A numerical coupling model for a multibody system with multiple lubricated clearance joints

The clearances of joints in a rigid multibody system may deteriorate the motion accuracy and even cause vibrations, noise and fatigue failure of structures. In over-constrained mechanisms, the number of degree-of-freedoms is more than that of independent coordinates which leads to numerical challenges in solving the underdetermined force equilibrium equations. A comprehensive study on the dynamic model and the performance of an over-constrained planar parallelogram mechanism with multiple clearance joints is presented in this paper. Since a common angular coordinate exists in the clearance joint associated with the redundant constraint, the degree-of-freedoms are revised by eliminating the number of redundant constraints. In planar analysis, the location of mass center and the orientation of the body reference with respect to the inertial frame are selected as the generalized coordinates of the components. Clearance joints are equivalent as the spring-damper elements and the contact forces are introduced into the dynamic equations by force constraints. The developed computational algorithm is implemented by MATLAB and may analyze the dynamic performance of this mechanism due to the elimination of kinematic constraints and the nonlinear contact-impact behavior in the clearance joints. Meanwhile, an orthogonal experimental design based on a quantitative analysis method demonstrates that the clearance size and the location of clearance joints affect the kinematic accuracy and counterbalance moment of the mechanism.

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

Multiple lubricated joints with long and short bearings in multibody mechanical systems - Modeling, simulation, and performance analysis

Over the last two decades, extensive work has been conducted on dynamic effect of joint clearances in multibody mechanical systems. In contrast, little work has been devoted to optimizing the performance of these systems. In this study, analysis of revolute joint clearance is formulated in term of a Hertzian-based contact force model. For illustration, the classical slider-crank mechanism with a revolute clearance joint at the piston pin is presented, and a simulation model is developed using the analysis/design code MSC.ADAMS. The clearance is modeled as a pin-in-a-hole surface-to-surface dry contact, with appropriate contact force model between the joint and bearing surfaces. Different simulations are performed to demonstrate the influence of the joint clearance size and the input crank speed on the dynamic behavior of the system with the clearance joint. An innovative design-of-experiment (DOE)-based method for optimizing the performance of a mechanical system with the revolute joint clearance for different ranges of design parameters is then proposed. Based on the simulation model results from sample points, which are selected by a Latin hypercube sampling (LHS) method, a polynomial function Kriging meta-model is established instead of the actual simulation model. The reason for development and use of the meta-model is to bypass computationally intensive simulations of a computer model for different design parameter values in place of a more efficient and cost-effective mathematical model. Finally, numerical results obtained from two application examples, considering the different design parameters, including the joint clearance size, crank speed, and contact stiffness, are presented for further analyzing the dynamics of the revolute clearance joint in a mechanical system. This allows for predicting the influence of design parameter changes, in order to minimize contact forces, accelerations, and power requirements due to the existence of joint clearance.

Dynamics modeling and quantitative analysis of multibody systems including revolute clearance joint

Clearance is inevitable for manufacture and assembly in the revolute joints of multibody systems. Excessive value of joint clearance will lead to the poor dynamic performance of mechanism, namely noise, vibration and fatigue failure. This paper presents the development of a dynamic model for planar multibody systems with clearance joints. Based on the continuous contact law, the contact force model proposed by Lankarani and Nikravesh is employed to describe the contact–impact phenomenon between pin and hole. And, the incorporation of the friction influence on revolute joint clearance is conducted by a modified friction force model. According to the geometric relationship between contact elements, the kinematics of the multibody systems is mapped into the global coordinate systems. Additionally, an experimental test platform is set up whereby a slider–crank mechanism with two clearance joints is used as an example to demonstrate the correctness and effectiveness of the proposed approach. Finally, the effects of joint clearance on the dynamic characteristics of planar multibody systems are investigated.

Collision and wear are common phenomena in revolute clearance joints, caused by the positional deviation between the journal and bearing centers. The freedom of motion and contact–impact characteristics are reflected in the mechanism’s movement. The penetration behavior of the clearance joint is described using modified elastic contact model combined with Coulomb’s friction. In addition, the dynamic model of a high-precision mechanism with a clearance joint is established using Largrange’s equation. A dynamic performance experiment is also conducted. The results prove the validity of the proposed method. The kinematic accuracy of this mechanism is then used to evaluate the stability and motion error in a case study. Furthermore, the influence of the clearance joint on the dynamic behavior of the high-precision mechanism is thoroughly analyzed. The results show that the fluctuation range of the slider’s dynamic repeated precision for slider is only 0.022 mm under high-speed conditions, meeting the design requirement.

In mechanical systems, the effect of friction on the dynamic response of the mechanism is unavoidable. In order to describe the friction behavior at the revolute joint of mechanical systems more accurately, the friction coefficient is modeled as a nonlinear function with respect to pressure and rotational speed based on material-level friction tests. Combined with the Ambrósio friction model, we propose a friction model with nonlinear friction coefficient, and the dynamics of a crank-slider mechanism containing a revolute clearance joint is analyzed based on the proposed model. The results show that the friction model with nonlinear friction coefficient can improve the accuracy of numerical simulation of the system and promote the capability of prediction of dynamic response of complex mechanical systems with joint clearance.

Modeling and simulation of wear in revolute clearance joints in multibody systems

There is still lack of effective modelling, simulation and optimisation methods for complex electromechanical system. In this paper, the dynamics model of the PMSM-precision reducer system is established using Lagrange-Maxwell equation. The simulation model and optimisation model of this system are set up with Modelica language. The simulation and optimisation of the system are realised in Dymola and JModelica.org platforms respectively. Simulation results show that the dynamics model of the system is correct. Optimisation results show that the system can quickly respond to the given speed and loads. The proposed modelling, simulation and optimisation method based on Modelica may be commonly applied to other complex electromechanical systems.

An enhanced formulation to model spatial revolute joints with radial and axial clearances

SUMMARYIn reality, clearances in the joints are inevitable due to tolerances, and defects arising from design and manufacturing. Therefore, poor dynamic performance, reduction in components component lifetimes and generation of undesirable vibrations result in impacts of mating parts in the clearance joint. In this study, the dynamic behavior of a planar mechanism with revolute joints, in the presence of clearances is investigated. A continuous contact force model, based on elastic Hertz theory together with a dissipative term, is used to evaluate the contact forces here. Moreover, using a contact model, the effects of working speed and clearance size on the dynamic characteristics of a planar mechanical system are analyzed and compared. Furthermore, numerical results for a 3RRR planar parallel manipulator with six revolute clearance joints are presented.

Analysis of angular errors of the planar multi-closed-loop deployable mechanism with link deviations and revolute joint clearances

A non-penetration approach of frictional contact analysis is presented for modeling revolute clearance joints of planar rigid multibody systems. In the revolute clearance joint, the motion modes of the journal are divided into three categories, namely, the free motion, collision, and permanent contact modes. The switch between different contact modes is identified by the state of the journal and bearing, including the gap and the normal relative velocity. When impact in the revolute clearance joint is detected, the collision process is simulated by the impulse-based differential approach, where Stronge’s improved model for restitution is employed to determine the relative velocity after impact. Instead of algebraic equations, the impact process is described by a set of ordinary differential equations (ODEs), which avoids solving complementarity problems. Moreover, in the permanent contact mode, the constraint-based approach and modified Coulomb’s friction law are adopted. The permanent contact mode maintains for most of the time and the governing ODEs are non-stiff. There is general agreement that the constraint-based approach is more efficient than the force-based method. A slider–crank mechanism with a revolute clearance joint is considered as a demonstrative application example where the comparison with the continuous contact force model is investigated.

This paper aims at investigating precisely the dynamic performance of deployable structure constituted by scissor unit mechanisms with clearance joint. Based on the motion law in real joints, the contact model is established using an improved Gonthier nonlinear continuous contact force model, and the friction effect is considered using LuGre model. Moreover, the resulting contact force is suitable to be included into the generalized force of the equations of motion of a multibody system and contributes to replace motion constraints. In the sequel of this process, the effect of joint clearance is successfully introduced into the dynamical model of scissor deployable structure and the dynamic characteristics of deployable structure with joint clearance are obtained using a direct default correction method, which can directly modify the coordinates and speed of the system to avoid the numerical results divergence. Also, the new hybrid contact force model of revolute joint clearance is verified through comparing with the original model. The numerical simulation results show that the improved contact model proposed here has the great merit that predicts the dynamic behavior of scissor deployable structure with joint clearance.