Joint Clearance Research Articles

Prediction of nonlinear vibration characteristics for high-speed and ultra-precision mechanism with clearance joints

The main purpose of this study is to present a comprehensive approach to illustrate the dynamic behavior of ultra-precision mechanism with clearance joints. According to geometrical features, the Largrange's equations of this mechanism is established. In order to describe the contact-impact process accurately, the models of dissipative contact force and modified friction force are introduced into the dynamic analysis model of this mechanism with clearance joints, which could describe the vibration characteristics clearly. Moreover, the experimental performance platform of high-speed and ultra-precision mechanism is designed and built. Then, the dynamic response of this mechanism is represented with the simulation and experiment, which demonstrates the effectiveness of proposed model. In addition, the probability statistics, largest Lyapunov exponent and bifurcation characteristics are employed to study the effects of clearance joints on the dynamic behavior of this mechanism.

Calibration of a (6 + 3)-DOF kinematically redundant parallel mechanism based on hybrid identification algorithm and two-step compensation strategy

To improve both the absolute accuracy and pose repeatability of a (6 + 3)-DOF kinematically redundant parallel mechanism (KRPM), a novel kinematic calibration method based on hybrid identification algorithm and two-step compensation strategy is proposed. Firstly, the error model is established, and the joint clearances are treated equivalently. On this basis, the global sensitivity index (GSI) is introduced to analyze the influence of parameter errors. Secondly, the absolute accuracy and pose repeatability are evaluated with the quasi-Monte Carlo simulation method (QMCSM) and the three-dimensional ellipsoidal error probability method (ESEPM). Thirdly, a hybrid identification algorithm combining Levenberg-Marquardt (LM) algorithm and adaptive differential evolution (ADE) algorithm is proposed to ensure the identification speed and accuracy. Finally, the error compensation is carried out by two steps. The experimental results show that the absolute accuracy and pose repeatability of the KRPM are improved by at least 52.8 % and 12.5 % respectively based on the novel method.

Influence of two kinds of clearance joints on the dynamics of planar mechanical system based on a modified contact force model

This study takes the slider-crank mechanism with revolute joint and translational joint as the research object and studies the contact force model of the clearance joint and the influence of the hybrid clearance joints on the nonlinear dynamic behavior of the mechanism. A modified contact force model is established based on the simplified elastic oscillator model, which can be used as a normal force in clearance joint. In the new contact force model, the component n of the indentation depth can be arbitrarily selected and it can support the calculation of contact force for both fully elastic recovery, non-elastic recovery and fully inelastic recovery. Based on the LuGre friction model, the tangential friction model of the clearance joint is given. Thus, the normal force and tangential force during the dynamic contact of the clearance joint are formed. Combining Lagrange’s equations of the first kind with the modified normal force and tangential friction force, the dynamic equations of the multi-body system with clearance joints are established. The Baumgarte stabilization method is used to improve the numerical stability. The correctness of the dynamic prediction model in the mechanism with clearance joint is verified by experiment. The dynamic analysis of the slider-crank mechanism with mixed clearance joints shows that the revolute clearance joint has a greater influence on the mechanism than the translational clearance, and the revolute clearance joint plays a leading role in the dynamic response.

Dynamic response investigation of high-speed structural redundant parallel manipulator considering multiple spatial revolute joints with radial and axial clearances

In order to grasp dynamic characteristics of the kind of high-speed structural redundant parallel manipulator in actual work, the dynamic response of a novel high-speed structural redundant parallel manipulator considering multiple spatial revolute joints with radial and axial clearances is studied. Firstly, the dynamic model of the novel high-speed parallel manipulator considering the multiple spatial revolute clearance joints is developed and verified. Then, the influences of different factors on dynamic characteristics of parallel manipulator are explored respectively. This paper contributes to explore the effect of revolute joints clearance on total property of the manipulator.

Dynamic Investigations on the Wear Behavior of a 3D Revolute Joint Considering Time-Varying Contact Stiffness: Simulation and Experiment

The existence of the relative radial and axial movements of a revolute joint’s journal and bearing is widely known. The three-dimensional (3D) revolute joint model considers relative radial and axial clearances; therefore, the freedoms of motion and contact scenarios are more realistic than those of the two-dimensional model. This paper proposes a wear model that integrates the modeling of a 3D revolute clearance joint and the contact force and wear depth calculations. Time-varying contact stiffness is first considered in the contact force model. Also, a cycle-update wear depth calculation strategy is presented. A digital image correlation (DIC) non-contact measurement and a cylindricity test are conducted. The measurement results are compared with the numerical simulation, and the proposed model’s correctness and the wear depth calculation strategy are verified. The results show that the wear amount distribution on the bearing’s inner surface is uneven in the axial and radial directions due to the journal’s stochastic oscillations. The maximum wear depth locates where at the bearing’s edges the motion direction of the follower shifts. These findings help to seek the revolute joints’ wear-prone parts and enhance their durability and reliability through improved design.

Time-dependent reliability analysis of planar mechanisms considering truncated random variables and joint clearances

The dimension variables and joint clearances are key factors affecting the motion accuracy of a mechanism. The existing time-dependent reliability analysis methods usually assume that the dimension variables follow ideal distribution, ignoring the truncation restrictions due to production and manufacturing. In addition, improper handling of the correlation between joint clearance variables leads to inaccurate calculation results. To address the above issues, this paper proposes a time-dependent kinematic reliability analysis method, in which the truncated random variables and joint clearances are comprehensively considered. Firstly, the complex correlation of clearance variables in the motion error function is processed by the dimension reduction method. Then, the truncated variables are converted into truncated standard normal variables. Furthermore, the envelope function method with expansion at the most probable point (MPP) is used to transform time-dependent reliability into time-independent reliability at multiple time points, greatly reducing computational complexity. On this basis, the saddlepoint method is used to fit the motion error cumulative distribution function at each time point, and the upper and lower bounds of failure probability are obtained through the Copula function and second-order narrow reliability bounds. The effectiveness of the proposed method is verified by a typical 4-bar linkage and a single crank double rocker mechanism.

Functionality and Mechanical Performance of Miniaturized Non-Assembly Pin-Joints Fabricated in Ti6Al4V by Laser Powder Bed Fusion.

In this work, additively manufactured pin-joint specimens are analyzed for their mechanical performance and functionality. The functionality of a pin-joint is its ability to freely rotate. The specimens were produced using laser powder bed fusion technology with the titanium alloy Ti6Al4V. The pin-joints were manufactured using previously optimized process parameters to successfully print miniaturized joints with an angle to the build plate. The focus of this work lies in the influence of joint clearance, and therefore all specimens were manufactured with a variety of clearance values, from 0 µm up to 150 µm, in 10 µm steps. The functionality and performance were analyzed using torsion testing and tensile testing. Furthermore, a metallographic section was conducted to visually inspect the clearances of the additively manufactured pin-joints with different joint clearance values. The results of the torsion and tensile tests complement each other and emphasize a correlation between the joint clearance and the maximal particle size of the powder utilized for manufacturing and the mechanical behavior and functionality of the pin-joints. Non-assembly multibody pin-joints with good functionality were obtained reliably using a joint clearance of 90 µm or higher. Our findings show how and with which properties miniaturized pin-joints that can be integrated into lattice structures can be successfully manufactured on standard laser powder bed fusion machines. The results also indicate the potential and limitations of further miniaturization.

Effect of Multi-Joint Clearance Coupling on Shimmy of Nose Landing Gear

The existence of joint clearances in the nose landing gear (NLG) is inevitable and significantly affects shimmy. It was found that the interaction of each joint clearance is closely related to the analysis of shimmy stability. In this study, the shimmy model of NLG with three-dimensional joint clearance was established by using LMS VirtualLab Motion. Based on the method of multibody dynamics (MBD), the load transfer mechanism at the joints of the NLG was analyzed, and the oscillation characteristics with multiple joint clearances were investigated. The results indicate that the radial and axial contact force of the joint decreases from bottom to top, and the radial contact forces are relatively high at the end positions of the connection shafts, resulting in uneven wear. When the joint clearance reaches a certain value, periodic shimmy of the NLG will occur, and an increase in torsional damping can reduce the amplitude of the shimmy. Therefore, this study reveals the influence of multi-position joint clearance coupling on shimmy, and provides a valuable insight for the maintenance and design of landing gear joints.

Vibration modelling analysis of defective parallel robots as machine tools for aerospace parts machining

The strict machining accuracy and surface finish requirements of manufactured products for aerospace parts make it particularly crucial to analyse the vibration performance of parallel robots as machining tools, which directly affects both of these factors. In this paper, a vibration modelling analysis for parallel robots with fewer-DOFs called defective parallel robots is presented, and the effects of four vibration models are also studied. The traditional spring-damping or elastic vibration models of two systems are presented, and the corresponding uncertain vibration systems are developed by considering the effects of gravity and the uncertain joint clearances. Taking a drilling defective parallel robot as an application example, four vibration models are derived, and the differences in natural frequency and vibration response are explored in numerical and experiment comparisons. The results shows that an uncertain system with six DOFs is closer to the experimental result (approximately 75.49%) than an elastic system (approximately 62.39%), which means that the accuracy has increased by 13.1%. The results of this paper reveal some of the reasons for the performance errors of the different vibration models for defective parallel robots, and the findings of this paper can provide a reference for the simplification and optimization of theoretical vibration models that ignore secondary factors.

Moment-Rotation Calculation Method and Parameter Analysis for Loose Continuous-Tenon Joint in Column-And-Tie Timber Structure

ABSTRACT To quantitatively calculate the moment-rotation relationship of loose continuous-tenon joints in traditional column-and-tie timber frame, the rotational deformation of loose joints is divided into two stages: free sliding and contact compression. Using constitutive, geometric, and equilibrium equations, a theoretical formula for moment-rotation is derived. The calculated values are then compared with experimental results to validate the accuracy of the theoretical calculation method. A sensitivity analysis is conducted on typical parameters, such as beam height, column diameter, joint clearance, and perpendicular compression modulus of wood, to explore their effects on the moment-rotation relationship of tenon joints. The results show that increasing the perpendicular compression modulus of wood leads to greater bending stiffness and load carrying capacity of tenon joints, with the latter increasing more significantly. In the elastic stage, the rotational stiffness of the joint increases with beam height or column diameter, while after entering the elastoplastic stage, the joint stiffness is less influenced by these factors. The initial rotational stiffness and load carrying capacity of the joint both decrease with joint clearance, and the effect of joint clearance on load carrying capacity decreases as the clearance increases when the joint enters the yielding stage.

Evaluation of Joint Clearance Effects on the Shimmy of Nose Landing Gear

Through the establishment of a three-dimensional joint clearance model, the effects of joint clearances at different positions on shimmy stability are evaluated. In this paper, considering the radial, axial and coupling characteristics of joint clearance, the shimmy multibody dynamics (MBD) model is applied to different joints in the nose landing gear (NLG) transmission system. It is proposed to evaluate the influence of joint clearance on shimmy from two aspects of position factor and wear factor. The study found that different joint clearances have different effects on shimmy: the joint clearance between the NLG and fuselage has little influence on shimmy; the larger axial clearance of upper and lower torque link joint will cause the shimmy of the NLG, but the radial clearance has no effect on shimmy; while the joint clearance between turning sleeve and upper torque link, lower torque link and piston only works in the axial and radial coupling. The reasons for the different influence characteristics of each joint space are analyzed. Consequently, studying and summarizing the influence of different clearance on shimmy is of great significance for the design and maintenance of the NLG joints.

Design-oriented dynamic model of deployable fin under time-varying elevated temperature environment

AbstractCoupling of clearance joint and harsh aerodynamic heating environment is an inevitable nonlinear factor in folding mechanism of the fin of high-speed aircrafts that remarkably modifies natural frequencies and modes of vibration from the initial design state. However, accurately predicting dynamic properties of deployable fin with full consideration of these effects is not common industry practice. A practical semi-analytical model based on Hertz contact theory and ESDU-78035 model is proposed in this study to investigate high-temperature connection stiffness of local hinged–locked mechanisms. Material property degradation and clearance variation caused by thermal expansion are comprehensively considered and quantified in this model. Vibration characteristics of the assembled deployable fin are then solved using finite element method (FEM). The real-time evolutionary process of thermal mode of the fin is discussed. And natural frequencies of fixed-value and time-varying connection stiffness are compared. The simulation results of this study demonstrate that the relative error of structure temperature between the sequential approach and fully coupled simulations is less than 6.98%. The connection stiffness (slope of the load-displacement curve) of the folding mechanism under high temperature conditions decreases by 3.52%, and the variation is mainly caused by the degradation of the elastic modulus of the material, while the clearance change due to the thermal expansion has no significant effect on the slope. The natural frequency of the deployable fin exhibits an inverse correlation with the temperature change trend, and the first three frequencies decrease by 1.67, 7.75, and 16.28 Hz compared to the initial value, respectively.

Failure modeling and reliability analysis for motion mechanism with clearance joints under plastic deformation and wear

The performance failure and reliability of motion mechanism has a significant effect on industry reliability, operation safety and production economy. Motion precise is one of the typical performance indicators especially for motion mechanism with multibody and joints. Size of joint clearance degenerates with usage such as wear and deformation. Repeated start-stop lead to impact stress and plastic deformation for clearance joint particularly for mechanism with high load and long working cycles. This study attempts to investigate the wear process and performance failure model of multibody mechanism with clearance joints considering plastic deformation and wear. Quantification of plastic deformation caused by repeated impact stress of joints is studied by formulation. Then, a novel wear process model is established, after which performance failure indicator is conducted. A linkage motion mechanism with multi revolution joints is studied to demonstrate proposed methods. This study provides valuable guidelines for degeneration prediction and reliability analysis of motion mechanism.

Dynamics and Wear Prediction of Mechanisms Considering Multiple Clearances and Coatings

The increase in joint clearance and system vibration caused by joint wear are important factors that may lead to the failure of the mechanism and a decrease in the motion accuracy of the actuator. In this paper, to investigate the impact of different numbers of spherical joint clearances on the dynamics performance of the mechanism and explore effective measures to reduce the vibration of the mechanism caused by multiple joint clearances, on the basis of the previous research on the mechanism dynamics when there is clearance in a single spherical joint, an improved contact force model is used to study the effects of coating, no coating, and different clearance quantities on the dynamics of a mechanism containing multiple spherical joint clearances. Moreover, the joint reaction forces and contact-impact forces under different working conditions are calculated. In order to reduce the difficulty of calculating the joint wear, an approximate calculation method for contact area is proposed, and an improved Archard wear model is employed to calculate and analyze the changes in wear amount under the influence of both spherical joint clearance and coating.

Flexible modeling and dynamics simulation of four-bar beating-up system with clearance

To explore the actual working characteristic of the beating-up mechanism on looms, the Step function is adopted to convert the beating-up resistance to an equivalent torque acting on the rocking shaft, and a new method of calculating and simulating the resistance is hereby raised. In accordance with the two-state joint clearance, the paper establishes a double-side model of the four-bar beating-up system in clearance status via ADAMS/View software, and under the consideration of both beating-up resistance and flexible deformation conditions, the contact simulation of beating-up motion with different clearances (0.01∼0.12 mm) is achieved. The main findings are as follows: the actual working condition could be reflected more accurately if the beating-up resistance and component flexibility are included into the simulation computing; from the perspective of the impact on sley moving and beating-up loads, 0.08 mm clearance is obviously less then another three clearances (0.01 mm, 0.04 mm and 0.12 mm); the multi-point contact and collision with peak load greater than 4000 N is existed in connecting rod bearing in the 0∼350 Hz low frequency area, which is likely to exacerbate the wear and fatigue rupture of the bearing; the dynamic shock load of rocking shaft on the loom frame is far greater than that of the crankshaft, indicating that the rocking shaft is the main carrier for delivering the beating-up power; compared to the clearance of 0.08 mm and 0.12 mm, the dynamic impact load generated by the clearance of 0.01 mm and 0.04 mm on the loom frame is obvious greater. In addition, under the clearance condition, transverse vibration could be occurred for the flexible crankshaft due to the deviation of its centroid trajectory, which is detrimental to vibration and noise reduction for the loom system. On the basis of the work, a number of viewpoints with theoretical and practical significance could be provided to the design of beating-up system on the loom with clearance.

Research on High Precision Stiffness Modeling Method of Redundant Over-Constrained Parallel Mechanism.

Traditional stiffness modeling methods do not consider all factors comprehensively, and the modeling methods are not unified, lacking a global stiffness model. Based on screw theory, strain energy and the virtual work principle, a static stiffness modeling method for redundant over-constrained parallel mechanisms (PMs) with clearance was proposed that considers the driving stiffness, branch deformation, redundant driving, joint clearance and joint contact deformation. First, the driving stiffness and branch deformation were considered. According to the strain energy and Castiliano's second theorem, the global stiffness matrix of the ideal joint mechanism was obtained. The offset of the branch was analyzed according to the restraint force of each branch. The mathematical relationship between the joint clearance and joint contact deformation and the end deformation was established. Based on the probability statistical model, the uncertainty of the offset value of the clearance joint and the contact area of the joint caused by the coupling of the branch constraint force was solved. Finally, taking a 2UPR-RR-2RPU redundant PM as an example, a stiffness simulation of the mechanism was carried out using the finite element method. The research results show that the high-precision stiffness modeling method proposed in this paper is correct, and provides an effective method for evaluating the stiffness performance of the PM.

The Horizontal Sonocapillary Effect in UltrasonicAssisted Soldering

In this work, the horizontal sonocapillary effect in ultrasonic-assisted soldering was investigated via numerical simulations and experiments. The numerical simulation results indicated that acoustic pressures in the liquid solder exhibited distinct sinusoidal features with negative offsets, forming a negative average acoustic pressure. When the ultrasonic vibrations were transmitted to the lower substrate in the joint clearance, the average acoustic pressures decreased from the acoustic pressure center to the filling front, forming a negative acoustic pressure gradient in the horizontal direction. As a result, the solder was sucked into the joint clearance by a large negative acoustic pressure. This sonocapillary effect was verified with experiments. In the calculation model, a high ultrasonic amplitude, a small joint clearance width, and a high base material stiffness increased the acoustic pressure and its average difference on the horizontal direction in the solder, which further improved the driving force of the sonocapillary effect. However, the wetting angle had a small influence on the sonocapillary effect.

Dynamic Analysis of a Delta Parallel Robot with Flexible Links and Joint Clearances

Delta robot is a lightweight parallel manipulator capable of accurately moving heavy loads at high speed and acceleration along a spatial trajectory. This intensive dynamic process may have a significant impact on the end-effector trajectory precision and motor behavior. The paper highlights the influence on the dynamic behavior of a Delta robot by considering individual and combined effects of clearances and friction in the spherical joints, as well as the flexibility of the rod elements. The CAD modeling of the Delta robot and its motion simulation on a representative spatial trajectory where the maximum allowed values of speed and acceleration are reached were performed using the Catia and Adams software packages. The obtained results show that the methods used were successfully applied and the effects are mutually interconnected, but not cumulative.

Dynamic response and nonlinear characteristics of multi-link mechanism with clearance joints

Dynamic response and nonlinear characteristics of multi-link mechanism with clearance joints

Fabrication of precise non‐assembly mechanisms by multi‐material fused layer modeling and subsequent heat treatment

AbstractAdditive manufacturing techniques offer several potentials for future design and production. One of these potentials is non‐assembly mechanisms, movable mechanisms which need no assembly after production. Especially non‐assembly mechanisms consisting of kinematic pairs face major tolerance issues. This work advances into the new field of non‐assembly mechanisms consisting of kinematic pairs from multi‐materials. The research described in this article shows how tolerance issues can be overcome by the deliberate use of intrinsic and printing‐induced shrinkage processes. Therefore, non‐assembly mechanisms produced by multi‐material printing using fused layer modeling (FLM) are heat‐treated after the printing process to reduce and adjust the joint clearance. It was found that PLA was a suitable material for this process due to its relaxation and recrystallisation behavior during heat treatment. The printing techniques and relevant shrinkage mechanisms were analyzed and explained. Furthermore, it was found that relaxation of orientations and recrystallization could be separated in two different heat treatment steps creating a possibility for “induced self‐healing.” In addition, tribological aspects of such mechanisms will be discussed.