B.1.1 Spur Gears With Gearwheels-10

CA LC U L AT I O N S · D ES I G N · A PPL I CAT I O N S B . 1 . 1

Spur gears with gear wheels made from Hostaform ®, Celanex ® and GUR ®

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Contents L Introduction

2.

3.

Requirements for spur gears

Principal specifications 3.1 Straight-toothed spur wheel

6. Calculation

3

7.

7.2

Complementary profile

20

4

7.3

Backlash

21

7.4

Reduction of

Helical spur wheel

5 6

3.4

Internal

7

8.

7

4.1

Materials

7

4.2

Material combinations

7

4.3

Lubrication

9

Straight-toothed

5.1

8.4

10

10

c

5.1.2 Tooth flank temperature 5.1.3 Loadbearing capacity of the tooth

Loadbearing capacity

11 12

root

of the tooth flank

14

5.1.5 Tooth deformation

14

5.3

Helical spur wheels Flow chart for designing spur gears using load characteristic c

5.4

Flow chart for

5.2

using tooth

designing spur strength for designing spur

5.5

5.6

using tooth flank stress Checking tooth deformation

15

17

gears 17

root

Flow chart

gears 18

18

Hostaform acetal

copolymer (POM)

Celanex polybutylene terephthalate (PBT)

Hostalen GUR ultrahigh molecular weight, high density polyethylene (PE-UHMW)

' =

registered trademark

22

24

24 25

26

Food processor attachment with gearwheels made from Hostaform and Celanex

27

9.

Explanation of symbols

28

loadbearing capacity

using load characteristic

5.1.4

Examples of applications 8.1 Pump drive for aquapick 8.2 Planetary gear for disc motor 8.3 Manually operated drive for window

20

10

spur wheels

5.1.1 Determination of

operating noise

verticals

Design calculations for straight-toothed and helical spur wheels

20

notes

4

Addendum modification

combination

19

Selection of module

3.3

toothing

Design

example

7.1

3.2

4. Materials and material

5.

3

10. Literature

29

1. Introduction

2.

Thermoplastic gearwheels have found wide application, particularly in precision drive system for watches, time switches, meters etc. which are produced in large num bers. In such applications, the low production cost made possible by injection moulding is a decisive factor in the choice of plastics.

Spur

Requirements for spur gears gears transmit rotary motion and power between

non-aligned

shafts. This power transmission

also involves The to

speed

requirements

or

generally

torque conversion.

for spur gears vary greatly according operating conditions. In watch

the type of gear and

constant torque transmission with low fric tion loss is necessary. In drives for meters and recording instruments, it is important to avoid jamming as a result

movements,

A

with

the drive

demanding application regard to being transmitted is gearing for small electrical appliances such as food processors, mixers, ironing presses, floor polishers etc. In addition to low cost production, a compelling argument for the use of engineering thermoplastics is their good sliding prop erties which make for silent running and maintenancefree operation. In the Hoechst range of engineering polymers, the Hostaform acetal copolymer grades and Celanex thermoplastic polyester grades offer a wide variety of possibilities for meeting the requirements more

power

of dirt contamination. Power gears

including

drives for

food processors, sewing machines, windscreen wipers, vehicle seat adjustment etc. must be capable of operating

wide temperature range and guaranteeing an adequate service life with low tooth flank wear. Another over a

important requirement in

which has

come more to

years and has actually favoured the is the demand for gears to operate as

recent

plastics as possible.

use

the fore of

silently

of different gears.

These various

special applications in which high chemical resis tance, e. g. against acids, is required, machined gear wheels made from the ultrahigh molecular weight poly ethylene Hostalen GUR are suitable. Hostalen GUR is also notable for its high resistance to abrasive wear. For

Gearwheels made from this material ideal for conditions

mud)

are

likely

to

in

are

which abrasive

therefore also

particles (dust,

get into the gear mesh.

requirements are met by different tooth designs (e. g. cycloidal or round flank toothing in watch mechanisms) and gear fits (quality classes) (see section 7.3).

In power gears, only involute teeth are used following designs are restricted to these.

and

so

the

3.1

The

Principal specifications

3.

following equations apply (see fig. 1):

Pitch diameter

d

Pitch circle

p

=

m

z

=

m

jt

[mm]

(1)

[mm]

(2)

Straight-toothed spur wheel

The

principle specifications

pitch

for

straight-toothed spur (fig. 1) according to the basic tooth profiles in DIN 867 (fig. 2) and DIN 58 400 (fig. 3) are the module m plus associated dimensions and

Tooth thickness

s

the number of teeth

Tooth space

e

Base circle diameter

db

wheels with involute teeth

Fig. on a

1 : Tooth

t.

dimensions, pitch surface and tooth

trace

ft

m

=

=

e

[mm]

(3)

[mm]

spur wheel

=

d

=

m

cos z

[mm]

cos

(4)

left flank

Pressure

angle

n

right flank

pitch surface

right tooth

1 mm the basic tooth pro For module values up to m file in DIN 58 400 (precision engineering) should be used =

and for

m

> 1

mm

the basic tooth

profile

in DIN 867

trace

(general

mechanical

engineering).

profile in DIN 58 400 has advantages over the profile in DIN 867:

the

The basic tooth

-

following

Greater engagement factor because common tooth height hg 2.2 m whereas in the basic tooth profile =

profile for spur wheels with invol ute teeth for general mechanical engineering, DIN 867 Fig.

according to

2: Basic tooth

-

mating profile

*

hg

=

2

m

(figs.

Reduced risk of jamming from dust

getting *|

DIN 867

into the tooth

backlash of SK

=

0.4

opposed to SK

=

0.25

or

2

and 3).

abraded

particles

root because of the greater 0.1 0.6 mm m where m =

m

-

with the basic tooth

as

profile

in DIN 867.

effective flank

a

nnerendofthe effective flank

~2Q H

flank

few

exceptions, it is usually possible to exchange a pair of gearwheels with teeth as specified in DIN 867 for a pair with teeth as in DIN 58 400. Even individual gearwheels with different basic tooth profiles can be paired together. With

In the

angel 2 a

English-speaking world,

(DP) quoted

For conversion

to

module the

profile for spur wheels with invol ute teeth for precision engineering, DIN 58 400

Fig.

3: Basic tooth

mating profile

m

=_[inch]

DP

[inch- H

=

m

profile reference line

effective flank

Example: DP m

=

=

inner end of the effective flank

"flank

angel

10 inch-'

-jL inch 25.4 10

2d =

the diametrical

pitch

in inch"1 is used instead of the module.

2.5

mm

following formula applies: (5)

Table 1 :

of different basic tooth

Comparison

profiles BS 978, Part 1 AGMA 20 706

DIN 58 400

DIN 867

Fig.

Fig.l 1

1

Tooth thickness

n

s

m

2

e

p F

2

Y*-m

=

=

yP

=

p 2V

y*-m

1

1

Tooth space

1

1

=

n

m

2

2.6

1

yr-m

1.4136m

y*-m

=

1

1 -p

=

1

1

T^m={p

1

1

yP

2

1.728

-X-m

m

=

yP 1 -p

for

m

m<0.6

Tooth

h

height

2.45

2.2

3.4m

2.4m

2.25m

m

+ 0.0508

for

m

m>0.6

Addendum ha

1

1

l.lm

m

1.5

1

m

1

m

m

for

m

m<0.6

Dedendum hf

1.25m 1.35

m

1.4m

1.4m

1.2

m

+ 0.0508

0.4m

0.4m

0.2

m

+ 0.0508

for

m>0.6 0.4

m

for

m<0.6

Backlash SK

0.25m

0.25

m

for

m>0.6

Table 1 compares the basic tooth profiles specified in DIN 867 and DIN 58 400, British Standard BS 978 and

Fig.

4: Effect of pressure

angle

on

tooth

shape

the American Gear Manufacturers' Association standard

ftftfb

20706.

With tant.

tooth stress, the tooth width b is impor Root stress af and flank stress OH are inversely pro

regard to

portionate for

a

given

circle of tooth width

tangential

b,

i.

e.

a

force Ft ;

b

on

the

pitch

(see section 5).

The pressure angle is established as 20 teeth (DIN 867 and others). Exceptions

for involute to

this rule

are

sometimes necessary, for example in order to reduce the critical tooth number. The effects of pressure angle on

tooth

shape

are

shown in

fig.

4.

With

increasing pressure angle, the tooth becomes more pointed but at the same time has a higher load-bearing capacity. Sliding conditions are improved.

Fig. 5: Production profile

of helical teeth with

oblique

normal

normal

profile

^=20

3.2

tool

Helical spur wheel

For helical spur wheels, the equations quoted in section 3.1 apply. One additional dimension is the helix angle ß

in the

pitch

circle

v

-iV-

direction

of rotation

(fig. 5). M

The helical teeth

are

produced by angling the

profile (normal module m).

In

transverse

normal

section

generating profile

FsÜSm: h- Pt

1

(see fig. 5), this gives but increased

tooth

a

profile pitch pt

transverse

with

straight

flanks

Fig.

cos

ß

cos

that the flanks of the helical spur wheel in are involutes (fig. 5).

so

of

contact

tool

(6)

it

mt-a

ß

modification, principal dimensions path

m =

Pt:

6: Addendum

A

profile

transverse

section

For the

pitch diameter, d

the

m

z

=

cos

The pressure

following applies:

angle

at

ß

[mm]

is calculated

(7)

by

the

equation

tan

tan t

(8)

=

cos

ß

Fig. 7: Effect of addendum shape

modification

on

tooth

toothing, tooth engagement no longer begins simultaneously over the whole tooth width as with straight-tooth gears but is spread over a finite angle of rotation. In this way, gear engage ment jolts are moderated and noise is reduced. The total As

a

result of the helical and ends

ratio er, i. e. how many teeth are engaged at the same time, is found from contact

on

average a

positive addendum modification

er

where ea

=

=

transverse contact

of

path

contact to

=

ratio

overlap ratio, Sß

=

ratio of the

the base

b

i

Bß

(9)

ea + %

tan

=

pitch, fig.

6

8 CL

(10)

Pt b normal teeth

3.3 Addendum

modification

The addendum modification is characterized

by the

dimensionless addendum modification coefficient

related

the module. The distance of the

x

profile (fig. 6) of the basic rack tooth profile from the rack pitch line of engagement WW is x m. to

centre

line MM

Addendum modification is carried

out to

c

negative addendum modification

-

-

-

specified centre distance balance the stresses between pinion and gearwheel avoid weakening the tooth root by an undercut (fig. 7 d) when there is a small number of teeth. adapt a pair of gearwheels

to a

The addendum modification coefficient is

positive

when

the addendum modification increases tooth thickness. d undercut

E

With

-

-

-

increasing

addendum modification,

4. Materials and material

combination

the outside diameter of the gearwheel da increases the flank curve is smaller and the tooth

tip

is

more

pointed (fig. 7). 4.1 Materials

3.4 Internal

toothing

Table 2

gives

range which

internally toothed wheel corresponds to a negative spur wheel. Hence helical toothing and addendum modi fication are possible.

a

survey of the

can

be used for

plastics in the gearwheels.

Hoechst

The

geometry of spur wheels remains valid if the number of teeth t and the The formulae for

calculating the

internally toothed wheel derived from as minus quantities and the addendum modification coefficient when increasing tooth thickness is definied as a plus (fig. 8). diameter of the

this

are

Depending on the ditions, the

most

requirements and operating con properties may be

gear

desirable material

rigidity for high tangential force and low peripheral speed toughness for jolt-stressed gears, e. g. reciprocating

-

-

motion

inserted

wear

-

resistance for

dry running.

Frequently silent gear operation is an additional priority. Fig.

8: Involute internal teeth

4.2 Material combinations

gearwheels slide against each other during engagement. The sliding speed created is not constant. It has a maximum value at the beginning of engagement, drops to 0 at the pitch point and then increases again to the end of engagement. The sliding speed vg, which averaged over tooth engagement is about 0.2 times peripheral speed v, causes friction

The teeth of

a

pair

of

between the tooth flanks.

vg

0.2

=*

v

dv

Through the use of internal toothing, it is possible to design planetary gears in which power transmission is spread over several planet wheels so that the relatively low strength and rigidity of plastics as compared with metals can be partially offset.

(11)

[m/s]

it

n

(12)

=

60

where d [m]

plastic gearwheels generally receive a once-only lubrication during assembly or, if this is not possible, run dry. Both in the case of solid/solid friction between dry-running gearwheels and the mixed friction to be expected with once-only lubrication, the combina tion of materials used has an important effect on the Spur

gears with

amount

of friction and

It is therefore

on wear.

important

to

aim for material combina

tions which

-

-

-

ensure

low friction and smooth,

even

sliding

show the least

possible wear have high thermal conductivity to heat quickly.

remove

frictional

Table 2 : Survey of the Hoechst Material

engineering plastics

Elastic

used for

gearwheels

Dimensional

Coefficient

modulus

stability

of linear

DIN 53 457

under heat

expansion

DIN 53 461

(method A)

Notes

special properties

on

material

between 20 and 100 C

DIN 53 752 N/mm2

C

K-i

Hostaform C 9021

2950

104

1.1 -10-4

standard

Hostaform C 2521

2750

101

1.1 -10-

withstands

Hostaform T 1020

2700

97

i.i-io-4

Hostaform C 27021

3000

107

1.1 -10-"

void-free parts increased rigidity,

Hostaform C 13021

3000

106

1.1 -10-4

Hostaform C 13031

3200

113

1.1 -10-4

}

grade jolt

basic

grades corresponding to required melt flowability

stress

small gear

dimensions

Hostaform C 902 IK

2950

99

i.i-io-4

reduced abrasion

Hostaform C 9021 TF

2400

98

1.1-10-*

running

Hostaform S 9063

2100

89

1.5-10-0

I

Hostaform S 9064

1700

83

1.6 -10-

1 low noise,

Hostaform S 27063

2200

91

1.5- 10-"

[ reduced abrasion,

Hostaform S 27064

1800

87

1.6-10-4

>

Celanex 2500

2600

60

1.3 -10-"

good sliding partner

850

47

2.0

low abrasion, chemical resistance

Hostalen GUR

Rapid or

removal of frictional heat is achieved if Hostaform paired with steel gearwheels. The steel

Celanex is

wheels should be hardened; the roughness height Rz of the tooth flanks should not exceed 2 //m, to minimize the

plastic gearwheel. Wear can be further redu plastic/steel gearwheel combinations if the modified grades Hostaform C 9021 K and C 9021 TF with improved sliding properties are used instead of the standard grades. If the gear only has to transmit low power inputs or if the total operating period is relatively short, gearwheels made from unhardened steel or nonferrous metals (brass, aluminium alloys) can be paired with plastic gearwheels. wear on

10-4

While for

even

in

dry

low friction coefficient

impact modified grades,

jolt stressed gearwheels

high-speed

for Hostaform

plastic should generally be plastics, in watches, meters and time switches, gearwheel pairs made from the same plas tic are frequently encountered although their tribological properties are poorer. paired

with steel

or

gears,

other

ced with

Surprisingly, wear properties are improved by the impact modification in the Hostaform S grades. This applies both to the combination of impact modified

grades with grades. Fig.

each other and their combination with basic

9 shows tooth flank

cated

gearwheel

wear

combinations

of the

Hostaform/Celanex and

Zj

nations exhibit

for different material combinations.

of solid/solid

plastic/steel

Hostaform/polyamide combi good sliding properties under conditions

or

mixed friction. In

combinations

comparison with they give rise to lower friction

coefficients and reduced wear. Their tendency to stickslip is also much reduced. On the other hand, the risk of overheating (melting of tooth flanks) is greater.

=

50/z2

=

54 and z,

=

40/z2

following unlubri-

(module =

2

mm) :

50 after 107 load

cycles Compared with the

combination Hostaform C 9021 /Hostaform C 9021, wear of the combination Hostaform S 9063/Hostaform S 9063 and Hostaform S 9064/Hostaform S 9064 is

negligibly

small.

Tooth flank

wear

of the combinations Hostaform

C 9021/Hostaform S 9063 and Hostaform C 90217

Hostaform S 9064 while combinations is still

slightly higher than in the above significantly lower than in the com-

bination Hostaform C 9021/Hostaform C 9021. In the combinations Hostaform C 9021/Hostaform S 9063 and

Fig.

9:

wear

Hostaform C 9021/Hostaform S 9064 in each

case

only

the

on

gearwheel

wear

Effect of

place impact

At 7

tj

0.25

steel, only

a

slight

pared with the

reduction in

modified

grades

is evident

wear

combination of basic

grades

with

10 shows the average

as com

|

g

with steel.

equilibrium temperature

wear

wheel 1: 0.55

wear

wheel 1 : 0.53

50/z2

=

Zj

=

0.20

0

0

un

Tfr

H

-^

occurs

u->

iTi

II

||

^

=

107 10 m/s

v

0

O

O

^

:

^ U"}

tT!

O 1/1

II

II

-

IÏ

-

-

<*ï

fi

§

g

0

TO

-* lA

o

Lfi

II

I

II

g Lf>

H

T*" in

o^

Om i\j

of materials. The lowest temperature in the combination Hostaform C 9021 /steel

pairings

§

§

sÖ

47*1

^

&

§

S

3

O->

o^

a--

U

U

^

^

^

5Ç

^

U

U

U

_^--_ s3

*1 ^D

r^

sD

O

\D O

CN

rf*$O O 00 o^ o

f^

O O>
c/5

c/i


o

0.05

**,

com

s

*

.


1

O

O

I

O ^

^

O"-

j

C/ï

.

s

g^-^. v>

rTj U

0

"^J

c/5

.

owing to the good thermal conduction of the steel gearwheel. The slightly higher temperatures in the

mm

19 N/mm2;

^t

"0

<^

different

mm

mm;

ul

-$ *">

of

54 with

wheel 2: 0.37 wheel 2: 0.43

dry-runni ig operation

o

the tooth flank in the combination

mm;

=2mm;N

m

0H

0.15

Fig.

tooth flank

U.JU

mrn

impact

on

took

made from

modified Hostaform. In the combination of the

modification

impact

in Hostaform/Hostaform combination

M

U

1 ii

rSi

s ~

!>

O

^

ov

en

*o

v)

r~i i i

1

|

binations Hostaform S 9063/steel and Hostaform S 9064/steel indicate the increased friction coefficient

of the

impact

modified

grades

when

sliding against

steel.

The combinations Hostaform C 9021/Hostaform S 9063

and Hostaform C 9021/Hostaform S 9064 (Nos. 4 and behave in a similar way, reaching a higher equilibrium

Fig. 10: Average equilibrium temperature of the tooth flanks in Hostaform/steel and Hostaform/Hostaform combinations (<JH flank stress,

see

section

5.1.4)

5)

temperature than the combinations Hostaform S 9063/ Hostaform S 9063 and Hostaform S 9064/Hostaform

10010

c

OH

=

30 N/mm2

S 9064. 11

90-

1

4.3 Lubrication

s gears with

plastic gearwheels are only rarely provided with splash lubrication because the cost of sealing the gear housing is high. The normal procedure is to give the gears a once-only grease lubrication during assembly. Although the grease is forced out of the tooth flanks during operation or is hurled out at high periphe ral speeds, the reduction in wear as compared with dryrunning gearwheels is considerable. Spur

1 1 shows the percentage

Fig. of

a

wear

Hostaform

under

i

I

OH

19 N/turn^

4

H

5* 60-

50

-

40

-

30

-

>

OH

=

25 N/mm2

7<

.

OH

=

19 N/mm2

steel

gearwheel paired gearwheel dry-running conditions and with initial once-only

lubricated one

gearwheel

a

conditions,

combination after 2

third of the value in

wear

of the

107 load is

dry-running operation. 20

The lubricants used

are

3.08

mineral-oil based greases

operating temperatures above rigidity decline as a result.

65 C.

Hardness and

=

=

m

=

b

=

50 54 2 mm 15 mm

6.7

to

ral-oil based greases at all temperatures. With Hostalen GUR, reversible diffusion of oil into the surface is likely

Wheel l:z,

Wheel2:z2 -

usually regulate consistency (multi-purpose greases). Through the use of special additions, adhesion of the grease to the plastic gearwheel surface can be improved. Hostaform and Celanex are resistant to mine with lithium soap

at

=

-

of the tooth thickness

with

lubrication. Under the chosen

only

8-

10

15

N-

m

20

Torque Md Wheel 1 1

2 3 4 5 6

S S C S S S

9064 9063 9021

9064 9063 9064

Wheel 2 steel steel steel C9021 C9021 S 9064

7 8

9 10 11

Wheel 1 S 9063 S 9064 C9021 C9021 S 9064

Wheel 2 S 9063 S 9064 C9021 C9021 S 9064

Fig.

Percentage decrease

11:

wear

against

in tooth thickness due

made from Hostaform

gearwheels gearwheels

in

to

5.

running

Design calculations for

straight-toothed ana helical

steel

spur wheels 5.1

20

A

Straight-toothed spur wheels

correctly designed pair of gearwheels

cated with oil

or

10

or

fracture when overloaded. therefore be based

e4ubncated^^'aSSembly 0.5

1.5

1.0

Number of load

2.0 -107

meet

oils. It has been observed that diester oils

swelling

of Celanex and increase

Celanex combinations.

wear

the tooth root, section

dry-running gearwheels, on the other hand, the wear on the intermeshing teeth is the predominant factor; there is also increased thermal stress owing to the

only a rough design calculation is required for the gearwheels, the distinction is not necessary. It is suffi cient to check loadbearing capacity with the c value or to use the c value to estimate the required dimensions of the gearwheel for a specified power input (section 5.1.1). If

cause

in Hostaform/

silicone oils have

Methyl softening effect in both Hostaform and phenylmethyl silicone oil has no effect.

on stress at

calculations should

greater friction. In this case, flank stress is the criterion which should be calculated, section 5.1.4.

cycles

resistance

cone

Design

5.1.3. With

higher requirements with regard to oxidation (ageing resistance), service temperature range or physiological safety (e. g. food transport or packaging), greases based on synthetic oils are used. Suitable oils include alkoxyfluoro oils, polyglycol ether oils and sili-

To

made from

Hostalen GUR, once-only lubri grease, will normally fail due to tooth

Hostaform, Celanex

a

Celanex while

symbols chosen here correspond to DIN 3990 "Calculating the loadbearing capacity of spur and bevel gears" and largely conform to those used in the VDI Guideline 2545 (VDI-Richtlinie 2545) "Gearwheels made from thermoplastics".

The

5.1.1 Determination

of loadbearing capacity using

load characteristic The load characteristic bles. It is

dependent

c

on

c

takes

account

of several varia

the combination of materials

used, loading conditions and tooth geometry. It is also influenced by lubrication, temperature and peripheral

speed.

There is

no

mathematical

relationship

between

these factors however. The load characteristic and is

c

is deter

valid for

only gearwheel experimentally pairs operating under similar conditions. In all other cases, deviations are likely but experience has shown mined

them

to

be small.

The load characteristic

c

10

=

c

is defined

T^-Seperm. bk'P

as:

[N/mrrf]

(13)

where

F, p

=

=

_Mi m

tangential force [N]

bk P

1000

9549.3

^=-1^r

P

^

[N-mm]

=

-n

(15)

30 9.549

pitch

[N m]

torque

Fig.

radius

[mm] power input [W] speed [min"']

n

1 2 shows

Hostaform

$a

temperature in the immediate ment of the gear [C]

/I P

A

dynamic friction coefficient of the mating materials power input [W] surface area of the gear housing [m2]

bk

smallest tooth width [mm]

module [mm] number of teeth (gearwheel 1 zli2 i tooth ratio z2/zt gear

P -

r

tooth flank temperature of gearwheel 1 wheel 2 [C]

or

gear

operating environ

m

n

P

$!,2 (14)

pitch [mm] (equation 2) module [mm] smallest tooth width [mm]

n

m

M

here

w

kz k3

peripheral speed [m/s] auxiliary value auxiliary value [K mVW]

K

index

v

or

2)

values for the different

permissible c grades as a function

of the number of load

The

following empirical

k2

2.5

values should be used:

cycles. 5.1.2 Tooth

strength dent. High tooth tooth The

root stress

permissible

k2 k3

temperature-depen reduce the permissible

7.0

Hostaform/Hostaform C

=

0

oil-lubricated gear /open gear with free

k3

=

0.04

depends among other factors on tooth flank temperature. In gearwheels with periphe ral speeds exceeding 5 m/s, the tooth flank temperature

k3

=

0.17

x

=

0.4

is calculated

x

stress

as:

to

0.13

=0.75

partially open air

cannot

^^a+0.136.P^.AiM7100.k2 5

closed gear Hostaform

freely

(basic grades) to

polyamide)

+63JE3l

H

J

/J.

=

0.20

,

=

0.18

Hostaform

^

=

0.05

A

[C] (16) B: It should be noted that in this numerical value

dry running

polyamide

Hostaform/Celanex

in the units

specified as follows:

and Celanex

Hostaform C 9021 K

Hostaform/Hostaform Hostaform/steel Celanex/steel

Lbk-Zij2-(v-m)*

equation (16), the values should be used

gear,

circulate

=

0.28

9021 K

access

(also applies z2 +

(basic grades)

=

air

temperatures and influence tooth deformation.

flank

Hostaform/Hostaform Hostaform/Celanex

of thermoplastics is

The

=

flank temperature

to

0.01

above material

combinations,

lubricated

Fig. 12: Load characteristic cperm. for gearwheels made from Hostaform (material combination Hostaform/ Hostaform

v

=

12

m/s)

107

10'

Number of load

cycles

11

With small gears, such as those used in neered drives, the ambient temperature

precision engi must

be assumed.

The additional frictional heat

insignificant

when the

arising as a result usually peripheral speed of the gearwheel

factor also

application

quoted

in DIN 3990

the value 1 like the other factors for which

is

given empirical

values for

plastic gearwheels

are

no

yet available.

shape factor YF takes into account the effect shape on force application on the tooth while the load proportion factor Ye allows for the effect of the transverse contact ratio. YF and Ye for straight-toothed 20) can be read off spur wheels (pressure angle a figs. 13 and 14. Strictly speaking these factors apply to metal gearwheels but they are also suitable for use in designing plastic gearwheels. In this case, however, they ignore the fact that the teeth of a plastic gearwheel deform more severely under load and that bottom clear ance and backlash change more when the gearwheel becomes hot than with metal gearwheels. A more precise calculation of tooth shape factor YF, particularly for spe cial profiles, can be carried out according to DIN 3990, sheet 2. For internally toothed spur wheels, the tooth shape factor is calculated as

The tooth

less than 5 m/s.

is

The so-called

of tooth

5.13

Loadbearing capacity of the

tooth

root

=

The basis for tooth

be

in the tooth

produced

The

design

following applies

is the flexural

root

by

for tooth

the

likely to tangential force Ft. stress

root stress

YF-Y85erpp

[N/mm']

(17)

'

U

JL11

where

permissible

OFP

tooth

root stress

[N/mm2]

(see equation 22)

tangential force on the pitch circle [N] shape factor, fig. 13; according to DIN 3990, part 3

Ft YF

Yf

tooth

load

=

"

e

Fig.

proportion factor, fig. 14; according to DIN 3990, part 3

transverse contact

(18)

shape factor YF (x factor)

=

2.06

1.18

-

h* tooth

h

height factor, h* tooth height

da outside diameter

ratio

13: Tooth

modification

YF

addendum

Fig.

=

=

m

df

root

-

h*)

(19)

^-df2 circle diameter

14: Load

spur wheels

3.8

(2.25

proportion factor Y8 for straight-toothed (a 20, x 0, i Za/zJ =

=

=

0.70

i=1.0

i=1.2\

0.65

i

=

2.0\^ \\\\ A\ ^v

1=3

i

S 0

0.60

i

I

=

\ \

ss

\ \N ^

10.0\

S\N^

VsYSN\\

a.

\A\\\s^

\\ V ?$ k s V SX ^s \ ss ^ ^ K \N S$§ ^ Vs sS: ^ > \^^^

0.55

\

"\

"^

15

20

25

30

40

Number of teeth

12

50 z

400

0.50

16

20

"N

"X

V , ',' 30

40

50

70

Number of teeth Zi

100

"X

"*

200

If the radius of the tooth

root curve is greater than the factor YS (according to DIN notch 0.25 x module, 3990 sheet 1) is given the value 1. With this proviso,

equation (17)

contains

no

Fig.

16:

Operating pressure angle wt

For teeth with addendum modification the

,<< ^

e

(tan EI

aA1)

here

KJ O

w.

tan A,

tan

the

EI,

=

tanAa

tan awt

are

(

1 +

(21)

tan a A2

values used in

auxiliary

transverse contact

i

i)

determining

Operating

-* U>

0.5

/, /

presure

(20)

2 Jt

0.6

/, '/

K> ^ tan

"s^

/ '/

angle -

//

1

^

/ 0.4

//

Y

0.3

ratio. *"* O

The function values for in

fig.

15

With D,

relation

in

=

-~, tan

and

tan E1

to an

A2 are

=

0

be read off

the value for

db2

Fig.

15:

contact

Graph to ratio

0.02

0.04

(x,

fig.

x2)/(z,

+

0.08

0.1

z2)

17: Tooth

root

strength oFlim for gearwheels

made

from Hostaform C 9021, C 2521, C 13021, C 27021, C 9021 K and C 9021 TF

tan A2.

assist calculation of

+

0.06

15 and

Fig.

-~,

0.2

shown

auxiliary factor D.

can

E1

tan

dbi with D2

u./

^

'/

a

-~-

wt

^ ^^

U O

wt

transverse

ratio is

=

tan

(^ u

notch factor. O

contact

and

transverse

e

1.0

0.8

0.6

0.4

105

107

10*

Number of load

0.2

[ 1.0

1.10

operating

pressure

toothed spur wheels in

1.30

1.20

Auxiliary

The

angel a fig. 16.

w,

1.40

is

plotted for straight-

permissible tooth root stress
OF

SF

=

SF

=

factor D

The

root

strength

(22)

of Hostaform is shown in

and of Celanex and Hostalen GUR in

fig.

18.

fig.

-

factor SF, the

following empirical values apply:

1.2 for normal 1.4 for

operating

frequent disengagement 1.3

-

special required.

cases,

even

engagement and

greater

safety

factors may be

permissible tooth root stress
The

the

lin

_ =

1.1

In

If The tooth

safety

For

cycles

17

a

gear

jams,

the teeth break off when the tooth

exceeds (TF 65 Hostaform C. stress

-

70

N/mm2, e.g. in the

case

root

of

13

Fig.

18: Tooth

The flank root

strength <7F!im for gearwheels

made

shape

factor is ZH

=

1.76 for

straight- toothed

20, without spur wheels with a pressure angle a addendum modification. For other pressure angles, the =

from Celanex and Hostalen GUR

at room

temperature

following equation applies: z

\

(24)

tana

normal pressure

wt

angle operating pressure angle

Fig.

19: Material factor

a

N/mm2

'

COSft

where

50

1/Ï

l -

Celanex

\ 40

flank temperature

ZM

as a

function of tooth

&

55

S

I

I

30

1 20

Hostalen GUR lubricated with water in oil emulsion

X 10 _,

dry-running 'also

1Q5

oil-lubricated)

10*

107

Number of load

5.1.4

Loadbearing capacity of the

10

cycles

tooth flank

Dry-running or once-only lubricated gearwheels made from plastic normally fail on overloading because of excessive tooth flank wear. Sometimes pitting occurs. In both

cases

flank

stress

For flank stress, the

(according to

0H is critical.

following equation applies

DIN 3990 sheet

1):

20

40

60

80

100

120

C

160

Tooth flank temperature I?

0H

=

1/b^d ^T1 '

'

Z

'

ZM

=

HP

[N/mm2] (23)

can

where OH flank

be read off

fig.

teeth, flank shape factor ZH

20.

stress

(Hertzian stress) [N/mm2] ÖHP permissible flank stress, fig. 21 [N/mm2] Ft tangential force on the pitch circle [N] bk smallest tooth width [mm] d pitch diameter [mm] tooth number ratio z2/zt ZH flank shape factor ZM material factor, fig. 19 V N/mm2

i

^_^_

14

With addendum modified

gives typical values for permissible flank stress ÖHP for Hostaform gearwheels at flank temperatures of & ^ 60C; fig. 22 does the same for Celanex. Fig.

21

5.1.5 Tooth

deformation

The noise of

intermeshing gearwheels

is increased

tooth defects and load-induced deformation of the

by

engaged teeth, which produces the same effect as a tooth defect during operation. Tooth deformation must there

Fig.

20: Flank

factor ZH for addendum modified

shape

teeth

fore be limited. z.u

displacement of the tooth tip in the circumferential direction (see fig. 23), the following equation applies: For

1.9

1.8

3Ft

À 2

bk

cos

Kt+t)

N

[mm]

(25)

v

\

1.7

\

V \

I

s

1.6

\

where

X

D,

X


\

M

smallest tooth width pressure

i

F

_C

tangential force [N]

F bk

1.5

angle

on

1.4

[mm]

the

pitch

circle

[

.

j

1.3

auxiliary value, fig. 24 auxiliary values, fig. 25

53

,

^

1.2

dynamic elastic moduli [N/mm2] of the gearwheel materials used, fig. 26 (DIN

*-^. *

1.1 -0.01

0.02

0

445)

Fig.

21 :

flank

+

x2)/(zi

Typical

stress

+

0.1

0.08

0.06

0.04

(x,

z2)

values for

permissible

oHp in Hostaform

gearwheels, without lubrication, peripheral speed v =12 m/s, flank temperature $

Number of load

ïs 60 C

cycles

Typical values for permissible 0Hp in Celanex gearwheels, peripheral speed v 10 m/s

Fig.

22:

flank

stress

=

a

Celanex 2500/steel,

dry-running b Celanex 2500/Hostaform C 9021, c

dry-running

Celanex 2300 GV 1/20/

Hostaform C 2521,

dry-running

d Celanex 2300 GV 1/20/

Number of load

Hostaform C 2521, once-only grease lubricated during assembly

cycles

tip under load is the criterion for tooth deformation. The permissible limit of this dis placement depends on the quiet-running and service life requirements which the gear has to meet. Experience has shown that the maximum permissible displacement is:

Displacement

of the tooth

If this value is exceeded,

operating noise

increases

sharply.

5.2 Helical spur wheels

normally designed with helical to reduce operating noise. Unlike with metal gearwheels, the increase in tooth root loadbearing capacity obtained through the use of helical teeth Plastic

gearwheels

are

teeth when the aim is

Vm,~o.i

mn

[mm]

(26)

15

and

represented by the factor Y^ (DIN 3990) is not absolutely guaranteed in the case of plastic gearwheels. It is therefore advisable to calculate the loadbearing capacity of the tooth root as for straight-toothed spur wheels.

On the other hand

relative the

movement

expected

applies to determination of flank stress. overlap is taken into account by the that the following equation applies for flank

same

ZE

so

stress

factor

I/ /

H

i+1

Ft '

T

T

~~î

bk-d

V

7

^-H

'

7 *4t

7

A;

'

by

a

factor of

1

ß

than

spur wheels. Tooth flank load far been determined for helical spur wheels. The values for straight-toothed spur wheels are therefore used as an approximate basis for calculation.

Fig.


is greater

-

straight-toothed

limits have

The

-

cos

with

The increased

wear

it is important to remember that the between the tooth flanks and hence

not so

25: Factor ip for

calculating tooth deformation

[N/mm*] (27)

i

where 2

=

]/f^

The

2

(28)

6s

'

overlap eas of the helical teeth by the equation

can

be

approximately

<

determined

8

8ßs

(ea

Fig.

see

section

COS'

ß

(29)

25

14

5.1.3)

23: Tooth deformation values

At and A2

50

100

26: Temperature curve of the dynamic elastic modulus E' for Hostaform C 9021, Celanex 2500 and Hostalen GUR, calculated from shear moduli

Fig.

driven i

40

30

Number of teeth ï\ j

^V

measured in accordance with DIN 53 445

"

(frequency about

wheel 2

10

(ISO 537)

Hz)

4000

Hostaform C 9021

N/mm2

3000

Celanex

w

Fig.

24: Factor y for

calculating tooth

deformation

2500

"T-T

J3

1

,

'S

Hostalen GUR

ä

1

2000

V

\ S

\

b>

§ 1000

Calculation section 6.

5.8 14

16

18

20

25

30

40 50

100 -20

Number of teeth

16

zt

example^ 20

40

Temperature

60

80 C

100

5.3 Flow chart for

characteristic

designing spur gears using load

5.4 Flow chart for

designing spur gears using tooth

strength

root

c

Given: Power

P

input

[W]

torque Md

Power

input

Speeds n,, n: [min"1]

Speeds

ni,n2

Operating time t pi]

Operating time t [h]

Selected:

Selected:

or

Pitch diameters dt, d2 Module

Tooth width b

9 %49

_

Module

P

.

.

*

'

_

torque Md

[N m]

[min"1]

d,, d2

[mm]

[mm]

m

Calculate

or

[mm]

tangential force Ft

as

in flow

chart 5.3

10 I*-"

__

[W]

Tooth width b

[mm]

tangential force Ft

F''-^

P

Pitch diameters

[mm]

[mm]

m

Calculate

[N m]

1-K.Ti _

f

j-jsjj

1

-f

where d

r

l

[mrnj

I ^

2-10'^-

=

Estimate tooth flank temperature $ to section 5.1.2

[N]

Calculate tooth Determine

0p r

=

m

Calculate load =

60

[N/nun]

-m

[N/mm*] *

tooth load

N

FL_ Yf Y, .

b

,

bk

root stress or

value

c

FI c=

according

n

cycle

shape factor YF from fig.

proportion

factor Yf from

13

fig.

14

number N

t

Determine load N

Compare calculated

c

=

60

n

cycle

number

t

value with

Cpfrm=f(N)seefig.l2

Compare calculated tooth
=

Check

root stress

Of with

f(N)

safety

factor S

=

^Ü* i

17

5.5 Flow chart for

flank

designing spur gears using tooth

stress

Given

Given: Power

Checking tooth deformation

5.6

P

input

Speeds

[W]

torque Md

or

[N m]

Operating time

force Ft

Tooth width

[min~1]

nl5 n2

Tangential

bk

[N]

[mm]

[h]

t

Selected: Pitch diameter Module

dl5 d2

[mm]

[mm]

m

Tooth width b

Calculate

displacement A

A

3Ft =

2

[mm] t=

bk for

cos

"(§+*) t

\LI

straight teeth, according

otherwise

Calculate

tangential

force Ft

as

Estimate tooth flank temperature & to section 5.1.2

according


from

fig.

24

ty

from

fig.

25

F

from

fig.

26

Check whether X < 0.1

H

l/Vd'1!1

=

ZH

stress

"

0H

ZH ZM (Ze) [N/mm2J '

'

1.76, for wheels without addendum modification

=

ZH from fig.

20 for addendum modified wheels

ZM from fig.

19

Z6 according

to

Determine load N

=

60

n

Compare <JHP

=

equation (28)

cycle

t

calculated tooth flank

Check safety factor S

=

OH

18

for helical spur wheels

number

f(N)

to

stress


tip

[mm]

L2/

equation (8)

in flow

chart 5.3

Calculate tooth flank

of the tooth

mn

6. Calculation

example

Ft

=

^k[N] 351 N

2

The last gear step m a domestic appliance drive is to be produced with two gearwheels made from Hostaform

37.5

Straight-toothed gearwheels are envisaged (basic profile according to DIN 867, no addendum modi fication). A service life of 107 load cycles is required at C 2521.

=

18.72 N c

12 =

Given:

The IS

input

P =5W

Speed,

wheel 1

ni

=

136 min"1

Wheel 1

zi

=

30

Wheel 2

z2

=

105

Gear ratio

i

=1

Helix

ß

=0

=

Module Pitch

m

diameter, wheel

1

Zi

m

Pitch

m

n

Tooth width

b

b)

TrqUe according to equation (15) M<j

mm

pt

=

=

=

load characteristic, read off

fig. 12,

1.7 N/mm2.

As

explained in section 5.1.2, it is not necessary to calculate the tooth flank temperature for small gear wheels provided their peripheral speed is less than

corresponds

to

ambient

temperature. 37.5

3,93

mm

mm

c) The tooth root equation (17).

stress

is calculated

OF

according to

mm

9549 3 =

0.397 N/mm2 < cperm.

5 m/s. In the present example, the peripheral speed is 0.267 m/s. It can therefore be assumed that the

3.5

di

=

=

12

=

mm

tooth flank temperature

1.25

=

3.93

mm

permissible

Cperm.

Zl

angle

=

The

a

Power

mm

18.72 N

tooth

maximum service temperature of about 30C. gearwheels will not be lubricated.

mm

=

P


-

-

=

[N mm]

-j-^ b

<

YF Y6

[N/mm2]

ÖFP

m

Hi

9549.3

Tooth

5

factor YF from

shape

fig.

13:

136 =

The

peripheral speed V

=

d, T

n

is calculated

v

n.

1000

5.236

d,

=

5.236

37.5

Load

in

So

136

=

fig.

14:

0.567

equation (17) gives:

lO"5

18. 72 N af

=

from

factor Y

proportion Y

mm

10~5

n,

YF=2.65

mm

as

[m/s] with dj

30

=

351 N

2.65

=

12

0.267 m/s =

mm

1.25

0.56

mm

1.875 N/mm2


Questions: a)

Does the load characteristic

b)

What is the calculated temperature of the tooth flank in operation?

c)

What is the tooth

c

fall within the

e)

is the flank

root

strength

for

Hostaform C 2521 is taken

permissible range?

d) What

The tooth

root stress

stress

OH

<7Flim

=

gearwheels made from fig. 17:

from

38N/mm2

(TF?

safety factor SH? the permissible

and the

Does tooth deformation exceed

Thus the tooth

occurring in operation permissible stress.

root stress

below the maximum

is far

limit?

d) a)

For load characteristic

c=-^-2cperm.

c

For flank

stress OH,

equation (23)

is used:

according to equation (13) OH

=

[N/mm2] where

l/b^Zi

'

ZH ZM '

^ (THP

[N/mm2]

,

=

=

=

^Y~

105

z2 i

'

c 3.5

30

19

Thus

ZH

=

ZM

=

we

1.76

The

page

14)

7.

from

N/mm2

fig.

stress:

The tooth

18.72 N

3.5 + 1

37.5

module

3.5

mm

notes

of module

root stress

N

1.76 -33 mm

Design

19

7.1 Selection

obtain for flank

inversely proportionate

to

the

mm2

J_ OF'

(30)

m

N/mm2<(THP

13.42

permissible

flank

stress oHp

is taken from

fig.

21

It therefore follows that with

a

larger module,

tangential force Ft

a

greater torque Md

=

and hence

be transmitted. For

module is limited OHP

<JF is

m

33^

-^

=

=

l/

33

-Ite

OH

(see

19 N/mm2

a

diameter

given gearwheel by possible a

the smallest

higher can

d, the

tooth number

^smallest"

This

gives

flank

a

safety

factor

(31)

=

mm*.

^smallest

HF

c

SH=

<7H

large module also means a large tooth height, which is advantage with regard to permissible centre distance tolerance (also affected by temperature changes). For A

19 N/mm2

an

_

~

13.42 N/mm2 =

e)

For tooth

centre

1.42

With

distance tolerance

regard

see

section 7.3.

tooth flank

wear, it is important to aim possible module because with a smaller module, frictional energy drops. Frictional energy is defined as the product of flank stress <JH and average sliding speed vg. Lower flank stress results from the smaller curvature, lower sliding speed from the smaller tooth height.

deformation, equation (25) applies

to

for the smallest

A

3Ft 2-b-cos

cos

Thus

*(^ + |f)

=

=

20

cos

=

E'2y

[mm]

0.9397

y

(from fig. 24)

=

6.8

Vi

(from fig. 25)

=

1.0

%

(from fig. 25)

=

1.0

E',

=

we

'

\F,

E'2 (from fig. 26)

7.2 2980 N/mm2

=

Complementary profile

In combination of

obtain for tooth deformation:

increased 3

A

18.72 N _

=

'

6 8

12

0.9397

mm

0.0114

/2mm2

\2980N

by the

use

of

a

plastic

can

be

complementary profiles (fig. 27). plastic gearwheel

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^M

mm.

Aperm.

=

0-1

'

Aperm.

=

0-1

'

=

0.125

[mm] according to equation (26)

mn

1-25

so no

mm

mm

The tooth deformation

20

gearwheel with

In this case, the tooth thickness of the

Fig.

of Aperm.

metal

'

2 =

a

wheel, the transmittable tangential force Ft

increased

occurring is thus only just operating noise is likely.

a

tenth

27:

Complementary profile

can

be increased

at

the expense of the tooth thickness of s to tooth

the metal wheel. The ratio of tooth thickness space

be up

e can

to

2

:

to

the nominal dimension for tooth thickness

dimension

the

impairing

1.

tooth thickness

=

quality

of the

=

tooth

(nominal

space)

without

The

position

gearwheel.

of

the tooth thickness tolerance range is indicated by small letters from h to a. The letter h denotes a theoretically

backlash-free gear engagement (upper limit of the range h corresponds to the nominal dimension for tooth thick

73 Backlash

The tooth

design

calculations

are

based

on

teeth free

ness).

from defects of dimensional variations. To compensate for unavoidable manufacturing error and heating up, deformation

during operation,

etc.

backlash

action

je

-

to

lower circiumferential

the letter

which allows the

a

Fig.

29:

System

of gear fits

Tolerance ranges for

centre

distance T

the distance measured

the line of action between the flanks of the

mating wheel (easy to measure with gauge) and circumferential backlash jv the pitch circle (fig. 28). and

a

-

-

Fig.

means

greatest clearance.

of tooth thickness. A distinction should be made between

line of

right

down

the

gearwheels must be designed with a certain backlash (flank clearance). Of the three different possibilities for providing backlash, DIN standards 3961-3967 and 58405 specify reduction etc.

A g tolerance range

backlash

28: Line of action backlash

je

along gearwheel 0--J

metal sheet measured

on

and circumferential

LLS

Tolerance ranges for tooth thicknesses Ts and tooth widths Tw

1

H*

c

bl

backlash j AÜO

T, Aau

13

-

A wo

Tw

I

-'

AWU~~

1

^ tN

without taking into account the radial eccentricity of the shafts, bearing clearance and shaft parallelity

.1

gives recommendations for the assignment of tolerance ranges which have proved successful for injec tion moulded plastic gearwheels. Table 3

By reducing the tooth thickness determined for the theoretical The

of backlash

amount

tolerance, manufacturing tions should

not

is

determined

by housing (dimensional devia backlash) and peripheral

smaller

eleminate the

The difference Aa. clearance.

the system of standard centre distance, the theoretical nominal centre distance (zero centre

If

given tolerances according to either the J or K ranges (K range 2 J range) to form 12 different quality classes. Quality class 1 specifies the closest and quality class 12 the widest tolerances. The circumferential backlash is also assigned 12 different tooth thickness tolerances ranges quality classes (h to a) according to the module and pitch diameter of the gearwheel and these classes are linked to centre distance quality classes (fig. 29). To achieve different backlashes within one quality class, the position of the tooth thickness tolerance

factor Ac

According to ao)

is

=

can

be shifted in the minus direction with respect

=

ao

a' is defined

as centre

relatively high operating temperatures

this

centre

distance clearance

by

must

which it is reduced

are

distance

expected, by the

be increased

owing to

thermal expan

sion.

For Ac the

following equation applies

Ac

=

ranges

a

accuracy

speed (thermal expansion).

distance

distance ao, the wheels operate in distance a' free from backlash.

centre

centre

ßi.z fj.2

A$

=

A#(Tt'ßl+r2-ß2) [mm]

coefficient of linear thermal

(32)

expansion

(table 2) [Kr1] pitch circle radii [mm] temperature difference K] 21

Table 3 : Tolerance range combinations for

Type of gear

injection moulded

Special features

teeth

Tolerances in accordance with DIN 58 405, sheet 2

gearwheels

High speed

highly

gear

stressed

1.5

centre

distance"""")

Tw::")

9J

ranges e.g. 9 ed

lightly

stressed

1.5

Tw*)

10J

ranges e.g. 10 ed

Drive

circumferential

assembly

1.5

backlash small

Tw:|-)

9J

ranges e.g. 9 ed

circumferential backlash

*) Tool **) Tool

large

Tw

10J

ranges e.g. 10 fed

correction

usually necessary correction may be necessary

depending on the

For the

the

2.0

temperature-dependent change following applies: Aje

=

2

Ac

sin

in

way in which the gear is mounted in the

design is achieved by e. g. thin, long teeth (fig. 30) or by incorporating radial slits in the carrier disc (fig. 31).

backlash,

[mm]

housing

A resilient

(33)

possibility is to connect the gearwheel rim to by spring elements (fig. 32) so that throught

Another the hub

Example:

deformation of these

The temperature of a pair of gearwheels made from Hostaform (centre distance a 80 mm) increases during

silent

operation

can

elements, backlash-free and hence

be achieved.

=

about 60 K.

According to equations 32 and 33 a reduction in backlash during operation of about 0.36 mm can be expected (coefficient of thermal expan sion for Hostaform ßL2 1,1 10~4). The specified back lash should therefore be increased by this amount. operation by

The

impact

modification of the

rial softer and

more

plastics renders the mate impact jolts are thus

resilient. The

less hard and operating

noise is

reduced.

=

The

operating

noise attributable

to

friction

can

be

reduced with suitable lubricants. To prevent notch effect at the tooth root, the radius of the tooth root fillet should be at least 0.25 module.

Fig.

30: Reduction of

teeth 7.4 Reduction

In addition

of operating noise

sliding tooth flanks, a significant contribution to operating noise. Impact jolts can be softened by using helical teeth, as already mentioned, and by impact jolts

-

-

-

-

tip

to

as

friction between the the

engage make

relief

resilient more

design

of the

gearwheels

flexible materials

modified tooth

22

gearwheels

shape.

operating noise by thin, long

Fig.

31: Reduction of

operating

noise

by

radial slits

in the carrier disc

radial slit

Fig.

32: Reduction of

connection of the

operating noise by flexible gearwheel rim and hub

23

8.

Examples of applications

8.1

Pump drive for aquapick

To

produce

water

is actuated via

pressure up

Tooth data:

to

about 10

bar,

a

pump

gearwheel made from Hostaform C 9021 with integral eccentric. The drive wheel is a metal pinion. This gearwheel combination, highly stressed on one side by the eccentric, is given an initial once-only lubrication with silicone grease and operates reliably in thousands of units.

Module

m

=

0.5

Metal

z,

=

12

pinion

n, up to 9000

Hostaform wheel

=

z2

da2 b

Gear

ratio

1

104

4

=

=

mm

mm

500

to

1040 min-1

^=8.67 Zl

min"1

(special teeth)

52.5

=

=

n2

24

mm

a

8.2

Planetary gear for disc motor

The

two-step planetary gear with gear wheels made from Hostaform C 9021 and C 2521 for the

photo

shows

Tooth data for the

a

golf trolley. The 12 volt disc motor and gear are incorporated directly into the trolley wheels pro viding a compact, spacesaving design. drive of

indentical steps:

Module

m

Sun wheel

z

=

46

b

=

11

z

=

42

b

=

8.5

2

=

b

=

=

1

mm

a

3

planet

wheels

Internal gear

Material for all the

Material for C2521

two

mm

mm

-120 35

mm

Hostaform C 9021

gearwheels: internally toothed sun

wheel: Hostaform

Gear ratio

itot. P

=

=

1

:

80

42 W

25

8.3

Manually operated drive for window

The window verticals tion

manually

passes

over an

are

brought

with the aid of

internally

a

into the

verticals

Tooth data:

required posi

Module

toothed wheel which transmits

the rotary motion via three double gearwheels to a sun wheel mounted in the housing. Hostaform C 9021 is used

as

the

gearwheel

m

0.7

=

mm

ball chain. The ball chain Chainwheel with internal teeth

-66

z=

da=

material.

-64

b

=

10

ï

=

12/18

b

=

5/3

z

=

36

b

=

5

mm

Planet wheels

(double gearwheels) Sun wheel

Gear ratio

26

i

=

mm

mm

1.83

8.4

Tooth data:

Food processor attachment with gearwheels made from

Hostaform

and Celanex

Module

m

Drive wheel

z

=

10

b

=

6

=

1

mm

This attachment is used for

whipping cream. For this reduce the speed of the pro

purpose it is necessary to 1800 min^1 via cessor from nj =

wheel

to n2

=

an

intermediate gear

900 min"1. This intermediate

gearwheel

Intermediate wheel

z

=

mm

40

made from abrasion resistant Hostaform C 9021 K drives

the mixing bowl n3

=

via a

second

gearwheel

which

turns at

b

=

z

=20

b

=

4.8

mm

200 min"1. The drive and driven wheels made from

Driven wheel

Celanex 2500 slide in the C 9021,

a

housing

made from Hostaform

material combination with low coefficient of

friction and

extremely low wear. Sliding properties improved by once-only lubrication during assembly.

further

7

mm

are

Power

input

P =50 W

27

9.

Explanation of symbols

Symbol

Unit

Explanation

a

mm

centre

a0

mm

zero centre

A

m2

surface

Symbol

distance

<

distance

area


of the gear

housing

<wt

Unit

Explanation

o

normal pressure

o

0

angle angle operating pressure angle transverse

pressure

b

mm

tooth width

bk

mm

smallest tooth width

ß <ß

c

N/mm2

load characteristic

e

transverse contact

d

mm

Bß

overlap ratio

S,

total

da db

(m)

diameter

mm

outside diameter

mm

base circle diameter

D

auxiliary

DP

inch"1

e

mm

E'

N/mm2

Ft

N

h

mm

diametral

factor

pitch (DP

tangential tooth height tooth height factor

helical teeth

)

=

the

pitch

&

c

#.

c

tooth flank temperature temperature in the operating environment of the gear

circle

K

A

mm

exponent (equation 16) deformation of the tooth

dynamic

P

tip

friction coefficient

addendum

OTp

N/mm2

tooth

root stress

dedendum

ÖFHm.

N/mm2

tooth

root

OFF

N/mm2

strength permissible tooth root

OH

N/mm2

flank

0HP

N/mm2

permissible flank stress auxiliary factor (equation 25) auxiliary factor (equation 25)

Z2 gear ratio

i

=

n.

n2

mm

line of

iv

mm

circumferential backlash

k m

mm

Md

N

n

mm"1

mm

action

backlash

auxiliary value (equation 16) module (normal module) torque

Rz

fj.m

s

mm

tooth thickness

P P

mm

r

mm

W

safety factor

SF SK

bottom clearance

t

h

operating

v

m/s

peripheral speed average sliding speed

m/s

time

X

addendum modification

\

load

YF

tooth

Ys

notch factor

z

number of teeth

ze ZH

flank

proportion (equation 17)

factor

shape factor (equation 17)

V N/mm2


V

stress

Indices

speed load cycle number pitch power input pitch radius roughness height

N

stress

=

)e

28

ratio with

mm

Zj

ZM

contact

ratio

mm

i

vg

expansion

angle

engagement factor with

Sas

tooth space dynamic elastic modulus on

coefficient of linear helix

helical teeth

(fig. 15)

force

h:;-

ha hf

pitch

K"1 o

overlap factor (equation 27) shape factor (equation 23) material factor (equation 23)

t

in

transverse

section

(except Ft) 1 2

relating to gearwheel relating to gearwheel

1 2

10. Literature [1]

Niemann, H. Winter: Maschinenelemente, vol II, Springer-Verlag G.

Berlin/Heidelberg/New York/Tokyo, [2]

1985

VDI 2545

Zahnräder

[3] DIN

aus

thermoplastischen Kunststoffen

3960

Begriffe und Bestimmungsgrößen für Stirnräder und Stirnradpaare mit Evolventenverzahnung [4]

DIN 58 405

der Feinwerktechnik

Stirnradgetriebe [5]

DIN 58 400

Bezugsprofil für Stirnräder mit Evolventenver zahnung für die Feinwerktechnik [6]

DIN 867

Bezugsprofil für Stirnräder mit Evolventenver zahnung für den allg. Maschinenbau [7]

DIN 3964

Achsabstandsabmaße und Gehäusen für

[8]

Achslagetoleranzen von Stirnradgetriebe

DIN 3967

Getriebe-Paßsystem, Flankenspiel,

Zahndicken

abmaße und Zahndickentoleranzen, Grundlagen, Berechnung der Zahndickenabmaße, Umrechnung der Abmaße für die verschiedenen Meßverfahren

[9]

H.

Hachmann,

Polyamide

E. Strickle:

als Zahnradwerkstoffe

Konstruktion 18

(1966)

3

29

In this technical information

Technical plastics

Design Calculations Applications Publications

so

far in this series:

This information is based

A. Technical plastics A. 1.1 Grades and A. 1.2 Grades and A. 1.4 Grades and A. 1.5 Grades and

A.2.1

A. 2. 2 Hostaform

-

calculation

-

-

-

Hostaform Hostacom Hostalen GUR

Celanex,

and is intended

edge products

and their

to

uses.

on our

present

It should

not

-

Characteristic values and

examples

B.2.2 Worm gears with

B.3.3 B.3.4 B.3.5

B.3.7

quality

of

our

products

is

must

General Conditions of Sale.

worm

Applications involving the use of the Hoechst materials Hostaform, Celanex and Hostalen GUR are devel opments or products of the plastics processing industry. Hoechst as suppliers of the starting material will be pleased to give the names of processors of plastics for technical applications.

wheels made from

of technical mouldings system Indirectly heated, conductive torpedo thermally Hot runner system Indirectly heated, thermally conductive torpedo Design principles and examples of moulds for processing Hostaform Machining Hostaform Design of mouldings made from engineering plastics Guidelines for the design of mouldings in engineering plastics Outsert moulding with Hostaform

C. Production

C.2.2

C.3.1 C.3.3

C.3.4

C.3.5

runner

-

-

©

Copyright by Hoechst Aktiengesellschaft

Issued in

30

be observed.

guaranteed under our

Design calculations for snap-fit joints in plastic parts Fastening with metal screws Plastic parts with integrally moulded threads Design calculations for press-fit joints Integral hinges in engineering plastics Ultrasonic welding and assembly of technical plastics

C.2.1 Hot

con

as guaranteeing specific properties of the products described or their suitability for a particular application.

Hostaform

B.3.2

of knowl on our

therefore be

Any existing industrial property rights

Characteristic values and

state

provide general notes

strued

The

Design of technical mouldings B.I.I Spur gears with gearwheels made from Hostaform, Celanex and Hostalen GUR

B.3.1

aims

examples

A. 2. 3 Hostacom

B.

properties properties properties properties

-

Vandar, Impet Calculations principles calculation

brochure, Hoechst

provide useful information for designers who want to exploit the properties of technical plastics such as Hostaform. In addition, our staff will be glad to advise you on materials, design and processing.

to

August 199672nd edition

World-Class Engineering Polymers

Contact Information

n Celanex® thermoplastic polyester (PBT)

Americas Ticona Engineering Polymers Product Information Service 8040 Dixie Highway Florence, KY 41042 USA Tel.: +1-800-833-4882 Tel.: +1-859-372-3244

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