A nonlinear friction coefficient model for dynamic analysis of multibody mechanical systems with joint clearance

Friction in joints significantly impacts the performance of mechanisms, and the friction coefficient varies with environment conditions. Accurately characterizing the friction coefficient has always been a challenge. In order to investigate the influence of friction coefficient on the dynamic properties of mechanisms, a dynamic model of crank-slider mechanism was constructed considering features such as joint clearance and time-varying nonlinear friction coefficient changing with pressure and speed. The dynamic response and wear prediction of the joint under the influence of nonlinear friction coefficient were analyzed. The results demonstrate that, the axis trajectories exhibit greatly changes on horizontal direction. At the same clearance, under conditions of nonlinear friction coefficients, the contact force is larger compared to that under constant friction coefficients, and the friction force increases with the increase in contact force. Both the contact force and friction force increase with the enlargement of the clearance, and as the clearance increases, the magnitude of the increase in contact force and friction force also increases. Additionally, the collision between the bushing and the pin leads to non-uniform wear on the inner surface of the bushing, with two wear peaks present corresponding to the two positions of highest contact force. Under conditions of nonlinear friction coefficients, the wear amount of the bushing significantly decreases, and the locations of the most severe wear locations of severe wear also change.

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

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.

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.

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

The study reported in this paper investigates the dynamic behavior of a semi-definite nonlinear mechanical structure. It consists of a cantilever beam with uniform thickness subjected to a harmonic excitation at the base; two hinged rigid plates are attached at its free end. The plates can execute oscillations in the horizontal plane without restoring moments. The friction at the hinges is modeled as a Coulomb type with a nonlinear friction coefficient. The excitation parameters at which chaotic motion of the hinged plates is initiated are investigated experimentally as well as numerically. It is shown that the prediction of the dynamic response of this semi-definite system is not accurate in the resonance region. The prediction fails due to the existence of chaotic behavior in that region. The measurement of the dynamic response of the system is conducted using a He-Ne laser system. The numerical results are found to be in a good agreement with the experimental findings.

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.

Uncertainties caused by measuring errors or incomplete knowledge affect the dynamic response and functional reliability of the mechanical system, particularly for the mechanisms with clearance joints. Considering that dependency between the interval parameters in the uncertain quantification of mechanical systems with clearance joints is prone to be ignored, in this article, a dynamic analysis procedure considering the correlation between interval parameters is presented. Firstly, the continuous contact force model and modified friction force model are embedded into the deterministic dynamic governing equations of the mechanical system with clearance joints derived by the Lagrangian method. To characterize the correlation between interval uncertainties, the convex ellipsoid model is employed, and a Chebyshev-based convex scanning method is developed to obtain the bounds of dynamic response. Finally, a robot manipulator with clearance joint considering dependent uncertainties is illustrated as an example to investigate the clearance effect and correlations between uncertainties on the dynamic behavior. In the numerical simulation, the geometrical parameters of the manipulator arm are regarded as dependent interval parameters. The results show that the dependence between interval uncertainties induces relatively conservative bounds and should be considered carefully in the case of a large clearance size existing in the mechanical system.

This article numerically investigates the effects of revolute joint clearance and structural flexibility on the overall dynamic characteristics of a deployable solar array system. Considering torque spring, close cable loop configuration, and lock mechanism, a typical mechanism composed of a main body with a yoke and two panels is used as a demonstration case to study the effects of clearance and flexibility on the dynamic response of the deployable solar array system in the deployment and lock process. The normal contact force model and tangential friction model in clearance joint are established using Lankarani Nikravesh model and modified Coulomb friction model, respectively. The numerical simulation results reveal that the coupling of clearance and flexibility makes different effects on the dynamic characteristics of the deployable space solar arrays for different operation stages. Besides, the clearance and flexibility of a mechanical system play crucial roles in predicting accurately the dynamic response of the system, which is the foundation of mechanism design, precision analysis, and control system design.

In machines and mechanisms, most of the clearance joints are designed to operate with lubricant fluid, which is an effective way of ensuring better performance of the mechanical systems. The differently located lubricated joints interact with each other, influencing the total performances of the mechanical system. In this study, a numerical coupling model for the dynamics and lubrication analyses of the multibody system with multiple lubricated clearance joints is established. This approach couples the dynamics model of the multibody system with the lubrication models of translational and revolute clearance joints. The dynamics model is established by the Lagrange’s method, while The lubrication models are solved using the finite element method. The hydrodynamic forces built up by the lubricant fluid are evaluated from the motion states of the system and then input into dynamics model of the multibody system. Finally, the proposed approach is applied to a four-stroke gasoline engine with the lubricated piston skirt-liner subsystem and lubricated bearing at the big end of the connecting rod.

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.

In general, joints are assumed without clearance in the dynamic analysis of multi-body echanical systems. When joint clearance is considered, the mechanism obtains two uncontrollable degrees of freedom and hence the dynamic response considerably changes. The joints’ clearances are the main sources of vibrations and noise due to the impact of the coupling parts in the joints. Therefore, the system responses lead to chaotic and unpredictable behaviors instead of being periodic and regular. In this paper, nonlinear dynamic behavior of a four-bar linkage with clearance at the joint between the coupler and the rocker is studied. The system response is performed by using a nonlinear continuous contact force model proposed by Lankarani and Nikravesh [1] and the friction effect is considered by a modified Coulomb friction law [2]. By using the Poincare portrait, it is proven that either strange attractors or chaos exist in the system response. Numerical simulations display both periodic and chaotic motions in the system behavior. Therefore, bifurcation analysis is carried out with a change in the size of the clearance corresponding to different values of crank rotational velocities. Fast Fourier Transformation is applied to analyze the frequency spectrum of the system response.

Due to kinematic function requirements, deployable structures inevitably have many clearance joints. The existence of clearance joints not only reduces the structural stiffness but also leads to complex nonlinear dynamic characteristics. This paper proposed a general numerical method based on the wave motion theory, which is able to analyze these complex nonlinear dynamic characteristics of frame structures with clearance joints. The dynamic model of frame structures with clearance joints is derived on the basis of continuous wave equations. The clearance joint is modeling by combining Lankarani and Nikravesh contact model with the Ambrósio friction model. The established dynamic model of frame structures is solved by the finite difference time domain (FDTD) method. A triangular frame structure with two clearance joints is taken as the numerical example for the verification of the proposed numerical method. Numerical results show that the longitudinal wave affects the distribution direction of contact positions and the transverse wave mainly affects the distribution range of contact positions. It has been also found that the introduction of torsional springs with reasonable pretension torque is able to significantly improve the distribution of contact positions and reduce state uncertainties of clearance joints in structural vibrations.

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.

Dynamics analysis of space robot manipulator with joint clearance