Investigation on effect of joint clearance on dynamics of four-bar mechanism

As a result of design, manufacturing and assembly processes or a wear effect, clearances are inevitable at the joints of mechanisms. In this study, dynamic response of mechanism having revolute joints with clearance is investigated. A four-bar mechanism having two joints with clearance is considered as a model mechanism. A neural network was used to model several characteristics of joint clearance. Kinematic and dynamic analyses were achieved using continuous contact mode between journal and bearing. A genetic algorithm was also used to determine the appropriate values of design variables for reducing the additional vibration effect due primarily to the joint clearance. The results show that the optimal adjusting of suitable design variables gives a certain decrease in shaking forces and their moments on the mechanism frame.     

Modeling and analysis of sliding joints with clearances in flexible multibody systems

The modeling of the sliding joint with clearance between a flexible beam and a rigid hole is investigated in this paper. The flexible beam is discretized using the three-dimensional curved Euler–Bernoulli beam element of the Absolute Nodal Coordinate Formulation, while the motion of the rigid hole is described by the Cartesian coordinates. Moreover, the cross sections of both the flexible beam and the rigid hole are assumed to be circular. The existing joints with clearances are mainly rigid joints with small clearances, and the contact detection algorithm adopted can solve only one pair of potential contact points within one section. In order to model the contact problem in the sliding joint with clearance, a new contact detection method based on the intersection of the rigid hole’s cross section and the flexible beam is proposed, which yields a two-dimensional contact detection problem. Based on the common-normal concept, the ellipse–circle contact detection problem within the hole’s cross section can be solved. The potential contact point on the hole’s cross section will be determined, and the closest point projection on the beam’s neutral axis can be defined further. The proposed contact detection method can deal with the sliding joint with large clearance and the multiple-point contact problem within one section. In addition, the penalty method is adopted to model the frictionless contact between the flexible beam and the rigid hole. Finally, two numerical examples about sliding joints with clearances, one with an initially curved beam under gravity and the other with a straight beam under zero gravity, are presented to demonstrate the influence of the clearance of sliding joint on the dynamic performance of flexible multibody systems.     

Simulation of Initially Slackened and Stiffened Structures by Virtual Distortions∗

ABSTRACT

Variational principles and computational methods for analysis of initially slackened and stiffened structures are discussed. The simulation of clearances or internal dry fraction in structural elements by virtual (eigen) distortions is applied. Considerations presented are used in the problem of nonstandard design of structural settings, with clearances or friction in the structural joints, for load capacity maximization.     

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.     

The effect of the lubricated revolute joint parameters and hydrodynamic force models on the dynamic response of planar multibody systems

In this work a comprehensive methodology for dynamic modeling and analysis of planar multibody systems with lubricated revolute joints is presented. In general, this type of mechanical systems includes journal-bearings in which the load varies in both magnitude and direction. The fundamental issues associated with the theory of lubrication for dynamically loaded journal-bearings are revisited that allow for the evaluation of the Reynolds equation for dynamic regime. This approach permits the derivation of the suitable hydrodynamic force laws that are embedded into the dynamics of multibody systems formulation. In this work, three different hydrodynamic force models are considered, namely the Pinkus and Sternlicht approach for long journal-bearings and the Frêne et al. models for both long and short journal-bearings. Results for a planar slider?Ccrank mechanism with a lubricated revolute joint between the connecting-rod and slider are presented and utilized to discuss the assumptions and procedures adopted throughout the present study. Different test scenarios are taken into account with the purpose of performing a comparative study for quantifying the effect of the clearance size, lubricant viscosity, input crank speed and hydrodynamic force model on the dynamic response of multibody systems with lubricated revolute joints. From the global results obtained from computational simulations, it can be concluded that the clearance size, the lubricant viscosity and the operating conditions play a key role in predicting the dynamic behavior of multibody systems.     

Condition Monitoring of Robot Joints Using Statistical and Nonlinear Dynamics Tools

This paper considers the problem for condition monitoring of robot joints employing measured acceleration signals. The study aims at (1) Determining features, to be extracted directly from the measured acceleration signals, to detect defects in robot joints and at (2) Finding features dependent on the size of the fault in order to quantify the present defects. The signals coming from intact robot joints and from joints containing backlash or clearance are analyzed using nonlinear dynamics as well as statistical tools. A method for defect detection that employs nonlinear autoregressive (AR) modeling of the acceleration signals is successfully applied to detect backlash and clearance in robot joints. Two procedures for defect quantification are considered – one of them based on the AR modeling and the other employing nonlinear dynamics and statistical features. The problems are considered in the context of a pattern recognition paradigm.     

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.      

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.     

The compliance contact model of cylindrical joints with clearances

This paper is concerned with the determination of the normal force-displacement (NFD) relation for the contact problem of cylindrical joints with clearance. A simple formulation for this contact problem is developed by modeling the pin as a rigid wedge and the elastic plate as a simple Winkler elastic foundation. The numerical results show that the normal displacement relation based on Hertz theory is only valid for the case of large clearance with a small normal load, and the NFD relation based on Persson theory is only effective in the case of very small clearance. The proposed approximate model in this paper gives better results than Hertz theory and Persson theory in a large range of clearances as seen from the comparison with the results of FEM. The project supported by the National Natural Science Foundation of (10272002; 60334030). The English text was polished by Keren Wang.     

Using a virtual skeleton to increase printability of topology optimized design for industry-class applications

This article broadens the scheme previously developed to associate topology optimization with additive manufacturing through the use of a virtual skeleton, consisting in solving the same physical problem with a discrete approach and then with a continuum one. This procedure for 3D designs is applied to various domain geometries, to demonstrate its pertinence on high-resolution industrial cases. An algorithm searching for the best printing direction, exploring the solid angle, is also described and validated; the surface-shaped presentation of the result allows immediate understanding of the influence of the discrete problem parameters, while its running time is much lower than a unique continuum optimization simulation, which proves the attractiveness of the method. In the three examples studied, the procedure outputs exhibit greater printability than the ones produced by traditional methods in each of the printing direction tested, albeit responsibility is left to the final user to choose his best trade-off. Furthermore, the unprintable zones are readily displayed to be either reworked or supported. Explanations about increase of convergence likelihood on discrete structures despite the geometry complexity of an industrial application are also provided and demonstrated.     

Elastodynamic behavior of balanced closed-loop mechanisms: numerical analysis of a four-bar linkage

This paper investigates the influence of two common techniques of static balancing on the dynamic performance of closed-chain linkages, by taking into account the flexibility of the mechanism components. The long-term goal of the research consists in enhancing the operation of parallel spatial robots by means of optimal balancing strategies. This contribution is primarily meant to provide the analysis method of the research and, for this purpose, it focuses on the planar four-bar linkage, intended as the simplest example of closed-chain mechanism. Firstly an original approach for the static balancing of planar linkages by means of constant-force generators is proposed. The implemented formulation, which permits to compute the balancing parameters of both counterweights and/or springs, is adopted for deriving a mass balanced and an elastically compensated variant of the studied four-bar linkage, respectively. Then the operation of the unbalanced linkage and its two balanced variants is numerically studied. The natural frequencies and mode shapes of these mechanisms are estimated by modal analysis, whereas the dynamic performance at different operating regimes is assessed by kineto-elastodynamic investigation and finally discussed.     

A loop-by-loop defect rectification procedure for optimal synthesis of Stephenson III path generators

This paper presents a formulation of constraints for the synthesis of Stephenson III mechanism and a loop-by-loop defect-rectification procedure. The procedure divides the Stephenson III mechanism into two loops, namely, Loop I, i.e., four-bar, and Loop II, i.e., five-bar mechanisms. Then, the defects are identified using the established methodology to formulate the defect-specific constraints in the simplified form. Based on the constraints, an optimization problem is formulated to synthesize a Stephenson III mechanism for path generation. A well-established meta-heuristic algorithm is used to solve the constrained optimization problem. For demonstrating the effectiveness of the formulated constraints, two numerical examples are considered, in which Stephenson III path generator mechanisms are synthesized. It is found that the mechanisms synthesized using the proposed procedure are defect-free when constraints are imposed, which is verified using the stick-diagram.

     

Trajectory optimization of a walking mechanism having revolute joints with clearance using ANFIS approach

Clearance as a real joint characteristic leads to deviation from desired trajectory in articulated mechanisms. This phenomenon makes the kinematic and dynamic performances of the mechanism worse. In this study, kinematic analysis of a Jansen’s mechanism used in a walking machine is performed. The model mechanism having two revolute joints with clearance is investigated for the trajectory analysis of the output link. It is clear that the mechanism’s trajectory is very sensitive to the clearance joint characteristics even if the clearance size is small. The adaptive network-based fuzzy inference system (ANFIS) is used to model the characteristics of joints with clearance. By using the suitable design variables and constraints, minimization of the trajectory errors arising from clearance is considered as an optimization problem. Optimization techniques are used to solve this problem for adjusting the optimum values of design variables. The obtained link dimensions show the success of the proposed modeling and optimization approach.     

重力场对人工肾透析性能的影响

通过数值模拟人工肾4种不同放置方式(水平放置透析液进出口朝上、水平放置透析液进 出口朝下、竖直放置血流向上、竖直放置血流向下)时尿素的传质情况，定性考察了重 力场对透析性能的影响，获得了各种放置情况下尿素的三维浓度场和清除率. 模拟结果显示， 重力场对人工肾传质影响显著. 在重力的影响下，竖直放置血流向上尿素清除率最高，水平 放置透析液进出口朝上清除率次之.     

On heat transfer in screw compressors

Heat transfer between the working fluid and machine parts within a screw compressor does not affect its performance significantly because the thermal energy dissipation is usually less than 1% of the compressor power input. However, it can be detrimental to the machine reliability because the fluid compression creates a non-uniform three dimensional temperature field leading to local distortions, which may be larger than the clearances between the machine parts. This phenomenon is widely known and special control procedures are required to allow for start-up and shut down, as well as for steady running operation. These measures are usually derived only from test-bench data and may result in larger clearances than necessary, thereby reducing the optimum performance.This paper gives an outline of two methods of computing heat transfer in a screw compressor; namely: by means of a quasi-one dimensional differential model and by three dimensional computational fluid dynamics (CFD). Both methods enable the clearance size for start-up and steady running conditions to be determined. The 3D CFD procedure is more accurate but requires a far longer running time. Two cases are considered: heat transfer in a dry screw compressor where fluid temperatures are high, and an oil-flooded screw compressor where fluid temperatures are relatively low but the convective heat transfer coefficient is substantially higher.     

Analysis of mechanisms with flexible beam-like links,rotary joints and assembly errors

The paper presents a method of modelling dynamics of mechanisms in which assembly errors can occur. One of the features of the method is that such errors can be included when the kinematics of the mechanism is modelled. A closed kinematic chain consisting of flexible and rigid links with one joint displaced and turned is discussed. Use of joint coordinates together with the rigid finite element method for discretisation of flexible links has allowed us to considerably decrease the size of the problem. Numerical simulations are carried out in order to analyse the influence of inaccurate assembly on the load on joints of a four-bar linkage.     

Modeling and simulation for wear prediction in planar mechanical systems with multiple clearance joints

Nonlinear Dynamics - The main goal of this work is to develop a comprehensive methodology for predicting wear in planar mechanical systems with multiple clearance joints and investigating the...     

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.     

On a Free Boundary Problem for the Curvature Flow with Driving Force

We study a free boundary problem associated with the curvature dependent motion of planar curves in the upper half plane whose two endpoints slide along the horizontal axis with prescribed fixed contact angles. Our first main result concerns the classification of solutions; every solution falls into one of the three categories, namely, area expanding, area bounded and area shrinking types. We then study in detail the asymptotic behavior of solutions in each category. Among other things we show that solutions are asymptotically self-similar both in the area expanding and the area shrinking cases, while solutions converge to either a stationary solution or a traveling wave in the area bounded case. We also prove results on the concavity properties of solutions. One of the main tools of this paper is the intersection number principle, however in order to deal with solutions with free boundaries, we introduce what we call “the extended intersection number principle”, which turns out to be exceedingly useful in handling curves with moving endpoints.     

Optimal truss design based on an algorithm using optimality criteria

A computational scheme is presented for the calculation of the optimal design of trusses. Constraints on the design variables (the cross-sectional areas) are considered. Linearly elastic behavior is assumed, and optimality criteria are derived, based on strain energy considerations. As in mathematical programming techniques, the optimum is approached through a sequence of designs, each differing slightly from its predecessor. The design changes to be made at each stage of the procedure are determined by application of the optimablity criteria. The formulation is sufficiently general to permit the solution of the problem of predicting both optimal member size and member layout-given the loads and the location of the joints. The procedure is illustrated with a number of numerical examples.