Nonsmooth spatial frictional contact dynamics of multibody systems
Nonsmooth dynamics algorithms have been widely used to solve the problems of frictional contact dynamics of multibody systems. The linear complementary problems (LCP) based algorithms have been proved to be very effective for the planar problems of frictional contact dynamics. For the spatial proble...
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| Published in | Multibody system dynamics Vol. 53; no. 1; pp. 1 - 27 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Dordrecht
Springer Netherlands
01.09.2021
Springer Nature B.V |
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| Online Access | Get full text |
| ISSN | 1384-5640 1573-272X |
| DOI | 10.1007/s11044-021-09786-w |
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| Abstract | Nonsmooth dynamics algorithms have been widely used to solve the problems of frictional contact dynamics of multibody systems. The linear complementary problems (LCP) based algorithms have been proved to be very effective for the planar problems of frictional contact dynamics. For the spatial problems of frictional contact dynamics, however, the nonlinear complementary problems (NCP) based algorithms usually achieve more accurate results even though the LCP based algorithms can evaluate the friction force and the relative tangential velocity approximately. In this paper, a new computation methodology is proposed to simulate the nonsmooth spatial frictional contact dynamics of multibody systems. Without approximating the friction cone, the cone complementary problems (CCP) theory is used to describe the spatial frictional continuous contact problems such that the spatial friction force can be evaluated accurately. A prediction term is introduced to make the established CCP model be applicable to the cases at high sliding speed. To improve the convergence rate of Newton iterations, the velocity variation of the nonsmooth dynamics equations is decomposed into the smooth velocities and nonsmooth (jump) velocities. The smooth velocities are computed by using the generalized-
a
algorithm, and the nonsmooth velocities are integrated via the implicit Euler algorithm. The accelerated projected gradient descend (APGD) algorithm is used to solve the CCP. Finally, four numerical examples are given to validate the proposed computation methodology. |
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| AbstractList | Nonsmooth dynamics algorithms have been widely used to solve the problems of frictional contact dynamics of multibody systems. The linear complementary problems (LCP) based algorithms have been proved to be very effective for the planar problems of frictional contact dynamics. For the spatial problems of frictional contact dynamics, however, the nonlinear complementary problems (NCP) based algorithms usually achieve more accurate results even though the LCP based algorithms can evaluate the friction force and the relative tangential velocity approximately. In this paper, a new computation methodology is proposed to simulate the nonsmooth spatial frictional contact dynamics of multibody systems. Without approximating the friction cone, the cone complementary problems (CCP) theory is used to describe the spatial frictional continuous contact problems such that the spatial friction force can be evaluated accurately. A prediction term is introduced to make the established CCP model be applicable to the cases at high sliding speed. To improve the convergence rate of Newton iterations, the velocity variation of the nonsmooth dynamics equations is decomposed into the smooth velocities and nonsmooth (jump) velocities. The smooth velocities are computed by using the generalized-
a
algorithm, and the nonsmooth velocities are integrated via the implicit Euler algorithm. The accelerated projected gradient descend (APGD) algorithm is used to solve the CCP. Finally, four numerical examples are given to validate the proposed computation methodology. Nonsmooth dynamics algorithms have been widely used to solve the problems of frictional contact dynamics of multibody systems. The linear complementary problems (LCP) based algorithms have been proved to be very effective for the planar problems of frictional contact dynamics. For the spatial problems of frictional contact dynamics, however, the nonlinear complementary problems (NCP) based algorithms usually achieve more accurate results even though the LCP based algorithms can evaluate the friction force and the relative tangential velocity approximately. In this paper, a new computation methodology is proposed to simulate the nonsmooth spatial frictional contact dynamics of multibody systems. Without approximating the friction cone, the cone complementary problems (CCP) theory is used to describe the spatial frictional continuous contact problems such that the spatial friction force can be evaluated accurately. A prediction term is introduced to make the established CCP model be applicable to the cases at high sliding speed. To improve the convergence rate of Newton iterations, the velocity variation of the nonsmooth dynamics equations is decomposed into the smooth velocities and nonsmooth (jump) velocities. The smooth velocities are computed by using the generalized-a algorithm, and the nonsmooth velocities are integrated via the implicit Euler algorithm. The accelerated projected gradient descend (APGD) algorithm is used to solve the CCP. Finally, four numerical examples are given to validate the proposed computation methodology. |
| Author | Hu, Haiyan Tian, Qiang Wang, Kun |
| Author_xml | – sequence: 1 givenname: Kun surname: Wang fullname: Wang, Kun organization: MOE Key Laboratory of Dynamics and Control of Flight Vehicle, School of Aerospace Engineering, Beijing Institute of Technology – sequence: 2 givenname: Qiang surname: Tian fullname: Tian, Qiang email: tianqiang_hust@aliyun.com organization: MOE Key Laboratory of Dynamics and Control of Flight Vehicle, School of Aerospace Engineering, Beijing Institute of Technology – sequence: 3 givenname: Haiyan surname: Hu fullname: Hu, Haiyan organization: MOE Key Laboratory of Dynamics and Control of Flight Vehicle, School of Aerospace Engineering, Beijing Institute of Technology |
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| Keywords | Nonsmooth Spatial frictional continuous contact Nonlinear complementary problem Cone complementary problem Generalized algorithm |
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| SubjectTerms | Algorithms Automotive Engineering Computation Control Dynamical Systems Electrical Engineering Engineering Friction Mechanical Engineering Multibody systems Nonlinear dynamics Optimization Velocity Vibration |
| Title | Nonsmooth spatial frictional contact dynamics of multibody systems |
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