Mechanism-oriented control for suppressing start-up judder of vehicle with automatic dry clutch: Experiment and simulation analysis

In this paper, a mechanism-oriented control strategy is proposed to cut off the introduction process of negative damping caused by the Stribeck effect for suppressing the vehicle start-up judder. From the experimental analysis, the characteristic frequency of start-up judder is mainly concentrated at about 8.25 Hz, coinciding with the first-order natural frequency of the driveline system. A 13-degree-of-freedom powertrain branched model is established, whose validity and accuracy in reflecting the characteristics of start-up judder are verified by comparing with the experimental results in time–frequency domain. The start-up judder mechanism is profoundly revealed through explaining the introduction of negative damping and the origin of characteristic frequency. The positive-feedback closed loop caused by the negative gradient characteristic of the Stribeck effect is the determining factor that promotes the aggravation of the fluctuation in the rotational speed of clutch-driven plate, which is the manifestation of the negative damping. The core idea of the mechanism-oriented control strategy is to cut off the positive-feedback closed loop, which is achieved by fine-tuning the position of release bearing. The judder-suppression performance behaves well both in simulation and in experiment.

Mechanism analysis of vehicle start-up judder based on gradient characteristic of Stribeck effect

This paper presents a profound mechanism investigation for vehicle start-up judder phenomenon using a combination of experiment and simulation. First, from the experimental analysis, the characteristic frequency of start-up judder is mainly concentrated at about 9 Hz. A 13-degree-of-freedom powertrain branched model is established to numerically reproduce experimental phenomenon. The validity and accuracy of simulation model in reflecting the characteristics of start-up judder are verified by the experimental results in time–frequency domain. Second, through analyzing clutch friction torque, it can be concluded that the closed-loop positive feedback mechanism caused by the negative gradient characteristic of Stribeck effect is the determining factor for the start-up judder. It promotes aggravated fluctuation in rotational speed of clutch driven plate. The introduction process of negative damping that makes powertrain system divergent is explained in detail. Finally, two theoretical measures are proposed to suppress the vehicle start-up judder. One of the measures is to diminish the absolute value of the negative gradient. It weakens the aggravation effect of the closed-loop positive feedback and hence attenuates the start-up judder. Another measure is to change to positive gradient. It forms a closed-loop negative feedback process that causes the almost disappearance of start-up judder. The effectiveness of the two suppression measures verifies the correctness of the start-up judder mechanism proposed in this paper.

Vibration Instability in a Large Motion Bistable Compliant Mechanism Due to Stribeck Friction

The present paper investigates friction-induced self-excited vibration of a bistable compliant mechanism. A pseudo-rigid-body representation of the mechanism is used containing a hardening nonlinear spring and a viscous damper. The mass is suspended from above with the spring-damper combination leading to the addition of geometric nonlinearity in the equation of motion and position- and velocity-dependent normal contact force. Friction input provided by a moving belt in contact with the mass. An exponentially decaying function of sliding velocity describes the friction coefficient and, thereby, incorporates Stribeck effect of friction. Eigenvalue analysis is employed to investigate the local stability of the steady-state fixed points. It is observed that the oscillator experiences pitchfork and Hopf bifurcations. The effects of the spring nonlinearity and precompression, viscous damping, belt velocity, and the applied normal force on the number, position, and stability of the equilibrium points are investigated. Global system behavior is studied by establishing trajectory maps of the system. Critical belt speed is derived analytically and shown to be only the result of Stribeck effect of friction. It is found that one equilibrium point dominates the steady-state response for very low damping and negligible spring nonlinearity. The presence of damping and/or spring nonlinearity tends to diminish this dominance.

Dynamic Analysis of Planar Mechanical Systems With Clearance Joint Based on LuGre Friction Model

A computational methodology to model and analyze planar rigid mechanical system with stick–slip friction in revolute clearance joint is presented. In this work, the LuGre friction model, which captures the Stribeck effect and spring-like characteristics for stiction, is employed to estimate the stick–slip friction in revolute clearance joint. A hybrid contact force model, combining Lankarani–Nikravesh model, and improved elastic foundation model, is used to establish contact model. The generalized-α method, which can dissipate the spurious high-frequency responses caused by the strongly nonlinear contact force and friction in numerical simulation, is adopted to solve the equations of motion and make the result closer to the physics of the problem. A slider-crank mechanism with revolute clearance joint based on LuGre friction model and modified coulomb friction model are simulated, respectively, and utilized to discuss the influences of the Stribeck effect and stiction on dynamic behavior of the mechanism. Different test scenarios are considered to investigate the effects of the clearance size and friction coefficient on the dynamic response of the mechanism. The results show that the mechanism based on LuGre friction model has better energy dissipation characteristics, while there are stiction phenomena of the contacting surfaces in many cases. When the relative velocity is zero or close to zero, the contact force of mechanism based on the LuGre friction model is significantly lower than that based on the modified coulomb friction model. Clearance size and friction coefficient obviously affect dynamic behavior of the mechanism.

Nonlinear Friction Compensation of a Flexible Robotic Joint with Harmonic Drive

To suppress the abrupt and unexpected turning velocity fluctuation of the industrial robot under the condition of trajectory tracking, a flexible robotic joint experimental setup with the harmonic drive was established. The measured friction with Stribeck effect and velocity were modeled by a simple polynomial fit method. Two friction compensation control strategies of feedforward and feedback were designed. The friction compensation experiments were carried out on the dSPACE system, the good restraint effect of fluctuation on the turning velocity was verified and the control accuracy of feedback compensation control strategy proved better.

Disc Brake Vibration Model Based on Stribeck Effect and Its Characteristics under Different Braking Conditions

A 7-degree-of-freedom (DOF) vibration model of a fixed-caliper disc brake system was developed herein based on the Stribeck effect. Furthermore, a dynamometer brake test was conducted to determine the characteristic system parameters of the 7-DOF vibration model. This model was developed to study the effects of braking conditions, such as disc rotational speed and brake pressure on brake noise. The complex eigenvalues of the system were also calculated to analyze the brake model stability under different braking conditions. The acceleration time history diagrams and phase plots were obtained by solving the equations of the system. The numerical calculation results showed that the brake noise increased with an increasing braking force and a decreasing breaking speed. These numerical findings were verified by the results of the dynamometer tests.

Self-Excited Torsional Oscillations under Locked-Wheel Braking: Analysis and Experiments

ABSTRACT This paper analyzes the effect of tire/vehicle parameters, specifically of tire/suspension torsional stiffnesses, on the stability of self-excited tire torsional oscillations during locked-wheel braking events. Using a torsionally flexible tire-wheel model and a dynamic tire-ground friction model, two system models for tire oscillations are considered: with suspension torsional compliance included in one but excluded in the other. Bifurcation analysis is conducted on both systems to derive the effect of tire/vehicle parameters on the stability. For the system without suspension torsional compliance, it is highlighted that the primary cause of unstable self-excited oscillations is the “Stribeck” effect in tire-ground friction. Based on the parameters obtained experimentally, the bifurcation surface of vehicle velocity with respect to tire/suspension torsional stiffness is also given. The effect of tire/suspension torsional stiffness to the stability of tire torsional oscillation is qualitatively validated via comparisons between locked-wheel braking simulations and experiments with tires with different torsional stiffnesses.