CH3 Worm Gear Design-2

8/10/2019 CH3 Worm Gear Design-2

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3.4 Design of Worm and Wormgear

Pitting, Scuffing and Wear first occur on the surface of wormgear.

Contact strength of tooth surface and bending strength of tooth.(1) Contact strength of tooth surface

For design:

2

2

1 2

HP 2

15000m d KT

z

For Checking: 2H HP2

1 2

9400E A V

TZ K K K

d d

T2-- Torque acting on wormgear, N.m;

K-- Coefficient of load, commonly in range of 1.0-1.4.

If well-distributed load, v23m/s and higher precise thanGrade 7, a smaller value. Otherwise, a bigger value.

HP -- Allowable contact stress of wormgear,

decided by material of wormgear.

1. Strength of wormgear


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For tin-free bronze, brass and cast iron, HP in Table 3-11;

For tin bronze, HP='HPZvsZN

'HPAllowable contact stress if load cycle number NL=107,

in Table 3-10.ZvsCoefficient of sliding speed, Fig. 3-10.

ZNCoefficient of contact fatigue life, Fig. 3-11.

Fig. 3-10 Coefficient of sliding speed

Injection

Churning

Zvs


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Fig. 3-11 Coefficient of contact/bending fatigue life

For cast iron

For bronze and brass

ZNo

rYN


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Table 3-11 Allowable contact stress of tin-free bronze, HP

Material of

wormgearM. of worm

Sliding speed vs, m/s

0.25 0.5 1 2 3 4 6 8

Al-

bronze

ZCuAl10Fe3

Steel,

Hardening - 250 230 210 180 160 120 90

ZCuAl10Fe3

Mn2

Steel,

Hardening- 250 230 210 180 160 120 90

BrassZCuZn38Mn2

Pb2

Steel,

Hardening-- 215 200 180 150 135 95 75

Grey

cast

iron

HT150,

HT200

Steel,

H.T.160 130 115 90 -- -- -- --

HT250Steel,

H.T./Hardening140 110 90 70 -- -- -- --

ZECoefficient of Elasticity, Table 3-12.

Material of

worm

Material of wormgear

Cast

tin bronze

Cast

Al bronze

Cast

Al brass

Grey cast

iron

Nodular cast

iron

Steel 155 156 157 162 182

Table 3-12 Coefficient of Elasticity


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Table 3-13 Overload Coefficient

Power sourceDriven machine

Uniform Moderate shock Heavy shock

Electrical motor,

Steam turbine0.8-1.25 0.9-1.5 1.0-1.75

Multi cylinder

engine0.9-1.5 1.0-1.75 1.25-2.0

Single cylinderengine

1.0-1.75 1.25-2.0 1.5-2.25

KAOverload coefficient, Table 3-13.

KVDynamic load coefficient

If v2

3m/s, KV

=1.0-1.1;

If v2>3m/s, KV=1.1-1.2.

KLoad distribution coefficient

If uniform load, K=1.0;

If variable load, K=1.1-1.3.


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(2) Bending strength of wormgear tooth

For design: 21 2 FS

FP 2

600m d KT Y

z

For Checking: 2 A V F FS FP

1 2

666T K K K Y Y

d d m

FPAllowable bending stress of wormgear, N/mm2, which

relates to the material of worm gear tooth, satisfying,FP= 'FPYN

'FP Allowable bending stress if number of load cycles

NL=106, Table 3-10.

YNCoefficient of bending fatigue life, Fig. 3-11.

YFSCombined coefficient of tooth profile, YFS=YFaFSa,

in Table 2-20 and Table 2-21,

Equivalent teeth number ze2=z2/cos3.

YCoefficient of lead angle, Y=1- /120.


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2. Stiffness of worm

Surface hardness of worm is high, but worm shaft will deform at

the engagement point under the radial force and tangential force.

A great deflection will cause unbalanced load or interference,and damage the engagement of worm and wormgear.

For Checking:

2 2

1 1 3

1 P48

t rF Fy L y

EI

Ft1Tangential force on worm;Fr1Radial force on worm;

EModulus of elasticity of worm material, if a steel worm,

E=2.07

105N/mm2;

IMoment of inertia at the critical section, mm4,

I=df14/64, where, df1dia. of dedendum circle;

L Span between supporting points, decided by structure design,

initial value L=0.9d2, d2-dia. of pitch circle of wormgear;

ypAllowable deflection, in the range of yp=(0.0010.0025)d1,

d1diameter of pitch circle of worm;


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3. Thermal equilibrium of worm drive

For the self-locking worm drive, the efficiency is as low as 50%.

Under closed and continuous driving conditions, there will be

overheatto deteriorate the lubrication.

Finally, it will cause failure.

In worm drive, the power of heat loss is

1 1sP P P1- Inputting power;

- Total efficiency.

Radiating power of in unit time is

1 2cP kA t t

k- Thermal conductivity,

14-17.5 W/(m2

.C) under good ventilation,8.7-10.5 W/(m2.C) under poor ventilation;

ACooling area, estimating by A=0.33(a/100)1.73, ais the

center distance between worm and worm gear, mm.

t1

Allowable temperature of lubrication, commonly 95;

t2Environment temperature, commonly 20.


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11 2

195

Pt t

kA

Worm drive must under the allowable temperature, so

If the thermal equilibrium can not be satisfied, Some measures

need to be adopted to increase heat dissipation .

Cooling waterVentilator Circulating lubrication

Fan

Oil Lubricating oil Oil pump

Cooler

Filter


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Example ProblemTry to design the worm drive for hoister.

Given:

(1) Inputting power of worm P1=7.5KW;

(2) Inputting rotational speed n1=1450r/min;(3) Speed ratio i=20;

(4) Load on driven machine is uniform;

(5) Slight shock from power source;

(6) Life expectancy is 5 years, 300 days/year, 8 hours/ day;(7) Worm is arranged below the wormgear;

(8) Small batch production;

Solution

(1) Worm type, precision grade and materialConsidering small inputting power, and medium inputting rotational

speed, we can choose ZA worm, and precision grade Grade 8.

Material of worm: Steel 45, Case hardening, Hardness HRC=45-50.

Material of wormgear: ZCuSn10P1, sand mould casting process.


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(2) Teeth of worm and wormgear

Speed ratio i=20, by Table 3-4, z1=2, z2=iz1=40.

Rotational speed of worm gear n2=n1/i=1450/20=72.5r/min.

(3) Allowable contact stress of worm gearMaterial of worm gear is tin bronze, so HP='HPZvsZN

By Table 3-10, 'HP=200N/mm2.

By Fig. 3-8, the estimated sliding speedv

s=7m/s, churning lubrication.By Fig. 3-10, Coefficient of sliding speed Zvs=0.87.

Wormgear rotates in unidirectional direction, No. of load cycle on

wormgear is

NL=60n2th=60

1

72.5

5

300

8=5.22

107

By Fig. 3-11, Coefficient of life ZN=0.8.

HP='HPZvsZN= 200N/mm2

0.87

0.8=139.2N/mm2


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(4) Designing by contact stress

Load coefficient K=1.1, by Table 3-8, the estimated efficiency of

worm drive =0.8, then the torque on worm gear is

T2= T1i =9550 P1/n1i =9550 7.5/1450 20 0.8=790.3 N.m2

2

1 2

HP 2

15000m d KT

z

By

2

2 3

1

150001.1 790.3 6309.12mm

139.2 40m d

By Table 3-3, m2d1is about 6400 mm3, then we have m=8mm,

d1=100mm, q=12.5.

(5) Calculating Geometrical parameters

Dia. of pitch circle of wormgear d2=mz2=840=320mm.

Lead angle of worm tan =z1/q=2/12.5=0.16, then =9.09.


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Face width of wormgear

2 2 0.5 1 2 8 0.5 12.5 1 mm=66.788mmb m q

We can set b2=68mm.

The center distance between worm and wormgear

a=0.5(d1+d2)=0.5(100+320)mm=210mm

(6) Linear speed ,and efficiency of worm gear

Linear speed of wormgear

v2=d2n2/(601000)=320725/(601000)=1.21m/s

Relative sliding speed

vs=v1/cos =d1n1/(60

1000)

cos 9.09=7.69m/sBy Table 3-7, Equivalent angle of frictione=1 03 =1.05 , we

have

1

tan tan 9.090.894

tan tan 9.09 1.05e


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Efficiency of churning 2=0.96, Efficiency of rolling bearing

3=0.99, we have

= 123=0.894

0.96

0.99=0.85

Approximating to the estimated

value

(7) Checking the contact strength

Torque on the worm gear

T2= T1i =9550 P1/n1i=9550 7.5/1450 20 0.85=839.7N.m

By Table 3-12, coefficient of elasticity ZE=155.

By Table 3-13, overload coefficient KA=1.

As v2=1.21m/s


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666T K K K


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2 A V

F FS

1 2

FP

666

666 790.3 1.05 14.04 0.92 8.03

100 320 8

T K K K Y Y

d d m

Bending strength is OK.

(9) Checking stiffness of worm

Tangential force

6

1

1

1

7.52 9.55 10

2 1450987.93N

100t

TF d

Radial force

3

2

r1 a

2

2 2 839.7 10tan tan 20 1910.2N

320

TF

d

Span between supporting points2

0.9 0.9 320 288L d

Moment of inertia at the critical section

44

6 4f1 100 2.5 8

2.01 10 mm64 64

dI

Allowable deflexion

10.001 0.001 100 0.1mmPy d

W h th d fl ti f


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We have the deflection of worm2 2

1 1 3

1

2 2

3

5 6

48

987.93 1910.2

28848 2.1 10 2.01 10

0.0025mm

t r

P

F Fy L

EI

y

Stiffness of worm is OK.

(10) Calculating the thermal equilibrium

Efficiency of worm drive =0.85, thermal conductivity

k=15W/(m2), temperature of environment t2=20,

Cooling area, estimated by

A=0.33(a/100)1.73=0.33(210/100)1.73=1.191m2

1

1 2

1 7500 1 0.85

20 82.97 9515 1.191

P

t tkA

Thermal equilibrium is OK.

(11) Calculating other geometrical parameters (Omitted)

(12) Designing structure (Omitted)

3 5 S f W G d i


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Worm structure:

Commonly Worm in a form of shaft worm shaft

3.5 Structure of Worm Gear drive

1) Non-tool withdrawal groove, by milling the worm teeth

2) Tool withdrawal groove, by turning the worm teeth

L

df1

L

df1

T. W. G. T. W. G.

W


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ormgear tooth width angle 90~130

Thickness of wormgear c 1.6m+1.5 mm

Width of flange B 0.75da 0.67 da

Dia. of wormgear addendum de2 da2 +2m da2 +1.5m da2 +2m

o. of thread z1 1 2 4

Wormgear structure

Unit wormgear Combined

by interference fit

de2

de2

de2

de2

BB B B

c cc

Combined

by bolt connection

Combined

by casting

Set screw 4~8, =2~3mm


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Documents

CH3 Worm Gear Design-2