平面轨迹机构运动误差的统计矩分析

周光钱; 佘霞; 李欣玲; 龙宇; 张均富

doi:10.13433/j.cnki.1003-8728.2016.1204

平面轨迹机构运动误差的统计矩分析

doi: 10.13433/j.cnki.1003-8728.2016.1204

1.
西华大学机械工程学院, 成都 610039

基金项目:

国家自然科学基金项目（51275425）资助

详细信息

作者简介:
周光钱(1989-),硕士研究生,研究方向为轨迹机构可靠性、稳健性设计,xiangguangqianjin@163.com

通讯作者:
张均富(联系人),教授,博士,zhang_junfu@126.com

计量
- 文章访问数: 113
- HTML全文浏览量: 19
- PDF下载量: 4
- 被引次数: 0
出版历程
- 收稿日期: 2015-04-17
- 刊出日期: 2017-01-05

Analyzing Statistical Moments of Motion Errors for Planar Path Linkage

1.
School of Mechanical Engineering, Xihua University, Chengdu 610039, China

摘要

摘要: 轨迹型机构的运动综合误差具有强非线性，采用泰勒级数线性化处理难以高精度求解其均值与方差。为此，提出采用变量降维算法对轨迹机构的运动综合误差进行概率建模。以平面四杆轨迹机构为例，考虑机构构件尺寸的随机性，基于运动学分析提出机构的运动综合误差模型，采用双变量降维方法将机构运动误差函数近似为系列双变量函数与单变量函数之和，并应用Gauss-Hermite积分公式对误差函数进行矩估计，由此导出机构运动综合误差的均值和方差。该方法处理实现了计算效率与精度的综合平衡。最后给出数值算例对所提方法的有效性进行验证。
- 平面轨迹机构 /
- 运动误差 /
- 统计矩 /
- 双变量降维方法
Abstract: Since the composite error of the motion of path generating mechanisms is multi-dimensional and strongly nonlinear, it is difficult to obtain the highly accurate mean and variance of the composite error with the Taylor series expansion. Therefore, this paper uses the dimensional reduction method to build the probabilistic model of the motion error. As an example, it presents a four-bar planar path linkage with random number of dimensions and establishes a model of the composite motion error based on kinematic analysis. With the bivariate dimension reduction method, the motion error is approximated by the sum of univariate and bivariate functions of dimensional variables. The Gauss-Hermite Quadrature rule is applied to evaluate the statistical moments of the motion error, and then its mean and standard deviation functions are derived. This application achieves an optimal balance between accuracy and efficiency. Finally, a numerical example is given to demonstrate the effectiveness of the bivariate dimensional reduction method.
- planar path mechanism /
- motion error /
- statistical moment /
- bivariate dimensional reduction method

HTML全文

参考文献(15)

[1]	Lin W Y. A GA-DE hybrid evolutionary algorithm for path synthesis of four-bar linkage[J]. Mechanism and Machine Theory, 2010,45(8):1096-1107
[2]	Sancibrian R, Viadero F, García P, et al. Gradient- based optimization of path synthesis problems in planar mechanisms[J]. Mechanism and Machine Theory, 2004,39(8):839-856
[3]	Vasiliu A, Yannou B. Dimensional synthesis of planar mechanisms using neural networks: application to path generator linkages[J]. Mechanism and Machine Theory, 2001,36(2):299-310
[4]	Nariman-Zadeh N, Felezi M, Jamali A, et al. Pareto optimal synthesis of four-bar mechanisms for path generation[J]. Mechanism and Machine Theory, 2009,44(1):180-191
[5]	张义民,黄贤振,贺向东.不完全概率信息牛头刨床机构运动精度可靠性稳健设计[J].机械工程学报,2009,45(4):105-110 Zhang Y M, Huang X Z, He X D. Reliability-based robust design for kinematic accuracy of the shaper mechanism under incomplete probability information[J]. Journal of Mechanical Engineering, 2009,45(4):105-110 (in Chinese)
[6]	Liu T S, Wang J D. A reliability approach to evaluating robot accuracy performance[J]. Mechanism and Machine Theory, 1994,29(2):83-94
[7]	Bhatti P K, Rao S S. Reliability analysis of robot manipulators[J]. Journal of Mechanisms, Transmissions, and Automation in Design, 1998,110(2):175-181
[8]	Zhang Y M, Huang X Z, Zhang X F, et al. System reliability analysis for kinematic performance of planar mechanisms[J]. Chinese Science Bulletin, 2009,54(14):2464-2469
[9]	Zhang J F, Du X P. Time-dependent reliability analysis for function generator mechanisms[J]. Journal of Mechanical Design, 2011,133(3):031005
[10]	成诚,张均富.平面轨迹机构的运动可靠性分析[J].机械科学与技术,2014,33(11):1633-1636 Cheng C, Zhang J F. Analysis of the kinematic reliability for planar path mechanisms[J]. Mechanical Science and Technology for Aerospace Engineering, 2014,33(11):1633-1636 (in Chinese)
[11]	Xu H, Rahman S. A generalized dimension-reduction method for multidimensional integration in stochastic mechanics[J]. International Journal for Numerical Methods in Engineering, 2004,61(12):1992-2019
[12]	Rahman S, Xu H. A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics[J]. Probabilistic Engineering Mechanics, 2004,19(4):393-408
[13]	Huang B Q, Du X P. Uncertainty analysis by dimension reduction integration and saddlepoint approximations[J]. Journal of Mechanical Design, 2006,128(1):26-33
[14]	Lee I, Choi K K, Du L, et al. Dimension reduction method for reliability-based robust design optimization[J]. Computers ＆ Structures, 2008,86(13-14):1550-1562
[15]	Wang J G, Zhang J F, Du X P. Hybrid dimension reduction for mechanism reliability analysis with random joint clearances[J]. Mechanism and Machine Theory, 2011,46(10):1396-1410