Design of Spur Gear

Design of Spur Gear

Spur gears or straight-cut gears are the simplest type of gear. They consist of a cylinder or disk with teeth projecting radially. Though the teeth are not straight-sided (but usually of special form to achieve a constant drive ratio, mainly involute but less commonly cycloidal), the edge of each tooth is straight and aligned parallel to the axis of rotation. These gears mesh together correctly only if fitted to parallel shafts. No axial thrust is created by the tooth loads. Spur gears are excellent at moderate speeds but tend to be noisy at high speeds.

Design Procedure for Spur Gears 

In order to design spur gears, the following procedure may be followed : 

1. First of all, the design tangential tooth load is obtained from the power transmitted and the pitch line velocity by using the following relation : 

WT = (P/v) * Cs 

where WT = Permissible tangential tooth load in newtons

P = Power transmitted in watts, 

v = Pitch line velocity in m/s = [π D N / 60]

D = Pitch circle diameter in meters

N = Speed in r.p.m.

CS = Service factor. 

The following table shows the values of service factor for different types of loads :

Types of Load	Type of service
	Intermittent or 3 hours	8-10 hours per day	Continuous 24 hours per day
Steady Load	0.8	1.00	1.25
Light Shock	1.00	1.25	1.54
Medium Shock	1.25	1.54	1.80
Heavy Shock	1.54	1.80	2.00

2. Apply the Lewis equation as follows :

-        W_T = (σ_O× C_v) b.π m.y

Notes:

(i) The Lewis equation is applied only to the weaker of the two wheels (i.e. pinion or gear).

(ii) When both the pinion and the gear are made of the same material, then pinion is the weaker.

(iii) When the pinion and the gear are made of different materials, then the product of (σ_w× y) or (σ_o× y) is the *deciding factor. The Lewis equation is used to that wheel for which (σ_w× y) or (σ_o× y) is less.

3. Calculate the dynamic load (WD) on the tooth by using Buckingham equation, i.e.

Where 

Where K = A factor depending upon the form of the teeth.

= 0.107, for 14.5° full depth involute system.

= 0.111, for 20° full depth involute system.

= 0.115 for 20° stub system.

E_P = Young's modulus for the material of the pinion in N/mm².

E_G = Young's modulus for the material of gear in N/mm².

e = Tooth error action in mm. The maximum allowable tooth error in action (e) depends upon the pitch line velocity (v) and the class of cut of the gears.

Where the value of C find out from the tables-

Material		Involute teeth form	Values of deformation factor (C) in N-mm
Pinion	Gear		Tooth error in action (e) in mm
			0.01	0.02	0.04	0.06	0.06
Cast Iron Steel Steel	Cast Iron Cast Iron Steel	14 .50	55 76 110	110 152 220	220 304 440	330 456 660	440 608 880
Cast Iron Steel Steel	Cast Iron Cast Iron Steel	200 Full Depth	57 79 114	114 158 228	228 316 459	342 474 684	456 632 912
Cast Iron Steel Steel	Cast Iron Cast Iron Steel	200 Stub	59 81 119	118 162 238	236 324 476	354 486 714	472 648 952

Table- Values of maximum allowable tooth error in action (e) verses pitch line velocity, for well cut commercial gears

Pitch Line Velocity m/sec	Tooth error in action (e) mm	Pitch Line Velocity m/sec	Tooth error in action (e) mm	Pitch Line Velocity m/sec	Tooth error in action (e) mm
1.25	0.0925	8.75	0.0425	16.25	0.0200
2.5	0.0800	10	0.0375	17.5	0.0175
3.75	0.0700	11.25	0.0325	20	0.0150
5	0.0600	12.5	0.0300	22.5	0.0150
6.25	0.0525	13.75	0.0250	25 & above	0.0125
7.5	0.0475	15	0.0225

Table- Values of tooth error in action (e) verses module

Module in mm	Tooth error in action (e) in mm
	First class commercial gears	Carefully Cut Gears	Precision gears
Up to 4	0.51	0.025	0.0125
5	0.055	0.028	0.015
6	0.065	0.032	0.017
7	0.071	0.035	0.0186
8	0.078	0.038	0.0198
9	0.085	0.042	0.021
10	0.089	0.0445	0.023
12	0.097	0.0487	0.0243
14	0.104	0.052	0.028
16	0.110	0.055	0.030
18	0.114	0.058	0.032
20	0.117	0.059	0.033

Note- In calculating the dynamic load (WD), the value of tangential load (WT) may be calculated by neglecting the service factor (CS) i.e. WT = P / v, where P is in watts and v in m/s.

4. Find the static tooth load (i.e. beam strength or the endurance strength of the tooth) by using the relation-

W_S = σ_e . b. π m. y_P

For Safety WS> WD

The value of (σ_e) find from the following table-

Material of pinion & gear	Brinell Hardness Number (B.H.N)	Flexural endurance gear (B.H.N.) limit (σe) in MPa
Grey Cast Iron	160	84
Semi-Steel	200	126
Phosphor bronze	100	168
Steel	150	252

5. Finally, find the wear tooth load by using the relation,

W_w = D_P .b.Q.K 

Where Q find out from following formulas

Where V.R = Velocity Ratio

K find out from following relationship-

Where Ep = Modulus of elasticity of Pinion.

EG = Modulus of elasticity of Gear.

The value of (σ_es) find from the following table-

Material of pinion & gear	Brinell Hardness Number (B.H.N)	Surface endurance limit (σes) in MPa
Grey Cast Iron	160	630
Semi-Steel	200	630
Phosphor bronze	100	630
Steel	150	350

·       The surface endurance limit for steel may be obtained from the following equation :

σ_es = (2.8 × B.H.N. – 70) N/mm²

The wear load (Ww) should not be less than the dynamic load (WD)

Numericals of Spur Gears- Click on Below Link-

Numericals of Spur Gear Design