Lubricated revolute joints in rigid multibody systems

The main purpose of this work is to present a general methodology for modeling lubricated revolute joints in constrained rigid multibody systems. In the dynamic analysis of journal-bearings, the hydrodynamic forces, which include both squeeze and wedge effects, generated by the lubricant fluid, oppose the journal motion. The hydrodynamic forces are obtained by integrating the pressure distribution evaluated with the aid of Reynolds’ equation, written for the dynamic regime. The hydrodynamic forces built up by the lubricant fluid are evaluated from the system state variables and included into the equations of motion of the multibody system. Numerical examples are presented in order to demonstrate the use of the methodologies and procedures described in this work.     

Simulation of planar flexible multibody systems with clearance and lubricated revolute joints

Modeling of clearance joints plays an important role in the analysis and design of multibody mechanical systems. Based on the absolute nodal coordinate formulation (ANCF), a new computational methodology for modeling and analysis of planar flexible multibody systems with clearance and lubricated revolute joints is presented. A planar absolute nodal coordinate formulation based on the locking-free shear deformable beam element is implemented to discretize the flexible bodies. A continuous contact-impact model is used to evaluate the contact force, in which energy dissipation in the form of hysteresis damping is considered. A force transition model from hydrodynamic lubrication forces to dry contact forces is introduced to ensure continuity in the joint reaction force. A comprehensive study with different lubrication force models has also been carried out. The generalized-α method is used to solve the equations of motion and several efficient methods are incorporated in the proposed model. Finally, the methodology is validated by two numerical examples.     

Modeling and simulation of planar multibody systems considering multiple revolute clearance joints

Nonlinear Dynamics - This paper presents a general procedure for dynamic modeling and simulation of planar multibody systems considering multiple revolute clearance joints. The normal contact force...     

Numerical and experimental investigation on multibody systems with revolute clearance joints

A comprehensive combined numerical and experimental study on the dynamic response of a slider-crank mechanism with revolute clearance joints is presented and discussed in this paper to provide an experimental verification and validation of the predictive capabilities of the multibody clearance joint models. This study is supported in an experimental work in a test rig, which consists of a slider-crank mechanism with an adjustable radial clearance at the revolute joint between the slider and the connecting rod. The motion of the slider is measured with a linear transducer and an accelerometer. Dynamic tests at different operating crank speeds and with several clearance sizes are performed. The maximum slider acceleration, associated with the impact acceleration, is used as a measure of the impact severity. The obtained results demonstrate the dynamical behavior of a multibody mechanical system with a clearance joint. Finally, the correlation between the numerical and experimental results is presented and discussed leading to validated models of clearance revolute joints.     

Dynamic analysis of planar rigid-body mechanical systems with two-clearance revolute joints

In this paper, the behavior of planar rigid-body mechanical systems due to the dynamic interaction of multiple revolute clearance joints is numerically studied. One revolute clearance joint in a multibody mechanical system is characterized by three motions which are: the continuous contact, the free-flight, and the impact motion modes. Therefore, a mechanical system with n-number of revolute clearance joints will be characterized by 3 ⁿ motions. A slider-crank mechanism is used as a demonstrative example to study the nine simultaneous motion modes at two revolute clearance joints together with their effects on the dynamic performance of the system. The normal and the frictional forces in the revolute clearance joints are respectively modeled using the Lankarani–Nikravesh contact-force and LuGre friction models. The developed computational algorithm is implemented as a MATLAB code and is found to capture the dynamic behavior of the mechanism due to the motions in the revolute clearance joints. This study has shown that clearance joints in a multibody mechanical system have a strong dynamic interaction. The motion mode in one revolute clearance joint will determine the motion mode in the other clearance joints, and this will consequently affect the dynamic behavior of the system. Therefore, in order to capture accurately the dynamic behavior of a multi-body system, all the joints in it should be modeled as clearance joints.     

Modeling 3D revolute joint with clearance and contact stiffness

The clearances in the kinematic joints are due to deformations, wear, and manufacturing errors; the accurate modeling of these effects in multibody analysis is a complex issue but in many practical applications, it is mandatory to take into them into account in order to understand the actual behavior of mechanical systems. In this paper, the authors present a general computer-aided model of a 3D revolute joint with clearance suitable for implementation in multibody dynamic solvers. While a perfect revolute joint imposes kinematic constraints, the proposed revolute joint with clearance leads to a force constraint. The revolute joint has been modeled by introducing a nonlinear equivalent force system, which takes into account the contact elastic deformations. The model depends on the structural and geometrical properties of materials in contact that have been investigated using finite element models. The purpose is to give a general approach to study the influence of actual joints on kinematic, dynamic, and structural behavior of mechanisms. The proposed model has been applied in dynamic simulations of a spatial slider-crank mechanism.     

含摩擦滑移铰平面多刚体系统动力学的数值算法

基于LuGre摩擦模型和线性互补问题(LCP)的数值算法,给出了具有双边约束含摩擦滑移铰平面多体系统动力学的数值算法.首先,根据滑移铰的特点,当间隙充分小时,将其视为双边约束,给出了滑移铰中滑道作用于滑块上的法向接触力的互补关系;LuGre摩擦模型能有效地描述机械系统中的黏滞与滑移运动,将该模型用于描述滑块与滑道间的摩擦力.其次,结合Baumgarte约束稳定化方法,应用第一类Lagrange方程,建立了该多体系统的动力学方程,给出了Lagrange乘子与滑移铰中作用于滑块上的法向接触力的关系式.然后,将滑块与滑道间多种接触状态的判断以及作用于滑块上的法向接触力的计算转换为线性互补问题的求解,并用常微分方程的数值算法求解该多体系统的动力学方程.最后,通过数值仿真算例揭示了滑移铰中滑块的黏滞与滑移现象,以及滑块在滑道内的多种接触状态;另外,在文中分别采用Coulomb干摩擦模型和LuGre摩擦模型,对算例中的某些工况进行了数值仿真,并且分别用本文方法得到的数值仿真结果与已有方法得到的数值仿真结果对比,表明了本文给出的方法的有效性.      

Dynamics analysis of 2-DOF complex planar mechanical system with joint clearance and flexible links

Joint clearance and flexible links are two important factors that affect the dynamic behaviors of planar mechanical system. Traditional dynamics studies of planar mechanism rarely take into account both influence of revolute clearance and flexible links, which results in lower accuracy. And many dynamics studies mainly focus on simple mechanism with clearance, the study of complex mechanism with clearance is a few. In order to study dynamic behaviors of two-degree-of-freedom (DOF) complex planar mechanical system more precisely, the dynamic analyses of the mechanical system with joint clearance and flexibility of links are studied in this work. Nonlinear dynamic model of the 2-DOF nine-bar mechanical system with revolute clearance and flexible links is built by Lagrange and finite element method (FEM). Normal and tangential force of the clearance joint is built by the Lankarani–Nikravesh and modified Coulomb’s friction models. The influences of clearance value and driving velocity of the crank on the dynamic behaviors are researched, including motion responses of slider, contact force, driving torques of cranks, penetration depth, shaft center trajectory, Phase diagram, Lyapunov exponents and Poincaré map of clearance joint and slider are both analyzed, respectively. Bifurcation diagrams under different clearance values and different driving velocities of cranks are also investigated. The results show that clearance joint and flexibility of links have a certain impact on dynamic behavior of mechanism, and flexible links can partly decrease dynamic response of the mechanical system with clearance relative to rigid mechanical system with clearance.     

A parametric study on the dynamic response of planar multibody systems with multiple clearance joints

A general methodology for dynamic modeling and analysis of multibody systems with multiple clearance joints is presented and discussed in this paper. The joint components that constitute a real joint are modeled as colliding bodies, being their behavior influenced by geometric and physical properties of the contacting surfaces. A continuous contact force model, based on the elastic Hertz theory together with a dissipative term, is used to evaluate the intrajoint contact forces. Furthermore, the incorporation of the friction phenomenon, based on the classical Coulomb’s friction law, is also discussed. The suitable contact-impact force models are embedded into the dynamics of multibody systems methodologies. An elementary mechanical system is used to demonstrate the accuracy and efficiency of the presented approach, and to discuss the main assumptions and procedures adopted. Different test scenarios are considered with the purpose of performing a parametric study for quantifying the influence of the clearance size, input crank speed, and number of clearance joints on the dynamic response of multibody systems with multiple clearance joints. Additionally, the total computation time consumed in each simulation is evaluated in order to test the computational accuracy and efficiency of the presented approach. From the main results obtained in this study, it can be drawn that clearance size and the operating conditions play a crucial role in predicting accurately the dynamic responses of multibody systems.     

Study of the effect of contact force model on the dynamic response of mechanical systems with dry clearance joints: computational and experimental approaches

The main objective of this work is to present a computational and experimental study on the contact forces developed in revolute clearance joints. For this purpose, a well-known slider-crank mechanism with a revolute clearance joint between the connecting rod and slider is utilized. The intra-joint contact forces that are generated at these clearance joints are computed by considering several different elastic and dissipative approaches, namely those based on the Hertz contact theory and the ESDU tribology-based cylindrical contacts, along with a hysteresis-type dissipative damping. The normal contact force is augmented with the dry Coulomb’s friction force. In addition, an experimental apparatus is used to obtained some experimental data in order to verify and validate the computational models. From the outcomes reported in this paper, it is concluded that the selection of the appropriate contact force model with proper dissipative damping plays a significant role in the dynamic response of mechanical systems involving contact events at low or moderate impact velocities.     

Modeling of joints with clearance in flexible multibody systems

This paper is concerned with the modeling of joints with clearance within the framework of finite element based dynamic analysis of nonlinear, flexible multibody systems. For actual joints, clearance, lubrication and friction phenomena can significantly affect the dynamic response of the system. In this work, the effects of clearance and lubrication are studied for revolute and spherical joints. The formulation is developed within the framework of energy preserving and decaying time integration schemes that provide unconditional stability for nonlinear, flexible multibody systems. Numerical examples are presented that demonstrate the efficiency and accuracy of the proposed approach. The importance of modeling structural damping and limited driving power are discussed.     

Spatial rigid-multibody systems with lubricated spherical clearance joints: modeling and simulation

The dynamic modeling and simulation of spatial rigid-multibody systems with lubricated spherical joints is the main purpose of the present work. This issue is of paramount importance in the analysis and design of realistic multibody mechanical systems undergoing spatial motion. When the spherical clearance joint is modeled as dry contact; i.e., when there is no lubricant between the mechanical elements which constitute the joint, a body-to-body (typically metal-to-metal) contact takes place. The joint reaction forces in this case are evaluated through a Hertzian-based contact law. A hysteretic damping factor is included in the dry contact force model to account for the energy dissipation during the contact process. The presence of a fluid lubricant avoids the direct metal-to-metal contact. In this situation, the squeeze film action, due to the relative approaching motion between the mechanical joint elements, is considered utilizing the lubrication theory associated with the spherical bearings. In both cases, the intra-joint reaction forces are evaluated as functions of the geometrical, kinematical, and physical characteristics of the spherical joint. These forces are then incorporated into a standard formulation of the system’s governing equations of motion as generalized external forces. A spatial four bar mechanism that includes a spherical clearance joint is considered here as an example. The computational simulations are carried out with and without the fluid lubricant, and the results are compared with those obtained when the system is modeled with perfect joints only. From the general results, it is observed that the system’s performance with lubricant effect presents fewer peaks in the kinematic and dynamic outputs, when compared with those from the dry contact joint model.     

柔性对多体系统中铰接副磨损的影响

通过集成柔性多体动力学与磨损计算程序,提出了一种用于对柔性多体系统中间隙铰接副部位的磨损进行了预测的方法.基于绝对节点坐标方法(ANCF)建立了柔性部件的多体动力学模型,引入Lankanrani和Nikravesh提出的连续接触力模型计算间隙铰接副部分的法向接触力,采用Lu Gre摩擦模型计算切向摩擦力,并利用基于Archard模型的迭代计算程序计算磨损.为了提高计算效率,引入了并行计算策略.最后,通过对一个含柔性连杆的曲柄滑块机构机构进行仿真计算,发现当考虑部件的柔性时,得到的间隙处的冲击力会大幅降低,预测的磨损量也随之降低,并且随着机构柔性的增强,这种效果更为明显.     

Modeling and analysis of rigid multibody systems with driving constraints and frictional translation joints

An approach is proposed for modeling and anal- yses of rigid multibody systems with frictional translation joints and driving constraints. The geometric constraints of translational joints with small clearance are treated as bilat- eral constraints by neglecting the impact between sliders and guides. Firstly, the normal forces acting on sliders, the driv- ing constraint forces （or moments） and the constraint forces of smooth revolute joints are all described by complementary conditions. The frictional contacts are characterized by a set- valued force law of Coulomb＇s dry friction. Combined with the theory of the horizontal linear complementarity problem （HLCP）, an event-driven scheme is used to detect the transi- tions of the contact situation between sliders and guides, and the stick-slip transitions of sliders, respectively. And then, all constraint forces in the system can be computed easily. Secondly, the dynamic equations of multibody systems are written at the acceleration-force level by the Lagrange multiplier technique, and the Baumgarte stabilization method is used to reduce the constraint drift. Finally, a numerical example is given to show some non-smooth dynamical behaviors of the studied system. The obtained results validate the feasibility of algorithm and the effect of constraint stabilization.     

A new model for dry and lubricated cylindrical joints with?clearance in spatial flexible multibody systems

A new approach to model and analyze flexible spatial multibody systems with clearance of cylindrical joints is presented in this work. The flexible parts are modeled by using absolute nodal coordinate formulation (ANCF)-based elements, while the rigid parts are described by employing the natural coordinate formulation (NCF), which can lead to a constant system mass matrix for the derived system equations of motion. In a simple way, a cylindrical joint with clearance is composed of two main elements, that is, a journal inside a bearing. Additionally, a lubricant fluid can exist between these two mechanical elements to reduce the friction and wear and increase the system??s life. For the case in which the joint is modeled as a dry contact pair, a technique using a continuous approach for the evaluation of the contact force is applied, where the energy dissipation in the form of hysteresis damping is considered. Furthermore, the frictional forces developed in those contacts are evaluated by using a modified Coulomb??s friction law. For the lubricated case, the hydrodynamic theory for dynamically loaded journal bearings is used to compute the forces generated by lubrication actions. The lubricated model is based on the Reynolds equation developed for the case of journal bearings with length-to-diameter ratios up to 1. Using this approach, the misalignment of the journal inside the bearing can be studied. Finally, two demonstrative examples of application are used to provide results that support the discussion and show the validity of the proposed methodologies.     

Dynamic analysis of planar mechanisms with revolute clearance joints based on two evaluation indices

Joint clearance is one of the most important factors that influence the dynamic performance of a mechanical system. In this study, a quantitative analysis method, which contains two clearance effect evaluation indices that can better evaluate influence of clearance joints on the dynamic performance of the mechanisms, is proposed. A dynamic modeling approach of planar mechanisms with clearance joints is introduced. A crank-slider mechanism with multiple clearance revolute joints is studied to support the proposed analysis methodology. Besides, different dynamic responses generated by different materials of the clearance joints are also investigated based on the clearance effect evaluation indices.     

An approach for calculating the dynamic load of deep groove ball bearing joints in planar multibody systems

This study is focused on dynamic modeling of planar multibody systems with multiple deep groove ball bearing joints, in which the radial clearance, contact deformation, and bearing kinematics are included. By using the approach presented, the variation of the joint reaction force and the dynamic load on each ball element in bearings can be simulated. The deep groove ball bearing joints are modeled by introducing a nonlinear force system, which takes into account the contact elastic deformations between the ball elements and the raceways. The contact force is calculated by the Hertzian contact deformation theory that accounts for the geometrical and material properties of the contacting bodies. A planar slider-crank mechanism with two deep groove ball bearing joints is chosen as an example to demonstrate the application of the methodologies presented in this paper. In this model, one bearing locates at the joint between the ground and crank, while the other one locates at the joint between the crank and connecting rod. By numerical calculation, the dynamic load distribution characteristics of bearings under real mechanism movement conditions are simulated. From the results, it can be concluded that the dynamic load on each rolling element varies differently and belongs to a variable load with the change of mechanism configuration. Load characteristic analysis is the foundation of developing research on the fatigue life and reliability of bearings. This study will provide a key mechanical support for the performance evaluation, dynamic design, and geometrical parameter optimization of the joint rolling element bearings.     

柔性多体系统中间隙铰接副的磨损预测

通过集成磨损计算与柔性多体动力学,对柔性系统中间隙铰接副部位的磨损进行了预测.基于绝对节点坐标方法（ANCF）建立了柔性部件的多体动力学模型,引入连续接触力模型计算间隙铰接副部分的接触力,并采用Archard磨损模型的迭代磨损计算程序预测磨损.为了得到在不同接触情况下的磨损系数,本文中采用了径向基神经网络处理试验数据.通过对含柔性连杆的曲柄滑块机构进行仿真计算,发现当考虑部件的柔性时,得到的间隙处的冲击力大幅降低,且预测的磨损量也略有降低,这种区别会随着仿真时间的增加而变得更加明显.     

一维滑块的向列相液晶润滑分析

基于一维向列相液晶的流动方程，研究了具有不同Leslie系数的5CB和MBBA向列相液晶在不同形状的平面滑块、指数型滑块以及双曲线型滑块中的润滑特性．结果表明：等效粘度、压力分布和载荷等在不同滑块润滑下均随向矢角度增加而增大；不同形状滑块的压力分布和载荷从小到大排列依次为平面滑块、指数型滑块和双曲线型滑块；可以通过向矢角度的变化控制摩擦系统的润滑性能．     

固液润湿性对流体动压润滑薄膜的影响

利用自行开发的微型面接触润滑油膜测量系统,研究了固液润湿性对流体动压润滑油膜厚度的影响.试验中以静止的微型滑块平面和旋转的光学透明圆盘平面形成润滑副.固液的润湿性通过接触角判定,不同材料的微滑块平面和润滑液体形成不同的界面.在保持载荷和面接触楔形角不变的条件下对油膜厚度-速度关系进行了测量.结果表明:对于固液润湿性强的界面,形成的油膜厚度与经典润滑理论有较好的一致性;当固液润湿性明显降低时,测量得到的油膜厚度减小.对于试验中观察到的界面效应,应用界面滑移理论进行了初步分析.