Full Text:   <1078>

Summary:  <275>

CLC number: 

On-line Access: 2022-07-19

Received: 2021-09-17

Revision Accepted: 2022-01-17

Crosschecked: 2022-07-19

Cited: 0

Clicked: 1030

Citations:  Bibtex RefMan EndNote GB/T7714


Guo-dong SA


-   Go to

Article info.
Open peer comments

Journal of Zhejiang University SCIENCE A 2022 Vol.23 No.7 P.527-542


A comparison of sensitivity indices for tolerance design of a transmission mechanism

Author(s):  Zhen-yu LIU, Han-chao XU, Guo-dong SA, Yu-feng LYU, Jian-rong TAN

Affiliation(s):  State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s):   sgd@zju.edu.cn

Key Words:  Transmission mechanism, Sensitivity analysis, Tolerance allocation, Hybrid simulation, Polynomial chaos expansion (PCE)

Zhen-yu LIU, Han-chao XU, Guo-dong SA, Yu-feng LYU, Jian-rong TAN. A comparison of sensitivity indices for tolerance design of a transmission mechanism[J]. Journal of Zhejiang University Science A, 2022, 23(7): 527-542.

@article{title="A comparison of sensitivity indices for tolerance design of a transmission mechanism",
author="Zhen-yu LIU, Han-chao XU, Guo-dong SA, Yu-feng LYU, Jian-rong TAN",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T A comparison of sensitivity indices for tolerance design of a transmission mechanism
%A Zhen-yu LIU
%A Han-chao XU
%A Guo-dong SA
%A Yu-feng LYU
%A Jian-rong TAN
%J Journal of Zhejiang University SCIENCE A
%V 23
%N 7
%P 527-542
%@ 1673-565X
%D 2022
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A2100461

T1 - A comparison of sensitivity indices for tolerance design of a transmission mechanism
A1 - Zhen-yu LIU
A1 - Han-chao XU
A1 - Guo-dong SA
A1 - Yu-feng LYU
A1 - Jian-rong TAN
J0 - Journal of Zhejiang University Science A
VL - 23
IS - 7
SP - 527
EP - 542
%@ 1673-565X
Y1 - 2022
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A2100461

sensitivity analysis is used to quantify the contribution of the uncertainty of input variables to the uncertainty of systematic output responses. For tolerance design in manufacturing and assembly, sensitivity analysis is applied to help designers allocate tolerances optimally. However, different sensitivity indices derived from different sensitivity analysis methods will always lead to conflicting results. It is necessary to find a sensitivity index suitable for tolerance allocation to transmission mechanisms so that the sensitivity results can truly reflect the effects of tolerances on kinematic and dynamic performances. In this paper, a variety of sensitivity indices are investigated and compared based on hybrid simulation. Firstly, the hybrid simulation model of the crank-slider mechanism is established. Secondly, samples of the kinematic and dynamic responses of the mechanism with joint clearances and link length errors are obtained, and the surrogate model established using polynomial chaos expansion (PCE). Then, different sensitivity indices are calculated based on the PCE model and are further used to evaluate the effect of joint clearances and link length errors on the output response. Combined with the tolerance-cost function, the corresponding tolerance allocation schemes are obtained based on different sensitivity analysis results. Finally, the kinematic and dynamic responses of the mechanism adopting different tolerance allocation schemes are simulated, and the sensitivity index corresponding to the optimal response is determined as the most appropriate index.




Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1]AbbiatiG, MarelliS, TsokanasN, et al., 2021. A global sensitivity analysis framework for hybrid simulation. Mechanical Systems and Signal Processing, 146:106997.

[2]AcharjeeS, ZabarasN, 2007. A non-intrusive stochastic Galerkin approach for modeling uncertainty propagation in deformation processes. Computers & Structures, 85(5-6):244-254.

[3]AmbayeGA, LemuHG, 2021. Dynamic analysis of spur gear with backlash using ADAMS. Materials Today: Proceedings, 38:2959-2967.

[4]BorgonovoE, 2007. A new uncertainty importance measure. Reliability Engineering & System Safety, 92(6):771-784.

[5]BorgonovoE, CastaingsW, TarantolaS, 2012. Model emulation and moment-independent sensitivity analysis: an application to environmental modelling. Environmental Modelling & Software, 34:105-115.

[6]CaiM, YangJX, WuZT, 2004. Mathematical model of cylindrical form tolerance. Journal of Zhejiang University-SCIENCE, 5(7):890-895.

[7]CaoYL, LiuYS, MaoJ, et al., 2006. 3DTS: a 3D tolerancing system based on mathematical definition. Journal of Zhejiang University-SCIENCE A, 7(11):1810-1818.

[8]CaoYL, MathieuL, JiangJ, 2015. Key research on computer aided tolerancing. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 16(5):335-340.

[9]CukierRI, FortuinCM, ShulerKE, et al., 1973. Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. I Theory. Journal of Chemical Physics, 59(8):3873-3878.

[10]DantanJY, BruyereJ, VincentJP, et al., 2008. Vectorial tolerance allocation of bevel gear by discrete optimization. Mechanism and Machine Theory, 43(11):1478-1494.

[11]DarlingtonRB, HayesAF, 2016. Regression Analysis and Linear Models: Concepts, Applications, and Implementation. The Guilford Press, New York, USA, p.8-30.

[12]DubowskyS, DeckJF, CostelloH, 1987. The dynamic modeling of flexible spatial machine systems with clearance connections. Journal of Mechanisms, Transmissions, and Automation in Design, 109(1):87-94.

[13]HainesRS, 1980. A theory of contact loss at resolute joints with clearance. Journal of Mechanical Engineering Science, 22(3):129-136.

[14]HeltonJC, DavisFJ, 2003. Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliability Engineering & System Safety, 81(1):23-69.

[15]IsukapalliSS, 1999. Uncertainty Analysis of Transport-Transformation Models. PhD Thesis, The State University of New Jersey, Piscataway, USA.

[16]IsukapalliSS, RoyA, GeorgopoulosPG, 2000. Efficient sensitivity/uncertainty analysis using the combined stochastic response surface method and automated differentiation: application to environmental and biological systems. Risk Analysis, 20(5):591-602.

[17]LinKS, ChanKY, LeeJJ, 2018. Kinematic error analysis and tolerance allocation of cycloidal gear reducers. Mechanism and Machine Theory, 124:73-91.

[18]LiuYY, GuoJK, LiBT, et al., 2019. Sensitivity analysis and tolerance design for precision machine tool. Journal of Mechanical Engineering, 55(17):145-152 (in Chinese).

[19]McKayMD, BeckmanRJ, ConoverWJ, 2000. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 42(1):55-61.

[20]MoS, LiZL, LiY, et al., 2011. Concurrent tolerance optimization design based on time value of money. Journal of Machine Design, 28(11):85-89 (in Chinese).

[21]SaltelliA, TarantolaS, 2002. On the relative importance of input factors in mathematical models: safety assessment for nuclear waste disposal. Journal of the American Statistical Association, 97(459):702-709.

[22]SaltelliA, RattoM, AndresT, et al., 2008. Global Sensitivity Analysis: the Primer. John Wiley & Sons Ltd., West Sussex, UK, p.1-165.

[23]SeneviratneLD, EarlesSWE, FennerDN, 1996. Analysis of a four-bar mechanism with a radially compliant clearance joint. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 210(3):215-223.

[24]ShannonCE, 1948. A mathematical theory of communication. The Bell System Technical Journal, 27(3):379-423.

[25]SobolIM, 1993. Sensitivity estimates for nonlinear mathematical models. Mathematical Modelling and Computational Experiments, 1:407-414.

[26]SobolIM, 2001. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation, 55(1-3):271-280.

[27]SoongK, ThompsonBS, 1990. A theoretical and experimental investigation of the dynamic response of a slider-crank mechanism with radial clearance in the gudgeon-pin joint. Journal of Mechanical Design, 112(2):183-189.

[28]SudretB, 2008. Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety, 93(7):964-979.

[29]TianQ, FloresP, LankaraniHM, 2018. A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints. Mechanism and Machine Theory, 122:1-57.

[30]WienerN, 1938. The homogeneous chaos. American Journal of Mathematics, 60(4):897-936.

[31]WienerN, TeichmannT, 1959. Nonlinear problems in random theory. American Institute of Physics, 12(8):52.

[32]ZhouSE, 2019. Assembly Modeling and Accuracy Analysis Method of Complex Product Based on Digital Twin. PhD Thesis, Zhejiang University, Hangzhou, China(in Chinese).

[33]ZieglerP, WartzackS, 2015. A statistical method to identify main contributing tolerances in assemblability studies based on convex hull techniques. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 16(5):361-370.

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE