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Research Papers

Geometric Error Modeling and Sensitivity Analysis of Single-Axis Assembly in Three-Axis Vertical Machine Center Based on Jacobian-Torsor Model

[+] Author and Article Information
Du Zhengchun

Mem. ASME
School of Mechanical Engineering,
Shanghai Jiao Tong University,
No. 800 Dongchuan Road,
Shanghai 200240, China
e-mail: zcdu@sjtu.edu.cn

Wu Jian

Mem. ASME
School of Mechanical Engineering,
Shanghai Jiao Tong University,
No. 800 Dongchuan Road,
Shanghai 200240, China
e-mail: wujian19920000@sjtu.edu.cn

Yang Jianguo

School of Mechanical Engineering,
Shanghai Jiao Tong University,
No. 800 Dongchuan Road,
Shanghai 200240, China
e-mail: jgyang@sjtu.edu.cn

1Corresponding author.

Manuscript received January 30, 2017; final manuscript received October 7, 2017; published online December 20, 2017. Assoc. Editor: Yan Wang.

ASME J. Risk Uncertainty Part B 4(3), 031004 (Dec 20, 2017) (12 pages) Paper No: RISK-17-1007; doi: 10.1115/1.4038170 History: Received January 30, 2017; Revised October 07, 2017

The influence of component errors on the final error is a key point of error modeling of computer numerical control (CNC) machine tool. Nevertheless, the mechanism by which the errors in mechanical parts accumulate to result in the component errors and then impact the final error of CNC machine tool has not been identified; the identification of this mechanism is highly relevant to precision design of CNC machine. In this study, the error modeling based on the Jacobian-torsor theory is applied to determine how the fundamental errors in mechanical parts influence and accumulate to the comprehensive error of single-axis assembly. First, a brief introduction of the Jacobian-torsor theory is provided. Next, the Jacobian-torsor model is applied to the error modeling of a single-axis assembly in a three-axis machine center. Furthermore, the comprehensive errors of the single-axis assembly are evaluated by Monte Carlo simulation based on the synthesized error model. The accuracy and efficiency of the Jacobian-torsor model are verified through a comparison between the simulation results and the measured data from a batch of similar vertical machine centers. Based on the Jacobian-torsor model, the application of quantitative sensitivity analysis of single-axis assembly is investigated, along with the analysis of key error sources to the synthetical error ranges of the single-axis assembly. This model provides a comprehensive method to identify the key error source of the single-axis assembly and has the potential to enhance the tolerance/error allocation of the single axis and the whole machine tool.

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Figures

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Fig. 1

Combination of typical features

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Fig. 2

Functional pairs (internal pairs and contact pairs)

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Fig. 3

Assembly flow of single-axis assembly of machine tool

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Fig. 4

The y-axis assembly of a three-axis vertical machining center VMC850B and its connection graph: (a) structure of a single-axis assembly and (b) connection graph of the single-axis assembly

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Fig. 5

Illustration of guide-slide subassembly and the related connection graph: (a) structure of guide-slide subassembly, (b) structure of base, (c) structure of the guide and slide, and (d) connection graph and assembly flow of guide-slide subassembly

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Fig. 6

Illustration of the cumulative lead error of ball screw [21]

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Fig. 7

Straightness of ball screw in the axis assembly

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Fig. 8

Illustration of ball screw subassembly and the related connection graph: (a) structure of ball screw subassembly and (b) connection graph and assembly flow of ball screw subassembly

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Fig. 9

Pitch, yaw, and rolling angle error around x/y/z axes of workbench

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Fig. 10

Structure of ball screw subassembly and local error transmission mechanism of ball screw

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Fig. 11

Multiple measurements of the positioning error of the machine tool VMC850B

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Fig. 12

Percentage contributions of key error sources (in bar graph) on uo, vo, wo and their accumulative percentage contributions (in line graph): (a) contributions on uo, (b) contributions on vo, and (c) contributions on wo

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