CN112270022A - Friction mechanics modeling method based on rubber-rough surface contact - Google Patents

Friction mechanics modeling method based on rubber-rough surface contact Download PDF

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CN112270022A
CN112270022A CN202011062061.2A CN202011062061A CN112270022A CN 112270022 A CN112270022 A CN 112270022A CN 202011062061 A CN202011062061 A CN 202011062061A CN 112270022 A CN112270022 A CN 112270022A
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dft
rubber
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刘延慧
肖旺新
包旭
肖神清
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Huaiyin Institute of Technology
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Abstract

The invention discloses a frictional mechanics modeling method based on rubber-rough surface contact. The method comprises the following specific steps: establishing a geometric model of the DFT rubber pad, obtaining a road profile, assuming a rubber sliding part and a road surface texture profile, calculating a control equation of rubber rough road surface contact, and calculating and measuring the characteristics of the DFT rubber pad based on a numerical resolution simplified algorithm. The invention solves the friction coefficient by establishing a Dynamic Friction Tester (DFT) rubber geometric model, acquiring a road profile, assuming a rubber sliding part and road surface textures, calculating a rubber rough surface contact control equation and establishing a rubber hysteresis friction calculation method of rubber rough surface contact based on numerical resolution, realizes the appearance quick detection instead of the field friction detection, improves the detection personal safety, reduces the cost and simultaneously improves the road surface anti-sliding performance.

Description

Friction mechanics modeling method based on rubber-rough surface contact
Technical Field
The invention belongs to the field of pavement characteristics and numerical analysis, and particularly relates to a frictional mechanics modeling method based on rubber-rough surface contact.
Background
The anti-skid performance is one of the main factors influencing the road driving safety, mainly depends on the friction force generated between the vehicle tire and the road surface, and influences the direction and the parking distance of the vehicle controlled by the driver. The frictional characteristics of the tire-road contact interface depend not only on the rubber texture, but also on the tire characteristics (tire geometry, inflation stress, tread depth, and rubber characteristics), operating conditions (slip rate and load), and road conditions (including dry, wet, snow, and ice). The manual method adopted at present for measuring the tire-road surface contact friction force has low efficiency, the detection speed cannot keep up with the road surface damage speed, a large amount of manpower and material resources can be wasted, and great safety threats can be generated to workers; therefore, the research on road surface skid resistance has attracted more and more attention, and the key to the research on road surface skid resistance is the friction force at the tire-road surface contact interface, so that the calculation of the friction coefficient for rubber rough road surface contact has become a hot spot. At present, the existing research technology is mostly constructed on the basis of physics, and the research is mostly carried out on the friction between a tire and a road surface by starting from a semi-empirical method and an experimental curve fitting method and a method for processing and analyzing a section.
However, the existing research techniques are mostly constructed on the basis of physics, and the tire-road friction is researched by starting from a semi-empirical method, an experimental curve fitting method and a method for processing and analyzing a section. The disadvantages are that: the research method is complex, and coefficients used in the model are difficult to calculate, do not conform to the actual situation, and even have uncertainty.
Disclosure of Invention
Aiming at the problems, the invention provides a frictional mechanics modeling method based on rubber-rough surface contact; the method is based on the frictional mechanical modeling of the rough rubber surface contact, and the frictional force of the tire-road surface contact is calculated through a model; the model is easy to implement, and the surface texture is the main input parameter. The model is applied to predicting the friction coefficient on the real road in the future, is easy to realize, greatly liberates manpower and material resources, and is lower in cost for road managers.
The technical scheme of the invention is as follows: the frictional mechanics modeling method based on rubber-rough surface contact comprises the following specific steps:
step (1.1), establishing a geometric model of the DFT rubber pad by referring to the actual geometric shape of the DFT;
step (1.2), acquiring a road profile by using CTM;
step (1.3), assuming the sliding state of the DFT rubber pad on the road surface texture to simplify the model;
step (1.4), determining a calculation control equation of the rough rubber road surface contact according to the contact state of the DFT rubber pad and the road surface;
step (1.5), calculating the average friction force of the road profile based on a numerical resolution simplification algorithm; and (1.6) determining the characteristics of the DFT rubber pad based on a bivariate Newton method numerical equation.
Further, in the step (1.1), in establishing a geometric model of the DFT rubber pad: the definition function g (x) of the geometric model is shown as formula (1):
Figure BDA0002712705650000021
the DFT actual geometry is defined as shown in equation (2):
h (x) ═ g (x) + max (g (x)) (2) wherein: g (x) represents a definition function, heDenotes the maximum DFT rubber mat thickness, x denotes the distance, L denotes the length of the DFT rubber mat, and h (x) denotes the DFT actual geometry.
Further, in the step (1.2), a concrete method for acquiring the road profile by using the CTM is as follows: measuring road surface textures by using a CTM (computer-to-machine) to obtain a height value of a road profile, taking the height value of the road profile as an input parameter of a friction mechanical model, and calculating to obtain the height of a section of a DFT (discrete Fourier transform) rubber pad in a road sliding range to form a road section diagram;
specifically, the road profile height of the input parameter is as shown in formula (3):
zi＝z_CTMi-max(z-CTMi) (3)
in the formula: z is a radical ofiIndicating road section height, CTMiRepresents the value obtained by the CTM at point i; z-CTMiRepresents the true height value, max (z _ CTM), of the road profile recorded by CTM at point ii) Representing the highest point of the road profile.
Further, in the step (1.3), the assumption of the sliding state of the DFT rubber pad on the road surface texture is to simplify the model specifically: the difficulty in calculating the contact parameters of the DFT rubber pad when moving on the road surface texture is that the contact state of any point in the contact area depends on the whole contact state, so that the movement of the rubber pad on the road surface is assumed.
Further, in the step (1.4), the calculation control equation for determining the contact of the rough rubber road surface according to the contact state of the DFT rubber pad and the road surface refers to: discretizing the DFT rubber pad into a plurality of small units; represented by i, j; wherein, the unit i represents the ith unit of the discretization rubber cushion, and the unit j represents the jth unit of the road section; u. ofijRepresenting the displacement of the rubber pad unit i corresponding to the road section unit j; at any time t, two situations occur between the DFT rubber mat and the road surface: the DFT rubber pad is contacted with the road surface, and the DFT rubber pad is far away from the road surface; specifically, the method comprises the following steps:
(1.4.1) when the DFT rubber pad is in contact with the road surface, the displacement u of the unit i at the time tijDepending on the overall displacement delta of the DFT rubber pad, the geometry h of the DFT rubber pad at that pointiHeight z of contact point with road surfacej(ii) a Contact force exists between the unit i and the unit j, and force F of the DFT rubber pad to the road surfaceijReaction force R of road surfaceijAnd adhesion FRijThere is a balance between; the formulas are shown in formulas (4) and (5):
Figure BDA0002712705650000031
wherein:
Figure BDA0002712705650000032
Figure BDA0002712705650000033
uij(t)＝δ(t)-hi-zj (5)
in the formula: t represents time;
Figure BDA0002712705650000034
representing the force of cell i acting on the road surface at time t,
Figure BDA0002712705650000035
representing the road surface reaction force at cell i at time t,
Figure BDA0002712705650000036
showing the local adhesion caused by the micro-texture at time t, which depends on the actual contact area AsTrue shear stress σ ins(ii) a K represents the modulus of elasticity of the spring, uij(t) represents the contact displacement of the unit i and the unit j at the time t, and C represents the damping viscosity; mu.sadhIs the coefficient of sticking friction; δ (t) represents the overall displacement of the DFT rubber pad at time t; h isiDFT rubber pad geometry h (x), z representing cell ijRepresents the height of cell j;
wherein the z-axis component of equation (4) balances the local normal load PijAs shown in formula (6):
Figure BDA0002712705650000037
wherein:
Figure BDA0002712705650000038
rewritable as follows:
Figure BDA0002712705650000039
in the formula: pij(t) represents the normal load at the time of t, and V represents the sliding speed of the DFT rubber pad; combining formula (6) with formulae (5), (7), and (8) yields the following formula, as shown in formula (9):
Figure BDA00027127056500000310
at an arbitrary time t, PiPositive, DFT rubber mat is far from road contact, as shown in equation (10):
Pij(t)>0 (10)
(1.4.2) when the DFT rubber pad is far away from the road surface to contact, three forces Fij、RijAnd FRijAre all zero; at this time, the displacement uijRepresents free relaxation; it is controlled by the self displacement before t-delta t and the mechanical property thereof; as shown in formulas (11) and (12):
Figure BDA0002712705650000041
Figure BDA0002712705650000042
wherein:
Figure BDA0002712705650000043
wherein t- Δ t represents a step time before time t;
equations (12) and (13) give the displacement of the DFT rubber mat away from road contact, as shown in equation (14):
Figure BDA0002712705650000044
at any time t, the contact stress is balanced with the total load applied to the DFT rubber mat, as shown in equation (15):
Figure BDA0002712705650000045
from the above formula, determine
Figure BDA0002712705650000046
I.e. the road reaction force at cell i at time t; the sum of their projected fields on the x-axis gives a force opposite to the direction of pad motion; the friction coefficient μ (t) at any time and at any position on the profile is calculated according to equation (16):
Figure BDA0002712705650000047
for each CTM road surface profile, calculating an average friction coefficient after the pad passes through the whole CTM road surface profile; by summarizing the number of each μ (t) divided by the road profile element, as shown in equation (17):
Figure BDA0002712705650000048
in the formula: mu.savThe calculated average friction coefficient of each road profile is expressed, and M represents the number of elements of the discrete road profile.
Further, in the step (1.5), a specific method for measuring the characteristics of the DFT rubber mat based on the bivariate newton's method numerical equation is as follows:
calculating the displacement of the rubber at the unit i at the unit position of the road section j by the formula (3) in the step (1.2) according to the mechanical property, the geometric shape of the DFT rubber pad, the road section obtained by the CTM and the working condition of a DFT instrument; assuming that any displacement is 0, calculating the local contact stress of the rubber at the cell position of the road section j by the formula (7) described in the step (1.4); assuming that any negative displacement is 0, recalculating the corresponding displacement by equation (2) as described in step (1.1); comparing the comprehensive stress of the global contact length with the DFT normal load, if equal, calculating the instantaneous friction by the formula (14) in the step (1.4), and moving all DFT rubber pad units to the next position of the section to carry out the step; if the penetration depth is not equal, setting a new penetration depth of the solid rubber on the road, and initializing the penetration depth of the solid rubber in the road for repeated cycle calculation; and finally, calculating the average friction force of the road section by the formula (15) in the step (1.4).
Further, in the step (1.6), the specific steps for determining the characteristics of the DFT rubber pad based on the bivariate newton's method numerical equation are as follows: approximating DFT rubber characteristics (C, K) through a numerical equation of a bivariate Newton method, wherein C represents rubber damping viscosity, and K represents rubber elastic modulus;
giving an initial pair of (C)0,K0) Calculating a code f (C, K, V), wherein V represents the DFT rubber pad sliding speed;
specifically, the problems to be solved are as follows:
f(C,K,V)-μDFT-V＝0 (18)
in the formula, muDFT-vRepresents the coefficient of friction of the DFT measured at a speed V on a given reference plane; v is 20 or 60 Km/h;
one of the surfaces was selected as a reference, the C and K values were set to DFT rubber properties and will be used for all simulations, and the above characterization procedure was repeated when the DFT rubber pad was replaced.
The invention has the beneficial effects that: the method comprises the steps of solving a friction coefficient by establishing a Dynamic Friction Tester (DFT) rubber geometric model, obtaining a road profile, assuming a rubber sliding part and road surface textures, calculating a rubber rough surface contact control equation and establishing a rubber hysteresis friction calculation method of rubber rough surface contact based on numerical resolution, so that rapid morphology detection is realized to replace on-site friction detection, the personal safety of detection is improved, the cost is reduced, and the road surface anti-sliding performance is improved; the friction coefficient calculation model established by the invention is simple and easy to realize, can intelligently and quickly measure the friction coefficient, and provides a new method for the friction coefficient calculation in the aspects of road surface anti-skid performance research and road surface noise reduction.
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FIG. 1 is a flow chart of the architecture of the present invention;
FIG. 2 is a flow chart of an algorithm based on numerical resolution in an embodiment of the present invention.
Detailed Description
In order to more clearly illustrate the technical solution of the present invention, the following detailed description is made with reference to the accompanying drawings:
as shown in the figure; the frictional mechanics modeling method based on rubber-rough surface contact comprises the following specific steps:
step (1.1), establishing a geometric model of the DFT rubber pad by referring to the actual geometric shape of the DFT;
step (1.2), acquiring a road profile by using CTM;
step (1.3), assuming the sliding state of the DFT rubber pad on the road surface texture to simplify the model;
step (1.4), determining a calculation control equation of the rough rubber road surface contact according to the contact state of the DFT rubber pad and the road surface;
step (1.5), calculating the average friction force of the road profile based on a numerical resolution simplification algorithm;
and (1.6) determining the characteristics of the DFT rubber pad based on a bivariate Newton method numerical equation.
Further, in the step (1.1), in the building of the geometric model of the DFT rubber pad, the geometric model is built with reference to its actual geometry: the definition function g (x) of the geometric model is shown as formula (1):
Figure BDA0002712705650000061
the DFT actual geometry is defined as shown in equation (2):
h(x)＝-g(x)+max(g(x)) (2)
in the formula: g (x) represents a definition function, heDenotes the maximum DFT rubber pad thickness, he6 mm; x represents the distance (describing the coordinates on the local x-axis), L represents the length of the DFT rubber mat, L ═ 20 mm; h (x) representsDFT actual geometry.
Further, in the step (1.2), a concrete method for acquiring the road profile by using the CTM is as follows: measuring road surface textures by using a CTM (computer-to-machine) to obtain a height value of a road profile, taking the height value of the road profile as an input parameter of a friction mechanical model, and calculating to obtain the height of a section of a DFT (discrete Fourier transform) rubber pad in a road surface sliding range to form a road section diagram;
specifically, the road profile height of the input parameter is as shown in formula (3):
zi＝z_CTMi-max(z_CTMi) (3)
in the formula: z is a radical ofiIndicating road section height, CTMiRepresents the value obtained by the CTM at point i; z _ CTMiRepresenting the true height value, max (z-CTM), of the road profile recorded by CTM at point ii) Representing the highest point of the road profile;
after this operation is performed, ziIs equal to zero; in addition, the longitudinal distance between two adjacent points is constant, equal to 0.87mm (CTM measurement scale).
Further, in the step (1.3), the assumption of the sliding state of the DFT rubber pad on the road surface texture is to simplify the model specifically: the difficulty in calculating the contact parameters of the DFT rubber pad when moving on the road surface texture is that the contact state of any point in the contact area depends on the whole contact state, so that the movement of the rubber pad on the road surface is assumed;
the assumption is mainly directed to the cross section of the rubber sliding part and the road surface texture, one of the main difficulties of the calculation of the contact parameters is that the behavior of any point in the contact area depends on the behavior of all other points in the whole contact; for example, in the contact of two elastic half-space objects, the displacement (and stress) at any point in the contact area will depend on the stress distribution in the whole contact area, so as to derive an integral equation; to simplify the model, the sliding part of the rubber is considered to consist of a series of individual Kelvin-Voigt elements spaced 0.87mm apart to match the discretization of the texture profile being measured; depth hiEach cell i of (a) has viscoelasticityBehavior, the displacement of which is independent of other elements; thus, the slider has a geometry hiIs described by its texture profile measured by the CTM, is considered to be a rigid semi-infinite body.
Further, in the step (1.4), the calculation control equation for determining the contact of the rough rubber road surface according to the contact state of the DFT rubber pad and the road surface refers to: discretizing the DFT rubber pad into a plurality of small units; represented by i, j; wherein, the unit i represents the ith unit of the discretization rubber cushion, and the unit j represents the jth unit of the road section; will uijRepresents the displacement of the rubber pad unit i corresponding to (in contact with or not in contact with) the road section unit j; at any time t, two situations occur between the DFT rubber mat and the road surface: the DFT rubber pad is contacted with the road surface, and the DFT rubber pad is far away from the road surface (the DFT rubber pad is not contacted with the road surface); specifically, the method comprises the following steps:
(1.4.1) when the DFT rubber pad is in contact with the road surface, the displacement u of the unit i at the time tijDepending on the overall (or solid) displacement δ of the DFT rubber pad, the geometry h of the DFT rubber pad at that pointiHeight z of contact point with road surfacej(ii) a Contact force exists between the unit i and the unit j, and force F of the DFT rubber pad to the road surfaceijReaction force R of road surfaceijAnd adhesion FRijThere is a balance between (due to micro-texture); the formulas are shown in formulas (4) and (5):
Figure BDA0002712705650000071
wherein:
Figure BDA0002712705650000072
Figure BDA0002712705650000073
uij(t)＝δ(t)-hi-zj (5)
in the formula:
Figure BDA0002712705650000074
representing the force of element i acting on the road surface at time t; t represents time;
Figure BDA0002712705650000075
representing the force of cell i acting on the road surface at time t,
Figure BDA0002712705650000076
representing the road surface reaction force at cell i at time t,
Figure BDA0002712705650000077
showing the local adhesion caused by the micro-texture at time t, which depends on the actual contact area AsTrue shear stress σ insThis is due to the energy dissipation mechanism of the rubber in the contact pad; k represents the modulus of elasticity of the spring, uij(t) represents the contact displacement of the unit i and the unit j at the time t, and C represents the damping viscosity; mu.sadhIs the coefficient of sticking friction; δ (t) represents the overall (or fixed) displacement of the DFT rubber pad at time t; h isiDFT rubber pad geometry h (x) representing unit i; z is a radical ofjRepresents the height of cell j;
wherein the z-axis component of equation (4) balances the local normal load PijAs shown in formula (6):
Figure BDA0002712705650000081
wherein:
Figure BDA0002712705650000082
rewritable as follows:
Figure BDA0002712705650000083
in the formula: pij(t) represents tThe normal load at the moment, V represents the sliding speed of the DFT rubber pad (taken as a constant); combining formula (6) with formulae (5), (7), and (8) yields the following formula, as shown in formula (9):
Figure BDA0002712705650000084
at an arbitrary time t, PiPositive, DFT rubber mat is far from road contact, as shown in equation (10):
Pij(t)>0 (10)
(1.4.2) when the DFT rubber pad is far away from the road surface to contact, three forces Fij、RijAnd FRijAre all zero; at this time, the displacement uijRepresents free relaxation; it is controlled by the intrinsic displacement before t- Δ t and its mechanical properties (elastic modulus K and viscosity C); as shown in formulas (11) and (12):
Figure BDA0002712705650000085
Figure BDA0002712705650000086
wherein:
Figure BDA0002712705650000087
wherein t- Δ t represents a step time before time t;
equations (12) and (13) give the displacement (relaxation) of the DFT rubber mat when it is in contact away from the road surface, as shown in equation (14):
Figure BDA0002712705650000088
at any time t, regardless of the location of the pad on the surface profile, the normal contact stress is balanced with the total load applied to the DFT rubber pad, as shown in equation (15):
Figure BDA0002712705650000091
from the above formula, determine
Figure BDA0002712705650000092
I.e. the road reaction force at cell i at time t; the sum of their projected fields on the x-axis gives a force opposite to the direction of pad motion (hysteresis friction); the friction coefficient μ (t) at any time and at any position on the profile is calculated according to equation (16):
Figure BDA0002712705650000093
for each CTM road surface profile, calculating an average friction coefficient after the pad passes through the whole CTM road surface profile; by summarizing the number of each μ (t) divided by the road profile element, as shown in equation (17):
Figure BDA0002712705650000094
in the formula: mu.savThe calculated average friction coefficient of each road profile is expressed, and M represents the number of elements of the discrete road profile.
Further, in the step (1.5), a specific method for measuring the characteristics of the DFT rubber mat based on the bivariate newton's method numerical equation is as follows:
calculating the displacement of the rubber at the unit i at the unit position of the road section j by the formula (3) in the step (1.2) according to the mechanical property, the geometric shape of the DFT rubber pad, the road section obtained by the CTM and the working condition of a DFT instrument; assuming that any displacement is 0, calculating the local contact stress of the rubber at the cell position of the road section j by the formula (7) described in the step (1.4); assuming that any negative displacement is 0, recalculating the corresponding displacement by equation (2) as described in step (1.1); comparing the comprehensive stress of the global contact length with the DFT normal load, if equal, calculating the instantaneous friction by the formula (14) in the step (1.4), and moving all DFT rubber pad units to the next position of the section to carry out the step; if the penetration depth is not equal, setting a new penetration depth of the solid rubber on the road, and initializing the penetration depth of the solid rubber in the road for repeated cycle calculation; finally, calculating the average friction force of the road section by the formula (15) in the step (1.4); the algorithm based on the numerical resolution is iterative computation, the average friction force of the road section is finally calculated by a target, the specific algorithm is shown in figure 2, and an equation is given for each step. Newton's numerical scheme is applied in loops with smaller algorithms and the convergence criterion is set by comparing the input load with the load calculated from the integral stress in the contact area, the error must be less than 1%.
Further, in the step (1.6), the specific steps for determining the characteristics of the DFT rubber pad based on the bivariate newton's method numerical equation are as follows: approximating DFT rubber characteristics (C, K) through a numerical equation of a bivariate Newton method, wherein C represents rubber damping viscosity, and K represents rubber elastic modulus;
giving an initial pair of (C)0,K0) Calculating a code f (C, K, V), wherein V represents the DFT rubber pad sliding speed;
specifically, the problems to be solved are as follows:
f(C,K,20)-μDFT20＝0
f(C,K,60)-μDFT60＝0 (18)
in the formula, muDFT-vShows the DFT coefficient of friction measured at a given reference level at speed V (here 20 and 60 km/h);
one of the surfaces is selected as a reference. Once the K and C values are found, they will be set to DFT rubber properties and will be used for all other simulations; of course, the same characterization process will be performed again when a new DFT rubber pad is started.
In this embodiment, 33 different test sites were collected, one friction and texture measurement was performed on the same test track at each test point, and the standard deviation of the 8 friction measurements performed with DFT on the test pavement ranged from 0.044 at 30Km/h to 0.038 at 60 Km/h.
Thus, the coverage factor is set to 2, the confidence interval is 95%, and the dispersion of friction data is μ at a speed of 60km/hmeasuredMu at + -0.076 and 30km/hmeasured+ -0.088; each surface has independent texture and friction, thus being distinguished from other surfaces; the test pavement covers all texture forms, all the texture forms are common forms of the pavement, and the collected textures range from smooth to micro texture and macro texture.
Through the specific implementation of the steps (1) to (6), the result is that:
the DFT rubber shows expected viscoelastic behavior to deformation of profile roughness; indeed, viscoelastic materials exhibit both viscous and elastic properties; therefore, contrary to the strain of an elastic material, which, after stretching, returns rapidly to its original state after stress relief, whereas a viscoelastic material, due to its viscoelastic properties, changes in strain over time, once strained, causing a time delay back to its original state, has the obvious above-described behavior; indeed, as the shim is moved over the surface, it is observed that the DFT rubber delays recovering its original height (before it is deformed by the asperities), resulting in an asymmetric normal stress distribution on the roughened surface; instantaneous friction is calculated at each movement step and displayed instantaneously on the graph.
The predicted value of the model and the measured value of the friction coefficient have good correlation; the results show that: the model predicted value has better correlation with the experimental result, the predicted value and the measured value follow the diagonal principle, and half of the predicted value is dispersed in the range of +/-0.10 of the diagonal; even if the model is not perfect, the conclusion can be drawn that the model well reproduces the physical principle of hysteresis friction force generation, thereby opening up a prediction method of the tire-road friction coefficient with better application value.
Therefore, the model provided by the invention has good correlation between the predicted value of the friction coefficient of the rough surface of the rubber and the measured value of DFT, the method has strong popularization value, and a solid foundation is laid for calculating the friction coefficient based on the modeling of the contact friction force of the rough surface of the rubber.

Claims (7)

1. The frictional mechanics modeling method based on rubber-rough surface contact is characterized by comprising the following specific steps of:
step (1.1), establishing a geometric model of the DFT rubber pad by referring to the actual geometric shape of the DFT;
step (1.2), acquiring a road profile by using CTM;
step (1.3), assuming the sliding state of the DFT rubber pad on the road surface texture to simplify the model;
step (1.4), determining a calculation control equation of the rough rubber road surface contact according to the contact state of the DFT rubber pad and the road surface;
step (1.5), calculating the average friction force of the road profile based on a numerical resolution simplification algorithm;
and (1.6) determining the characteristics of the DFT rubber pad based on a bivariate Newton method numerical equation.
2. The modeling method of friction mechanics based on rubber-rough surface contact as claimed in claim 1, characterized in that in step (1.1), in building a geometric model of DFT rubber pad: the definition function g (x) of the geometric model is shown as formula (1):
Figure FDA0002712705640000011
the DFT actual geometry is defined as shown in equation (2):
h(x)＝-g(x)+max(g(x)) (2)
in the formula: g (x) represents a definition function, heDenotes the maximum DFT rubber mat thickness, x denotes the distance, L denotes the length of the DFT rubber mat, and h (x) denotes the DFT actual geometry.
3. The modeling method of friction mechanics based on rubber-rough surface contact as claimed in claim 1, characterized in that in step (1.2), the concrete method of obtaining road profile by CTM is: measuring road surface textures by using a CTM (computer-to-machine) to obtain a height value of a road profile, taking the height value of the road profile as an input parameter of a friction mechanical model, and calculating to obtain the height of a section of a DFT (discrete Fourier transform) rubber pad in a road sliding range to form a road section diagram;
specifically, the road profile height of the input parameter is as shown in formula (3):
zi＝z_CTMi-max(z_CTMi) (3)
in the formula: z is a radical ofiIndicating road section height, CTMiRepresents the value obtained by the CTM at point i; z _ CTMiRepresents the true height value, max (z _ CTM), of the road profile recorded by CTM at point ii) Representing the highest point of the road profile.
4. The modeling method of friction mechanics based on rubber-rough surface contact as claimed in claim 1, characterized in that in step (1.3), the sliding state of DFT rubber pads on road surface texture is assumed to simplify the model specifically: the difficulty in calculating the contact parameters of the DFT rubber pad when moving on the road surface texture is that the contact state of any point in the contact area depends on the whole contact state, so that the movement of the rubber pad on the road surface is assumed.
5. The modeling method of friction mechanics based on rubber-rough surface contact as claimed in claim 1, wherein in step (1.4), the calculation control equation for determining the rubber rough road surface contact according to the DFT rubber pad and road surface contact state is: discretizing the DFT rubber pad into a plurality of small units; represented by i, j; wherein, the unit i represents the ith unit of the discretization rubber cushion, and the unit j represents the jth unit of the road section; u. ofijRepresenting the displacement of the rubber pad unit i corresponding to the road section unit j; at any time t, two situations occur between the DFT rubber mat and the road surface: the DFT rubber pad is contacted with the road surface, and the DFT rubber pad is far away from the road surface; specifically, the method comprises the following steps:
(1.4.1) when the DFT rubber pad is in contact with the road surface, the displacement u of the unit i at the time tijDepending on the overall displacement delta of the DFT rubber pad, the geometry h of the DFT rubber pad at that pointiHeight z of contact point with road surfacej(ii) a Contact force exists between the unit i and the unit j, and force F of the DFT rubber pad to the road surfaceijReaction force R of road surfaceijAnd adhesion FRijThere is a balance between; the formulas are shown in formulas (4) and (5):
Figure FDA0002712705640000021
wherein:
Figure FDA0002712705640000022
Figure FDA0002712705640000023
uij(t)＝δ(t)-hi-zj (5)
in the formula: t represents time;
Figure FDA0002712705640000024
representing the force of cell i acting on the road surface at time t,
Figure FDA0002712705640000025
representing the road surface reaction force at cell i at time t,
Figure FDA0002712705640000026
showing the local adhesion caused by the micro-texture at time t, which depends on the actual contact area AsTrue shear stress σ ins(ii) a K represents the modulus of elasticity of the spring, uij(t) represents the contact displacement of the unit i and the unit j at the time t, and C represents the damping viscosity; mu.sadhIs the coefficient of sticking friction; delta (t) denotes DFT rubberIntegral displacement of the rubber pad at the moment t; h isiDFT rubber pad geometry h (x), z representing cell ijRepresents the height of cell j;
wherein the z-axis component of equation (4) balances the local normal load PijAs shown in formula (6):
Figure FDA0002712705640000027
wherein:
Figure FDA0002712705640000028
rewritable as follows:
Figure FDA0002712705640000031
in the formula: pij(t) represents the normal load at the time of t, and V represents the sliding speed of the DFT rubber pad; combining formula (6) with formulae (5), (7), and (8) yields the following formula, as shown in formula (9):
Figure FDA0002712705640000032
at an arbitrary time t, PiPositive, DFT rubber mat is far from road contact, as shown in equation (10):
Pij(t)>0 (10)
(1.4.2) when the DFT rubber pad is far away from the road surface to contact, three forces Fij、RijAnd FRijAre all zero; at this time, the displacement uijRepresents free relaxation; it is controlled by the self displacement before t-delta t and the mechanical property thereof; as shown in formulas (11) and (12):
Figure FDA0002712705640000033
Figure FDA0002712705640000034
wherein:
Figure FDA0002712705640000035
wherein t- Δ t represents a step time before time t;
equations (12) and (13) give the displacement of the DFT rubber mat away from road contact, as shown in equation (14):
Figure FDA0002712705640000036
at any time t, the contact stress is balanced with the total load applied to the DFT rubber mat, as shown in equation (15):
Figure FDA0002712705640000037
determining R 'by the formula'ij(t), the road surface reaction force at cell i at time t; the sum of their projected fields on the x-axis gives a force opposite to the direction of pad motion; the friction coefficient μ (t) at any time and at any position on the profile is calculated according to equation (16):
Figure FDA0002712705640000038
for each CTM road surface profile, calculating an average friction coefficient after the pad passes through the whole CTM road surface profile; by summarizing the number of each μ (t) divided by the road profile element, as shown in equation (17):
Figure FDA0002712705640000039
in the formula: mu.savThe calculated average friction coefficient of each road profile is expressed, and M represents the number of elements of the discrete road profile.
6. The modeling method of friction mechanics based on rubber-rough surface contact as claimed in claim 1, characterized in that in step (1.5), the specific method for determining the characteristics of DFT rubber pad based on bivariate newton's numerical equation is as follows:
calculating the displacement of the rubber at the unit i at the unit position of the road section j by the formula (3) in the step (1.2) according to the mechanical property, the geometric shape of the DFT rubber pad, the road section obtained by the CTM and the working condition of a DFT instrument; assuming that any displacement is 0, calculating the local contact stress of the rubber at the cell position of the road section j by the formula (7) described in the step (1.4); assuming that any negative displacement is 0, recalculating the corresponding displacement by equation (2) as described in step (1.1); comparing the comprehensive stress of the global contact length with the DFT normal load, if equal, calculating the instantaneous friction by the formula (14) in the step (1.4), and moving all DFT rubber pad units to the next position of the section to carry out the step; if the penetration depth is not equal, setting a new penetration depth of the solid rubber on the road, and initializing the penetration depth of the solid rubber in the road for repeated cycle calculation; and finally, calculating the average friction force of the road section by the formula (15) in the step (1.4).
7. The modeling method of friction mechanics based on rubber-rough surface contact as claimed in claim 1, characterized in that in step (1.6), the specific steps of determining the characteristics of DFT rubber pad based on bivariate newton's numerical equation are as follows: approximating DFT rubber characteristics (C, K) through a numerical equation of a bivariate Newton method, wherein C represents rubber damping viscosity, and K represents rubber elastic modulus;
giving an initial pair of (C)0,K0) Calculating a code f (C, K, V), wherein V represents the DFT rubber pad sliding speed;
specifically, the problems to be solved are as follows:
f(C,K,V)-μDFT-V＝0 (18)
in the formula, muDFT-vRepresents the coefficient of friction of the DFT measured at a speed V on a given reference plane; v is 20 or 60 Km/h;
one of the surfaces was selected as a reference, the C and K values were set to DFT rubber properties and will be used for all simulations, and the above characterization procedure was repeated when the DFT rubber pad was replaced.
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