Vision measuring method for the involute profile of a gear
shaft

Jianwei Miao; Jianwei Miao; Qingchang Tan; Siyuan Liu; Haojing Bao; Xianbao Li

doi:10.1364/AO.388175

Applied Optics
Vol. 59,
Issue 13,
pp. 4183-4190
(2020)
•https://doi.org/10.1364/AO.388175

Vision measuring method for the involute profile of a gear shaft

Jianwei Miao, Qingchang Tan, Siyuan Liu, Haojing Bao, and Xianbao Li

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Jianwei Miao, Qingchang Tan, Siyuan Liu, Haojing Bao, and Xianbao Li, "Vision measuring method for the involute profile of a gear shaft," Appl. Opt. 59, 4183-4190 (2020)

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Abstract

Since the involute profile error of a gear shaft influences its transmission performance, it is desirable to accurately and quickly measure its involute profiles. With the advantages of low cost, universal applicability and in situ detection, a vision measuring method for multiple involute profiles of a gear shaft is developed only using one image in this study. The base circle radius and initial position angle of the involute are obtained by geometrically fitting the involute profile. The correctness and reliability of the method are tested by measuring the pitch deviation of the gear shaft; a specialized experiment is carried out; and the factors affecting the measurement accuracy also are analyzed.

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Equipment	Model No.	Main Parameters
CCD camera	JAI CCD camera	Resolution: $1376 \times 1024$
Lens	M0814-MP	Focal length: 25 mm
Calibration board	CBC75mm-2.0	Precision of the grid: 1 µm
Background light	CCS LFL-200	Electric source:12 V/10 W

Parameters	Module	Tooth Number	Pressure Angle
Gear shaft I	4	22	20°
Gear shaft II	5	21	20°

		Measurement Value		Reference Value		Error
Gear shaft No.		Left	Right	Left	Right	Left	Right
I	$Δ P_{1}$	0.022	−0.005	−0.001	−0.009	0.023	0.004
	$Δ P_{2}$	0.018	−0.004	0.001	−0.007	0.017	0.003
	$Δ P_{3}$	−0.026	0.004	−0.010	−0.001	−0.016	0.005
	$Δ P_{4}$	−0.003	0.035	0.001	0.004	−0.004	0.031
	$Δ P_{5}$	−0.019	0.008	−0.001	0.005	−0.018	0.003
	$Δ P_{6}$	−0.018	−0.003	0.005	0.002	−0.023	−0.005
II	$Δ P_{1}$	−0.014	−0.034	0.003	−0.049	−0.017	0.015
	$Δ P_{2}$	0.006	−0.050	0.019	−0.055	−0.013	0.005
	$Δ P_{3}$	0.045	−0.031	0.073	−0.018	−0.028	−0.013
	$Δ P_{4}$	0.042	0.029	0.072	0.014	−0.030	0.015
	$Δ P_{5}$	0.047	0.005	0.088	0.041	−0.041	−0.036
	$Δ P_{6}$	0.051	0.028	0.097	0.081	−0.046	−0.053

Tooth Profile	$r_{k}$	Mean Value μ	Standard Deviation $σ$	Known Values	Measurement Values	Errors
Left	49.5942	0	0.1	4.9081	4.9081	0
	49.5942	0.1	0.2	4.9081	5.0081	0.1
	49.5942	0	0.2	4.8097	4.8097	0
	49.5942	0.2	0.5	4.8097	5.0097	0.2
Right	49.5942	0	0.2	4.7461	4.7461	0
	49.5942	−0.1	0.3	4.7461	4.6461	−0.1
	49.5942	0	0.4	4.6601	4.6601	0
	49.5942	−0.2	0.3	4.6601	4.4601	−0.2

Gear End Face No.	$X_{0}$	$Y_{0}$
I	−73.6403	−19.1974
II	−73.6569	−19.1896

Gear Shaft No.		I	II
The camera coordinates of $O_{w 0}$	$x$	−91.6743	−94.9755
	$y$	8.2311	6.6354
	$z$	429.9032	402.3853
The world coordinates of $O_{w 0}$	$X$	−91.6872	−94.9664
	$Y$	6.7258	7.6425
	$Z$	−429.9266	−402.3696
The Z-coordinate	$Z_{0}$	−430.2166	−402.6596

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Applied Optics