SPUR GEAR DESIGN

Contents

9.1 Problem 1 Analysis

9.2 Problem 2 Spur gear

9.1 PROBLEM 1 – SPUR GEAR DESIGN

In a conveyor system a step-down gear drive is used. The input pinion is

made of 18 eeth, 2.5 mm module, 20o full depth teeth of hardness 330Bhn and runs

at 1720 pm. The driven gear is of hardness 280Bhn and runs with moderate shock

at 860 pm. Face width of wheels is 35 mm. The gears are supported on less rigid

ountings, less accurate gears and contact across full face may be assumed. The

ultimate tensile strength of pinion and gear materials is 420 and 385MPa

respectively. The gears are made by hobbing process. Find the tooth bending

strength of both wheels and the maximum power that can be transmitted by the

drive with a factor of safety 1.5. The layout diagram is shown in

The bending fatigue stress is found from AGMA equation as,

We know that,

Substituting values from table 1,

Data given for gear and pinion

Using the values from

V = π dn/60000 = π x 45 x 1720/60000

= 4.051m/s

We know that

J values for pinion and gear

The J value is obtained from Fig. 9.2 for sharing teeth as in practice. Ko and Km

values are obtained from Tables 9.3 and 9.4 for the given conditions.

SPUR GEAR –TOOTH BENDING STRESS (AGMA)

Overload factor Ko

Load distribution factor Km

Properties of pinion and gear

SPUR GEAR – PERMISSIBLE TOOTH BENDING STRESS (AGMA)

Endurance limit of the material is given by:

σe = σe’ kL kv ks kr kT kf km

Where, σe’ is the endurance limit of rotating-beam specimen

From table 9.5,

kL = load factor

= 1.0 for bending loads

kv = size factor

= 1.0 for m < 5 mm and

= 0.85 for m > 5 mm

ks = surface factor, is taken from Fig.9.3 based on the

ultimate tensile strength of the material for cut, shaved, and ground gears.

kr = reliability factor given in Table 9.5.

kT = temperature factor

= 1 for T≤ 350oC

= 0.5 for 350 < T ≤ 500oC

Reliability of 90%, working temperature <150o C and reversible is assumed.

kf = 1.0 since it is taken in J factor.

km = 1.0 for reverse bending assumed here

K terms of pinion and gear

Reliability factor R

Permissible bending stress

Hence the design equation from bending consideration is,

Factor of safety required = 1.5

Strength values of pinion and gear

shows that the pinion is weaker than gear. And maximum tangential force that can

be transmitted is: Ft= 947 N

So, the maximum power that can be transmitted is:

W = Ft v / 1000

= 947 x 4.051 /1000

= 3.84 kW

PROBLEM 2

SPUR GEAR DESIGN

In a conveyor system a step-down gear drive is used. The input pinion is made

of 18 teeth, 2.5 mm module, 20o full depth teeth of hardness 340Bhn and runs at

720rpm. The driven gear is of hardness 280Bhn and runs with moderate shock at

860 rpm. ace width of wheels is 35mm. The gears are supported on less rigid

mountings, less ccurate gears and contact across full face may be assumed. The

ultimate tensile strength of pinion and gear materials is 420 and 385MPa

respectively. The gears are made by hobbing process. From surface durability

consideration, find the maximum power that can be transmitted by the drive with a

factor of safety 1.2 for a life of 108 cycles. Drive layout is shown in the Fig

Data given:

i = n1/n2 = 1720/860 = 2

Z2= Z1 x i = 18 X 2 = 36

Data given for pinion and gear

Properties of gear and pinion

Solution:

The induced dynamic contact stress is given by equation below,

When both pinion and gear material are made up of steel, from Table

SPUR GEAR – CONTACT STRESS

Elastic coefficient Cp for spur gears in

Substituting the values from table

From table 3 and 4,

V = π dn/60000 = π x 45 x 1720/60000

= 4.051m/s

For hobbed gear,

K Values of pinion and gear

Substituting values from Table 14, we have,

Surface fatigue strength of the material is given by,

σsf = σsf‘ KL Kr KT

From table 10, for steel life is 107 cycles & reliability 99% and from Table 9.15,

σsf’ = 28(Bhn) – 69 = 2.8x340 – 69 = 954MPa

KL = 0.9 for 108 cycles from Fig.9.2

KR = 1.0. for 99% reliability from

SPUR GEAR – SURFACE FATIGUE STRENGTH

Surafce fatigue strength σsf for metallic spur gears (107 cycle life 99%

reliability and temperature <120 0 C)

SPUR GEAR – ENDURANCE SPUR

Reliability factor KR

SPUR GEAR – ALLOWABLE SURFACE FATIGUE STRESS (AGMA)

We know that,

[ σH ] = σSf / fs = 954/1.2 = 795MPa

For factor of safety fs = 1.2

Design equation is, σH ≤ [ σH ]

26.051 √ Ft = 795 Ft = 931 N

Maximum Power that can be transmitted is,

W = Ft V/1000 = 931x4.051/1000 = 3.51kW