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The Prediction of the Angular Transmission Error of a Harmonic Drive by Measuring Noncontact Tooth Profile and Considering Three-dimensional Tooth Engagement

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Abstract

The importance of robots is growing in manufacturing of the new normal era caused by the 4th industrial revolution and the pandemic. Harmonic drive is widely used as a precision reducer for the joint motion control of industrial robots. The angular transmission error (ATE) is an important performance indicator that greatly affects the position accuracy and vibration of a robot. This paper presents a novel method of predicting the ATE of a harmonic drive by measuring noncontact tooth profile and considering 3-dimensional tooth engagement. The tooth profile of the harmonic drive was measured with a commercial noncontact coordinate measuring machine, and the tooth pitch error was extracted using several mathematical techniques. The ATE considering 3D tooth engagement was predicted by introducing a triangular engagement coefficient. The ATE errors of 9 harmonic drives assembled with 3 flex splines (F/S) and 3 circular splines (C/S) were predicted and the superiority of the proposed method was verified by experimentally measuring their ATE.

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Abbreviations

a i , b i :

Coefficient of Fourier series

c f, c c :

Center of a tooth of the F/S and the C/S

E :

Angular transmission error

e i :

Error of tooth engagement

k 1 , k 3 :

Stiffness coefficient for tooth engagement

N :

Reduction ratio of a harmonic drive

n :

The number of simultaneous tooth engagement

p f , p c :

Accumulated pitch error of the F/S and the C/S

r c :

Pitch circle radius of the C/S

w i :

Triangular engagement coefficient

θ w, θ f :

Rotational angle of the W/G and the F/S

ω f,ω c :

Fundamental frequency of the pitch errors of the F/S and the C/S

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Authors and Affiliations

  1. School of Mechanical Engineering, Soongsil University, Hyungnam Engineering Building 408, Sangdo-Ro, Dongjak-Gu, Seoul, 06978, Republic of Korea

    Beom-Seok Kim & Hyeong-Joon Ahn

  2. Department of Mechanical Engineering, Graduate School, Soongsil University, Hyungnam Engineering Building 416, Sangdo-Ro, Dongjak-Gu, Seoul, 06978, Republic of Korea

    Seung-Tae Jeong

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  1. Beom-Seok Kim
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Kim, BS., Jeong, ST. & Ahn, HJ. The Prediction of the Angular Transmission Error of a Harmonic Drive by Measuring Noncontact Tooth Profile and Considering Three-dimensional Tooth Engagement. Int. J. Precis. Eng. Manuf. 24, 371–378 (2023). https://doi.org/10.1007/s12541-022-00760-w

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