Numerical study of parametric effects on the dynamic response of planar multi-body systems with differently located frictionless revolute clearance joints

Abstract

This paper numerically investigates the parametric effects of differently located frictionless revolute clearance joints on the overall dynamic characteristics of a multi-body system. A typical planar slider–crank mechanism is used as a demonstration case in which the effects of clearance size and the input speed on the dynamic response of the mechanism with a revolute clearance joint between the crank and connecting rod, and between the connecting rod and slider are separately investigated with comprehensive observations numerically presented. It is observed that, different joints in a multi-body system have different sensitivities to the clearance size, and changing the driving speed of a mechanism makes the behavior of the mechanism to change from either periodic to chaotic, or chaotic to periodic depending on which joint has clearance. Therefore the dynamic behavior of one clearance revolute joint cannot be used as a general case for a mechanical system. Also the location of the clearance revolute joint, the clearance size and the operating speed of a mechanical system, play a crucial role in predicting accurately the dynamic responses of the system.

Introduction

The dynamic modeling of multi-body systems is a key aid in the analysis, design, optimization, control, and simulation of mechanisms and manipulators. However, clearance, friction, impact and other phenomena associated with real joints have been routinely ignored in order to simplify the dynamic model. The increasing requirement for high-speed and precise machines, mechanisms and manipulators demands that the kinematic joints be treated in a realistic way. This is because in a real mechanical joint, a clearance which permits the relative motion between the connected bodies as well as the components assemblage, is always present. The clearance no matter how small it is, can lead to vibration and fatigue phenomena, premature failure and lack of precision or even random overall behavior. For instance, clearance at joints in a robot has been observed to decrease the positioning accuracy which is a key factor in achieving robotic tasks such as maintenance and assembly. This has led Wanghui et al. [1] to present a novel method based on trajectory planning to avoid the detachment of revolute and spherical joints of a manipulator with clearances. Also the clearances at joints have been observed to cause significant errors in function and path generation mechanisms due to the caused variations in mechanism performance. This has led to recent research activities [2], [3], [4], [5] aimed at developing methodologies for optimizing performance and link parameters in path and function generation mechanisms. Using a reheat-stop-valve of a steam turbine, Dong et al. [6] demonstrated that the clearance size besides other factors leads to uncertainties in the dynamic performance of a mechanism.

There is a significant amount of available literature which discuses theoretical and experimental analysis of imperfect kinematic joints in a variety of planar and spatial mechanical systems with rigid or flexible links [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [2], [3], [4], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40]. Many of these works focus on the planar systems in which only one kinematic joint is modeled as an imperfect joint [7], [8], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [21], [22], [23], [24], [26], [2], [3], [4], [29], [30], [33], [34], [35], [36], [37], [38]. Although, the results from such experimental and analytical models have been shown to provide important insights on the behavior of mechanical systems with imperfect joints, the models do not allow for study of the interactions of multiple kinematic imperfect joints. Furthermore a real mechanical system does not have only one real joint, but practically all joints are real. This led several researchers such as Flores [41] and Cheriyan [42] to strongly recommend for their work to be extended to include multi-body mechanical systems with multiple imperfect joints, and with a variety of joints such as prismatic and universal joints. Few recent papers by Erkaya and Uzmay [25], [28], and by Flores [39] have considered the nonlinear dynamic analysis of multi-body systems with two imperfect joints. However in these research papers, only mechanisms with rigid links have been considered and the interaction effects of the imperfect joints on the overall response of a multi-body system were not investigated. Also, Erkaya and Uzmay [25], [28] modeled the clearance in the journal bearing as a massless imaginary link whose length is equal to the clearance size. This assumption is not valid especially at large clearances because the journal and bearing will not be in contact at all times.

However majority of these works have assumed that differently located revolute joints in a multi-body system when modeled as clearance joints affect the dynamic behavior of the system in a similar manner. Hence the inherent observations derived from investigating the dynamic behavior of one clearance revolute joint have been used as general cases for a mechanical system. Therefore, the primary objective of this research work is to investigate numerically if differently located revolute joints in a multi-body system when modeled as clearance joints affect the behavior of the system in a similar dynamic manner or not. The influence of the main parameters on the dynamic characteristics of a rigid-planar multi-body mechanical system with differently located revolute clearance joints without friction is numerically quantified. The selected parameters are the clearance size and the input crank speed. This work will provide inherent information which can be of great use in the analysis of multi-body systems with clearance joints especially as it regards to the effective design and control tasks of these systems. This study will also form a base towards the investigation of dynamic interaction of multiple revolute clearance joints in a multi-body mechanical system.

Specifically, this work addresses planar mechanical systems with rigid links and with differently located revolute clearance joints without friction. However the flexibility of links, dry friction at the revolute clearance joints and lubrication effects have been shown to significantly affect the dynamic response of multi-body systems. Flores et al. [23], [37], [43] showed that the existence of dry friction at joint clearances causes high peaks on the kinematic and dynamic responses when compared to those obtained with lubricated model, and the performance of the lubricated joint is closer to that of an ideal joint. Schwab et al. [22] demonstrated that the effect of a lubricant in a revolute clearance joint is to significantly smoothen and reduce peak values of responses developed by the contact-impact forces at the joint. The authors also showed that if the links are considered flexible, the dynamic responses are further smoothened and the peak values further reduced. Imedi and Romdhane [27] showed that a flexible link in a mechanism plays a role of suspension in the mechanism by smoothening the dynamic responses and reducing the peak values, and the dynamic behavior is more periodic as compared to rigid link case.