Mechanical Elastic Wheel Research Articles

Steady-state rolling resistance prediction model of non-pneumatic tyres considering tread temperature: theory and experiment

Non-pneumatic tires have potential advantages over pneumatic tires, including lower rolling resistance. First, a non-pneumatic mechanical elastic wheel (ME-Wheel) was designed. Based on its structural characteristics, a tread temperature prediction model under steady-state rolling conditions was established, and the accuracy of the established model was verified through temperature measurement experiments. Combined with the tread temperature prediction model, a steady-state rolling resistance prediction model of ME-Wheel was established, and the basic parameters (ground length CL , ground width CW , radial stiffness SR ) required for the model were identified through experiments. Finally, the experimental data were compared with the predicted values under different speed and load conditions. The results showed that the average simulation value of the rolling resistance coefficient of ME-Wheel was 0.01853, which was positively correlated with speed and load. The test results and predicted values showed a similar trend under the same operating conditions, with a maximum error of less than 3.5%. This proved that the novel non-pneumatic tyre steady-state rolling resistance prediction model based on tread temperature could accurately predict the steady-state rolling resistance of tyres. This research addresses a significant topic in tyre technology and has the potential to influence future designs and optimizations of non-pneumatic tyres.

Mechanism of resistance to deformation for damaged mechanical elastic wheel: Rubber damage research based on peridynamic

As a type of non-pneumatic wheel, mechanical elastic wheel (MEW) can is resistant to deformation and continue to be used when rubber is damaged by the bullet. In order to prove the deformation resistance ability of MEW, the model of rubber damaged by bullet based on the non-ordinary state-based peridynamic is proposed for the first time. By considering the two conditions with bullet penetrating and staying in rubber respectively, the model is simulated and predicted. The results show that the simulations about the model of rubber damaged by bullet is consistent with experiments, the validity of the model is verified. It explains the physical process of penetrating bullet hole being smaller than the bullet diameter, and explains the reasons for the rubber forming bulge after bullet staying in rubber. The MEW damaged by bullet still has the running ability, the damage wheel does not have obvious secondary damage after running, and MEW has the deformation resistance ability after bullet damage. It has reference significance for the research of rubber tearing problem.

Modeling Control and Forecasting Nonlinear Systems Based on Grey Signal Theory

Based on this article, a fuzzy NN (neural network) based on the EBA (evolved bat algorithm) was developed to devise adaptive control with gray signal prediction to provide asymptomatic stability and increased driving comfort. The method is used to assess plant nonlinearity and to perform structural tracking of the signal. The set of Gray’s differential equations is applied to Gray’s model (GM) (n, h), which has been an active system model. In the model, n is the order of the Gray’s differential equation and h is the number of variables considered. In this paper, a GM(2.1) has been utilised to achieve advanced nonlinear motion of a system, allowing the controller to demonstrate the efficiency and stability of the whole system in a Lyapunov-like expression. The controller design standard for a MEW (mechanical elastic wheel) is presented, creating a realistic framework in mathematical for practical engineering applications.

Neural ordinary differential gray algorithm to forecasting nonlinear systems

Due to the feasibility of the gray model for predicting time series with small samples, the gray theory is well investigated since it is presented and is currently evolved in an important manner for forecasting small samples. This study proposes a new gray prediction criterion based on the Neural Ordinary Differential Equation (NODE), which is named the NODGM (Neural Based Ordinary Differential gray Mode). This mode permits the forecasting approximation to be learned by a training process which contains a new whitening equation. It is needed to prepare the structure and time series, compared with other models, according to the regularity of actual specimens in advance, therefore this model of NODGM can provide comprehensive applications as well as learning the properties of distinct data specimens. In order to acquire a better model which has highly predictive efficiency, afterwards, this study trains the model by NODGM meanwhile using the Runge-Kutta method to obtain the prediction sequence and solve the model. The controller establishes an advantageous theoretical foundation in adapting to novel wheels and comprehensive spreads the utilize extent of Mechanical Elastic Vehicle Wheel (MEVW).

Integrated Control of Active Front Wheel Steering and Active Suspension Based on Differential Flatness and Nonlinear Disturbance Observer

Mechanical elastic wheel (MEW) has the advantage of explosion-proof, which helps to guarantee the safety and maneuverability of the automobile. Aiming to improve the stability of vehicles matching with MEW, this paper proposes an integrated control strategy that combines the active front steering and the active suspension systems. The integrated controller consists of feed-forward and feedback controllers. Firstly, the differential flatness system of the vehicle is constructed concerning the coupling among yaw, lateral, and roll motion. And the flatness based feed-forward control inputs of the desired front wheel angle and active roll moment are derived. At the same time, the backstepping-adaptive feedback controllers for yaw rate and roll angle are designed. Then, the feed-forward and feedback controllers are coordinated and their weight coefficients are adjusted according to the sideslip angle. Furthermore, this paper also adopts a nonlinear disturbance observer to estimate the vertical load of MEW. The influence of the vertical load is fully considered when estimating the equivalent cornering stiffness of each MEW, so as to realize the online adjustment of the controller parameters. Finally, the maneuver tests of step input steering and double lane change are simulated, respectively. The results show that the proposed control strategy yields a better control effect than the fuzzy-PID controller, and the performance of the vehicle matching with MEW has been significantly improved.

Integrated tire slip energy dissipation and lateral stability control of distributed drive electric vehicle with mechanical elastic wheel

Stability and energy consumption have always been important issues in electric vehicle research. Excessive slip energy not only aggravates tire wear, but also consumes energy of electric vehicle. In order to ensure the lateral stability and to reduce the slip energy dissipation of the distributed drive electric vehicle (DDEV) equipped with Mechanical Elastic Wheel (MEW), an integrated framework considering both tire slip energy dissipation and lateral stability control is proposed. The SESC (Slip Energy and Stability Control) is a hierarchical control framework for DDEV with MEW. A PID speed tracking controller and an (Integral Terminal Slide Mode) ITSM controller are designed at the upper-level controller. The ITSM controller can improve the lateral stability of the vehicle by obtaining the desired yaw moment. Speed tracking controller can stabilize the speed of the vehicle and obtain the desired longitudinal force. At the lower-level controller, the brush model of the MEW is proposed to express tire slip energy. In order to reduce the error of the vehicle dynamics and the slip energy dissipation, a mixed objective function including a holistic corner controller (HCC) and a minimum tire slip energy characterization is proposed. The proposed control framework is verified by Carsim and Matlab/Simulink under emergency simulation conditions. The simulation results show that the SESC based method can improve the lateral stability of DDEV with MEW effectively, and has better performance compared with fuzzyPID+AD based method. Meanwhile, the SESC achieves less slip energy than conventional torque distribution method.

Rideability analysis of mechanical elastic wheel in damaged conditions

In this paper, it is first time to study rideability of mechanical elastic wheel (MEW) in damaged conditions and discuss whether the wheel with local damage conditions will be failure during running. This paper is first time to propose a rideability evaluation method of damaged MEW. For getting the parameters about displacement acceleration of rings and tensile force of chains required from the evaluation method, a rigid-flexible coupling model ‘ring model’ of running MEW was established, the solution method of the model was also given by travelling mode superposition method. The ring model was compared with the experiment and finite element method to verify its accuracy. With using the verified ring model, the rideability simulation was analyzed under eight kinds of speeds and six kinds of damaged working conditions. The results show that: MEW with one or two damaged chains still has the receptible rideability and is not failure, and it provides security for the safe driving of vehicles in emergency situations; when damaging three chains, the wheel can be used to run at low speeds, the rideability of wheel at high speeds will deteriorate and the wheel will be failure; the rideability of MEW with axisymmetric chain damage is better than that with neighboring chain damage; it also finds that the simulation calculation time of ring model is much lower than that of finite element method, the time cost will be saved.

Lateral Stability Control of Distributed Drive Electric Vehicle with Mechanical Elastic Wheel

Lateral Stability Control of Distributed Drive Electric Vehicle with Mechanical Elastic Wheel

NN model-based evolved control by DGM model for practical nonlinear systems

This article develops an evolutionary bat algorithm (EBA) based fuzzy neural network (NN), which is applied to the adaptive controller in a plant, for the purpose of ensuring the asymptotic stability and heightening the stability of the vehicle. With a gray signal predictor, the Lyapunov theory as well as the backstepping method are adopted to ensure the non-linearity of the controlled system and derive the evolutionary control law of the signal tracking. The discrete gray model (DGM) (2,1) is used to predict the future motion of the nonlinear system, so that the fuzzy controller can ensure the Lyapunov stability and the feasibility of the parallel distributed compensation (PDC) scheme through the Lyapunov type lemma. The controller design is demonstrated in practical nonlinear systems, for a mechanical elastic wheel (MEW), as a feasible mathematical framework for the matching of this circular object revolving on an axle.

Backstepping sliding-mode control for active suspension system matching mechanical elastic wheel with uncertainties

For the purpose of anti-puncture and lightweight, a new type of mechanical elastic wheel (MEW) is constructed. However, the large radial stiffness of MEW has a negative effect on ride comfort. To make up for the disadvantage, this paper proposes a novel control strategy consisting of backstepping control and integral sliding-mode control, considering the uncertainties of active suspension and MEW. First, an active suspension system matching MEW is established, discussing the impact of uncertainties. The nonlinear radial characteristic of MEW is fitted based on the previous experiment results. Then, in order to derive ideal motions, an ideal suspension system combining sky-hook and ground-hook damping control is introduced. Next, ignoring the nonlinear characteristics and external random disturbance, a backstepping controller is designed to track ideal variables. Combined with the backstepping control law, an integral sliding-mode control strategy is given, further taking parameter uncertainty and external disturbance into account. To tackle chattering problem, an adaptive state variable matrix is applied. By using Lyapunov stability theory, the whole scheme proves to be robust and convergent. Finally, co-simulations with Carsim and MATLAB/Simulink are carried out. By analyzing the simulation results, it can be concluded that the vehicle adopting backstepping sliding-mode control performs best, with excellent real-time performance and robustness.

Decoupling control of active suspension and four-wheel steering based on Backstepping-ADRC with mechanical elastic wheel

Mechanical elastic wheel (MEW) has the advantages of explosion-proof and prick-proof, which is conducive to the safety and maneuverability of the vehicle. However, the research on the performance of the full vehicle equipped with MEW is rare. Considering the particular properties of the radial and cornering stiffness of MEW, this paper aims to take into account both ride comfort and yaw stability of the vehicle equipped with the MEW through a nonlinear control method. Firstly, a 9-DOF nonlinear full vehicle model with the MEW tire model is constructed. The tire model is fitted based on experimental data, which corrects the impacts of vertical load on the cornering characteristic of the MEW. Then the full vehicle system is decoupled into four subsystems with a single input and a single output each according to active disturbance rejection control (ADRC) technology. In this process, the coupling relationship between different motions of the original system is regarded as the disturbance. Afterward, a novel nonlinear extended state observer is proposed, which has a similar structure of traditional linear extended state observer but smaller estimation error. Next, the control law of Backstepping-ADRC for different subsystems are derived respectively based on the Lyapunov theory. For the first time, the Backstepping-ADRC method is applied to the decoupling control of four-wheel steering and active suspension systems. Furthermore, the parameters of the controllers are adjusted through a multi-objective optimization scheme. Finally, simulation results validate the effectiveness and robustness of the proposed controller, especially when encountering some disturbances. The indices of vehicle body attitude and ride comfort are improved significantly, and also the yaw stability is guaranteed simultaneously.

Radial stiffness analysis of circular ring with uncertain boundary conditions: Mechanical elastic wheel as an example

The paper studies the radial stiffness of mechanical elastic wheel (MEW), which is regarded as a circular ring with uncertain boundary conditions for the first time, and proposes a ring-chain model to solve the radial stiffness of the ring. Different from assuming the boundary conditions by experience or building finite element model with complex processes from previous researches, the ring-chain model coupling circular ring model and dynamics of multi-rigid body is accurate and simple to find the loaded positions of ring and make the boundary conditions clear. The results show that the ring-chain model can be solved to get the deformations and loaded positions of ring, the radial stiffness of MEW is large, and the radial displacement of MEW increases non-linearly. The results are consistent with that from finite element model under the same settings, but the time cost of ring-chain model is less. In addition, the influence factors of ring radial stiffness are also found and analyzed. The method presented in this paper can provide data for the response analyses of vehicle and references for the analysis of circular ring with uncertain boundary conditions.

Grey Signal Predictor and Fuzzy Controls for Active Vehicle Suspension Systems via Lyapunov Theory

In order to investigate and decide that the vehicle asymptotic vibration stability and improved comfort, the present paper deals with a fuzzy neural network (NN) evolved bat algorithm (EBA) backstepping adaptive controller based on grey signal predictors. The Lyapunov theory and backstepping method is utilized to appraise the math nonlinearity in the active vehicle suspension as well as acquire the final simulation control law in order to track the suitable signal. The Discrete Grey Model DGM (2,1) have been thus used to acquire prospect movement of the suspension system, so that the command controller can prove the convergence and the stability of the entire formula through the Lyapunov-like lemma. The controller overspreads the application range of mechanical elastic vehicle wheel (MEVW) as well as lays a favorable theoretic foundation in adapting to new wheels.

Torque vectoring algorithm based on mechanical elastic electric wheels with consideration of the stability and economy

How to coordinate the relationship between stability and economy according to the current motion state of the vehicle is an urgent problem to be considered in torque distribution. To solve this problem, a novel torque vectoring algorithm is proposed based on a novel type of mechanical elastic electric wheel. The tire model of mechanical elastic wheel is identified based on Fibonacci tree. Considering the nonlinearity of tire force, a linear parameter-varying linear quadratic regulator upper controller based on a 2-degree of freedom (DOF) model is designed. In addition, considering the inaccuracy of the vehicle model, a nonlinear model predictive control is designed based on the 7-DOF model. For the lower controller, a torque allocation algorithm considering stability and economy is proposed, which ensures the stability of the vehicle and reduces the energy consumption of the powertrain. Moreover, the weight distribution of stability and economy is dynamically coordinated based on the phase portrait. Finally, the algorithm is verified under the conditions of low adhesion road, joint road, driving cycle and hardware-in-the-loop test. The results show that the proposed torque vectoring algorithm can ensure the vehicle handling stability and improve the energy efficiency of the powertrain at the same time.

Theoretical analysis on cornering properties of the mechanical elastic wheel based on a mixed modelling method

The mechanical elastic wheel (MEW) is a new type of non-pneumatic tyre, which is characterised by the elastic-rings and hinge-groups to replace the compressed air of ordinary tyres. A mixed modelling method was used to theoretically analyse steady-state cornering properties of MEW. Considering structure properties and using the basic theory of the brush model, a simplified theoretical model for steady-state cornering properties of MEW was set up. Test data of MEW cornering properties under different vertical loads was used to establish the fitting models on half contact length, lateral stiffness and sliding friction coefficient. Based on the steady-state cornering simplified model and the fitting models, the MEW cornering mixed model was constructed. Comparing theory simulation result with test result, it is indicated that the mixed model has relatively high prediction accuracy. Therefore, certain reference could be provided for optimising MEW structure and improving cornering performance.

Theoretical analysis on cornering properties of MEW based on mixed modelling method

The mechanical elastic wheel (MEW) is a new type of non-pneumatic tyre, which is characterised by the elastic-rings and hinge-groups to replace the compressed air of ordinary tyres. A mixed modelling method was used to theoretically analyse steady-state cornering properties of MEW. Considering structure properties and using the basic theory of the brush model, a simplified theoretical model for steady-state cornering properties of MEW was set up. Test data of MEW cornering properties under different vertical loads was used to establish the fitting models on half contact length, lateral stiffness and sliding friction coefficient. Based on the steady-state cornering simplified model and the fitting models, the MEW cornering mixed model was constructed. Comparing theory simulation result with test result, it is indicated that the mixed model has relatively high prediction accuracy. Therefore, certain reference could be provided for optimising MEW structure and improving cornering performance.

Integrated optimization for mechanical elastic wheel and suspension based on an improved artificial fish swarm algorithm

This paper aims to provide a baseline for the future optimum design of the Mechanical Elastic Wheel (MEW), and improve the ride comfort of the vehicle equipped with the MEW. A new factor δ is introduced, which is the ratio of the length of hinge groups to the thickness of elastic wheel. The influence of δ on the MEW radial stiffness is studied based on finite element analyses and experimental verification. The stiffness characteristics with δ are fitted by means of artificial neural network. A quarter-car model is established, combining the MEW and the hydro-pneumatic suspension. A multi-objective optimization is proposed, where an improved Pareto Artificial Fish Swarm Algorithm is applied to attain the appropriate parameters of both suspension and MEW. The results after optimization illustrate that the root mean square value of body vertical acceleration, suspension working space and dynamic tyre load are reduced by 43.88%, 24.38% and 46.46% respectively. In addition, the power spectral densities of three indexes are all dropped. This method proposed by this paper not only offers an optimal matching between the MEW and the hydro-pneumatic suspension, but also has the reference value for improving vehicle ride comfort.

Integrated yaw and rollover control based on differential braking for off-road vehicles with mechanical elastic wheel

Aiming at the issue of yaw and rollover stability control for off-road vehicles with non-pneumatic mechanical elastic wheel (MEW), an integrated control system based on fuzzy differential braking is developed. By simplifying the structure of the MEW, a corresponding fitting brush tire model is constructed and its longitudinal and lateral tire force expressions are set up, respectively. Then, a nonlinear vehicle simulation model with MEW is established to validate the proposed control scheme based on Carsim. The designed yaw and rollover control system is a two-level structure with the upper additional moment controller, which utilizes a predictive load transfer ratio (PLTR) as the rollover index. In order to design the upper integrated control algorithm, fuzzy proportional-integral-derivative (PID) is adopted to coordinate the yaw and rollover control, simultaneously. And the lower control allocator realizes the additional moment to the vehicle by differential braking. Finally, a Carsim-simulink co-simulation model is constructed, and simulation results show that the integrated control system could improve the vehicle yaw and roll stability, and prevent rollover happening.

Adaptive backstepping control with grey signal predictor for nonlinear active suspension system matching mechanical elastic wheel

Abstract In order to stabilize the attitude and improve ride comfort of vehicles equipped with mechanical elastic wheel (MEW), an adaptive backstepping controller with grey signal predictor is presented for active suspension system, considering the uncertainty and nonlinearity of suspension and MEW. The MEW’s mathematical model is established through experiments firstly. Then the ideal suspension motions are generated according to a designed hybrid damping control. To track these ideal signals, Lyapunov theory and the thought of backstepping are used to estimate the nonlinearity of active suspension and obtain final control laws. Grey DGM (2,1) model is further applied to derive future motions of suspension, thus commands can be carried out in advance to realize control in time. The stability and convergence of whole scheme are also proved by Lyapunov-like lemma. Finally, simulations on two different road profiles (step and pulse) show that this strategy can effectively suppress the vertical motion of vehicle body by 19.7% and pitch motion by 9.5% respectively compared with that without control. And furthermore, the bounce of wheels is also decreased at the same time. The controller expands the application of MEW and establishes a good theoretical foundation for the novel wheels’ matching.

Thermodynamics modeling of a novel nonpneumatic mechanical elastic wheel for predicting its mechanical–thermal behavior

An advanced thermodynamics model based on brush-type tire model was developed here to investigate the mechanical–thermal behavior of a novel nonpneumatic mechanical elastic wheel (ME-wheel), operating under rolling conditions. Herein, first, we proposed a novel brush-type tire physical model wherein the factors of realistic tire deformable and frictional behavior were introduced. Next, the heat generation and dissipation mechanism of ME-wheel was investigated to develop its thermal model. By combining the brush-type tire physical model and thermal model through the factors involving tire deformable energy loss and frictional power loss, we established this thermodynamics model to predict the temperature-dependent mechanical characteristics and corresponding thermal behavior of ME-wheel under rolling operating conditions. It is found that the computation results agree well with the obtained experimental data (tire static and dynamics testing), which demonstrated the capability of this model in precisely predicting the mechanical characteristics and thermal behavior of ME-wheel, particularly those designed for off-road vehicle under typical real operating conditions.