Mathematical Model Of Wear Research Articles

Оцінка ресурсу фрикційних поверхонь гальмівних дискових механізмів за показниками відносного зношення для легкових автомобілів

Modern development of vehicle designs requires paying great attention to braking properties, which will depend on the design parameters of the brake mechanisms. The article discusses a scheme where a disc brake is installed on the front wheels, and drum brakes are installed on the rear wheels. From the diagram of the distribution of forces that act on the vehicle during braking, the maximum friction forces for the front and rear axles were determined. A general formula was obtained for the braking distance of a vehicle, during which wear of the brake mechanism occurs. We used the results of the well-known theory of friction and wear by I.V. Kragelsky. The mathematical wear model was built for each friction pair. The wear model takes into account the design parameters of the vehicle, the wear resistance coefficient of materials, the initial braking speed of the vehicle, the mileage and braking distance. The main design parameters of the brake system are the friction radius, the kinematic rolling radius of the wheel, and the amount of drive pressure.
 To assess the service life of the brake mechanism, it was proposed to use such an indicator as the relative wear of associated parts. A formula has been obtained for calculating this indicator based on changes in geometric parameters and operating modes of the brake mechanism under operating conditions. A forecast was made of the service life of the brake mechanisms of the front and rear axles of passenger cars, which is proposed to be carried out according to the indicator of relative wear of friction surfaces. Graphic dependences of the distribution of relative wear of the friction surfaces of brake mechanisms for Chevrolet Aveo and Forza cars were constructed. It was shown using the example of Chevrolet Aveo passenger cars that the relative wear of the front axle brakes is maximum and it varies from 22.5 to 26.1%, and for the rear axle this figure varies from 21.0 to 22.5%. The service life of the brake disc is 4.44 times greater than the service life of the friction lining for the Chevrolet Aveo. For the Forza car this figure is 4.76. The results of the work can be used to estimate the residual life of brake mechanisms, taking into account operating conditions.

Use of synchrotron X-rays for direct observation of wear damage in optically-opaque contacts by means of CT imaging and X-ray diffraction

In a simulated in-situ experiment annular contacts of 6082-T6 aluminium alloy were first exposed to various degrees of fretting wear, before synchrotron X-ray CT and diffraction were applied to examine the extent and development of wear damage. The wear volumes measured and development of the wear rate were consistent with the mathematical wear model of Fillot, Iordanoff & Berthier. Thickness and porosity of the worn zone were measured and the contact area between wearing elements estimated. Developments of residual strain and tribologically transformed structure were investigated through X-ray diffraction. This study demonstrates, for the first time, the value and viability of observing and quantifying wear through combination of X-ray CT and diffraction opening a path towards in-situ observations of wear.

EVALUATION OF WEAR RESISTANCE OF FRICTION SURFACES FOR DISC BRAKES OF PASSENGER CARS

A mathematical model of wear of friction surfaces of disc brake mechanisms of a passenger car during braking is proposed. For passenger cars, the work of the created algorithm is considered, the results of the program and the analysis of the results of the computational experiment are given. The prospects for further research to determine the wear resistance coefficient of materials for mating parts of disc brake mechanisms are also considered.

Checking the adequacy of the mathematical model of the wear of electric brushes, taking into account the dynamics of their interaction with the collector

The adequacy of the mathematical model of the wear of electric brushes of direct current collector machines, taking into account the dynamics of their interaction with the collector surface, is verified. The wear of electric brushes in laboratory conditions and during operation of traction motors of rolling stock is analyzed. Comparison of the results of modeling and experimental studies using different criteria showed that the mathematical model of brush wear can be used to forecast the residual life of electric brushes with a given accuracy. Keywords: electric motor, electric brush, wear, mathematical modeling, forecasting, residual life. hvv-omgups@mail.ru, popovomsk@yandex.ru

Estimation of Wear Resistance for Multilayer Coatings Obtained by Nitrogenchroming

This article deals with improving the wear resistance of multilayer coatings as a fundamental problem in metal surface treatment, strengthening elements of cutting tools, and ensuring the reliability of machine parts. It aims to evaluate the wear depth for multilayer coatings by the mass loss distribution in layers. The article’s primary purpose is to develop a mathematical method for assessing the value of wear for multilayer steel-based coatings. The study material is a multilayer coating applied to steel DIN C80W1. The research was performed using up-to-date laboratory equipment. Nitrogenchroming has been realized under overpressure in two successive stages: nitriding for 36 h at temperature 540 °C and chromizing during 4 h at temperature 1050 °C. The complex analysis included several options: X-ray phase analysis, local micro-X-ray spectral analysis, durometric analysis, and determination of wear resistance. These analyses showed that after nitrogenchroming, the three-layer protective coating from Cr23C6, Cr7C3, and Cr2N was formed on the steel surface. Spectral analysis indicated that the maximum amount of chromium 92.2% is in the first layer from Cr23C6. The maximum amount of carbon 8.9% characterizes the layer from Cr7C3. Nitrogen is concentrated mainly in the Cr2N layer, and its maximum amount is 9.4%. Additionally, it was determined that the minimum wear is typical for steel DIN C80W1 after nitrogenchroming. The weight loss of steel samples by 25 mg was obtained. This value differs by 3.6% from the results evaluated analytically using the developed mathematical model of wear of multilayer coatings after complex metallization of steel DIN C80W1. As a result, the impact of the loading mode on the wear intensity of steel was established. As the loading time increases, the friction coefficient of the coated samples decreases. Among the studied samples, plates from steel DIN C80W1 have the lowest friction coefficient after nitrogenchroming. Additionally, a linear dependence of the mass losses on the wearing time was obtained for carbide and nitride coatings. Finally, an increase in loading time leads to an increase in the wear intensity of steels after nitrogenchroming. The achieved scientific results are applicable in developing methods of chemical-thermal treatment, improving the wear resistance of multilayer coatings, and strengthening highly loaded machine parts and cutting tools.

Improving the mathematical model of wear of contact elements of pantograph during very high-speed movement

The long-term development program of the Russian Railways holding provides for a comprehensive modernization of the railway infrastructure by The least expensive of these measures is the use of contact elements with an extended service life, providing reliable, economical and environmentally friendly transmission of electricity to rolling stock. In accordance with the program developed and successfully tested at OSTU, the methodology for conducting experimental studies of contact pairs of current collector devices for conducting a test cycle requires specialized experimental complexes, as well as significant time and resources. To reduce the volume of experimental studies, a combined method is used - a combination of the required minimum of experimental studies of real objects (or their analogues) and calculation methods based on mathematical modeling of processes occurring in contact pairs of current collector devices. However, the use of existing mathematical models for predicting wear under conditions of very high-speed movement is not accurate enough due to the lack of consideration of the aerodynamic effects and the speed of the rolling stock on current collection processes. This article discusses the improvement of the electrical component of the wear model of the elements of contact pairs of current collector devices under conditions of very high-speed movement. The histograms of the electrical wear of contact elements obtained by calculation using the existing and improved mathematical models are presented.

Plastic strength of cutting parts of tools from STM when there is turning heat-resistant alloys

The article is devoted to the modeling of physical and chemical creep process, which determines the plastic strength of cutting parts at the vertices of the tools from STM. The creep process is associated with the phenomena of diffusion and diffusion wear of the tool from STM in the zone of quasi-brittle transition (that is, the temperature transition of tool STM from brittle to plastic state at high cut-ting temperatures) with thin turning of heat-resistant alloys and steels. Turning of heat-resistant alloys at high cutting temperatures, corresponding to the quasi-brittle transition, allows the machining process at ultra-high cutting speeds, which expands the application of tools from STM. We have created mathematical model of wear and destruction of the cutting part at the top of the tool and STM due to diffusion phenomena in the process of thin turning of a heat-resistant alloy.

Research and development of a probability mathematical wear model of automobile friction joints

The existing approaches related to the mathematical description of the wear process are analyzed. A new mathematical wear model for automobile friction joints, based on an infinite power series, has been substantiated. This model takes into account the random nature of the wear process and the nonlinearity of the wear accumulation during the breaking-in period and normal operation of the detail. It is convenient for engineering estimations and does not require complex calculations. The article is recommended for agricultural specialists, scientists, teachers, graduate students, undergraduates and students of agricultural universities for the program track “Agricultural Engineering”.

A wear model for subrough surface contacts of martensitic steels

This article includes an analysis of techniques for determining wear of contact areas to show two lines of wear research – due to deformations and adhesion forces. It has been established that surface subroughness is not presently taken into account in calculations of wear despite the fact that this surface property is of increasing research interest. The paper aims to develop a mathematical model of wear for subrough surface contacts in the context of deformation and theories of adhesion. Mathematical wear modelling for subrough surfaces is based on studies on causes of their formation due to phase and structural heterogeneity of the material. The article considers contact interaction at the level of surface subroughness; physics of interaction of contact areas at the level of surface subroughness; a mathematical model of deformation and adhesive wear for subrough surface contacts of martensitic steels; some analytical dependences of the theoretical model for a body-centred tetragonal lattice. Analysis of the theoretical concepts shows that wear of subrough surface contacts depends largely on the deformation component, while the adhesive component is significant only during the ‘bedding-in’ period for a friction couple. The materials of the article can be used to calculate the wear for contact areas at the level of surface subroughness.

Wear of Induction Cladded Coating in the Abrasive Mass at Various Speeds and Impact Angles

The wear of induction cladded coating during motion was investigated through the abrasive mass at a speed of 1.0 to 3.0 m/s and the impact angle of abrasive particles with a worn surface of 0° to 90°. Cladding was performed by using Ni-Cr-Si-B-Fe flame spraying powder. Experimental research was carried out by using the Response Surface Method (RSM) and Central Composite Design (CCD). Analysis of variance proved that both motion speed and impact angle had significant impact on the wear of coating, both individually and interactively. Motion speed had the greatest influence, and the interaction of speed and angle had the least influence. The wear rate increased along with the motion speed increase, and the influence of the impact angle depends on the wear speed. At a speed of 1 m/s, the wear increases along with the increase of angle from 0° to 45° and then continues to decrease up to the angle of 90°. At a speed of 2 m/s, the wear increases along with the angle increase from 0° to 30° and then continues to decrease up to the angle of 90°. At a speed of 3 m/s, the wear increases along with the angle increase from 0° to 20° and then decreases as the angle increases up to 90°. Based on the statistical data processing, this research developed the mathematical model of wear in the form of quadratic polynomial that describes the influences of input variables in individual and interactive form.

SIMULATION OF WEAR IN A SPHERICAL JOINT WITH A POLYMERIC COMPONENT OF THE TOTAL HIP REPLACEMENT CONSIDERING ACTIVITIES OF DAILY LIVING

The present study assesses the impact of the main typical activities of patients' daily living (ADL) after total hip arthroplasty (THA) on the wear parameters of sliding couple's materials by simulating linear and volumetric wear according to the Archard's law in a spherical joint with a polymeric element of the total hip replacement (THR). The mathematical wear model, built on the basis of algorithms and custom codes of the finite element analysis in ANSYS and MATLAB software systems, has been studied numerically. The activities used in the model are: level walking, stair ascending-stair descending, chair sitting-chair rising, and deep squatting. They were described by typical waveforms of the angular displacements of the THR's femoral component and the waveforms of the applied force. The results of the simulation show that for the same duration the overall wear value with ADL is significantly higher than in the case of level walking according to the requirements of ISO 14242-1. Therefore, the evaluation of the wear value for ADL is more informative for predicting the functional life time of the THR. Analysis of the simulation results shows that the amount of wear calculated for all activities separately is practically the same as the overall wear value obtained at summary action of ADL. This effect of the independence of contributions to the total amount of wear of each activity makes it possible to significantly simplify the solution of the problem of wear estimation for typical activities, including stochastic ones.

Remaining Vehicles Useful Lifetime Estimation Based on Operation Conditions Measurement

The article describes a prognostic approach to estimating the remaining useful lifetime of cars and trucks based on the known monitoring data. The algorithm for the calculation of remaining useful lifetime uses the information about the technical state of the vehicles obtained from sensors of onboard measuring system. The remaining useful lifetime prediction is based on the comparison of the current technical state of a vehicle with the expected state which is determined by the mathematical model of wear for given mileage. The result of the comparison is used for the evaluation of the operation conditions that allows predicting the remaining useful lifetime of vehicle. The proposed approach is well suited to be integrated into onboard automobile equipment and may be applicable to a wide variety of automotive, aircrafts and similar industries.

A comparative study of wear laws for soft-on-hard hip implants using a mathematical wear model

Wear of UHMWPE acetabular components is the most serious threat to the long-term success of hip replacements. Consequently numerical and experimental wear simulations are of great interest. The present study proposes a mathematical wear model and compares the most recent wear laws, based on the so-called cross-shear (CS) effect. Simulations highlighted the variability of wear predictions with the wear factors/laws. Moreover a sensitivity analysis underlined that the kinematic conditions affect volumetric/linear wear more than the loading ones. This study confirms the importance of the CS in wear predictions even if some critical issues are still open, requiring further investigations.

Wear of symmetrical wedge-shaped tillage tools

Results of wear investigations on steel samples in the laboratory and on ridger shares in field conditions are presented. Wear was determined by measurements of the change in length and thickness of shares, and from the weight of samples. Relative resistance against abrasive wear was determined for four grades of steel, considering the type and condition of the soil. The effect of steel hardness and microstructure on wear was analysed. It was found that the abrasive wear resistance of steel increased with a decrease of carbide size and with an increase of volume fraction of carbide in the metal microstructure. The loss of share thickness due to wear was linearly related to the distance travelled, and the wear of cutting edges was related to the distance travelled and the distance of the measurement point from the share point, by power functions. A mathematical model of wear of a symmetrical wedge-shaped tillage tool was determined.

Predictive model for ball mill wear

Ball mills, characteristic of the mineral processing industry, are used to reduce ore from one size distribution to another. Wear is associated with comminution mechanisms found in the ball charge which in turn affects grinding performance. In this work, ball mill wear, as a function of mill operating variables, is determined using a mathematical wear model. The wear model incorporates the energy dissipated in crushing, tumbling and grinding zones of the charge profile with adhesive and abrasive wear descriptions. This model has been added to a ball charge motion model allowing the simulation of mill wear rates as well as ball mill element wear and its affect on grinding performance. Simulation results presented show the interaction between wear and grinding performance. Further work is necessary to validate charge and wear model results using industrial data.

Model of mechanical wear based on Markov processes

1. An analytical expression was obtained for the distribution of the working life for mechanical wear; the parameters of the distribution have specific physical significance and are determined by a special experiment. 2. The diffusional distribution of the life, as shown by preliminary estimates, does not disagree with experimental data and, together with other distributions, may be used for the treatment of statistical data on the life of couplings. Since the diffusional distribution was obtained on the basis of an analysis of wear kinetics, its use in estimating wear resistance is preferable to the use of other distributions based on different considerations (Weibull distribution, gamma distribution, normal distribution, etc.). 3. In the procedure proposed for determining the distribution law of the life, active use was made of a priori information on failure (the steady character of failure, i.e., the linear variation of the mean value and the dispersion), so that data on the lifetime can be extrapolated. Thus, the model of wear proposed may serve as the basis for the development of methods and means of accelerated testing for wear resistance. 4. By means of the mathematical model of wear proposed, it is fairly simple to obtain all the statistical characteristics of the reliability of coupling components necessary for engineering calculations.