Kinematic and dynamic analysis of pseudo-rigid body model of compliant dwell mechanism

doi:10.3785/j.issn.1006-754X.2022.00.021

Chin J Eng Design

2022, Vol. 29

Issue (2): 202-211 DOI: 10.3785/j.issn.1006-754X.2022.00.021

Modeling, Simulation, Analysis and Decision

Kinematic and dynamic analysis of pseudo-rigid body model of compliant dwell mechanism

Ya-ping DU(

),Chun-hua ZHAO(

),Jia-hui GUO,Chuan ZHOU,Li-qiang ZHANG

School of Mechanical and Automotive Engineering，Shanghai University of Engineering Science，Shanghai 201620，China

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Abstract

Aiming at the large deformation, large deflection and other geometric nonlinear behaviors of the flexible component of the compliant dwell mechanism in motion, the pseudo-rigid body model method was used to analyze this kind of nonlinear large deformation system. Firstly, based on large deflection theory, the buckling analysis of large deformation flexible beam was carried out. The first and second kinds of elliptic integral were used to simulate the flexible beam whose initial state was straight beam, and the load-displacement relation formula was obtained by polynomial fitting. Combined with boundary conditions and force characteristics, the equivalent nonlinear spring pseudo-rigid body model of flexible beam was obtained. On this basis, the kinematic equation of the mechanism was established by using Newton's law, the position of the slider when the crank rotated at a uniform speed was obtained by MATLAB/Simulink modeling and simulation. So the slider displacement curve with double stop characteristics of the mechanism was obtained, the relationship between the slider displacement and time and crank angle was revealed, and the accuracy of the theoretical model was verified by ADAMS(automatic dynamic analysis of mechanical systems) simulation. Secondly, in order to improve the operation accuracy and working performance of the compliant dwell mechanism, its frequency characteristics were studied. Using Lagrange equation, the dynamic model of the mechanism was established from the whole, the analytical expression of the natural frequency of the compliant dwell mechanism was derived, and the influence of section parameters of flexible long beam, length of flexible beam and material performance parameters on the natural frequency of the mechanism were analyzed. The results showed that different parameters had different influences on the natural frequency of the mechanism, so the influences of various parameters on the dynamic characteristics of the mechanism should be comprehensively considered in the optimal design of the compliant dwell mechanism. The research results lay a foundation for the optimal design of compliant dwell mechanism.

Key words： compliant dwell mechanism large deflection theory pseudo-rigid body model motion characteristic natural frequency

Received: 02 March 2021 Published: 06 May 2022

CLC:

TH 113

Corresponding Authors: Chun-hua ZHAO E-mail: duyaping1209@foxmail.com;zchh226@163.com

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Cite this article:

Ya-ping DU,Chun-hua ZHAO,Jia-hui GUO,Chuan ZHOU,Li-qiang ZHANG. Kinematic and dynamic analysis of pseudo-rigid body model of compliant dwell mechanism. Chin J Eng Design, 2022, 29(2): 202-211.

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https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2022.00.021 OR https://www.zjujournals.com/gcsjxb/Y2022/V29/I2/202

柔顺停歇机构伪刚体模型的运动学和动力学分析

针对柔顺停歇机构的柔性构件在运动中产生的大变形、大挠度等几何非线性行为，采用伪刚体模型法来分析该类非线性大变形系统。首先，基于大挠度理论对大变形柔性梁进行屈曲分析，运用第一、第二类椭圆积分模拟初始状态为直梁的柔性梁，用多项式拟合得到其载荷—位移关系式。结合边界条件与受力特性，得到柔性梁的等效非线性弹簧伪刚体模型。在此基础上，运用牛顿定律建立机构运动学方程，通过MATLAB/Simulink建模仿真求得曲柄匀速转动时滑块的位置，得到机构具有双停歇特性的滑块位移曲线，揭示了滑块位移与时间以及曲柄转角之间的关系，并通过ADAMS （automatic dynamic analysis of mechanical systems，机械系统动力学自动分析）仿真验证了理论模型的准确性。其次，为了提高柔顺停歇机构的操作精度和工作性能，对其频率特性进行研究。运用Lagrange方程从机构整体出发建立其动力学模型，推导出柔顺停歇机构固有频率的解析表达式，分析了柔性长梁的截面参数、柔性梁长度和材料性能参数对机构固有频率的影响。结果表明，不同的参数对机构固有频率的影响是不同的，因此在进行柔顺停歇机构的优化设计时要综合考虑各参数对机构动力特性的影响。研究结果为柔顺停歇机构的优化设计奠定了一定基础。

关键词： 柔顺停歇机构, 大挠度理论, 伪刚体模型, 运动特性, 固有频率

Fig.1 Schematic diagram of compliant dwell mechanism

Table 1 Relevant parameters of compliant dwell mechanism

Fig.2 Stress of flexible long beam

Fig.3 Deformation of flexible long beam

Fig.4 Load-displacement curve of flexible long beam

Fig.5 Pseudo-rigid body model of flexible beam

Fig.6 Pseudo-rigid body model of compliant dwell mechanism

Fig.7 Position analysis of the slider

Fig.8 Stress of the slider

Fig.9 Mathematical model of mechanism motion with crank angle as input and slider displacement as output

Fig.10 Variation curve of slider displacement with time

Fig.11 Variation curve of slider displacement with crank angle

Fig.12 Influence of section thickness of flexible long beam on natural frequency of mechanism

Fig.13 Influence of section width of flexible rod on natural frequency of mechanism

Fig.14 Influence of length of flexible long beam on natural frequency of mechanism

Fig.15 Influence of the length of flexible short beam on natural frequency of mechanism

柔性梁材料	E/GPa	ρ/（g/cm³）	$E ρ / 103 N ? m k g 12$	ω/Hz
聚丙烯	1.38	0.90	1.238 28	5.378 5
聚乳酸	3.50	1.25	1.673 32	8.563 9
铍青铜	126	8.30	3.896 24	23.594 2
钛合金	114	4.40	5.090 10	38.729 3
铝合金	71.7	2.71	5.143 69	48.789 1
弹簧钢	207	7.68	5.191 64	57.624 0

Table 2 Natural frequency of mechanism with different flexible beam materials

Fig.16 Influence of the value of

E ρ

on natural frequency of mechanism


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