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Research Papers

Virtual Model of Gear Shaping—Part II: Elastic Deformations and Virtual Gear Metrology

[+] Author and Article Information
Andrew Katz, Fathy Ismail

Precision Controls Laboratory,
Department of Mechanical and
Mechatronics Engineering,
University of Waterloo,
Waterloo, ON N2 L 3G1, Canada

Kaan Erkorkmaz

Precision Controls Laboratory,
Department of Mechanical and
Mechatronics Engineering,
University of Waterloo,
Waterloo, ON N2 L 3G1, Canada
e-mail: kaane@uwaterloo.ca

1Corresponding author.

Manuscript received July 28, 2017; final manuscript received March 5, 2018; published online April 16, 2018. Assoc. Editor: Laine Mears.

J. Manuf. Sci. Eng 140(7), 071008 (Apr 16, 2018) (10 pages) Paper No: MANU-17-1484; doi: 10.1115/1.4039651 History: Received July 28, 2017; Revised March 05, 2018

Elastic deflection of cutting tools relative to the workpiece is one of the major factors contributing to dimensional part inaccuracies in machining. This paper examines the effect of tool deflection in gear shaping and its effect on the gear's profile form error, which can cause transmission error and noise during gear operation. To simulate elastic tool deflection in gear shaping, the tool's static stiffness is estimated from impact hammer testing. Then, based on simulated cutter-workpiece engagement and predicted cutting forces, the elastic deflection of the tool is calculated at each time-step. To examine the effect of tool deflection on the profile error of the gear, a virtual gear measurement module is developed and used to predict the involute profile deviations in the virtually machined part. Simulated and measured profile deviations were compared for a one-pass external spur gear process and a two-pass external spur gear process. The simulated profile errors correlate very well with the measured profiles on the left flanks of the workpiece teeth, which are cut by the leading edges of the cutter teeth. However, additional research is needed to improve the prediction of the right flanks, which are cut by the trailing edges of the cutter teeth.

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Figures

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Fig. 1

Elastic deformation of cutting tool due to cutting forces

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Fig. 2

Measured and fit receptance FRF of the 5.08 module spur gear shaper assembly

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Fig. 3

Measured and fit receptance FRF of the workpiece

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Fig. 4

Definition of profile and lead curve in gear inspection and corresponding metrics: (a) profile and lead curves, (b) total error, form error, and slope error, and (c) pitch error

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Fig. 5

Segmenting cross section into tooth subgroups based on the middle points: (a) finding tooth flank middle points in the cross section and (b) segmenting points into tooth subgroups

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Fig. 6

Calculation of first tooth angle by finding the mean point

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Fig. 7

Calculation of profile deviation

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Fig. 8

Virtual gear inspection module

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Fig. 9

Simulated and measured profile deviations for single-pass process

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Fig. 10

Leading/left and trailing/right flank in gear shaping

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Fig. 11

Simulated and measured profile deviation metrics for single-pass process

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Fig. 12

Simulated and measured profile deviations for two-pass process

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Fig. 13

Simulated and measured profile deviation metrics fore two-pass process

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