Gear Tolerance Modeling with Small Displacement Torsor and Response Surface Method

doi:10.7652/xjtuxb201709011

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Gear Tolerance Modeling with Small Displacement Torsor and Response Surface Method

更新时间：2025-07-09

- Gear Tolerance Modeling with Small Displacement Torsor and Response Surface Method
- Vol. 51, Issue 9, Pages: 77-84+91(2017)
- 作者机构：
  
  合肥工业大学机械工程学院,合肥,230009
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb201709011
  CLC： TH115
- Online First：10 September 2017，
  
  Published：2017
- 稿件说明：
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Gear Tolerance Modeling with Small Displacement Torsor and Response Surface Method[J]. 2017, 51(9): 77-84+91.
DOI：

Gear Tolerance Modeling with Small Displacement Torsor and Response Surface Method[J]. 2017, 51(9): 77-84+91. DOI： 10.7652/xjtuxb201709011.

摘要

为了更高效更合理地开展齿轮公差分析及优化

提出一种小位移旋量与响应面法相结合的齿轮公差分析模型构建方法。以齿轮安装公差为例

依据齿轮精度标准

利用小位移旋量公差建模理论建立了齿轮安装公差数学模型; 基于该公差模型

结合齿面接触分析原理编制了计及误差的齿面接触分析模拟程序

并分析了不同变动要素对传动误差的影响; 利用拉丁超立方试验方法采样并结合最小二乘法

构建了齿轮公差变动要素与传动误差之间的二阶响应面近似模型

从而得到了齿轮公差分析模型。实例分析结果表明:该方法建模精度较高

实用性好

可为齿轮公差分析和综合等提供参考。

Abstract

To conduct tolerance analysis of gears more effectively and reasonably

a new tolerance analysis modeling approach for gears based on small displacement torsor(SDT)and response surface method is proposed. Taking the installation tolerance of a gear for example

the mathematical model for installation tolerance of the gear is built based on SDT theory and in accordance with gear precision standard. Based on this model and tooth contact analysis(TCA)

a simulation program considering the errors is coded and the effects of different variation factors on transmission error are analyzed. A second-order response surface approximate model of gear transmission error is built based on Latin hypercube sampling and the least squares method

hence the tolerance analysis model of gears is obtained. An example is analyzed and the result indicates that the proposed method has high modeling accuracy and good practicability

and may provide a reference for gear tolerance analysis and synthesis.

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Keywords

references

吴昭同, 杨将新. 计算机辅助公差优化设计 [M]. 杭州: 浙江大学出版社, 1999: 1-7.

徐旭松, 杨将新, 曹衍龙, 等. 一种面向可装配性的公差分析方法 [J]. 中国机械工程, 2008, 19(24): 2976-2981.

XU Xusong, YANG Jiangxin, CAO Yanlong, et al. A tolerance analysis method for feasibility of assembly [J]. China Mechanical Engineering, 2008, 19(24): 2976-2981.

REQUICHA A A G. Toward a theory of geometric tolerancing [J]. International Journal of Robotics Research, 1983, 2(4): 45-60.

DESROCHERS A, CLÉMENT A. A dimensioning and tolerancing assistance model for CAD/CAM systems [J]. International Journal of Advanced Manufacturing Technology, 1994, 9(9): 352-361.

BOURDET P, MATHIEU L, LARTIGUE C, et al. The concept of the small displacement torsor in metrology [G]. Series on Advances in Mathematics for Applied Sciences: 40 Advanced Mathematical Tools in Metrology: Ⅱ. Singapore: World Scientific, 1996: 110-122.

ASANTE J N. A small displacement torsor model for tolerance analysis in a workpiece-fixture assembly [J]. Journal of Engineering Manufacture, 2009, 223(8): 1005-1020.

BARKALLAH M, JABALLI K, LOUATI J, et al. Three-dimensional quantification of the manufacturing defects for tolerances analysis [J]. Multidiscipline Modeling in Materials and Structures, 2012, 8(1): 43-62.

DAVIDSON J K, MUJEZINOVI A, SHAH J J. A new mathematical model for geometric tolerances as applied to round faces [J]. Journal of Mechanical Design, 2002, 124(4): 609-622.

MUJEZINOVIC A, DAVIDSON J K, SHAH J J. A new mathematical model for geometric tolerances as applied to polygonal faces [J]. Journal of Mechanical Design, 2004, 126(3): 504-518.

吴玉光. 基于真实机器的装配公差分析方法 [J]. 中国科学: 技术科学, 2014, 44(9): 991-1003.

WU Yuguang. Assembly tolerance analysis method based on the real machine model [J]. Scientia Sinica: Techonogica, 2014, 44(9): 991-1003.

徐旭松, 杨将新, 曹衍龙, 等. 渐开线圆柱斜齿轮齿面的公差建模 [J]. 浙江大学学报(工学版), 2008, 42(11): 1946-1950.

XU Xusong, YANG Jiangxin, CAO Yanlong, et al. Tolerance modeling of involute helical gear tooth surface [J]. Journal of Zhejiang University(Engineering Science), 2008, 42(11): 1946-1950.

BRUYÈRE J, DANTAN J Y, BIGOT R, et al. Statistical tolerance analysis of bevel gear by tooth contact analysis and Monte Carlo simulation [J]. Mechanism Machine Theory, 2007, 42(10): 1326-1351.

徐旭松. 基于新一代GPS的功能公差设计理论与方法研究 [D]. 杭州: 浙江大学, 2008: 26-27.

胡洁, 吴昭同, 杨将新. 基于旋量参数的三维公差累积的运动学模型 [J]. 中国机械工程, 2003, 14(2): 127-130.

HU Jie, WU Zhaotong, YANG Jiangxin. Kinematic model of 3D tolerance accumulation based on screw parameter [J]. China Mechanical Engineering, 2003, 14(2): 127-130.

吕程, 艾彦迪, 余治民. 蒙特卡罗与响应面法相结合的圆柱度公差模型求解 [J]. 西安交通大学学报, 2014, 48(7): 53-59.

LÜ Cheng, AI Yandi, YU Zhimin. Cylindricity tolerance model solution combining Monte Carlo simulation with response surface method [J]. Journal of Xi'an Jiaotong University, 2014, 48(7): 53-59.

中国国家标准化管理委员会. 圆柱齿轮检验实施规范: GB/Z 18620.3—2008[S]. 北京: 中国标准出版社, 2008.

LITVIN F L, FUENTES A. Gear geometry and applied theory [M]. Cambridge, UK: Cambridge University Press, 2004: 375-403.

林超, 魏沛堂, 朱才朝. 平行轴变齿厚斜齿轮传动接触分析 [J]. 重庆大学学报(自然科学版), 2012, 35(12): 1-6.

LIN Chao, WEI Peitang, ZHU Caichao. Tooth contact analysis of helical beveloid gear with parallel axis [J]. Journal of Chongqing University(Natural Science Edition), 2012, 35(12): 1-6.

沈云波, 方宗德, 赵宁, 等. 斜齿面齿轮几何传动误差的设计 [J]. 航空动力学报, 2008, 23(11): 2147-2152.

SHEN Yunbo, FANG Zongde, ZHAO Ning, et al. Design of geometry transmission errors of helical face-gear drive [J]. Journal of Aerospace Power, 2008, 23(11): 2147-2152.

吴序堂. 齿轮啮合原理 [M]. 2版. 西安: 西安交通大学出版社, 2009: 1-11.

吕辉, 于德介, 谢展, 等. 基于响应面法的汽车盘式制动器稳定性优化设计 [J]. 机械工程学报, 2013, 49(9): 55-60.

LÜ Hui, YU Dejie, XIE Zhan, et al. Optimization of vehicle disc brakes stability based on response surface method [J]. Journal of Mechanical Engineering, 2013, 49(9): 55-60.

刘文卿. 实验设计 [M]. 北京: 清华大学出版社, 2005: 59-61.

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