CN116930059A - Characterization method of thermal coupling friction coefficient of tire rubber - Google Patents
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Abstract
The application discloses a characterization method of a thermal coupling friction coefficient of tire rubber, and belongs to the field of rubber detection. Aiming at the problem of insufficient friction performance research of tread rubber at different tread temperatures in the prior art, the application comprises the following steps: 1) Determining factors affecting the friction characteristics of the tire rubber; 2) Constructing a friction model at normal temperature according to the factors determined in the step 1); 3) Heating the tire rubber, and analyzing the functional relation between the temperature and the friction coefficient; 4) And constructing a thermal coupling model of the friction coefficient based on the friction model at normal temperature determined in the step 2) and the functional relation between the temperature and the friction coefficient in the step 3). According to the technical scheme, a rubber thermal coupling friction model is constructed, the friction performance of tread rubber at different tread temperatures, sliding speeds and contact pressures is represented, and theoretical support is provided for improvement of driving safety.
Description
Technical Field
The application relates to a characterization method of a thermal coupling friction coefficient of tire rubber, and belongs to the field of marine communication.
Background
The tire is a ring-shaped elastic rubber product which is assembled on an automobile and rolls in a grounding way, and is used as the only part of the vehicle which is contacted with the road surface during the running process, and the advantages and disadvantages of the friction performance directly influence the running safety.
Main raw materials for manufacturing tires: and (3) rubber. It has viscoelastic, nonlinear, temperature sensitive and other properties, and the friction mechanism is different from that of metal material, and has typical thermodynamic coupling characteristic.
The dynamic friction characteristics of rubber are related to various factors such as speed, pressure and temperature, and the friction performance of rubber can show considerable difference under different working conditions.
Due to the thermal coupling characteristics of rubber, tread rubber temperature has a non-negligible effect on tire friction performance. The prior art models characterizing the friction properties of rubber often do not take into account the effect of temperature on friction properties, or only take into account temperature as a function of sliding speed.
For example, chinese patent 202210979684.9 discloses a method for accurately modeling a vehicle tire and an application thereof, which includes the steps of creating a simplified physical model of the tire considering the hysteresis characteristics of the tire, introducing a spring damping hysteresis system describing the force displacement characteristics of a viscoelastic material, then combining an RC operator, creating a composite force deformation relation characteristic model of the spring damping hysteresis system in the loading and unloading process, dividing the interaction relation between the tire and the ground in a pure working condition into a loading stage and an unloading stage, and creating a semi-empirical tire model with uniform longitudinal slip and lateral bias working condition expression based on the hysteresis characteristics in an SAE tire coordinate system.
The friction coefficient is solved by a rubber hysteresis friction calculation method based on rubber-rough surface contact, which is disclosed in Chinese patent 202011062061.2 and comprises the steps of establishing a dynamic friction tester rubber geometric model, acquiring a road profile, presuming a rubber sliding part and road surface textures, calculating a rubber rough surface contact control equation and establishing rubber rough surface contact based on numerical resolution.
According to the estimation method of the road surface friction coefficient disclosed in the Chinese patent 201811418159.X, according to the tire slip angle, the tire lateral force and the steering rate generated by the lateral operation of a driver on a vehicle, a corresponding classifier set is selected to calculate the road surface friction coefficient; and determining the calculated maximum road surface friction coefficient as a final road surface friction coefficient.
In the prior art, in various related characterization methods, a technical scheme for taking the temperature as an independent parameter to consider the influence of the temperature on the friction characteristics does not exist, the friction performance of the tread rubber at different tread temperatures is not sufficiently researched, and theoretical support can not be provided for improvement of driving safety.
Disclosure of Invention
Aiming at the problem of insufficient friction performance research of tread rubber at different tread temperatures in the prior art, the application provides a characterization method of thermal coupling friction coefficient of the tire rubber, a thermal coupling friction model of the rubber is constructed, the friction performance of the tread rubber at different tread temperatures, sliding speeds and contact pressures is characterized, and theoretical support is provided for improvement of driving safety.
In order to solve the technical problems, the technical scheme adopted by the application is that the characterization method of the thermal coupling friction coefficient of the tire rubber comprises the following steps:
1) Determining factors affecting the friction characteristics of the tire rubber;
2) Constructing a friction model at normal temperature according to the factors determined in the step 1);
3) Heating the tire rubber, and analyzing the functional relation between the temperature and the friction coefficient;
4) And constructing a thermal coupling model of the friction coefficient based on the friction model at normal temperature determined in the step 2) and the functional relation between the temperature and the friction coefficient in the step 3).
Optimally, in the characterization method of the thermal coupling friction coefficient of the tire rubber, in the step 1), determining factors influencing the friction characteristic of the rubber, and selecting tread temperature, sliding speed and contact pressure as parameters for constructing a friction model.
In the step 2), a friction model of friction coefficient, sliding speed and contact pressure at normal temperature is constructed through experimental data.
Optimally, in the characterization method of the thermal coupling friction coefficient of the tire rubber, in the step 4), a functional relation of the friction coefficient to the tread temperature, the sliding speed and the contact pressure, namely the thermal coupling model of the friction coefficient is established based on a friction model of the friction coefficient, the sliding speed and the contact pressure at normal temperature and a functional relation of the temperature and the friction coefficient.
Optimally, in the characterization method of the thermal coupling friction coefficient of the tire rubber, in the step 1), determining factors influencing the friction characteristic of the rubber, selecting tread temperature, sliding speed and contact pressure as parameters for constructing a friction model, wherein μ=μ (p, v, T), wherein T is tread temperature, p is contact pressure, and v is sliding speed;
establishing a friction model of friction coefficient, sliding speed and contact pressure at normal temperature as
Wherein a is 1 、a 2 、b 1 、b 2 Is constant, a 1 、a 2 B, related to the ground contact shape of the rubber and the road surface roughness 1 、b 2 Is related to the material physical properties of the rubber and the sensitivity of pressure and speed.
Optimally, in the characterization method of the thermal coupling friction coefficient of the tire rubber, in the step 3), a functional relation between the friction coefficient and the temperature is established, wherein the characterization method is characterized in that:
wherein t is m Indicating the maximum friction coefficient correspondenceAnd the alpha and beta represent the gradient characteristics of the curve, and the Y represents the height characteristics of the curve.
Optimally, in the characterization method of the thermal coupling friction coefficient of the tire rubber, in the step 4), the established thermal coupling comprehensive friction model is characterized as follows:
wherein alpha and beta are rubber viscoelasticity correlation coefficients, gamma is a temperature correlation coefficient, t m A is the temperature corresponding to the maximum value of mu 1 、a 2 B, related to the ground contact shape of the rubber and the road surface roughness 1 、b 2 The temperature t is the temperature, the contact pressure p is the contact pressure, and the sliding speed v is the sensitivity of the physical properties, pressure and speed of the rubber itself.
Optimally, the characterization method of the thermal coupling friction coefficient of the tire rubber is characterized in a thermal coupling comprehensive friction modelWherein e is obtained by the following formula,
wherein A is a pre-factor, E is apparent activation energy, R is molar gas constant, T is thermodynamic temperature, and k is rate coefficient.
Optimally, the characterization method of the thermal coupling friction coefficient of the tire rubber is characterized by a friction model of the friction coefficient, the sliding speed and the contact pressure at normal temperatureWherein a is 1 、a 2 、b 1 、b 2 Is a parameter obtained by fitting test data at 25℃by μ (T) =μ (T-T) 0 ) Performing variable displacement, wherein t 0 ＝25℃。
The beneficial effects of the application are as follows:
according to the technical scheme, the factors such as the contact pressure, the rubber temperature and the sliding speed are considered in the expression of the rubber friction coefficient, the thermal coupling comprehensive friction model is constructed, the friction coefficient change trend caused by the change of the contact pressure, the rubber temperature and the sliding speed can be expressed more accurately, and theoretical support is provided for improvement of driving safety.
Drawings
FIG. 1 is a structural flow diagram of the present application;
FIG. 2 is a graph showing the relationship between the friction coefficient of the rubber wheel and the abrasive belt under different pressures and temperatures;
FIG. 3 is a graph showing the relationship between the friction coefficient of the rubber wheel and the abrasive belt at different speeds and temperatures;
FIG. 4 is a graph of the fit results of a thermal coupling comprehensive friction model and experimental data at different pressures;
fig. 5 is a graph of the fit results of the thermal coupling integrated friction model and experimental data at different speeds.
Detailed Description
The application provides a method for constructing a rubber thermal coupling friction model, which comprises the following steps:
(1) Determining factors influencing the friction characteristics of rubber, and selecting tread temperature, sliding speed and contact pressure as parameters for constructing a friction model;
(2) Constructing a friction model of friction coefficient, sliding speed and contact pressure at normal temperature through experimental data;
(3) Analyzing the functional relationship of temperature and friction coefficient by heating the tread rubber;
(4) And establishing a functional relation of the friction coefficient to the tread temperature, the sliding speed and the contact pressure, namely a thermal coupling model of the friction coefficient, based on the friction model of the friction coefficient, the sliding speed and the contact pressure at normal temperature and the functional relation of the temperature and the friction coefficient.
The tread temperature, sliding speed and contact pressure are selected as parameters for constructing a friction model, and the parameters include: μ=μ (p, v, T), where T is tread temperature, p is contact pressure, v is slip speed.
Due to the non-linearity and viscoelastic properties of rubber, the friction coefficient as a function of tread temperature, slip velocity and contact pressure cannot be characterized by a simple linear relationship. In this example, a thermal coupling model of the coefficient of friction as a function of tread temperature, slip velocity and contact pressure was constructed in the following manner.
Firstly, a friction model of friction coefficient, sliding speed and contact pressure at normal temperature is established according to a large number of tests and curve characteristic analysis, and the friction model is a power function relation and is characterized in that:
wherein a is 1 、a 2 、b 1 、b 2 Is constant, a 1 、a 2 B, related to the ground contact shape of the rubber and the road surface roughness 1 、b 2 Is related to the material physical properties of the rubber and the sensitivity of pressure and speed. The above parameters can be obtained by measuring the friction coefficient of a fixed sliding speed or contact pressure at normal temperature, using fitting means.
Second, local molecules between the rubber and the road surface are adhered due to intermolecular forces, and the adhered portion is stretched to break and then relaxed during sliding.
Both adhesion formation and fracture are a thermal activation rate process that can be described by the Arrhenius equation:
wherein A is a factor before, E is apparent activation energy, R is molar gas constant, T is thermodynamic temperature, k is a rate coefficient, and the size of the rate coefficient reflects the formation of adhesion and the speed of fracture.
Friction essentially involves molecular adhesion and cleavage, so that the friction versus temperature is similar to the rate coefficient versus thermodynamic temperature in the Arrhenius equation, i.e., an exponential function model based on e.
The curve of coefficient of friction versus temperature is characterized by a bell-shaped curve with a maximum of coefficient of friction in the first quadrant. Establishing a functional relation between friction coefficient and temperature according to the curve characteristics, wherein the functional relation is characterized in that:
wherein t is m And the temperature corresponding to the maximum friction coefficient is represented, alpha and beta represent the gradient characteristics of the curve, and gamma represents the height characteristics of the curve.
Finally, as the friction coefficient is the same as the variation trend of the sliding speed and the contact pressure at different temperatures, curves among different temperatures are in a multiple relation, and a thermodynamic coupling comprehensive friction model established according to curve characteristics is characterized in that:
wherein alpha and beta are rubber viscoelasticity correlation coefficients, gamma is a temperature correlation coefficient, t m A is the temperature corresponding to the maximum value of mu 1 、a 2 B, related to the ground contact shape of the rubber and the road surface roughness 1 、b 2 Is related to the material physical properties of the rubber and the sensitivity of pressure and speed.
The model is suitable for the friction process of rubber and dry road surface with linear speed difference, t is temperature, and the unit is DEG C; p is the contact pressure, and the unit is N; v is the sliding speed in mm/s.
A in μ (p, v) 1 、a 2 、b 1 、b 2 Is a parameter fitted using test data at 25 ℃, and is determined by μ (T) =μ (T-T) 0 ) Performing variable displacement to eliminate the influence of temperature, wherein t 0 ＝25℃。
The technical scheme of the application is further described below with reference to specific embodiments.
In this example, a rubber abrasion test apparatus was used, as shown in chinese patent 202111375593.6, by which a rubber sample was subjected to a friction performance test. The equipment adopts a friction mode of a rubber wheel and a plane friction pair, and a rubber wheel sample is required to be prepared before an experiment.
Taking the tread formula and the preparation process of a certain manufacturer as an example, the 3# smoke rubber, N115 and other fillers are used for preparing rubber, and rubber wheel samples are prepared through plasticating, mixing and vulcanization processes.
The specific formula is as follows: 100 parts of natural rubber, 53 parts of N115 carbon black, 7 parts of 175GR white carbon black, 2 parts of stearic acid, 3.5 parts of zinc oxide, 1 part of microcrystalline wax, 2 parts of 4020 anti-aging agent, 1.5 parts of RD anti-aging agent, 1.2 parts of oil-filled sulfur, 5 parts of cut-resistant resin and 1.1 parts of CZ rubber accelerator.
The specific operation during plastication is as follows: the open rubber mixing mill is used, the rotating speed of the front wheel is set to be 18 revolutions per minute, the rotating speed of the rear wheel is set to be 25 revolutions per minute, the roller spacing is set to be 1.5mm, the roller is operated for 30 seconds at the temperature of 40 ℃, and rubber is sheared into small blocks after being thinned, so that the rubber is conveniently put into an internal mixer for the next working procedure.
The specific operation during mixing is as follows: using an internal mixer, putting most of natural rubber, setting the feeding temperature to be 80 ℃, the rubber discharging temperature to be 140 ℃ and the rotating speed of a rotor to be 80 revolutions per minute.
Starting a rotor, and rapidly throwing the residual natural rubber; adding stearic acid and zinc oxide at 90 seconds;
half of the carbon black is added at 150 seconds; adding antioxidant such as RD,4020, microcrystalline wax and the other half of carbon black at 240 seconds; sweeping the materials near the feed inlet and the upper top bolt into the internal mixer chamber at 330 seconds; and discharging the glue at 420 seconds.
An open mill was used, the roll gap was set at 1.5mm, the roll temperature was 40 ℃, the front wheel speed was 18rpm, and the rear wheel speed was 25rpm. And (3) putting rubber into the left and right cutters after wrapping the rollers, putting an accelerator and sulfur on the surface of the rubber material, reducing the roller spacing to 0.5mm after the left and right cutters are respectively rotated for 6 times along with the continuous rotation of the roller, reducing the baffle distance to a proper spacing, and repeating the triangular wrapping for 6 times. Increasing the roll spacing to 1.5mm, increasing the baffle distance at two sides to about 20cm, and exhausting air and then discharging glue for many times at a glue middle cutter after roll wrapping.
After the sheet is removed, the rubber compound is placed for more than 8 hours, and the next working procedure is prepared.
The specific operation during vulcanization is as follows: and (3) placing the vulcanizing mould on a flat plate of a flat vulcanizing machine, preheating for 20 minutes, and smearing a release agent on the inner surface of the mould.
Two rubber wheels can be vulcanized simultaneously in each vulcanization, 85g of rubber compound is placed at each rubber wheel, and a plurality of rubber blocks with proper shapes are sheared when the rubber compound is placed, so that gaps among the dies are filled. Setting the vulcanizing temperature of the vulcanizing machine to be 151 ℃ and the vulcanizing time to be 30min.
And after vulcanization is finished, the mold is taken down and opened, and the rubber wheel is gently tapped for multiple times to separate the rubber wheel from the mold, so that irreversible physical damage to rubber on the surface of the rubber wheel caused by adhesion between rubber and the inner side surface of the mold is avoided. The excess portion of the rubber wheel is removed by a tool such as scissors, and is trimmed to a cylindrical shape. The metal brush or sand paper is used for cleaning the mould, and residual rubber on the surface of the mould is removed, so that the accumulation of rubber dirt is prevented from affecting the dimensional accuracy.
After the rubber wheel is manufactured, the surface of the rubber wheel needs to be pre-ground to expose the fresh surface, so that the defect on the surface of the sample can be eliminated, and the sample can be uniformly stressed when friction is carried out.
The specific operation of the premiller is as follows: the linear speed of the rubber wheel is set to be 0.8m/s, the linear speed of the abrasive belt is set to be 0.5m/s, the deflection angle and the inclination angle are set to be 0 degrees, the contact pressure is set to be 200N, and the time is set to be 8min.
The sliding speed, the contact pressure and the rubber temperature are selected as parameters, the deflection angle and the inclination angle are 0 degrees, experiments under different working conditions are respectively carried out, and the experimental scheme is as follows:
the four conditions of contact pressure of 100N, 200N, 300N and 400N are selected under the condition that the linear speed difference is 0.3m/s and the temperature is 25 ℃.
The friction coefficient test results are respectively as follows: 0.65, 0.48, 0.40, 0.35.
Five cases were selected in which the contact pressure was 200N and the temperature was 25℃and the line speed difference was 0m/s, 0.1m/s, 0.2m/s, 0.3m/s, and 0.4 m/s.
The friction coefficient test results are respectively as follows: 0.31, 0.37, 0.42, 0.48, 0.61.
Fitting the experimental data with a friction model curve, wherein the friction model is characterized in that:
the fitting result is a1= 12.1476, a2= 0.3204, b1= -0.4440, b2=1.550.
Five conditions of 25 ℃,40 ℃, 55 ℃, 70 ℃ and 85 ℃ are selected for repeated experiments, the test results are shown in the following tables (friction coefficient tables of rubber wheels and abrasive belts under different pressures and temperatures, friction coefficient tables of rubber wheels and abrasive belts under different speeds and temperatures), and the curves are shown in fig. 2 and 3.
Friction coefficient meter for rubber wheel and abrasive belt under different pressure and temperature
Friction coefficient meter for rubber wheel and abrasive belt at different speeds and temperatures
Experimental data was split into two parts, one for modeling and one for validating the model.
Fitting through friction experimental data results of variable pressure, variable sliding speed and 200N contact pressure at 25 ℃ and variable temperature at 300mm/s sliding speed, wherein the established friction model is characterized in that:
the fitting result is α= 0.6278, β= 0.001974, γ=0.980, tm=68.
In summary, the thermal coupling friction model constructed by the rubber prepared by the formula is characterized in that:
the verification of the friction model was performed by the results of friction experiment data with contact pressures of 100N, 300N, 400N and slip speeds of 0mm/s, 100mm/s, 200mm/s, 400 mm/s.
The fit results of the thermal coupling comprehensive friction model and experimental data under different contact pressures are shown in fig. 4, and the fit results of the experimental data under different sliding speeds are shown in fig. 5. The curve is a thermodynamic coupling comprehensive friction model, and the discrete points are experimental data.
Taking fig. 4 as an example, part of the experimental data at 40 ℃ and 55 ℃ is slightly lower than the predicted model value, and especially the experimental data at the contact pressure of 300N has a certain gap from the predicted model value, which may be caused by excessive tension of the abrasive belt at the contact pressure of 300N.
Besides individual data, the whole experimental data and the model predictive values have little difference, for example, in fig. 4, the predictive errors at the temperature of 70 ℃ are 1.16%, 2.81% and 1.56% respectively, and the errors are within 5%, so that the built thermal coupling comprehensive friction model can accurately express the friction coefficient change trend caused by the contact pressure, the rubber temperature and the sliding speed change.
It should be understood that the above description is not intended to limit the application to the particular embodiments disclosed, but to limit the application to the particular embodiments disclosed, and that various changes, modifications, additions and substitutions can be made by those skilled in the art without departing from the spirit and scope of the application.
Claims (8)
1. A characterization method of thermal coupling friction coefficient of tire rubber is characterized by comprising the following steps: the method comprises the following steps:
1) Determining factors affecting the friction characteristics of the tire rubber;
2) Constructing a friction model at normal temperature according to the factors determined in the step 1);
3) Heating the tire rubber, and analyzing the functional relation between the temperature and the friction coefficient;
4) And constructing a thermal coupling model of the friction coefficient based on the friction model at normal temperature determined in the step 2) and the functional relation between the temperature and the friction coefficient in the step 3).
2. The method for characterizing a thermal coupling friction coefficient of a tire rubber according to claim 1, wherein:
in the step 1), factors influencing the friction characteristics of rubber are determined, and tread temperature, sliding speed and contact pressure are selected as parameters for constructing a friction model.
In the step 2), a friction model of friction coefficient, sliding speed and contact pressure at normal temperature is constructed through experimental data.
3. The method for characterizing a thermal coupling friction coefficient of a tire rubber according to claim 2, wherein:
in the step 4), based on the friction model of the friction coefficient, the sliding speed and the contact pressure at normal temperature and the functional relation of the temperature and the friction coefficient, a thermal coupling model of the friction coefficient, which is the functional relation of the friction coefficient to the tread temperature, the sliding speed and the contact pressure, is established.
4. The method for characterizing a thermal coupling friction coefficient of a tire rubber according to claim 2, wherein: in the step 1), determining factors influencing the friction characteristics of rubber, and selecting tread temperature, sliding speed and contact pressure as parameters for constructing a friction model, wherein μ=μ (p, v, T), wherein T is tread temperature, p is contact pressure and v is sliding speed;
establishing a friction model of friction coefficient, sliding speed and contact pressure at normal temperature as
Wherein a is 1 、a 2 、b 1 、b 2 Is constant, a 1 、a 2 B, related to the ground contact shape of the rubber and the road surface roughness 1 、b 2 Is related to the material physical properties of the rubber and the sensitivity of pressure and speed.
5. The method for characterizing a thermal coupling friction coefficient of a tire rubber according to claim 2, wherein: in step 3), a functional relationship of the friction coefficient with temperature is established, characterized by:
wherein t is m And the temperature corresponding to the maximum friction coefficient is represented, alpha and beta represent the gradient characteristics of the curve, and Y represents the height characteristics of the curve.
6. A method of characterizing the thermal coupling coefficient of friction of a tire rubber according to claim 3, wherein: in the step 4), the established thermodynamic coupling comprehensive friction model is characterized by:
wherein alpha and beta are rubber viscoelasticity correlation coefficients, gamma is a temperature correlation coefficient, t m A is the temperature corresponding to the maximum value of mu 1 、a 2 B, related to the ground contact shape of the rubber and the road surface roughness 1 、b 2 The temperature t is the temperature, the contact pressure p is the contact pressure, and the sliding speed v is the sensitivity of the physical properties, pressure and speed of the rubber itself.
7. The method for characterizing a thermal coupling friction coefficient of a tire rubber according to claim 6, wherein: integrated friction model by thermal couplingWherein e is obtained by the following formula,
wherein A is a pro-factor, E is apparent activation energy, R is molar gas constant, T is thermodynamic temperatureK is the rate coefficient.
8. The method for characterizing a thermal coupling friction coefficient of a tire rubber according to claim 4, wherein: friction model of friction coefficient, sliding speed and contact pressure at normal temperatureWherein a is 1 、a 2 、b 1 、b 2 Is a parameter obtained by fitting test data at 25℃by μ (T) =μ (T-T) 0 ) Performing variable displacement, wherein t 0 ＝25℃。
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