The polytope-based tolerance analysis in design process uses a finite set of constraints to represent specifications and propagates these constraints to any objective point in the Euclidean space. The operations of Minkowski sum and intersection on polytopes are well suited to serial and parallel assemblies. The polytope model has been applied to complex assemblies which contain a large number of joints and geometrical tolerances. However, the previous studies on this model consider toleranced features as surfaces of perfect form. The ignorance of form defects in tolerance analysis would result in a significant loss in accuracy and reliability. In this paper, an extension of the polytope model for tolerance analysis considering form defects is described in which the skin model shape representing the physical shape of the product is adopted to simulate the actual toleranced feature in place of the substitute one used conventionally. The combination of polytope model and skin model shape is expected to inherit many of the advantages of each model, combining easy-to-use tolerance propagation and form defects representation with accuracy guarantees. To demonstrate the method and its respective application, a case study of an assembly is illustrated in detail. The proposed method further enhances the capability of the polytope model in handling form defects and provides more realistic assembly results that approximate the actual assembly conditions for design evaluation.
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June 2019
Research-Article
Form Defects Consideration in Polytope-Based Tolerance Analysis
Ting Liu,
Ting Liu
Key Laboratory of Advanced Manufacturing
Technology of Zhejiang Province,
School of Mechanical Engineering,
Zhejiang University,
Hangzhou 310027, China
e-mail: tingliu@zju.edu.cn
Technology of Zhejiang Province,
School of Mechanical Engineering,
Zhejiang University,
Hangzhou 310027, China
e-mail: tingliu@zju.edu.cn
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Laurent Pierre,
Laurent Pierre
LURPA,
ENS Paris-Saclay,
University Paris-Sud,
Université Paris-Saclay,
Cachan 94235, France
e-mail: laurent.pierre@ens-paris-saclay.fr
ENS Paris-Saclay,
University Paris-Sud,
Université Paris-Saclay,
Cachan 94235, France
e-mail: laurent.pierre@ens-paris-saclay.fr
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Nabil Anwer,
Nabil Anwer
LURPA,
ENS Paris-Saclay,
University Paris-Sud,
Université Paris-Saclay,
Cachan 94235, France
e-mail: nabil.anwer@ens-paris-saclay.fr
ENS Paris-Saclay,
University Paris-Sud,
Université Paris-Saclay,
Cachan 94235, France
e-mail: nabil.anwer@ens-paris-saclay.fr
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Yanlong Cao,
Yanlong Cao
State Key Laboratory of Fluid Power and
Mechatronic Systems,
School of Mechanical Engineering,
Zhejiang University,
Hangzhou 310027, China;
Key Laboratory of Advanced Manufacturing
Technology of Zhejiang Province,
School of Mechanical Engineering,
Zhejiang University,
Hangzhou 310027, China
e-mail: sdcaoyl@zju.edu.cn
Mechatronic Systems,
School of Mechanical Engineering,
Zhejiang University,
Hangzhou 310027, China;
Key Laboratory of Advanced Manufacturing
Technology of Zhejiang Province,
School of Mechanical Engineering,
Zhejiang University,
Hangzhou 310027, China
e-mail: sdcaoyl@zju.edu.cn
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Jiangxin Yang
Jiangxin Yang
Key Laboratory of Advanced Manufacturing
Technology of Zhejiang Province,
School of Mechanical Engineering,
Zhejiang University,
Hangzhou 310027, China
e-mail: yangjx@zju.edu.cn
Technology of Zhejiang Province,
School of Mechanical Engineering,
Zhejiang University,
Hangzhou 310027, China
e-mail: yangjx@zju.edu.cn
Search for other works by this author on:
Ting Liu
Key Laboratory of Advanced Manufacturing
Technology of Zhejiang Province,
School of Mechanical Engineering,
Zhejiang University,
Hangzhou 310027, China
e-mail: tingliu@zju.edu.cn
Technology of Zhejiang Province,
School of Mechanical Engineering,
Zhejiang University,
Hangzhou 310027, China
e-mail: tingliu@zju.edu.cn
Laurent Pierre
LURPA,
ENS Paris-Saclay,
University Paris-Sud,
Université Paris-Saclay,
Cachan 94235, France
e-mail: laurent.pierre@ens-paris-saclay.fr
ENS Paris-Saclay,
University Paris-Sud,
Université Paris-Saclay,
Cachan 94235, France
e-mail: laurent.pierre@ens-paris-saclay.fr
Nabil Anwer
LURPA,
ENS Paris-Saclay,
University Paris-Sud,
Université Paris-Saclay,
Cachan 94235, France
e-mail: nabil.anwer@ens-paris-saclay.fr
ENS Paris-Saclay,
University Paris-Sud,
Université Paris-Saclay,
Cachan 94235, France
e-mail: nabil.anwer@ens-paris-saclay.fr
Yanlong Cao
State Key Laboratory of Fluid Power and
Mechatronic Systems,
School of Mechanical Engineering,
Zhejiang University,
Hangzhou 310027, China;
Key Laboratory of Advanced Manufacturing
Technology of Zhejiang Province,
School of Mechanical Engineering,
Zhejiang University,
Hangzhou 310027, China
e-mail: sdcaoyl@zju.edu.cn
Mechatronic Systems,
School of Mechanical Engineering,
Zhejiang University,
Hangzhou 310027, China;
Key Laboratory of Advanced Manufacturing
Technology of Zhejiang Province,
School of Mechanical Engineering,
Zhejiang University,
Hangzhou 310027, China
e-mail: sdcaoyl@zju.edu.cn
Jiangxin Yang
Key Laboratory of Advanced Manufacturing
Technology of Zhejiang Province,
School of Mechanical Engineering,
Zhejiang University,
Hangzhou 310027, China
e-mail: yangjx@zju.edu.cn
Technology of Zhejiang Province,
School of Mechanical Engineering,
Zhejiang University,
Hangzhou 310027, China
e-mail: yangjx@zju.edu.cn
1Corresponding author.
Contributed by the Design for Manufacturing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 19, 2018; final manuscript received October 16, 2018; published online January 31, 2019. Assoc. Editor: Rikard Söderberg.
J. Mech. Des. Jun 2019, 141(6): 061702 (16 pages)
Published Online: January 31, 2019
Article history
Received:
June 19, 2018
Revised:
October 16, 2018
Citation
Liu, T., Pierre, L., Anwer, N., Cao, Y., and Yang, J. (January 31, 2019). "Form Defects Consideration in Polytope-Based Tolerance Analysis." ASME. J. Mech. Des. June 2019; 141(6): 061702. https://doi.org/10.1115/1.4041784
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