Section 3, the replacement modulus Ered in N / m2, the equivalent curvature radius red in m and the r m must be used in Equation (D.1). A decisive input variable is the dynamic viscosity of the lubricant at ambient pressure and wheel mass temperature, the oil becom 0M. due to the wheel mass temperature of the noteworthy considered. Overtemperatures of the worm wheel opposite From the local quantities hmin, the mean value hminm is formed. hminm is the minimum lubrication gap thickness averaged over engagement area. For the meaning of the mean value hminm it should be noted: Since in the cylindrical worm of the flank shape I approximately in the middle of the wheel flank, the summed velocity v ™ becom conditions of the EHD theory [16] are no longer fulfilled there and in the environment. Last but not least, it is doubtful whether an a permissible in order to grasp the physical event correctly. The considerations show that the calculated lubrication gap thicknesses regarded as a physically measurable quantity. After evaluation of test results, however, the integral mean value hminm used is at least one relevant characteristic 57

DIN 3996:2012-09 58

C The wear travel sWm traveled during the service life is calculated from the number of cycles of the worm wheel NL and the mean sliding path sgm of the worm edge within the Hertzian

The local gli

v * n2the component of v * 2 perpend

v * g the sliding speed between the flanks of

bH half the Hertzian flattening width a

The glideslope size and changes sgB is by itself the flattening width of point to point and point in the Hertzian engagement area. thus dependent on the local load. Size sgB is sgB a local arithmetic me

DIN 3996:2012-09

Annex F (informative) Notes on calculating the wear rate

The calculation method described here was based on experiments with bronze wheels and oils, both of which came from one bat experience, considerable material and oil charge influence is to be expected. Experiments and practical experience show that the to a very large dispersion and classification of unknown lubricants is only possible to a limited extent, even with a known information given here on wear behavior, in principle only the examined pairings can be calculated. Furthermore, the following restrictions must be observed:

The calculation approach applies to uniform operation and running-in gearboxes. High wear levels due to overloading or impermi not taken into account.

The calculation applies to gear units with case-hardened and ground screw and Ra1 = 0.5 m; Larger roughnesses can cause sig of wear, especially during the run-in

59

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60

Annex G (informative) Notes on tooth foot bearing capacity

The calculations apply to the root strength of the wheel teeth when paired with case-hardened 16MnCr5 screws. In experiments on dura strength always break the gear teeth in gears with bronze wheels; on wheels made of gray and nodular cast iron materials usually break t

The fatigue strength values for the plasticizing materials (CuSn bronzes) are already partly in the plastic range. If slight plastic deform these values are expected. Otherwise, the reduced fatigue strength values are used. The yield value was based on average va microstructure formation. The time-constant load for these worm wheel materials is to be understood as a kind of damage line which ru area and is limited by the definition of a permissible quality deterioration (plastic deformation) for the worm wheel. For the more brittle and harder aluminum bronze, the difference between the plastic and the elastic state is less. For gray cast iron and spheroidal graphite, the fatigue and fatigue strength values are in the elastic range.

Determining the tooth root stress takes into account the reduction in the thickness of the root of the tooth due to wear, which weakens th pitting occurs, the wheel tooth can also be weakened thereby. However, this can not be taken into account by a flat-rate calculation appro

DIN 3996:2012-09 Annex H (informative) Lifetime estimation of dimpled wheel sets In the following, a service life estimation of dimpled wheel sets based on wear resistance is presented. The service life of a worm gear can be divided into three characteristic phases: Phase I: pitting formation phase, number of cycles NLI Phase II: Dimple growth phase, number of cycles NLII Phase III: Wear phase, number of load cycles NLIII The achievable load cycles in phases I to III can be combined according to equation (H.1) to a required or a life-determining number of cycles NL: NNNN L LI LII LIII (H.1)

Phase I covers the time until the first pitting. The beginning of the pitting is defined by the pitting characteristic value AP10 = 2%. The number of cycles NLI of the pitting which depends on the respective op determined in accordance with equation (H.2) as a function of Hm and vgm: N LI 10 6 3ln860,01 v gm vref ln666,4078,28exp 520 Hm limH61 (H.2) with vref = 3 m / s, vgm according to equation (9), Hlim from Table 8 and Hm according to equation (16)

The phase II characterized by pitting growth directly follows the pitting phase (phase I) and ends at the latest when a maximum pitting area AP 10, max. For a given (permissible) dimple fraction AP10, zul ( of cycles NLII is calculated according to equation (H.3) (AP10, zul is to be used in percent): N LII (A p10, perm 10) 2 6 212,16 (Hm ) 180 541.1exp Hm 581.0 BC gm ref (H.3) LimH limHvThe following plausibility check must also be carried out. It must apply: NNN LI LII II) L (I (H.4)

With: N II) L (I 103 6 v gm vref ln047,4924,24exp 520 Hm Limh (H.5)

DIN 3996:2012-09

Reduction of the pit surface in Phase III is due to the predominant wear behavior in this phase. The number of cycles of phase determined from equation (H.1). The number of cycles NLIII is only reached if there is sufficient wear resistance. The we determined according to [10]. It should be noted, however, that instead of the wear intensity JW or the flank removal Wn, the we or the flank abrasion WPn according to equation (H.6) or (H.7) must be used. LLIII 0III LLII 0III I0 LLI 0I NS ML WP) (5.0 NN J NN JJ NN J WW J (H.6) The wear intensity J0I is determined by equations (67) to (77), the wear intensity J0III according to equation (H.7). 0I p 0III JW J (H.7) The damage factor WP is calculated according to equation (H.8). 75.0W p 25 KW (H.8) The calculation method presented here is based on experiments that cover the following boundary conditions: Operating mode: constant with previous inlet average flank pressure Hm: 330 ... 620 N / mm2 mean sliding speed vgm: 1 ... 7.5 m / s Center distance a: 65 ... 160 mm Nominal ratio iN: 10 ... 20 Starting roughness Ra1: 0.4 ... 0.5 m Material pairing: 16MnCr5E / CuSn12Ni2-C-GZ Lubrication: Polyglycol ISO VG 220 at oil = 80 ° C For worm gears operated within these constraints, the calculation method shows good results. For other constraints, calcula verified by experiment if possible. DIN 3996:2012-09

Annex I (informative)

Examples

a) Example 1: Calculation of the efficiency and the safety for a standard worm

gear (flank shape I) at a given load

given:

Generation angle: 0 = 20 ° Center distance: a = 100 mm Teeth ratio: u = 41: 2 Axial module of the worm: mx = 4 mm Profile displacement factor of the worm wheel: X2 = 0 avg. Pitch angle: m = 12.53 ° av.

root diameter of the screw: df1 = 26.4 mm ave. Worm wheel diameter: dm2 = 164 mm root circle diameter of the worm wheel: df2 = 154.4 mm wheel width: b2H = 31.0 mm sprocket thickness: sk = 10 mm d bearing: l1 = 150 mm power at the worm wheel: P2 = 4.5 kW speed at the worm shaft: n1 = 1 500 min- 1 required lifetime with continuous continuous operation: Lh = 25,000 h;

Material pairing: worm made of 16MnCr5, case hardened and ground from CuSn12Ni2-C-GZ; Lubrication with splash lubrication (worm wheel immersed), polyglycol; Gearbox with fan, 40 = 220 employees 37 mm = 0.5 m, worm wheel 2 2 / s; Radial shaft seals oil15 = 1,02 kg / dm3;

on the worm shaft.

Searched:

Efficiency and safety at an application factor KA = 1.0

Calculated (general sizes):

Moment at the worm wheel: T2 = 30 / P2 u / n1 = 587.28 Peripheral force according to equation (4): Ftm2 = 7 162.0 N Sliding speed according to equation (9): vgm = 2.9 m / s characteristic value for the me

to Eq. (10): pm * = 0.94703 characteristic value for the min. av. Grease gap thickness according to Eq. (12): h * = 0.06918 characteristic for the mean. Slideway according to equation (14): s * = 30.283 mea equation (16): Hm = 368.52 N / mm2 average glide path according to equation (27): sWm = 813 190 mm

63

DIN 3996:2012-09 64

Calculated (efficiency): Basic friction coefficient according to equation (52): 0T = 0.0245 Mean tooth friction coefficient according to equation (46): zm = 0.0234 with YS = 1; YG = 1.006; YW = 0.95 and YR = 1 gear efficiency according to equation (44): z = 90.0% total power lo equation (35): PV = 0.81 kW gear loss power according to equation (61): PVz = 0.48 kW idling power loss after Equation (36): PV Storage Loss (Employed Storage) According to Eq. (40): PVLP = 0.13 kW Sealing loss power according to equation (42): PVD = 0.046 kW Total efficiency according to equation (33): ges = 84.7% Calculated (wear): Oil sump temperature according to equation (115): with 0 = 20 ° and c0 = 22.94; c1 = 0.206 for housing with fan S = 73.2 ° Wheel mass temperature according to equation (128): with L = 24440 W / (m2K) and AR = 0.00508 m2 M = 77.1 ° min. Mean lubrication gap thickness according to equation (18): at OM = 0.064 Ns / m2 hminm = 0.246 m characteristic value according to equation (78): with WS = 2.623 and WH = 1.0 KW = 0.646 Wear intensity according to equation (72): JOT = 51.347 10œ11 Wear intensity according to equation (66): JW = 89.857 10œ11 W according to equation (65): Wn = 0.731 mm Limit value of wear abrasion (here 0.3 mx cos m, da Wlimn = 1.17 mm not specified) according to equation (88): Wear resistance according to equation (63): SW = 1.6 Calculated (Dimple): Threshold of flank compression according to equation (91): with Zh = 1; Zv = 0.85; ZS = 1 and Zoil = 1 pitting security according to equation (89): HG = 442.76 N / mm2 SH = 1.2 Calculated (deflection): Occurring deflection of the screw according to Eq. (101): m = 0.030 mm Bend limit according to equation (103): lim Bend resistan equation (99): S = 0.08 mm = 2.63 DIN 3996:2012-09 Calculated (tooth fracture): Thrust nominal voltage according to equation (106):

with Ye = 0.5; YF = 1.20 and sf2 = 9.671 mm, taking into account the decrease in tooth thickness due to wear s = Wn / cos m; Wn from equation (65); Y = 1.0244 and YK = 1 65 F = 35.522 N / mm2 Limit value of the rated thrust stress according to equation (112): FG = 90 N / mm2 (no quality deterioration accepted) Tooth-breaker safety according to equation (104): SF = 2.53 Calculated (overtemperature): Temperature safety Slim = 100 ° C) according to equation (113): ST = 1.37 b) Example 2: Calculation of efficiency and service life for a worm gear (Edge shape I) at a given load given: Generation angle: Center distance: a 0 = 20 ° = 65 mm Number of teeth ratio: u = 40: 1 Axial module of the worm: mx = 2.5 mm Profile displacement: X2 = 0.25 avg. Pit Screw diameter: dm1 m = 4.97 ° = 28.75 mm med. Worm wheel diameter: dm2 = 101.25 mm Wheel width: b2H = 22.0 mm Distance between the worm shaf 100 mm Moment at the worm wheel: Speed at the worm shaft: T2 n1 = 300 Nm = 150 rpm Material pairing: worm made of 16MnCr5, worm wheel made of CuSn12Ni2-C-GZ; Lubrication 1 oil15 Radial Sh kg / dm3; Splash lubrication; on the snail. case hardened with polyglycol; and ground 40 = 460 mm 2 / s; 100 with = 60 ram1 2 = / s; 0.5 m, Gearbox without fan, mounted storage, Wanted: Efficiency and service life with regard to wear (continuous continuous operation, pointed wheel tooth head) wit application factor KA = 1.0 (with a small center distance and low drive speed, wear is the limiting load capacity criterion)

Berechnet (allgemeine Größen): Leistung am Schneckenrad: P2 = 30 T2 n1/u = 117,81 W Umfangskraft nach Gleichung (4): Ftm2 = 5 925,93 N Gleitgeschwindigkeit nach Gleichu Kennwert für die mittl. Hertzsche Pressung nach Gl. (10): Kennwert für die min. mittl. Schmierspaltdicke nach Gl. (12): Kennwert Gleitweg nach Gleichung (14): mittlere Flankenpressung nach Gleichung (16): vpgm mhs* * * Hm = 0,23 m/s = 0,962 = 0,0763 = = 73,58 506,50 N/mmCalculated (general sizes): Worm gear power: P2 = 30 T2 n1 / u = 117.81 W circumferential force according to equation (4): Ftm2 = 5 925.93 N sliding speed equation (9): characteristic value for the mean. Hertzian pressure according to Eq. (10): characteristic value for the min. av. Grea according to Eq. (12): characteristic value for the mean Glide path according to equation (14): mean flank pressure according to e vpgm mhs * * * Hm = 0.23 m / s = 0.962 = 0.0763 = = 73.58 506.50 N / mm2 2

DIN 3996:2012-09 66 Calculated (efficiency): Basic friction coefficient according to equation (52): 0T = 0.0457 Mean tooth friction coefficient according to equation (46): zm = 0.0516 with YS = 1.24; YG = 0.96; YW = 0.95 and YR = 1 gear efficiency according to equation (44): total power loss according to equation (35): PV z = 62.5% = 82.3 W gear loss power according to power loss according to equation (36): bearing power dissipation (salaried storage) according to Eq. (40): Sealing loss performance according to equation (42): PPV0 Vz PVLP PVD = 67.5 W = 4.6 W = 8.8 W = 1.5 W overall efficiency according to equation (33): ges = 58.9% Calculated (wear): Oil sump temperature according to equation (116): with 0 = 20 ° and c0 = 6.394; c1 = 0.064 for housing without fan S = 44.0 ° Wheel mass temperature according to equation (128): with L = 4190 W / (m2K) and AR = 0.00223 m2 M = 51.2 ° min. Mean lubrication gap thickness according to equation (18):

at OM = 0,284 Ns / m2 hminm = 0,0927 m characteristic value according to equation (78): with WS = 1.554 and WH = 0.587 KW = 0.0845

Wear intensity according to equation (72): JOT = 2.498 10 -8 Wear intensity according to equation (66): JW = 4.371 10 -8 Permissible wear according to equation (84): Flank removal in normal section from with SWmin = SW = 1.1 Wlimn Wn = 2.1 mm = 1.91 mm Mean glide path from equation (65): Permissible number of cycles from equation (27): sWm NL = 43 658 mm = 2.7 106 load change lifetime from equation (28): with a wear resistance SW = 1.1. Lh = 12 065 h c) Example 3: Calculation of efficiency and service life for a worm gear (Edge shape I) at a given load given: Generation angle Center distance a 0 = 20 ° = 400 mm Teeth ratio u = 49: 4 Axial module of the screw mx = 13.5 mm Profile displacement: X2 = 0.13 avg. Pitch angle: avg. Screw diameter: dm1 m = 21.8 °

= 135 mm med. Worm wheel diameter dm2 = 665 mm Wheel width: b2H = 110 mm Distance of the worm shaft bearing: l1 = 1 000 mm Moment on the worm wheel: Speed at the worm: T2 n1 = = 13 3 000

Material pairing: worm made of 16MnCr5, case hardened from CuSn12Ni2-C-GZ; Lubrication injection lubrication, gearbox without fan, polyglycol, employed 40 = bearings, 220 and mm2 ground / s; 1 radia mmRa2 / s; 1 = 0.5 oil15 on = m, 1.02 of the worm wheel worm. kg / dm3,

DIN 3996:2012-09 Searched:

Density and lifetime for dimples (continuous continuous operation) at an application factor KA = 1.0 (with large center distance and high drive speed, dimples are the limiting load-bearing cri Calculated (general sizes): Output power: Peripheral force according to equation (4): 67 P2 Ftm2 = / 30 T2 n1 / u = 333.4 kW

= 39 097,7 N sliding velocity according to equation (9): characteristic value for the mean. Hertzian pressure according to Eq. (10): characteristic value for the min. av. Grease gap thickness ac characteristic value for the mean Glide path according to equation (14): mean flank pressure according to equation (16): vpgm mh * * s * Hm = 22.8 m / s = 1.026 = 0.0591 = = 17.35 225.57 N / mm2 Calculated (efficiency): Basic friction coefficient according to (49): 0T = 0,021 Mean tooth friction coefficient according to equation (46) with YS = 0.5; YG = 1.088; YW = 0.95 and YR = 1 zm = 0.0108 Gear efficiency according to equation (44): total power loss according to equation (35): PV z = 96.9% = 14.76 kW gear loss power according to equation (61): No-load power loss according to equation (36): bearing power dissipation (in-service storage) according to Eq. (40): Sealing loss performance according to equation (42): PVz PV0 PVLP PVD = 10.04 kW = 1.54 kW = 2.53 kW = 0.644 kW Total efficiency according to equation (33): ges = 95.8% Calculated (Dimple): Survival Factor: with and Zv HlimT = 0.43; = 520 ZS N / mm = 0.95; 2 To = 0.918; Zoil = 1.0 ZH = 1.15 from equation (91) and equation (89) Lifetime from equation (92): with a pitting security SH = 1.0. Lh = 10 890 h

DIN 3996:2012-09

68 references [1] Dinter, R .: FVA Research Project No. 237. Determine and increase the screw carrying capacity limits. FVA No. 518 (1997) [2] Dierich, H .: Further development of the theory for the determination of Hertzian pressures and friction pay in gears of worm gears. Diss. Uni. Bochum (1989) [3] Dolschel, A .: FVA Research Project No. 69 / III. Calculation of power loss and heat Household of non power-split transmissions, FVA No. 625 (2001) [4] Dowson, D .; Higginson, GR: Elastohydrodynamic Lubrication. Oxford: Pergamon Press (1966) [5] Höhn, B.-R .; Michaelis, K .; Stone Rover, K .; Winter, H .: Friction numbers and efficiencies at Worm gears. VDI Report No. 905, pp. 105œ120, (1991) [6] Lange, N .: FVA Research Project No. 141 / II. Schneckenradfressen II. FVA No. 584 (1999) [7] Lutz, M .: Methods for arithmetical determination and optimization of contact patterns on worm driven. Dissertation TU Munich (2001) [8] Mathiak, D .: FVA Research Project No. 70. Gearwheel root strength of worm wheels. FVA-Heft No. 153 (1983) [9] Nass, U .: FVA Research Project No. 205. Worm wheel bronzes. FVA No. 476 (1996) [10] Neupert, K .: FVA Research Project No. 12 / III. Tests on the influence of the size on the efficiency and flank load capacity of taking into account the lubricant viscosity. FVA No. 312 (1990) [11] Niemann, G .; Winter, H .: Machine Elements Vol. III. Correct reprint, Springer-Verlag (1986) [12] Predki, W .: Hertzian pressures, lubrication gap heights and efficiencies of worm gears. Diss. University of Bochum (1982) [13] Rank, B .: FVA Research Project No. 12 / IV. Pit carrying capacity worm gear. FVA-Heft No. 494 (1996) [14] Simon, M .: Measurement of elastohydrodynamic parameters and their effect on the Pit carrying capacity of tempered discs and gears. Dissertation TU Munich (1984) [15] Steingröver, K .: FVA Research Project No. 141. Eating with Worm Gearboxes. FVA-Heft No. 390 (1993) [16] Stößel, K .: Friction numbers under elastohydrodynamic conditions. Dissertation TU Munich (1973) [17] Vill, D .: FVA Research Project No. 155. Computer program package for the calculation of screw Gear Splines, User Guide (1990) [18] Vogelpohl, G .: Reliable plain bearings. Springer-Verlag (1958) [19] Wellauer. JE; Borden, DL: Analysis of factors used for strength rating of worm wheel gear teeth. AGMA 229.18 (1974) [20] Wilkesmann, H .: Calculation of worm gears with different tooth profile shapes. Diss. TU Munich (1974)