Effect of friction coefficients on the dynamic response of gear systems

The inevitable deterioration of the lubrication conditions in a gearbox in service can change the tribological properties of the meshing teeth. In turn, such changes can significantly affect the dynamic responses and running status of gear systems. This paper investigates such an effect by utilizing virtual prototype technology to model and simulate the dynamics of a wind turbine gearbox system. The change in the lubrication conditions is modeled by the changes in the friction coefficients, thereby indicating that poor lubrication causes not only increased frictional losses but also significant changes in the dynamic responses. These results are further demon-strated by the mean and root mean square values calculated by the simulated responses under different friction coefficients. In addition, the spectrum exhibits significant changes in the first, second, and third harmonics of the meshing components. The findings and simulation method of this study provide theoretical bases for the development of accurate diagnostic techniques.

Negative differential friction coefficients of two-dimensional commensurate contacts dominated by electronic phase transition

Friction force(f)usually increases with the normal load(N)macroscopically,according to the classic law of Da Vinci–Amontons(f=μN),with a positive and finite friction coefficient(μ).Herein near-zero and negative differential friction(ZNDF)coefficients are discovered in two-dimensional(2D)van der Waals(vdW)magnetic CrI_(3)commensurate contacts.It is identified that the ferromagnetic–antiferromagnetic phase transition of the interlayer couplings of the bilayer CrI_(3)can significantly reduce the interfacial sliding energy barriers and thus contribute to ZNDF.Moreover,phase transition between the in-plane(p_(x)and p_(y))and out-of-plane(p_(z))wave-functions dominates the sliding barrier evolutions,which is attributed to the delicate interplays among the interlayer vdW,electrostatic interactions,and the intralayer deformation of the CrI_(3)layers under external load.The present findings may motivate a new concept of slide-spintronics and are expected to play an instrumental role in design of novel magnetic solid lubricants applied in various spintronic nano-devices.

Development and validation of an integrated mechatronic apparatus for measurement of friction coefficients of agricultural products

An integrated mechatronic apparatus was developed based on tilting plate method in order to precisely measure static friction coefficient(SFC)and dynamic friction coefficient(DFC)of agricultural products.The apparatus consisted of two main parts(mechanical and electrical parts).The main element of mechanical part was rotary container.Meanwhile,the electrical part included control,display,goniometer,level controller,rotational power supply,and infrared unit.The apparatus was initially simulated in simulation environment and practically calibrated to achieve high precision measurements.To appraise performance of the apparatus,the SFC and DFC of three grains were measured on five contact surfaces.Experiments were also conducted by means of a typical apparatus operating based on puling force method.Some statistical descriptor parameters such as mean absolute percentage error(MAPE),average of absolute values of measurement errors(AAVME),maximum of absolute values of measurement errors(MAVME),and correlation coefficient were used to compare accuracy of the apparatus with the typical one.The acceptable AAVME(<10%),MAVME(<10%),MAPE(<5%),and correlation coefficient(>0.9)indicated high accuracy,stability,and efficiency of the apparatus for automatic measurements of the SFC and DFC.From practical point of view,the mechatronic apparatus would be a beneficial tool for experimental,educational,demonstrational,and research works.

Study of the Judder Characteristics of Friction Material for an Automobile Clutch and Test Verification

The friction judder characteristics during clutch engagement have a significant influence on the NVH of a driveline.In this research,the judder characteristics of automobile clutch friction materials and experimental verification are studied.First,considering the stick-slip phenomenon in the clutch engagement process,a detailed 9-degrees-of-freedom(DOF)model including the body,each cylinder of the engine,clutch and friction lining,torsional damper,transmission and other driveline parts is established,and the calculation formula of friction torque in the clutch engagement process is determined.Second,the influence of the friction gradient characteristics on the amplification or attenuation of the automobile friction judder is analyzed,and the corresponding stability analysis and the numerical simulation of different friction gradient values are carried out with MATLAB/Simulink software.Finally,judder bench test equipment and a corresponding damping test program are developed,and the relationship between the friction coefficient gradient characteristics and the system damping is analyzed.After a large number of tests,the evaluation basis of the test is determined.The research results show that the friction lining with negative gradient characteristics of the friction coefficient will have a judder signal.When the friction gradient value is less than-0.005 s/m,the judder signal of the measured clutch cannot be completely attenuated,and the judder phenomenon occurs.When the friction gradient is greater than-0.005 s/m,the judder signal can be significantly suppressed and the system connection tends to be stable.

Effects of multiple shapes for steady flow with transformer oil+Fe_(3)O_(4)+TiO_(2) between two stretchable rotating disks

In this study,we examine the effects of various shapes of nanoparticles in a steady flow of hybrid nanofluids between two stretchable rotating disks.The steady flow of hybrid nanofluids with transformer oil as the base fluid and Fe_(3)O_(4)+TiO_(2)as the hybrid nanofluid is considered.Several shapes of Fe_(3)O_(4)+TiO_(2)hybrid nanofluids,including sphere,brick,blade,cylinder,and platelet,are studied.Every shape exists in the same volume of a nanoparticle.The leading equations(partial differential equations(PDEs))are transformed to the nonlinear ordinary differential equations(ODEs)with the help of similarity transformations.The system of equations takes the form of ODEs depending on the boundary conditions,whose solutions are computed numerically by the bvp4c MATLAB solver.The outputs are compared with the previous findings,and an intriguing pattern is discovered,such that the tangential velocity is increased for the rotation parameter,while it is decreased by the stretching values because of the lower disk.For the reaction rate parameter,the concentration boundary layer becomes shorter,and the activation energy component increases the rate at which mass transfers come to the higher disk but have the opposite effect on the bottom disk.The ranges of various parameters taken into account are Pr=6.2,Re=2,M=1.0,φ_(1)=φ_(2)=0.03,K=0.5,S=-0.1,Br=0.3,Sc=2.0,α_(1)=0.2,γ=0.1,E_(n)=2.0,and q=1.0,and the rotation factor K is within the range of 0 to 1.

Dual Extended Kalman Filter for Combined Estimation of Vehicle State and Road Friction

Vehicle state and tire-road adhesion are of great use and importance to vehicle active safety control systems. However, it is always not easy to obtain the information with high accuracy and low expense. Recently, many estimation methods have been put forward to solve such problems, in which Kalman filter becomes one of the most popular techniques. Nevertheless, the use of complicated model always leads to poor real-time estimation while the role of road friction coefficient is often ignored. For the purpose of enhancing the real time performance of the algorithm and pursuing precise estimation of vehicle states, a model-based estimator is proposed to conduct combined estimation of vehicle states and road friction coefficients. The estimator is designed based on a three-DOF vehicle model coupled with the Highway Safety Research Institute（HSRI） tire model; the dual extended Kalman filter （DEKF） technique is employed, which can be regarded as two extended Kalman filters operating and communicating simultaneously. Effectiveness of the estimation is firstly examined by comparing the outputs of the estimator with the responses of the vehicle model in CarSim under three typical road adhesion conditions（high-friction, low-friction, and joint-friction）. On this basis, driving simulator experiments are carried out to further investigate the practical application of the estimator. Numerical results from CarSim and driving simulator both demonstrate that the estimator designed is capable of estimating the vehicle states and road friction coefficient with reasonable accuracy. The DEKF-based estimator proposed provides the essential information for the vehicle active control system with low expense and decent precision, and offers the possibility of real car application in future.

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.

Road Friction Estimation under Complicated Maneuver Conditions for Active Yaw Control

Road friction coefficient is a key factor for the stability control of the vehicle dynamics in the critical conditions. Obviously the vehicle dynamics stability control systems, including the anti-lock brake system（ABS）, the traction control system（TCS）, and the active yaw control（AYC） system, need the accurate tire and road friction information. However, the simplified method based on the linear tire and vehicle model could not obtain the accurate road friction coefficient for the complicated maneuver of the vehicle. Because the active braking control mode of AYC is different from that of ABS, the road friction coefficient cannot be estimated only with the dynamics states of the tire. With the related dynamics states measured by the sensors of AYC, a comprehensive strategy of the road friction estimation for the active yaw control is brought forward with the sensor fusion technique. Firstly, the variations of the dynamics characteristics of vehicle and tire, and the stability control mode in the steering process are considered, and then the proper road friction estimation methods are brought forward according to the vehicle maneuver process. In the steering maneuver without braking, the comprehensive road friction from the four wheels may be estimated based on the multi-sensor signal fusion method. The estimated values of the road friction reflect the road friction characteristic. When the active brake involved, the road friction coefficient of the braked wheel may be estimated based on the brake pressure and tire forces, the estimated values reflect the road friction between the braked wheel and the road. So the optimal control of the wheel slip rate may be obtained according to the road friction coefficient. The methods proposed in the paper are integrated into the real time controller of AYC, which is matched onto the test vehicle. The ground tests validate the accuracy of the proposed method under the complicated maneuver conditions.

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.

Modeling and Calculation of Impact Friction Caused by Corner Contact in Gear Transmission

Corner contact in gear pair causes vibration and noise,which has attracted many attentions.However,teeth errors and deformation make it difficulty to determine the point situated at corner contact and study the mechanism of teeth impact friction in the current researches.Based on the mechanism of corner contact,the process of corner contact is divided into two stages of impact and scratch,and the calculation model including gear equivalent error-combined deformation is established along the line of action.According to the distributive law,gear equivalent error is synthesized by base pitch error,normal backlash and tooth profile modification on the line of action.The combined tooth compliance of the first point lying in corner contact before the normal path is inversed along the line of action,on basis of the theory of engagement and the curve of tooth synthetic complianceload-history.Combined secondarily the equivalent error with the combined deflection,the position standard of the point situated at corner contact is probed.Then the impact positions and forces,from the beginning to the end during corner contact before the normal path,are calculated accurately.Due to the above results,the lash model during corner contact is founded,and the impact force and frictional coefficient are quantified.A numerical example is performed and the averaged impact friction coefficient based on the presented calculation method is validated.This research obtains the results which could be referenced to understand the complex mechanism of teeth impact friction and quantitative calculation of the friction force and coefficient,and to gear exact design for tribology.

Dry Friction and Wear Characteristics of Impregnated Graphite in a Corrosive Environment

Tribological properties of impregnated graphite are greatly influenced by preparation technology and working conditions and it’s highly susceptible to corrosion environmental impacts,but the experimental research about it are few.In this paper,three kinds of impregnated graphite samples are prepared with different degree of graphitization,the tribological properties of these samples in the dry friction environment and in a corrosive environment are analyzed and contrasted.The tribo-test results show that the friction coefficient of samples is reduced and the amount of wear of samples increase when the graphitization degree of samples increases in dry friction condition.While in a corrosive environment（samples are soaked N2O4）,the friction coefficient and amount of wear are changed little if the graphitization degree of samples are low.If the degree of graphitization increase,the friction coefficient and amount of wear of samples increase too,the amount of wear is 2 to 3 times as the samples tested in the non-corrosive environment under pv value of 30MPa？m/s.The impregnated graphite,which friction coefficient is stable and graphitization degree is in mid level,such#2,is more appropriate to have a work in the corrosion conditions.In this paper,preparation and tribological properties especially in corrosive environment of the impregnated graphite is studied,the research conclusion can provide an experimental and theoretical basis for the selection and process improvement of graphite materials,and also provide some important design parameters for contact seal works in a corrosive environment.

The Influence of Normal Load and Sliding Speed on Frictional Properties of Skin

The study of frictional properties of human skin is important for medical research, skin care products and textile exploi- tation. In order to investigate the influence of normal load and sliding speed on the frictional properties of skin and its possible mechanism, tests were carded out on a multi-specimen friction tester. When the normal load increases from 0.1 N to 0.9 N, normal displacement and the friction coefficient of skin increase. The friction coefficient is dependent on the load, indicating that both adhesion and deformation contribute to the friction behaviour. The deformation friction was interpreted using the plough model of friction. When sliding speed increases from 0.5 mm·s^-1 to 4 mm·s^-1, the friction coefficient increases and ＂stick-slip＂ phenomena increase, indicating that hysteretic friction contributes to the friction. The hysteretic friction was in- terpreted using schematic of energy translation during the rigid spherical probe sliding on the soft skin surface, which provides an explanation for the influence of the sliding speed on the frictional characteristics of the skin.

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.

Friction and wear properties of copper matrix composites reinforced by tungsten-coated carbon nanotubes

Carbon nanotubes （CNTs） were coated by tungsten layer using metal organic chemical vapor deposition process with tungsten hexacarbonyl as a precursor. The W-coated CNTs （W-CNTs） were dispersed into Cu powders by magnetic stirring process and then the mixed powders were consolidated by spark plasma sintering to fabricate W-CNTs/Cu composites. The CNTs/Cu composites were fabricated using the similafprocesses. The friction coefficient and mass wear loss of W-CNTs/Cu and CNTs/Cu composites were studied. The results showed that the W-CNT content, interfacial bonding situation, and applied load could influence the friction coefficient and wear loss of W-CNTs/Cu com- posites. When the W-CNT content was 1.0 wt.%, the W-CNTs/Cu composites got the minimum friction coefficient and wear loss, which were decreased by 72.1% and 47.6%, respectively, compared with pure Cu specimen. The friction coefficient and wear loss of W-CNTs/Cu composites were lower than those of CNTs/Cu composites, which was due to that the interracial bonding at （W-CNTs）-Cu interface was better than that at CNTs-Cu interface. The friction coefficient of composites did not vary obviously with increasing applied load, while the wear loss of composites increased significantly with the increase of applied load.

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.

Friction and wear behaviors of biodegradable Mg-6Gd-0.5Zn-0.4Zr alloy under simulated body fluid condition

The friction and wear behaviors of biodegradable Mg-6Gd-0.5Zn-0.4Zr(wt%,GZ60K)alloy were evaluated under simulated body fluid(SBF)condition using ball-on-disk configuration and compared with those under dry sliding condition.The results show that under dry sliding and SBF conditions,the friction coefficient declines with increasing applied load and keeps stable with prolonging sliding time.The friction coefficient of the alloy effectively decreases in SBF as compared to dry sliding due to lubrication caused by SBF.The real wear rates under SBF condition are lower than those under dry sliding condition for each parameter.Nevertheless,the nominal wear rates are higher in SBF which are attributed to the more mass loss caused by corrosion but not wear.Both the nominal wear rate in SBF and the dry sliding wear rate increase with increasing applied load,and they decline firstly and then keep stable with prolonging sliding time.It is concluded that the wear of the alloy is restricted by the SBF,but the corrosion of the alloy is aggravated by the wear.

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.

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.

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.