Kinematic accuracy and nonlinear dynamics of a flexible slider-crank mechanism with multiple clearance joints

Highlights

• An efficient action prediction method of a flexible slider-crank mechanism with multiple clearance joints is proposed.

• The dynamic characteristics is computed based on the rotational speed fluctuation test data.

• The effects of external load on the stability analysis of slider-crank mechanism is studied.

• The probability density distribution is used to describe the bifurcation and chaos.

Abstract

Clearance joint appears in the multibody system and it could cause the uncertainty of motion. A general method for dynamic modelling and analysis of slider-crank mechanism with multiple clearance joints is presented and discussed in this work. The contact-impact characteristics of clearance joint are described by the nonlinear continuous contact force model. With flexible link taken into account, the dynamic characteristics of slider-crank mechanism with multiple clearance joints are analyzed based on the presented model. Then, the dynamic response of a flexible slider-crank mechanism is measured to clarify how to clearance joints can cause the vibration phenomenon of multibody system. Moreover, the stability and chaos analysis are conducted with the purpose of performing a parametric study, which quantifies the effects of clearance size and rotational speed on dynamic behavior of multibody system with multiple clearance joints. The numerical results indicate that the dynamic behavior of a flexible slider-crank mechanism depends on the characteristics of clearance joints.

Introduction

For the requirement of high precision, the accuracy is an essential element in the design of multibody systems. However, the existence of clearance would cause the worse dynamic characteristics of mechanism, namely vibration, wear and fatigue (Lai et al., 2017a; Li et al., 2019; Khemili and Romdhane, 2008; Xu and Yang, 2016; Wang et al., 2016a). Then, how to establish an effective model for describing the dynamic behavior of mechanical systems with multiple joint clearances is attracted many researchers (Tian et al., 2018; Yang et al., 2015, 2016; Zhao et al., 2015; Zheng et al., 2016a; Erkaya and Uzmay, 2008; Liu et al., 2015; Zhan et al., 2018). For instance, high-precision press system is the machine tool for manufacturing the high-precision part, such as automobile parts, stator and rotor. The transmission mechanism is similar to a slider-crank mechanism and the clearance joints are subordinate to the mechanical systems. Although the size of clearance is small, the trajectory of slider would deviate and the quality of production cannot be assurance. Therefore, the type of clearance joint and the illustration of contact-impact characteristics are always discussed in recent years (Yao et al., 2015; Lai et al., 2017b).

A significant amount of references represents the modelling method of revolute joint and translational joint considering clearance, and the contact-impact characteristics of clearance joint are also discussed (Zhao et al., 2019; Erkaya, 2013; Guo et al., 2019). Flores et al. (Flores and Ambrósio, 2010; Machado et al., 2012a) proposed a comprehensive method to describe the contact-impact characteristics in multibody systems, which could automatically adjust the time step. The numerical results showed this method had a good computational efficiency and it was suitable to different state (non-contact and contact). With the nonlinear stiffness coefficient taken into account, Bai and Zhao, 2012, 2013 developed a hybrid contact force model for illustrating the dynamic behavior of revolute joint with clearance. The case study demonstrated that the model was simplicity used in the planar mechanical systems. Moreover, Alves et al. (2015) conducted a comparative study of viscoelastic contact models. Based on the Hertz contact theory, the effects of restitution coefficient on the contact-impact characteristics of solids were discussed. Varedi et al. (2015) analyzed the feature of revolute joint clearance and proposed an optimization method to reduce the undesirable effects of revolute joint clearance. And, an application case was employed to demonstrate the efficiency of this method. Zhang (Zhang and Zhang, 2017) introduced an approach for minimizing the influence of revolute joint clearance on the dynamic characteristics of planar redundantly actuated mechanism. The two-step Bathe integration method was used to solve the restrained equations of revolute joint clearances. In addition, the 3D revolute joint with clearance was established by Cavalieri and Cardona (2018). On account of the non-smooth model, the equations of motion were solved and the numerical examples illustrated the preferable adaptability of this methodology. On the other hand, the model of translational joint clearance was introduced by Flores and Leine (Flores et al., 2010a). The contact type and constraint condition were discussed in this work. The Moreau time-stepping method was employed to solve the linear complementarity problem. Meanwhile, the model of translational joint with clearance was extended by Zhuang and Wang, 2013, 2014, which illustrated the problem of contact situation between slider and guideway. The introduction of Baumgarte's stabilization method could decrease the constraint drift. Considering the effects of variable stiffness, a new model of 3D translational joint with clearance was developed by Wu and Sun (Wu et al., 2020). Based on the Monte Carlo method, the dimensionless factor varying the ratios of contact region sides was obtained and the influences of inclination angle and initial impact velocity on the dynamic characteristics in solids were investigated.

It is important to note that the influence of multiple clearance joints on the dynamic behavior of multibody systems (Ma et al., 2015a; Li et al., 2018a; Xu, 2017; Kong and Tian, 2020). Li at al (Li et al., 2015a). proposed a model for describing the angular errors in mechanical system with joint clearances. The effectiveness of proposed model was demonstrated by the Monte Carlo method and the probability density functions were also given out. Considering the effects of flexible characteristics, Tian et al. (Wang et al., 2016b; Tian et al., 2017a) established the dynamic analysis model of mechanical systems with uncertain joint clearance. Based on the ANCF, the simulation results could illustrate that the clearance and flexible effected on the nonlinear dynamics and chaotic control. The numerical investigation of effects of joint clearance and flexible link on the dynamic response of multibody systems was conducted by Zheng (Zheng et al., 2016b, 2019). The multilink mechanism was used as an application case for demonstrating the accuracy of proposed model. The journal center path of revolute joint and acceleration of slider were shown. In addition, the nonlinear dynamics of slider-crank mechanism with multiple clearance joints were discussed by Yaqubi et al. (2016). In this work, the Poincare maps and bifurcation diagrams were employed to represent the effects of multiple clearance joints on the nonlinear behavior of slider-crank mechanism. With the multiple clearance joints taken into account, the nonlinear vibration behavior of mechanical system was conducted by Salahshoor and Ebrahimi (Salahshoor et al., 2016, 2018). Based on the method of multiple scales, the primary resonance and internal resonance were discussed detailedly. In order to obtain the dynamic analysis results of slider-crank mechanism accurately, Li et al., 2016, 2018b made a general method for studying the dynamic behavior of slider-crank with flexible components and clearance joints. Compared with traditional methods, the proposed approach could provide optimization results for the design of mechanical systems. Based on the L-N model and elastic foundation model, Ma (Ma et al., 2016; Ma and Qian, 2017) investigated the influence of multiple revolute clearance joints on the planar multibody systems. The location and size of clearance joints (27 kinds) were listed. Then, the motion trajectory of slider and contact force were given out. Meanwhile, Erkaya (Erkaya et al., 2015a; Erkaya, 2019) conducted a comparative study for illustrating how to minimize the effects of clearance joint and flexible link on the dynamic response of slider-crank mechanism. The experiment could not only demonstrate the effectiveness of proposed method, but also revealed the joint clearance effected on actuator power consumption in multibody systems.

However, the most work conduct the multiple clearance joints in the mechanical systems and the investigation of clearance both revolute joint and translational joint has not almost been found. In this paper, a suitable method to indicate the dynamic characteristics of the flexible slider-crank mechanism considering multiple clearance joints (both revolute joint and translational joint). The flexible characteristics of link is established by ANSYS and the natural frequency is obtained. Based on the continuous contact force model, the effects of revolute joint and translational joint with clearance on the contact-impact characteristics are represented. Then, compared with the experimental data, the nonlinear dynamic characteristics and chaotic analysis are discussed.