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Spur - Gears - Metric - XLS: Tooth Normal Force

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Spur_Gears_Metric.

xls
Spreadsheet to estimate gear tooth strength
Production gears must be designed using the Lewis Form Factor or FEA
By Alex Slocum 1/18/01, last modified 9/28/2007 by Alex Slocum
Enters numbers in BOLD, Results in RED
Inputs
Desired torque transmission, T (N-mm, in-lb) 12 0.1
Maximum conservative achievable torque transmission
(C35 stress ratio = 1) (N-mm, in-lb) 654 5.8
Pressure angle, f (deg, rad) 20 0.3491
Module, M 1
Pitch, P 25.4
Number of teeth on pinion, Np 24
Number of teeth on gear, Ng 96 T
Center distance tolerance, Ctol (mm) 0.01 no
Face width, w (mm) 5 f
Pinion yeild stress, sigp (N/mm^2, psi) 41 5944
Gear yield stress, sigg (N/mm^2, psi) 41 5944
Stress concentration factor at tooth root, scf 1.25
Outputs
Gear ratio, mg 4
Pinion pitch diameter, Dp (mm) 24.00
Gear pich diameter, Dg (mm) 96.00
Center distance, C (mm) 60.01
Tooth thickness at base tt (mm) 1.73 Dpitc
Addendum, a (mm) 1.00
Dedendum, b (mm) 1.25
Clearance, cl (mm) 0.25
Pinion tooth force (normal to radius), Fp (N) 1.00
Gear tooth separation force (parallel to radius) Fs (N) 0.36
Tooth section parameters
Chordal area, Ac (mm^2) 8.6394
First Moment, Q (mm^3) 3.73E+00
2nd moment of area ("moment of inertia") I (mm^4) 2.15E+00
Pinion tooth stresses (stress ratio must be less than 1) s ratio
Transverse shear stress of the tooth (F/A) (N/mm^2) 0.14 0.01
Bending induced shear stress (FQ/wI) (N/mm^2) 0.43 0.02
Bending stress (F*b*c/I) (psi) 0.50 0.01

From FEA of one tooth from MOD 1 gear


load normal to the tooth (N) 1
load normal to pitch radius (N) 0.94
max stress from FEA (N/m^2, N/mm^2) 500000 0.5
maximum tangential load (N) 78
maximum torque (N-mm) 934
Safe Von Mises stress (psi) Maximum Von Mises stress (MPa)
Plastic Unfilled Glass-filled Plastic Unfilled Glass-filled
ABS 3000 6000 ABS 21 41
Acetal 5000 7000 Acetal 35 48

Nylon 6000 12000 Nylon 41 83


Polycarbonate 6000 9000 Polycarbonate 41 62
Polyester 3500 8000 Polyester 24 55
Polyurethane 2500 Polyurethane 17

Tooth
normal
force Pressure angle f

Tangential
force

Dpitch/2
Modulus of elasticity
psi Gpa
2.96E+07 204
1.00E+07 69

1.50E+06 10
400000 2.8
500000 3.4
300000 2.1

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