Methodology of contact stress analysis of gearwheel by means of experimental photoelasticity

Peter Frankovský; Oskar Ostertag; František Trebuňa; Eva Ostertagová; Michal Kelemen

doi:10.1364/AO.55.004856

Applied Optics
Vol. 55,
Issue 18,
pp. 4856-4864
(2016)
•https://doi.org/10.1364/AO.55.004856

Methodology of contact stress analysis of gearwheel by means of experimental photoelasticity

Peter Frankovský, Oskar Ostertag, František Trebuňa, Eva Ostertagová, and Michal Kelemen

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Peter Frankovský, Oskar Ostertag, František Trebuňa, Eva Ostertagová, and Michal Kelemen, "Methodology of contact stress analysis of gearwheel by means of experimental photoelasticity," Appl. Opt. 55, 4856-4864 (2016)

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Abstract

The subject of this paper is the analysis of contact stresses that occur between the teeth of a gear. The analysis was carried out by means of reflection photoelasticity, which is an experimental method rarely used in this field. Contact stresses assessed in the experiment are compared with values assessed through an analytical calculation while using the Airy stress function or Hertzian relations.

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Optical-deformation constant $K$ [–]	0.15
Modulus of elasticity $E$ [MPa]	2500
Poisson’s ratio $μ$ [–]	0.38
Maximum temperature [°C]	150

Order of Isochromatic Fringes $N$ [–]	Difference of Principal Normal Stresses $σ_{1} - σ_{2}$ [MPa]
0.49	48.85
0.98	97.70
1.47	146.55
1.63	162.46
1.96	195.40
2.23	222.26
2.45	244.30
2.71	273.11
2.94	293.10

Point	$2 b$ [mm]	$β_{i}$ [°]	$τ_{12 (i)}$ [MPa]	$σ_{\max (i)}$ [MPa]
1		17	48.85	524.9
2	0.2	36	97.70	522.2
3		59	146.55	537.1

Point	$z_{i}$ [mm]	$σ_{\max}$ [MPa]	$β_{i}$ [°]	$σ_{1}$ [MPa]	$σ_{2}$ [MPa]	$τ_{12}$ [MPa]
1	0		180	−528.1	−528.1	0
2	0.10		90	−95.9	−432.1	168.1
3	0.16	528.1	59	−29.0	−317.4	144.1
4	0.26		36	−6.8	−204.4	98.8
5	0.60		17	−0.7	−99.0	49.2

$l = 23 mm$	Width of gearing, contact length
$l_{1} = 416 mm$	Length of the loading arm loaded on its end
$l_{2} = 78 mm$	Teeth contact radius
$F = 1308 N$	Force in the contact place of two teeth
$G = 25 kg$	Load gravity on the end of the arm
$g = 9.81 {ms}^{- 2}$	Gravity acceleration
$E = 2.1 \cdot 10^{5} MPa$	Young’s modulus of elasticity
$μ = 0.3$	Poisson’s ratio
$φ = 20 °$	Meshing angle
$m = 3 mm$	Modulus of teeth
$z_{1} = z_{2} = 52$	Number of teeth

$F$ [N]	Force applied to teeth
$2 b$ [mm]	Contact width
$σ_{\max}$ [MPa]	Maximum stress in contact point
$σ_{1}$ [MPa]	Principal normal stress in the direction of axis $z$
$σ_{2}$ [MPa]	Principal normal stress in the direction of axis $y$
$τ_{12}$ [MPa]	Shear stress

Abstract

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Equations (14)

Applied Optics