Chapter 9 Spur Gear Design. Pinion. Gear. Lecture Steps:. Quick review, gear geometry (Chapter 8) Transmitted loads (overhead) Review bending stress, bending stress number, St, allowable bending stress number, Sat and adjusted allowable bending stress number, S’at .
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Bending Stress No:
Required Allowable Bending Stress No:
Contact Stress No:
Required Allowable Contact Stress No:
A gear pair is to be a part of the drive for a milling machine requiring 20 hp with the pinion speed at 550 rpm and the gear speed to be between 180 and 190 rpm.
Driven = Milling Machine
Power = 20 hp
Pinion Speed = 550 rpm
Output Speed = 180 -190 rpm ≈ 185 rpm
Continuous Use = 30,000 hours
Compact Gear Design
Assume: Light Shock Driver and Moderate Shock Driven
Ko = 1.75 (Table 9-5, page 389)
PDesign = (Ko)(PInput)
Pd = 5 T/in
Dp = 4.80 in
DG = 14.2 in
Np = 24 teeth
NG = 71 teeth
Check physical size!!
Pitch Line Speed
Note: Use Input Power Here as Ko is applied Later!
Quality Number, Qv = 6 (Table 9-2, Page 378)
More precision, higher quality number!
Cp = 2300 (Table 9-9, Page 400)
Softer material, more relative deformation, therefore contact area increases and stress decreases
Pinion: JP = .36
Gear: JG = .415
Figure 9-17, Page 387
I = .108
Equation 9-16, Page 390; Equation is solved on next slide
ks = 1.0 since Pd ≥ 5
For this problem, specify a solid gear blank KB = 1.00
KB = 1.00 for mB = 1.2 or larger
We are assuming a solid gear blank for this problem, but if not then use:
Min Rim Thickness = (1.2)(.45 in) = .54 in
Min back-up ratio
SF = 1.25 (Mid-Range)
CH =1.00 for early trials until materials have been specified. Then adjust CH if significant
differences exist in the hardness of the pinion and the gear.
KR = 1.5 (for 1 in 10,000 failures)
Qv comes from Figure 9-21
Kv can be calculated like in above equations or taken from Figure 9-21.
Equations are more accurate.
Ncp = (60)(L)(n)(q)
L = 30,000 hours from Table 9-7
n = 550 rpm
q = 1 contacts
Ncp = (60)(30,000 hours)(550 rpm)(1 contact) = 9.9x108 cycles
NcG = (60)(30,000 hours)( 185.92 rpm)(1 contact) = 3.34656x108 cycles
Satp = 34,324.5 psi = HB 270
These stresses are OK
SatG = 28,741.9 psi = HB 215
Go to appendix A3 or A4 and spec out material that meets this hardness requirement! Example AISI 1040, Temper at 900 F
Sacp = 261,178 psi
These Stresses are WAY too HIGH!
Values are off table!
SacG = 245,609 psi
Contact stresses are too High. Must iterate until stress are low enough until
a usable material can be found.
NOTE: Contact Stress generally controls. If material cannot be found for bending,
contact stress is too high!
Iterate! Decrease Pdand increase F
Excel is a GREAT tool to use for these Iterations.
This problem solved after third iteration using Excel