Nonlinear Friction Research Articles

A Terminal Residual Vibration Suppression Method of a Robot Based on Joint Trajectory Optimization

Vibration problems have become one of the most important factors affecting robot performance. To this end, a terminal residual vibration suppression method based on joint trajectory optimization is proposed to improve the accuracy and stability of robot motion. Firstly, based on the characteristics of the friction nonlinearity due to joint coupling and physical feasibility of dynamic parameters, a semidefinite programming method is used to identify dynamic parameters with actual physical meaning, thereby obtaining an accurate dynamic model. Then, based on the result of the residual vibration time domain analysis, a joint trajectory optimization model with the goal of minimizing joint tracking error is established. The Chebyshev collocation method is used to discretize the optimization model. The dynamic model is used as the optimization constraint, and barycentric interpolation is used to obtain the optimized joint motion trajectory. Finally, industrial robot experiments prove that the vibration suppression method proposed in this article can reduce the maximum acceleration amplitude of residual vibration by 62% and the vibration duration by 71%. Compared with the input shaping method, the method proposed in this paper can reduce the terminal residual vibration more effectively and ensure the consistency of running time and trajectory.

Discrete-Time Event-Triggered Type-2 fuzzy wavelet neural network control for Multi-Motor servo system

This paper investigates a discrete-time event-triggered adaptive neural network control scheme for a multi-motor servo system (MMSS) to realize a desired position tracking performance. First, a discrete-time model of the MMSS, including a dead-zone and a nonlinear friction, is established based on the Euler’s discretization. Then, a discrete-time adaptive neural network controller is designed by integrating a type-2 fuzzy wavelet neural network (T2FWNN) and the backstepping technology. The neural network is not only used to estimate uncertain nonlinearities, but also can handle the non-causal problem caused by the conventional backstepping method. Meanwhile, a fixed threshold event-triggered mechanism along with the incorporation of a dead-zone operator is superimposed into the actual controller thus saving communicational resources. Besides, stability analysis proves that all the signals in the closed MMSS are bounded, and the position tracking error converges to a small neighborhood of the origin. Finally, abundant simulation experience results demonstrate the effectiveness and robustness of the proposed scheme.

Robust controller design and experimental validation based on bounded uncertainty for collaborative industrial robots.

In this paper, derived from the proportional-derivative control and robust control, a novel practical robust control method based on a dynamic feedforward model is established by taking six-axis motion cooperative industrial robots as the research object. The nonlinear friction, parameter uncertainty, and external disturbance are taken into consideration while establishing the dynamic model of the cooperative industrial robot. The method includes a proportional-derivative control and a robust control. Lyapunov theory is used to analyze the proposed controller, and it is shown that this method can guarantee uniformly bounded and uniformly final bounded systems. Simulation and experiment results show that the proposed controller is better than proportional-integral-derivative control and mode-based proportional-derivative control in stability tracking performance and robustness. In addition, the CSPACE platform for rapid controller prototyping may reduce the arduous programming effort and offer a lot of ease for the trials.

An online payload identification method based on parameter difference for industrial robots

AbstractAccurate online estimation of the payload parameters benefits robot control. In the existing approaches, however, on the one hand, only the linear friction model was used for online payload identification, which reduced the online estimation accuracy. On the other hand, the estimation models contain much noise because of using actual joint trajectory signals. In this article, a new estimation algorithm based on parameter difference for the payload dynamics is proposed. This method uses a nonlinear friction model for the online payload estimation instead of the traditionally linear one. In addition, it considers the commanded joint trajectory signals as the computation input to reduce the model noise. The main contribution of this article is to derive a symbolic relationship between the parameter difference and the payload parameters and then apply it to the online payload estimation. The robot base parameters without payload were identified offline and regarded as the prior information. The one with payload can be solved online by the recursive least squares method. The dynamics of the payload can be then solved online based on the numerical difference of the two parameter sets. Finally, experimental comparisons and a manual guidance application experiment are shown. The results confirm that our algorithm can improve the online payload estimation accuracy (especially the payload mass) and the manual guidance comfort.

A Novel Friction Compensation Method for Machine Tool Drive Systems in Insufficient Lubrication.

Friction is the dominant factor restricting tracking accuracy and machining surface quality in mechanical systems such as machine tool feed-drive. Hence, friction modeling and compensation is an important method in accurate tracking control of CNC machine tools used for welding, 3D printing, and milling, etc. Many static and dynamic friction models have been proposed to compensate for frictional effects to reduce the tracking error in the desired trajectory and to improve the surface quality. However, most of them focus on the friction characteristics of the pre-sliding zone and low-speed sliding regions. These models do not fully describe friction in the case of insufficient lubrication or high acceleration and deceleration in machine tool systems. This paper presents a new nonlinear friction model that includes the typical Coulomb-Viscous friction, a nonlinear periodic harmonic friction term for describing the lead screw property in insufficient lubrication, and a functional component of acceleration for describing the friction lag caused by the acceleration and deceleration of the system. Experiments were conducted to compare the friction compensation performance between the proposed and the conventional friction models. Experimental results indicate that the root mean square and maximum absolute tracking error can be significantly reduced after applying the proposed friction model.

Modeling method and dynamic analysis of blade with double friction damping structure considering time-varying pressure distribution

A modeling and analytical method considering contact interface pressure characteristics is presented in this paper. Firstly, a high-fidelity model of a blade with a double friction damping structure is established by solid element, and a three-dimensional friction contact element is used to describe the nonlinear friction interface between the blade contact interfaces. Then, the static pressure distribution characteristics of the contact interface of the blade are obtained through the experimental device of the blade with double friction damping structure, and the accuracy of the pressure characteristics is verified. Based on the static pressure distribution, the time-varying dynamic pressure formula of blade contact interface is derived. The influence of the pressure distribution on the contact characteristics of the contact interface is analyzed and applied to the dynamic calculation of the rotating blade. The influence of different parameters on the blade dynamics is obtained. And the optimum mass ratio of the under-platform damper is obtained by simulating the operation condition of the aero engine blade acceleration process.

The optimal nonlinear inertial amplifier friction bearings for liquid storage tanks: an analytical study

The optimal nonlinear inertial amplifier friction bearings for liquid storage tanks: an analytical study

Dynamic analysis and optimization of a novel Dual-valve heave compensator for heavy lifting operations

Traditional Passive Heave Compensator (PHC) requires set parameters before operation according to the specific sea conditions, making it difficult to adapt to complex and variable working environments. This study aims to enhance the environmental adaptability of classical PHC by proposing a novel concept of Dual-valve Heave Compensator (DHC) based on the traditional PHC framework. By modulating the hydraulic and pneumatic throttle valve openings dynamically, the DHC system facilitates adjustments extensively in damping and stiffness, significantly enhancing compensation performances. As an enhancement over traditional models, this study incorporates a coupled dynamic model that accounts for critical influencing factors, including gas temperature and nonlinear friction. A linearized equation for the dynamic stiffness of DHC has been developed based on the small deviation linearization method, extensively analysing the effects of pneumatic parameters on the stiffness characteristics. Furthermore, a design framework employing Latin Hypercube Sampling (LHS) design, Radial Basis Function (RBF) surrogate model, and Non-dominated Sorting Genetic Algorithm-II (NSGA-II) has been specifically developed to address the multi-objective optimization challenges presented by DHC systems. The case study indicates that the optimized DHC can achieve up to 86% compensation accuracy under a 250-ton load with harmonic excitation and offers adjustments flexibly for various operational conditions. Contrary to conventional wisdom, minimal valve openings significantly enhance compensation accuracy during some intervals of irregular wave excitation. These findings confirm the superior performance and potential of DHC relative to traditional PHCs under complex marine environments.

Investigation of friction induced vibrations on a nonlinear two degree of freedom mathematical model and experimental validation

This article investigates the dynamic behavior of a low order nonlinear mathematical model, which is developed based on an existing mass-sliding belt experiment. First, the proposed model is developed with kinematic and friction nonlinearities, and the corresponding governing equations are obtained. Governing equations are then solved numerically for certain operating parameters, and the characteristics of different dynamic responses are investigated. It is observed from the numerical solutions that the dynamic response of the system can be deterministic or chaotic based on the set of operating parameters. Furthermore, the period doubling mechanism is found to be the path from deterministic to chaotic behavior. Second, experiments are performed at a wide range of operating parameters in order to calculate the dynamic friction coefficient, which are used in artificial neural network models for the generation of friction models as functions of operating parameters. It is observed that these operating parameters have significant influence on the variation of the dynamic friction coefficient. Third, the friction models developed with artificial neural network approach are implemented in the nonlinear mathematical model, and numerical solutions are obtained at the same operating parameters. Finally, the numerical results of the low order nonlinear mathematical model are compared to the experimental data, and it is concluded that there is a good correlation between the model predictions and measurements from the perspectives of fundamental frequencies and the characteristics of the dynamic responses. Hence, a better insight about the dynamic response behavior of the mass-sliding belt experiment is achieved through the bifurcation analyses.

Enhanced suppression of vibration response and energy transfer by using nonlinear hysteresis friction damper

Enhanced suppression of vibration response and energy transfer by using nonlinear hysteresis friction damper

Modelling and application of typical nonlinear torsional elements in vibro-impact analysis of pickup truck driveline system

The torsional element method for the dynamic modelling of torsional system was proposed by Crowther and Zhang, which provides a modular modeling approach with high modeling efficiency and has a good application prospect in vibro-impact analysis of vehicle driveline system. The main purpose of this paper is to further enrich the element types of the torsional element method and to establish a nonlinear dynamic model for a pickup truck driveline system by applying the torsional element method to analyze the vibro-impact phenomenon. A general nonlinear clearance element with different contact stiffness and damping, a nonlinear friction element with smooth Stribeck effect and a nonlinear multistage stiffness-damping element with different torque transfer characteristics are developed. A dynamic lumped parametric model with 10 degrees of freedom for a pickup truck driveline system is established by assembling the developed nonlinear torsional elements. The transient vibro-impact phenomenon caused by the clearance, the stick-slip phenomenon caused by the friction and the transient hysteresis cycle phenomenon caused by the nonlinear multistage damper during transient engagement of clutch are numerically investigated. Furthermore, a real-vehicle experimental study is conducted to confirm the transient vibro-impact phenomenon in pickup truck driveline system during transient clutch engagement and to verify the correctness of the dynamic lumped parameter model. On these bases, the influence of the key parameters of the nonlinear torsional element on the transient vibro-impacts are investigated, the effective engineering countermeasures to reduce the vibro-impact of the vehicle driveline system are put forward.

Combining finite-time control and prescribed tracking performance for uncertain PMSM driven steer-by-wire system with unknown disturbance

To solve the uncertainties in permanent magnet synchronous motor (PMSM) driven steer-by-wire (SbW) system, a prescribed-performance-control (PPC) based finite-time fuzzy controller is proposed. Specifically, the dynamics of SbW system driven by PMSM is analyzed, and combine PPC technology to transform the tracking error coordinates. Then, the velocity signal is obtained from the sigmoid function-based tracking differentiator by using the position signal. To solve the problem of mismatched disturbance, fuzzy logic system (FLS) are used as a universal approximator to estimate the lumped nonlinear friction and other unknown functions, the boundary of lumped disturbance is estimated by the designed adaptive updating law. By fusing the designed virtual controller and the intermediate control law, the controller needs no precise parameters of system, under which the effect of uncertainty of control gain can be compensated completely. Finally, rigorous theoretical analysis based on the Lyapunov stability theory is provided to demonstrate the finite-time stability of the closed-loop system under consideration. Simulation and experiment results are presented to show the effectiveness of the developed control approach, and some comparisons are given to show the rapid and accurate position tracking control performance.

Axial transfer characteristics of a drillstring in conjunction with bit penetration behavior in horizontal wells

Nonlinear friction and interaction between bit and rock often result in a lower weight on bit (WOB) than the intended design value. The analysis of the dynamic transmission mechanism of a drillstring in complex horizontal wells is a crucial engineering problem that aims to enhance drilling efficiency. In this paper, a mechanical model was developed, integrating nonlinear bit penetration behavior and variable axial loads, aiming to unveil the nonlinear axial vibration characteristics and elucidate the transmission mechanisms within the drillstring. Notably, the mean value of axial force distributed along the drillstring is dictated by wellhead pulling force, while the amplitude is shaped by the interaction between bit and rock, and rotary speed. In calculated examples for horizontal wells, the analysis reveals that significant losses in power axial transmission, resulting in WOB is only 38% of the intended value. And reducing the wellhead pulling force by 30 kN leads to a maximum increase in WOB only of 9.51 kN. Extended region in drillstring with negative axial forces exhibit maximum values 5–6 times higher than the WOB. Specific zones, such as 20 m–40 m and 0–20 m from the bit, experience axial force fluctuation amplitudes of 40.5% and 138.8% of the mean value respectively, with the latter identified as an intense vibration zone, while the acceleration values 0–10 m from the bit signal a high-risk zone. In prolonged horizontal section, stability issues manifest, with spiral buckling observed in the holding section and sinusoidal buckling in the horizontal section. Mitigating the synchronous vibrations between the bit and the surrounding drillstring can effectively reduce the intensity of axial vibration. To ensure successful drilling to target formation, adjusting the wellhead pulling force to keep the WOB in the range of 60–90 kN and limiting the rotary speed to 90 r/min are recommended practices. This comprehensive analysis offers valuable insights for optimizing drilling parameters, pinpointing high-vibration zones, and mitigating risks associated with drilling, providing a holistic approach to enhancing drilling efficiency.

A three-loop physical parameter identification method of robot manipulators considering physical feasibility and nonlinear friction model

A three-loop physical parameter identification method of robot manipulators considering physical feasibility and nonlinear friction model

ДИНАМІЧНА МОДЕЛЬ ІТЕРАЦІЙНОГО ЕЛЕКТРОПРИВОДА ПОДАЧІ З ДВОМА ГВИНТОВИМИ ПЕРЕДАЧАМИ ДЛЯ ПРЕЦИЗІЙНИХ ВЕРСТАТІВ ТА ОБРОБНИХ ЦЕНТРІВ

A variant of a simplified design diagram is proposed and the corresponding kinematic diagram of a two-motor gearless drive mechanism with two screw gears (SG) is given for an iterative two-channel electric drive for the longitudinal feed of the working tool (worktable with a product) of a coordinate multi-purpose metal-cutting machine of especially high precision, model 24K70AF4. Compensators of the negative dynamic interaction of load control channels have been determined. A generalized dynamic model of the cutting process has been constructed, taking into account both the inertia of the cutting process and the influence of the machine “WT-cutter” elastic system dynamics. A dynamic model of a conditional compensator for the cutting process is determined and calculated. A refined mathematical model of motion in steady-state feed modes of the two-channel electric drive has been obtained, taking into account the compensation of the dynamic interaction of the channels on the load and the influence of friction nonlinearities in the drive mechanism and the working tool of the machine. A structural-algorithmic diagram of an iterative two-channel compensated feed electric drive with two SGs and subordinated adjustment of control channels has been designed. The diagram includes a generalized dynamic model of the cutting process and a dynamic model of the corresponding conditional compensator for the cutting process, and also takes into account the main static moments of resistance and nonlinearity of friction in the drive load. References 13, tables 2, figures 5.

Hybrid method for hydraulic transient analysis of liquid pipe networks based on characteristic lines and equivalent circuits

Water hammer poses a significant concern in the transportation of pipelines and pipe networks. Due to the passage of reflection of water hammer waves at nodes, a large number of high-frequency pressure fluctuation signals appear in the pipe network, demanding an intensive computational workload. A novel hybrid method based on characteristic lines and equivalent circuits is proposed for the accurate and fast simulation of pipe networks. Multiple methods are employed for the simulation of pipelines and pipe networks, followed by a comparative analysis. The accuracy of the hybrid method is validated by comparing the proposed method with simulation results of commercial software. The hybrid method reduces the significant computational workload inherent in the classic method of characteristics and enhances the accuracy at high frequencies in the state-of-the-art elastic water column model. A trade-off between simulation accuracy and computation speed is achieved by adjusting the time step. The accuracy of calculating higher-frequency pressure fluctuations is further validated with an increase in the pipe diameter and a corresponding reduction in the friction loss. Generally, this method enables the simultaneous descriptions of high-frequency characteristics and nonlinear friction loss, enhancing calculation speed with little impact on the accuracy. The results demonstrate that the proposed model can be utilized for the transient analysis of pipe networks, providing support for predicting system performance and designing optimal strategies.

Nonlinear Slippage of Tensile Armor Layers of Unbonded Flexible Riser Subjected to Irregular Loads

The unbonded flexible riser has been increasingly applied in the ocean engineering industry to transport oil and gas resources from the seabed to offshore platforms. The slippage of helical layers, especially the tensile armor layers of unbonded flexible risers, contribute to the nonlinear hysteresis phenomenon, which is a research hotspot and difficulty. In this paper, on the basis of a typical eight-layer unbonded flexible riser model, the nonlinear slippage of a tensile armor layer and the corresponding nonlinear behavior of an unbonded flexible riser subjected to irregular external loads are studied by numerical modeling with detailed cross-sectional properties of the helical layers, and are verified through a theoretical method considering the coupled effect of the external loads on the unbonded flexible riser. Firstly, the balance equation of each layer considering the effect of external loads is established based on functional principles, and the overall theoretical model of the unbonded flexible riser is set up in consideration of the contact between adjacent layers. Secondly, the numerical modeling of each separate layer within the unbonded flexible riser, including the actual geometry of the carcass and pressure armor layer, is established, and solid elements are applied to all the interlayers, thus simulating the nonlinear contact and friction between and within interlayers. Finally, after verification through test data, the behavior of the unbonded flexible riser under the cyclic axial force, torsion, bending moment, and irregular external and internal pressure is studied. The results show that the tensile armor layer can slip under irregular loads. Additionally, some suggestions related to the analysis of unbonded flexible risers under irregular loads are drawn in the end.

Online identification and feed-forward compensation of nonlinear friction in servo system based on RBF neural network model

In this paper, an online identification and compensation method of nonlinear friction based on radial basis function (RBF) neural network model is proposed for the influence of nonlinear friction on machining accuracy in the low speed process of servo feed system of CNC machine tools. First, a three-layer single-input-output RBF neural network model is established for describing the nonlinear friction of servo feeding system. Second, the neural network online learning algorithm is improved based on adaptive gain, which improves the stability and accuracy of the algorithm. Finally, experiments were carried out on a three-axis milling machine to compensate the friction in the servo feed system in real time based on the online identification results. The results show that the method can effectively improve the online identification accuracy and convergence rate, and effectively improved the low-speed performance of the servo feed system.

Research on High-Stability Composite Control Methods for Telescope Pointing Systems under Multiple Disturbances.

During the operation of space gravitational wave detectors, the constellation configuration formed by three satellites gradually deviates from the ideal 60° angle due to the periodic variations in orbits. To ensure the stability of inter-satellite laser links, active compensation of the breathing angle variation within the constellation plane is achieved by rotating the optical subassembly through the telescope pointing mechanism. This paper proposes a high-performance robust composite control method designed to enhance the robust stability, disturbance rejection, and tracking performance of the telescope pointing system. Specifically, based on the dynamic model of the telescope pointing mechanism and the disturbance noise model, an H∞ controller has been designed to ensure system stability and disturbance rejection capabilities. Meanwhile, employing the method of an H∞ norm optimized disturbance observer (HODOB) enhances the nonlinear friction rejection ability of the telescope pointing system. The simulation results indicate that, compared to the traditional disturbance observer (DOB) design, utilizing the HODOB method can enhance the tracking accuracy and pointing stability of the telescope pointing system by an order of magnitude. Furthermore, the proposed composite control method improves the overall system performance, ensuring that the stability of the telescope pointing system meets the 10 nrad/Hz1/2 @0.1 mHz~1 Hz requirement specified for the TianQin mission.

Optimizing Reverse-Engineered Finite Element Models for Accurate Predictions of Experimental Measurements

This study investigates the challenges of reverse engineering in finite element modelling of sheet metal forming, specifically for the Volvo XC90 front door inner component. Advanced models incorporating anisotropic behaviour of steel and non-linear friction are compared against actual real-world measurements. The methodology involves simplifying complex continuous parameters into more manageable representative data sets and assessing model accuracy under both uniform and varied blank holder force settings, guided by measured contact pressure distributions. Although the results indicate an improvement in accuracy, they underscore the need for additional methodological improvements and more accurate replication of tooling effects to enhance the fidelity and effectiveness of these models.