spur gear design final
TRANSCRIPT
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