Machine Design II Prof. K.Gopinath & Prof. M.M.Mayuram Indian Institute of Technology Madras Module 2- GEARS Lecture 9 - 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 teeth, 2.5 mm module, 20 o full depth teeth of hardness 330Bhn and runs at 1720 rpm. The driven gear is of hardness 280Bhn and runs with moderate shock at 860 rpm. Face width of wheels is 35 mm. The gears are supported on less rigid mountings, 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 Fig 9.1. Fig 9.1 Conveyor drive layout
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Machine Design II Prof. K.Gopinath & Prof. M.M.Mayuram
Indian Institute of Technology Madras
Module 2- GEARS
Lecture 9 - 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
teeth, 2.5 mm module, 20o full depth teeth of hardness 330Bhn and runs at 1720 rpm.
The driven gear is of hardness 280Bhn and runs with moderate shock at 860 rpm. Face
width of wheels is 35 mm. The gears are supported on less rigid mountings, 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 Fig 9.1.
Fig 9.1 Conveyor drive layout
Machine Design II Prof. K.Gopinath & Prof. M.M.Mayuram
Indian Institute of Technology Madras
Solution:
The bending fatigue stress is found from AGMA equation as,
tv o mK K
FK
b m J (9.1)
We know that, Z2= Z1 x (N1/N2)
Substituting values from table 1,
Z2= 18 X (1720/860) = 36
Table 9.1 Data given for gear and pinion
N Z m d b
Pinion 1720rpm 18 2.5 mm 45 mm 35 mm
Gear 860 rpm 36 2.5 mm 90 mm 35 mm
Using the values from Table 9.1,
V = π dn/60000 = π x 45 x 1720/60000
= 4.051m/s
We know that 0.5
v
50 (200V)K
50
(9.2)
Table 9.2 J values for pinion and gear
Z J (sharing) Kv Ko Km
Pinion 18 0.338 1.569 1.25 1.6
Gear 36 0.385 1.569 1.25 1.6
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.
Machine Design II Prof. K.Gopinath & Prof. M.M.Mayuram
Indian Institute of Technology Madras
Fig.9.2 - Geometric Factor J
SPUR GEAR –TOOTH BENDING STRESS (AGMA)
Table 9.3 - Overload factor Ko
Driven Machinery
Source of power Uniform Moderate Shock Heavy Shock
Uniform 1.00 1.25 1.75
Light shock 1.25 1.50 2.00
Medium shock 1.50 1.75 2.25
Machine Design II Prof. K.Gopinath & Prof. M.M.Mayuram
Indian Institute of Technology Madras
Table 9.4 - Load distribution factor Km
Face width ( mm)
Characteristics of Support 0 - 50 150 225 400 up
Accurate mountings, small bearing
clearances, minimum deflection, precision
gears
1.3
1.4
1.5
1.8
Less rigid mountings, less accurate gears,
contact across the full face
1.6
1.7
1.8
2.2
Accuracy and mounting such that less than
full-face contact exists
Over
2.2
Over
2.2
Over
2.2
Over
2.2
For pinion:
(9. 3)
tv o m
t
t
K K
F1.569x1.25x1.6
35x 2.5x0.338
= 0.1061 F
FK
b m J
x
And for Gear:
(9.4)
tv o m
t
t
σ = K K
F1.569x1.25x1.6
35= x
x 2.5x0.385
= 0.0932 F
FK
b m J
Fatigue strength of the material is given by,
σe = σe’ kL kv ks kr kT kf km (9.5)
Table 9.5 Properties of pinion and gear
Prop. σut MPa σ’e=0.5σut MPa kL Kv ks
Pinion 420 210 1 1 0.8
Gear 385 187.5 1 1 0.8
Machine Design II Prof. K.Gopinath & Prof. M.M.Mayuram