Partial Time-Varying Coefficient Regression and Autoregressive Mixed Model

Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressive mixed models are constants. However, for complicated data, the coefficients of covariates may change with time. In this article, we propose a kind of partial time-varying coefficient regression and autoregressive mixed model and obtain the local weighted least-square estimators of coefficient functions by the local polynomial technique. The asymptotic normality properties of estimators are derived under regularity conditions, and simulation studies are conducted to empirically examine the finite-sample performances of the proposed estimators. Finally, we use real data about Lake Shasta inflow to illustrate the application of the proposed model.

Partial Time-Varying Coefficient Regression and Autoregressive Mixed Model

Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressive mixed models are constants. However, for complicated data, the coefficients of covariates may change with time. In this article, we propose a kind of partial time-varying coefficient regression and autoregressive mixed model and obtain the local weighted least-square estimators of coefficient functions by the local polynomial technique. The asymptotic normality properties of estimators are derived under regularity conditions, and simulation studies are conducted to empirically examine the finite-sample performances of the proposed estimators. Finally, we use real data about Lake Shasta inflow to illustrate the application of the proposed model.

Approach to estimation of vehicle-road longitudinal friction coefficient

According to the road adaptive requirements for the vehicle longitudinal safety assistant system an estimation method of the road longitudinal friction coefficient is proposed.The method can simultaneously be applied to both the high and the low slip ratio conditions. Based on the simplified magic formula tire model the road longitudinal friction coefficient is preliminarily estimated by the recursive least squares method.The estimated friction coefficient and the tires model parameters are considered as extended states. The extended Kalman filter algorithm is employed to filter out the noise and adaptively adjust the tire model parameters. Then the final road longitudinal friction coefficient is accurately and robustly estimated. The Carsim simulation results show that the proposed method is better than the conventional algorithm. The road longitudinal friction coefficient can be quickly and accurately estimated under both the high and the low slip ratio conditions.The error is less than 0.1 and the response time is less than 2 s which meets the requirements of the vehicle longitudinal safety assistant system.

Effect of friction coefficient in deep drawing of AA6111 sheet at elevated temperatures

The effect of friction coefficient on the deep drawing of aluminum alloy AA6111 at elevated temperatures was analyzed based on the three conditions using the finite element analysis and the experimental approach.Results indicate that the friction coefficient and lubrication position significantly influence the minimum thickness,the thickness deviation and the failure mode of the formed parts.During the hot forming process,the failure modes are draw mode,stretch mode and equi-biaxial stretch mode induced by different lubrication conditions.In terms of formability,the optimal value of friction coefficient determined in this work is 0.15.At the same time,the good agreement is performed between the experimental and simulated results.Fracture often occurs at the center of cup bottom or near the cup corner in a ductile mode or ductile-brittle mixed mode,respectively.

Nominal friction coefficient in spread formulas based on lead rolling experiments

Friction coefficients in spread formulas were studied under low width-to-thickness ratio. The effects of all the factors on friction were considered as different roughness of surfaces. After lead rolling experiments in 5 different roughness grades, friction coefficients were obtained. With changing width-to-thickness ratio, reduction rate and ratio of diameter of roller to thickness, all the nominal friction coefficients which can be used in these formulas were calculated. Then, a fitting expression was proposed, comparing with the results measured in 232 times tests, the errors of the nominal friction coefficients calculated by the expression are mostly less than 12%. After a certain times self-learning, the errors are no more than 2%. With the varying nominal friction coefficients, the spread will be predicted more accurately. When the nominal friction coefficient is used to predict the spread under the real working condition, the results calculated are also in agreement with the measured ones, and the errors are less than 2%. This credible reference and solution about how to set the friction coefficient in spread formulas would also be used in practical industrial production.

Estimation of Road Friction Coefficient in Different Road Conditions Based on Vehicle Braking Dynamics

The accurate estimation of road friction coeffi- cient in the active safety control system has become increasingly prominent. Most previous studies on road friction estimation have only used vehicle longitudinal or lateral dynamics and often ignored the load transfer, which tends to cause inaccurate of the actual road friction coef- ficient. A novel method considering load transfer of front and rear axles is proposed to estimate road friction coef- ficient based on braking dynamic model of two-wheeled vehicle. Sliding mode control technique is used to build the ideal braking torque controller, which control target is to control the actual wheel slip ratio of front and rear wheels tracking the ideal wheel slip ratio. In order to eliminate the chattering problem of the sliding mode controller, integral switching surface is used to design the sliding mode sur- face. A second order linear extended state observer is designed to observe road friction coefficient based on wheel speed and braking torque of front and rear wheels. The proposed road friction coefficient estimation schemes are evaluated by simulation in ADAMS/Car. The results show that the estimated values can well agree with the actual values in different road conditions. The observer can estimate road friction coefficient exactly in real-time andresist external disturbance. The proposed research provides a novel method to estimate road friction coefficient with strong robustness and more accurate.

Identification of Maximum Road Friction Coefficient and Optimal Slip Ratio Based on Road Type Recognition

The identification of maximum road friction coefficient and optimal slip ratio is crucial to vehicle dynamics and control.However,it is always not easy to identify the maximum road friction coefficient with high robustness and good adaptability to various vehicle operating conditions.The existing investigations on robust identification of maximum road friction coefficient are unsatisfactory.In this paper,an identification approach based on road type recognition is proposed for the robust identification of maximum road friction coefficient and optimal slip ratio.The instantaneous road friction coefficient is estimated through the recursive least square with a forgetting factor method based on the single wheel model,and the estimated road friction coefficient and slip ratio are grouped in a set of samples in a small time interval before the current time,which are updated with time progressing.The current road type is recognized by comparing the samples of the estimated road friction coefficient with the standard road friction coefficient of each typical road,and the minimum statistical error is used as the recognition principle to improve identification robustness.Once the road type is recognized,the maximum road friction coefficient and optimal slip ratio are determined.The numerical simulation tests are conducted on two typical road friction conditions（single-friction and joint-friction）by using CarSim software.The test results show that there is little identification error between the identified maximum road friction coefficient and the pre-set value in CarSim.The proposed identification method has good robustness performance to external disturbances and good adaptability to various vehicle operating conditions and road variations,and the identification results can be used for the adjustment of vehicle active safety control strategies.

Study on Quantitative Relationship between Surface Wettability and Frictional Coefficient of Liquid Flowing in a Turbulent Horizontal Pipe

This paper had investigated the effects of surface wettability on the frictional resistance of turbulent horizontal flow for tap water in five pipes made of various materials and four kinds of liquids in a polytetrafluoroethylene(PTFE) pipe,with the same inner diameter of 14 mm. Pressure drops were measured under different flow rates through an experimental flow loop. The contact angles and adhesion work of liquids in contact with pipe surfaces were determined using a contact angle meter. Based on the dimension and regression analyses, two kinds of modified relationships between the frictional coefficient and the surface wettability were established according to the measured results corresponding to tap water in five pipes and four liquids in PTFE pipe. The experimental results show that the surface wettability has some influence on frictional coefficient of the studied liquids flowing in macroscale pipes, and the frictional coefficient decreases with the increase of the contact angle at the same Reynolds number. Meanwhile the effect of wettability on the hydrophobic surface is greater than that on the hydrophilic one. The frictional coefficients predicted by the modified formulas have verified to be in good agreement with the experimental values, the relative errors of which are within ±6% and ±3% for the tap water flowing in five different pipes and four kinds of liquids flowing in PTFE pipe, respectively.

Effect of Friction Coefficient on Deep Drawing of 6A16 Aluminum Alloy for Automobile Body

Based on the ABAQUS/Explicit finite element method,the forming force changing trend of deep drawing test for 6A16 aluminum alloy plate after pre-aging and storage at room temperature for one month was simulated under friction coefficient ranging from 0 to 0.22.The lubricants selected for the tests were mechanical oil,butter and dry film lubricant,and the friction coefficient of these lubricants were 0.05,0.10 and 0.15,respectively.Microstructural evolution of 6 A16 aluminum alloy plate during drawing forming was investigated by OM,SEM and EBSD.The results showed that,with the increase of friction coefficient,the stress,strain and deformation degree in deformation zone increased,while the grain size in deformation zone decreased.Thus,the hardness of the cup-typed component increased with the increase of friction coefficient.Butter-lubricated cups had the highest tensile strength and yield strength after paint-bake cycle.The combination of simulation results and microstructure analysis of 6A16 aluminum alloy plate after drawing forming indicates that the appropriate lubricant is butter.

Experimental investigation of friction coefficient in tube hydroforming

The friction coefficient between tube and die in guide zone of tube hydroforming was obtained. In hydroforming, the tube is expanded by an internal pressure against the tool wall. By pushing the tube through tool, a friction force at the contact surface between the tube and the tool occurs. In guiding zone, the friction coefficients between tube and die can be estimated from the measured axial feeding forces. In expansion zone, the friction coefficients between tube and die can be evaluated from the measured geometries of expanded tubes and FE analysis.

Effect of Tension on Friction Coefficient Between Lining and Wire Rope with Low Speed Sliding

In order to obtain the exact friction coefficient between lining and wire rope, the tension of wire rope is studied as a factor which affects this coefficient. A mechanical model of a wire rope subjected to axial load was established to determine the torque of the wire rope. The contact motion between lining and wire rope was regarded as a screw rotation and the axial force of the lining resulting from the torque of the wire rope was analyzed. Theoretical formulas relating tension of the wire rope and the friction coefficient was obtained. Experiments between lining and wire rope with low sliding speed were carried out with friction tester made by us. Experimental results show that increment of the friction coefficient is proportional to that of the tension of the wire rope with a low sliding speed. The experimental results agree with the theoretical calculation; the errors are less than 6%, which oroves the validity of the theoretical model.

Analysis of sliding electric contact characteristics in augmented railgun based on the combination of contact resistance and sliding friction coefficient

The contact resistance between the armature and rails is an important indicator of the contact characteristics in electromagnetic launches.As the contact resistance depends not only on the contact state but also on the contact stress and temperature,there are some limitations in analyzing the contact characteristics using only the contact resistance.In this paper,the contact characteristics of the augmented railgun are analyzed by the combination of contact resistance and sliding friction coefficient.Firstly,the theoretical calculation model of the contact resistance and friction coefficient of the augmented electromagnetic railgun is established.Then the contact resistance and friction coefficient are calculated by the measured values of the muzzle voltage,rail current and armature displacement.Finally,the contact characteristics are analyzed according to the features of the waveforms of the contact resistance and the friction coefficient,and the analysis conclusions are verified by experimental rail images.The results showed that:the aluminum melt film gradually formed on the contact surface reduces the contact resistance and the friction coefficient;the wear and erosion of the armature cause deterioration of the contact state;after the transition,the reliability of the sliding contact between the armature and rails decreases,resulting in an increase in contact resistance.

The Frictional Coefficient of Bovine Knee Articular Cartilage

The normal displacement of articular cartilage was measured under load and in sliding, and the coefficient of friction during sliding was measured using a UMT-2 Multi-Specimen Test System. The maximum normal displacement under load and the start-up frictional coefficient have similar tendency of variation with loading time. The sliding speed does not significantly influence the frictional coefficient of articular cartilage.

GENERAL DECAY FOR A VISCOELASTIC EQUATION OF VARIABLE COEFFICIENTS WITH A TIME-VARYING DELAY IN THE BOUNDARY FEEDBACK AND ACOUSTIC BOUNDARY CONDITIONS

A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered.Under suitable assumptions, general decay results of the energy are established via suitable Lyapunov functionals and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term and the elements of the matrix A and the kernel function g.

Driving force coordinated control of an 8x8 in-wheel motor drive vehicle with tire-road friction coefficient identification

Because of the complexities of tire-road interaction,the wheels of a multi-wheel distributed electricdrive vehicle can easily slip under certain working conditions.As wheel slip affects the dynamic per-formance and stability of the vehicle,it is crucial to control it and coordinate the driving force.With this aim,this paper presents a driving force coordination control strategy with road identification for eight-wheeled electric vehicles equipped with an in-wheel motor for each wheel.In the proposed control strategy,the road identification module estimates tire-road forces using an unscented Kalman filter al-gorithm and recognizes the road adhesion coefficient by employing the recursive least-square method According to road identification,the optimal sip ratio under the current driving condition is obtainedand a controller based on sliding mode control with a conditional integrator uses this value for accel-eration slip regulation.The anti-slip controller obtains the adjusting torque,which is integrated with the driver-command-based feedforward control torque to implement driving force coordination control.The results of hardware-in-loop simulation show that this control strategy can accurately estimate tire-roadrces as well as the friction coefficient,and thus,can effectively fulfill the purpose of driving force coordinated control under different driving conditions.

Influences of Bias Voltage and Target Current on Structure,Microhardness and Friction Coefficient of Multilayered TiAlN/CrN Coatings Synthesized by Cathodic Arc Plasma Deposition

Multilayered TiAlN/CrN coatings have been synthesized on stainless steel substrates by cathodic arc plasma deposition using TiAl and Cr targets.Influences of the bias voltage,cathode current ratio ITiAl/ICr,and deposition pressure on the hardness and friction coefficient of the coatings were investigated.The measurement revealed existence of two cubic phases,face-centercubic （Cr,Al）N and（Ti,Al）N,in the coatings deposited under various bias voltages except for the coating deposited at -400 V,which is amorphous.The hardness of the coatings was strongly dependent on the Itial/Icr ratio and deposition pressure,and reached a maximum of 33 GPa at an ITiAI/ICr ratio of 1.0 and a pressure of 1.0 Pa.The incorporation of the element chromium can reduce the density of pinholes in the coatings and assist the optimization of deposition conditions for high quality TiAlN/CrN coatings.

Tire Road Friction Coefficient Estimation:Review and Research Perspectives

Many surveys on vehicle traffic safety have shown that the tire road friction coefficient(TRFC)is correlated with the probability of an accident.The probability of road accidents increases sharply on slippery road surfaces.Therefore,accurate knowledge of TRFC contributes to the optimization of driver maneuvers for further improving the safety of intelligent vehicles.A large number of researchers have employed different tools and proposed different algorithms to obtain TRFC.This work investigates these different methods that have been widely utilized to estimate TRFC.These methods are divided into three main categories:off-board sensors-based,vehicle dynamics-based,and data-driven-based methods.This review provides a comparative analysis of these methods and describes their strengths and weaknesses.Moreover,some future research directions regarding TRFC estimation are presented.

Studies on the Coefficient of Friction During the Oblique Impact of a Hard Sphere Against a Ductile Solid Target

Following the original approach of Bowden and Tabor and introducing state variables, an effective friction coefficient μ_e for solid particle erosion is defined as a combination of shearing term and ploughing term. In the case of continuous sliding, based on considering the interaction between asperities under certain condition, it is indicated that during the oblique impact of a hardened steel sphere against a mild steel target, a possible value of μ_e is 0.05, which was chosen in all of the calculations by Hutchings for consistency with both experiments and calculations. In the case of continuous ploughing, it is shown that the value of μ_e is a function of the impact process and the initial impact angle and is greater than 0.05 on an average for Hutchings' experiments. It is suggested that the variation of sliding, rolling and ploughing state at each instant in the impact process makes “the coefficient of friction” equal to 0.05 for Hutchings' experiments, and in general, makes the effective friction coefficient during particle impact on metal far less than the friction coefficient during simple continuous sliding on an average.

Effects of Inter-Particle Frictional Coefficients on Evolution of Contact Networks in Landslide Process

During the process of landslide, its dynamic mechanism is important to understand and predict these kinds of natural hazard. In this paper, a new method, based on concepts of complex networks, has been proposed to investigate the evolution of contact networks in mesoscale during the sliding process of slope. A slope model was established using the discrete element method (DEM), and influences of inter-particle frictional coefficients with four different values on?dynamic landslides were studied. Both macroscopic analysis on slope?landslide?and mesoanalysis on structure evolution of contact networks, including the?average degree, clustering coefficient?and N-cycle, were done during the process?of landslide. The analysis results demonstrate that: 1) with increasing inter-particle?frictional coefficients, the displacement of slope decreases and the stable angle of slope post-failure increases, which is smaller than the peak internal frictional angle;2) the average degree decreases with the increase of inter-particle frictional coefficient. When the displacement at the toe of the slope is smaller,?the average degree there changes more greatly with increasing inter-particle?frictional coefficient;3) during the initial stage of landslide, the clustering coefficient?reduces sharply, which may leads to easily slide of slope. As the landslide?going?on, however, the clustering coefficient?increases denoting increasing stability?with?increasing inter-particle frictional coefficients. When the inter-particle?frictional coefficient is smaller than 0.3, its variation can affect the clustering coefficient?and stable inclination of slope post-failure greatly;and 4) the number of?3-cycle increases, but 4-cycle and 5-cycle decrease with increasing inter-particle frictional coefficients.

Measurement of friction coefficient in aluminum sheet warm forming

Aluminum alloy sheets are used more and more to manufacture auto panels. Because the friction behavior is very complicated, it is necessary to study the friction during the aluminum sheet warm forming process. The author has designed a new probe sensor based on an online tribotest method which directly measures friction coefficient in the forming process. Experiments of cup drawing have been conducted and the friction coefficients under different forming conditions have been measured. The results indicate that the forming parameters, such as forming temperature, blankholding force and lubrication status have great effect upon the friction coefficient.