CN104517039A - Tire side-tipping side-inclining steady-state aligning torque characteristic radius semi-empirical modeling method - Google Patents

Abstract

The invention belongs to the technical field of tire dynamics and discloses a tire side-tipping side-inclining steady-state aligning torque characteristic radius semi-empirical modeling method. The method comprises decomposing aligning torque in the condition of non-linear stacking of the tire side-tipping side-inclining into side-inclining side force aligning torque, side-tipping side force aligning torque and side-tipping longitudinal force aligning torque, and tire side-tipping side-inclining steady-state aligning torque test data are obtained by testing through a tire mechanical characteristic test table, and parameters of the built tire model are obtained by identification through a curve fitting technology. The model has the advantages of being high in accuracy, clear in parameter physical meaning, capable of meeting theoretical boundary conditions and high in predictive capacity and can be used for high-accuracy car dynamic simulation.

Description

Tyre side canting inclined stable state aligning torque characteristic semiempirical modeling method

Technical field

The invention belongs to tire dynamics technical field, particularly relate to a kind of tyre side canting inclined stable state aligning torque characteristic semiempirical modeling method, the inclined test figure of tyre side canting obtained is tested by tire mechanical property testing platform, adopt the parameter of curve fitting technique identification tire model, obtain tyre side canting inclined stable state aligning torque model, for vehicle dynamics simulation.

Background technology

Tire is the vitals on automobile, and the acting force between car load and ground is all transmitted by tire.Mechanics of tire characteristic is the basis of automotive performance design and study, and has important impact to the performance such as security, operational stability, ride comfort of automobile.

Tire model sets up the relation between tire motion parameter and tire six square phase, and namely tire in certain operating conditions, can realize the various operating condition emulation of tire.Due to tire in the process of moving stressed very complicated, different according to the change of the factors such as the form of pavement properties, the speed of a motor vehicle, vertical load, fricative temperature and tire, therefore the foundation of tire model is the Focal point and difficult point that Chinese scholars research is discussed always.

Tire model has a significant impact the development of vehicle dynamics simulation technology and simulation result, and the precision of tire model must match with auto model precision, therefore selects accurate tire model to be vital.Because tire has the complicacy of structure and the non-linear of mechanical property, realistic tire model easy to use is again selected to be the key setting up Virtual Sample Vehicle model.

Patent of the present invention relates to the steady tire model of behaviour, mainly contains magic formula, UniTire, Fiala, UA, 5.2.1 model and TM-easy tire model etc. at present for grasping the steady tire model analyzed.Above tire model is when expressing tyre side canting inclined stable state aligning torque characteristic or adopt simplification theoretical expression or adopt pure experimental formula, causes the problems such as model parameter physical significance is indefinite, model prediction ability is not high.Patent of the present invention obtains according to the inclined Brush Model analysis of tyre side canting, the method of lateral deviation side force aligning torque, inclination side force aligning torque and inclination longitudinal force aligning torque Nonlinear Superposition is adopted to express tyre side canting inclined stable state aligning torque characteristic, Model Parameter has clear and definite physical significance, and model accuracy is high and predictive ability is strong.

Summary of the invention

In order to overcome above-mentioned the deficiencies in the prior art, the invention provides a kind of tyre side canting inclined stable state aligning torque characteristic semiempirical modeling method, the aligning torque of inclined for tyre side canting steady-state characteristic is decomposed into the Nonlinear Superposition of lateral deviation side force aligning torque, inclination side force aligning torque and inclination longitudinal force aligning torque.Set up tyre side canting inclined stable state aligning torque model, tested the inclined aligning torque test figure of tyre side canting obtained by tire mechanical property testing platform, adopt curve fitting technique identification to obtain the parameter of built tire model, for vehicle dynamics simulation.

The technical solution adopted in the present invention is: inclined for tyre side canting stable state aligning torque characteristic is decomposed into lateral deviation side force aligning torque, rolls side force aligning torque and the Nonlinear Superposition M rolling longitudinal force aligning torque _z=M _{z α}+ M _{z γ y}+ M _{z γ x}.

1, lateral deviation side force aligning torque model is:

$\left\{\begin{array}{c}{D}_{x0}=m_1+m_2\·F_m+m_3\·{F_{\mathrm{zn}}}^2\\ D_1=m_4\·\exp (-\frac{F_{\mathrm{zn}}}{m_5})\\ D_2=m_6\·\exp (-\frac{F_{\mathrm{zn}}}{m_7})\\ D_e=m_8+m_9\·F_{\mathrm{zn}}+m_{10}\·{F_{\mathrm{zn}}}^2\\ D_x=D_e+(D_{x0}-D_e)\·\exp (-D_1\·|{\mathrm{\φ}}_y|-D_2\·{{\mathrm{\φ}}_y}^2)\\ M_{\mathrm{z\α}}=F_{\mathrm{y\α}}\·D_x\end{array}\right.$

Wherein the implication of parameter is as follows:

M ₁: initial constant term of returning the positive arm of force

M ₂: load is on the initial coefficient of first order returning the impact of the positive arm of force

M ₃: load is on initial quadratic coefficients of returning the impact of the positive arm of force

M ₄: single order Curvature factor affecting parameters 1

M ₅: single order Curvature factor affecting parameters 2

M ₆: second order curvature Effects of Factors parameter 1

M ₇: second order curvature Effects of Factors parameter 2

M ₈: the constant term of the positive arm of force of ending back

M ₉: load is on the coefficient of first order of the positive arm of force impact that ends back

M ₁₀: load is on the quadratic coefficients of the positive arm of force impact that ends back

φ _y: based on the intermediate variable in the tyre side canting inclined stable state side force characteristics modeling method of Nonlinear Superposition

D _x: lateral deviation returns the positive arm of force

F _{y α}: the lateral deviation side force that the tire model based on Nonlinear Superposition calculates, side force model is F _y=F _{y α}+ F _{y γ},

Wherein lateral deviation side force F _{y α}computing formula is:

Wherein, the meaning of each parameter expression is:

S ₁: the horizontal-shift of side drift angle

S ₂: the effectively relation amplitude coefficient of side drift angle and nominal side drift angle

S ₃: load is to the constant term coefficient of lateral deviation stiffness effect

S ₄: load is to the Monomial coefficient of lateral deviation stiffness effect

S ₅: load is to the quadratic term coefficient of lateral deviation stiffness effect

S ₆: side rake angle is to the quadratic term coefficient of lateral deviation stiffness effect

S ₇: load is to Curvature factor affecting parameters 1

S ₈: load is to Curvature factor affecting parameters 2

S ₉: static friction coefficient when load is zero

S ₁₀: side drift angle and side rake angle direction are to the influence coefficient of static friction

S ₁₁: the difference of static friction coefficient when large load and load are zero

S ₁₂: lateral sliding speed is to the influence coefficient of friction factor

F _z: tyre load

F _z0: tire normal load, determine by the load index of 0.8 times, load index can obtain from the specifications and models of tire

V _r: tire rolling speed

α: slip angle of tire

α _e: the effective side drift angle of tire

γ: tyre side inclination angle

K _y: tire cornering stiffness

E _y: the tyre curvature factor

μ _y: tire coefficient of friction

With effective side drift angle α _ereplace slip angle of tire α to calculate Wheel slip and return positive arm of force D _x, effective side drift angle α _eall convergence slip angle of tire α when little slippage and large slippage between tire and road surface, positive side rake angle and positive side drift angle time, effective side drift angle α _ebe greater than slip angle of tire α, positive side rake angle and minus side drift angle time, effective side drift angle α _eabsolute value be less than the absolute value of slip angle of tire α.

2, side force aligning torque model is rolled

Roll side force aligning torque M _{z γ y}with effective side drift angle α _erelevant, α _em when being 0 _{z γ y}be 0, along with effective side drift angle α _ethe increase M of absolute value _{z γ y}first increase and reduce to 0 afterwards, rolling side force aligning torque model is:

$\left\{\begin{array}{c}{K}_{\mathrm{m\γy}}=m_{11}+m_{12}\·F_{\mathrm{zn}}+m_{13}\·{F_{\mathrm{zn}}}^2\\ M_{\mathrm{z\γy}}=K_{\mathrm{mry}}\·\mathrm{sgn}\left(\mathrm{\γ}\right)\·(1-\cos \left(m_{14}{\mathrm{\α}}_e\right))\end{array}\right.$

Wherein, the meaning of each parameter expression is:

M ₁₁: load offside incline side force aligning moment stiffness impact constant term coefficient

M ₁₂: load offside incline side force aligning moment stiffness impact Monomial coefficient

M ₁₃: load offside incline side force aligning moment stiffness impact quadratic term coefficient

M ₁₄: side drift angle offside inclines the affecting parameters of side force aligning torque

K _mry: roll side force aligning moment stiffness

3, longitudinal force aligning torque model is rolled

Roll longitudinal force aligning torque M _{z γ x}with effective side drift angle α _erelevant, α _em when being 0 _{z γ x}maximum, along with effective side drift angle α _ethe increase M of absolute value _{z γ x}reduce to 0, rolling longitudinal force aligning torque model is:

$\left\{\begin{array}{c}{K}_{\mathrm{m\γx}}=m_{15}+m_{16}\·F_{\mathrm{zn}}+m_{17}\·{F_{\mathrm{zn}}}^2\\ M_{\mathrm{z\γx}}={-K}_{\mathrm{mrx}}\·\mathrm{sgn\γ}\·\mathrm{sech}\left(\frac{{\mathrm{\φ}}_y}{m_{18}}\right)\end{array}\right.$

Wherein, the meaning of each parameter expression is:

M ₁₅: load is on the constant term coefficient rolling the impact of longitudinal force aligning moment stiffness

M ₁₆: load is on the Monomial coefficient rolling the impact of longitudinal force aligning moment stiffness

M ₁₇: load is on the quadratic term coefficient rolling the impact of longitudinal force aligning moment stiffness

M ₁₈: side drift angle is to the affecting parameters rolling longitudinal force aligning torque

K _mrx: roll longitudinal force aligning moment stiffness

Wherein, s ₁, s ₂, s ₃, s ₄, s ₅, s ₆, s ₇, s ₈, s ₉, s ₁₀, s ₁₁, s ₁₂, s ₁₃, s ₁₄, s ₁₅, s ₁₆for side force model parameter to be identified, m ₁, m ₂, m ₃, m ₄, m ₅, m ₆, m ₇, m ₈, m ₉, m ₁₀for lateral deviation returns the parameter of the positive arm of force, m ₁₁, m ₁₂, m ₁₃, m ₁₄, m ₁₅, m ₁₆, m ₁₇, m ₁₈for aligning torque model parameter to be identified, vertical load F _z, normal load F _z0, slip angle of tire α, tyre side tilt angle gamma be the input quantity of model, the inclined stable state aligning torque M of tyre side canting _zfor the output quantity of model, all the other parameters are model intermediate variable.

Tyre side canting inclined stable state aligning torque characteristic semiempirical modeling method specifically comprises the following steps:

The first step: be arranged on tire mechanical property testing platform by test request by needing the tire of the inclined steady-state characteristic model of establishment side canting, complete stable state mechanical property testing under the inclined operating mode of tyre side canting, record test figure, test figure at least comprises tyre side tilt angle gamma, side drift angle α, vertical load F _z, tire rolling speed V _r, side force F _yand aligning torque M _z, normal load F _z0determine by the load index of 0.8 times, load index can obtain from the specifications and models of tire;

Second step: the tyre side inclination angle adopting curve fitting technique to obtain from the first step, side drift angle, vertical load and side force test figure, identification obtains Wheel slip side force F _{y α}and effective side drift angle α _e, by effective side drift angle α _ecalculate Wheel slip and return positive arm of force D _x, and then obtain lateral deviation side force aligning torque M _{z α};

3rd step: the tyre side inclination angle adopting curve fitting technique to obtain from the first step, side drift angle, vertical load and aligning torque test figure, identification obtains all parameter m to be determined in tyre side canting inclined stable state aligning torque model ₁₁, m ₁₂, m ₁₃, m ₁₄, m ₁₅, m ₁₆, m ₁₇, m ₁₈, set up the inclination lateral deviation stable state aligning torque characteristic model of this tire.

Described curve fitting technique can adopt least square method, genetic algorithm etc.

Compared with prior art, the invention has the beneficial effects as follows:

1. patent of the present invention obtains according to the inclined Brush Model analysis of tyre side canting, adopts the method for lateral deviation side force aligning torque, inclination side force aligning torque and inclination longitudinal force aligning torque Nonlinear Superposition to express tyre side canting inclined stable state aligning torque characteristic;

2. Model Parameter has clear and definite physical significance;

3. model accuracy is high;

4. meet theoretical boundary condition, predictive ability is strong.

Accompanying drawing explanation

Fig. 1 is tire mechanical property testing platform;

Fig. 2 is the implementing procedure figure of the inventive method;

Fig. 3 is that typical case rolls lateral deviation operating mode tyre moment steady-state characteristic curve;

Fig. 4 decomposes from inclination lateral deviation tyre moment the lateral deviation side force aligning torque curve obtained;

Fig. 5 decomposes from inclination lateral deviation tyre moment the inclination side force aligning torque curve obtained;

Fig. 6 decomposes from inclination lateral deviation tyre moment the inclination longitudinal force aligning torque curve obtained;

Fig. 7 rolls lateral deviation operating mode 0 degree of side rake angle side force identification result curve;

Fig. 8 rolls lateral deviation operating mode 6 degree of side rake angle side force identification result curves;

Fig. 9 rolls lateral deviation operating mode-6 to spend side rake angle side force identification result curve;

Figure 10 rolls lateral deviation operating mode 0 degree of side rake angle aligning torque identification result curve;

Figure 11 rolls lateral deviation operating mode 6 degree of side rake angle aligning torque identification result curves;

Figure 12 rolls lateral deviation operating mode-6 to spend side rake angle aligning torque identification result curve;

Figure 13 rolls lateral deviation operating mode 10 degree of side rake angle aligning torque identification result curves;

Figure 14 rolls lateral deviation operating mode-10 to spend side rake angle aligning torque identification result curve;

Figure 15 rolls lateral deviation operating mode 15 degree of side rake angle aligning torque identification result curves;

Figure 16 is vertical load total aligning torque identification result curve when be 5005.1N side rake angle being 6 degree;

The lateral deviation side force aligning torque curve that Figure 17 is vertical load to be decomposited when be 5005.1N side rake angle being 6 degree;

The inclination side force aligning torque curve that Figure 18 is vertical load to be decomposited when be 5005.1N side rake angle being 6 degree;

The inclination longitudinal force aligning torque curve that Figure 19 is vertical load to be decomposited when be 5005.1N side rake angle being 6 degree.

Embodiment

Below in conjunction with accompanying drawing, the present invention is further described.This method verifies that tire used is GeneralP215/70R16 99S tire, tire pressure is 262kPa, test figure under utilizing the test of the tire mechanical property testing platform shown in Fig. 1 to obtain the inclined operating mode of tyre side canting, utilize the tyre side canting inclined stable state aligning torque characteristic semiempirical modeling method of inventing, adopt curve fitting technique, pick out the parameter of tire model.Concrete steps are as follows:

The first step: General P215/70R16 99S tire is arranged on tire mechanical property testing platform as shown in Figure 1, stable state mechanical property testing under the inclined operating mode of tyre side canting is completed by test request as shown in table 1, record test figure, test figure comprises tyre side inclination angle, side drift angle, vertical load, tire rolling speed, side force and aligning torque;

Table 1 test request

Second step: the tyre side inclination angle adopting curve fitting technique to obtain from the first step, side drift angle, vertical load and side force test figure, identification obtains Wheel slip side force F _{y α}and effective side drift angle α _e, it is as shown in table 2 that identification obtains all parameters to be determined in the side force model of the inclined steady-state characteristic of tyre side canting, side force identification result curve as shown in Fig. 7,8,9, by effective side drift angle α _ecalculate Wheel slip and return positive arm of force D _x, and then obtain lateral deviation side force aligning torque M _{z α}=F _{y α}d _x, return positive arm of force D _xparameter as shown in table 3;

Table 2 side force parameter

Parameter	Parameter value
		s1	-0.000933287
s2	0.187178829

s3	0.081740439
		s4	0.051857804
s5	0.034281361
		s6	10.98848437
s7	1.045918699
		s8	0.82085454
s9	1.774814355
		s10	0.05873428
s11	0.973171657
		s12	1.327434196
s13	-5358.787416
		s14	-6419.344965
s15	1410.596107
		s16	1.61393815

Table 3 lateral deviation returns positive arm of force parameter

Parameter	Parameter value
		m1	-0.07227821
m2	-0.066010994
		m3	-0.002608773
m4	1.297002171
		m5	105746.1822
m6	-0.859879162
		m7	77785.6785
m8	0.004401635
		m9	-0.000334013
m10	0.00814403

3rd step: the tyre side inclination angle adopting curve fitting technique to obtain from the first step, side drift angle, vertical load and aligning torque test figure, identification obtains all parameter m to be determined in tyre side canting inclined stable state aligning torque model ₁₁, m ₁₂, m ₁₃, m ₁₄, m ₁₅, m ₁₆, m ₁₇, m ₁₈, as shown in table 4, set up the inclination lateral deviation stable state aligning torque characteristic model of this tire.

Table 4 model parameter

Parameter	Parameter value
		m11	-6.243376875
m12	6.287808167

m13	16.68964112
		m14	-14.48682227
m15	154.9439434
		m16	202.6030222
m17	47.5500795
		m18	0.799140111

The curve fitting technique adopted is least square method.The inclination lateral deviation operating mode done comprises: load is respectively 5000N, 8300N, 11500N, side rake angle be respectively 6 degree ,-6 degree, 10 degree ,-10 degree and 15 degree, side drift angle from-25 spend change to 25 degree.Fitting result is as shown in Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15.Be 5005.1N by vertical load, the aligning torque (Figure 16) of side rake angle when being 6 degree be decomposed into lateral deviation aligning torque (Figure 17), roll side force aligning torque (Figure 18) and roll longitudinal force aligning torque (Figure 19), can see that model has higher precision, and Model Parameter there is clear and definite physical significance.

Claims (7)

1. tyre side canting inclined stable state aligning torque characteristic semiempirical modeling method, is characterized in that: by the stable state aligning torque M under inclined for tyre side canting operating mode _zbe decomposed into lateral deviation side force aligning torque M _{z α}, roll side force aligning torque M _{z γ y}with inclination longitudinal force aligning torque M _{z γ x}nonlinear Superposition.

2. tyre side canting according to claim 1 inclined stable state aligning torque characteristic semiempirical modeling method, is characterized in that: described lateral deviation side force aligning torque M _{z α}equal Wheel slip side force F _{y α}positive arm of force D is returned with Wheel slip _xproduct, with effective side drift angle α _ereplace slip angle of tire α to calculate Wheel slip and return positive arm of force D _x, effective side drift angle α _eall convergence slip angle of tire α when little slippage and large slippage between tire and road surface, positive side rake angle and positive side drift angle time, effective side drift angle α _ebe greater than slip angle of tire α, positive side rake angle and minus side drift angle time, effective side drift angle α _eabsolute value be less than the absolute value of slip angle of tire α.

3. tyre side canting according to claim 1 inclined stable state aligning torque characteristic semiempirical modeling method, is characterized in that: roll side force aligning torque M _{z γ y}with effective side drift angle α _erelevant, α _em when being 0 _{z γ y}be 0, along with effective side drift angle α _ethe increase M of absolute value _{z γ y}first increase and reduce to 0 afterwards.

4. tyre side canting according to claim 1 inclined stable state aligning torque characteristic semiempirical modeling method, is characterized in that: roll longitudinal force aligning torque M _{z γ x}with effective side drift angle α _erelevant, α _em when being 0 _{z γ x}maximum, along with effective side drift angle α _ethe increase M of absolute value _{z γ x}reduce to 0.

5. tyre side canting according to claim 1 inclined stable state aligning torque characteristic semiempirical modeling method, is characterized in that: the inclined stable state aligning torque M of described tyre side canting _zmodel is:

$\left\{\begin{array}{c}{F}_{\mathrm{zn}}=\frac{F_z-F_{z0}}{F_{z0}}\\ K_{\mathrm{m\γy}}=m_{11}+m_{12}\·F_{\mathrm{zn}}+m_{13}\·{F_{\mathrm{zn}}}^2\\ M_{\mathrm{z\γy}}=K_{\mathrm{mry}}\·\mathrm{sgn}\left(\mathrm{\γ}\right)\·(1-\cos \left(m_{14}{\mathrm{\α}}_e\right))\\ K_{\mathrm{m\γx}}=m_{15}+m_{16}\·F_{\mathrm{zn}}+m_{17}\·{F_{\mathrm{zn}}}^2\\ M_{\mathrm{z\γx}}=-K_{\mathrm{m\γx}}\·\sin \mathrm{\γ}\·\mathrm{sech}\left(\frac{{\mathrm{\φ}}_y}{m_{18}}\right)\\ M_z=M_{\mathrm{za}}+M_{\mathrm{z\γy}}+M_{\mathrm{z\γx}}\end{array}\right.$

Wherein, m ₁₁, m ₁₂, m ₁₃, m ₁₄, m ₁₅, m ₁₆, m ₁₇, m ₁₈for model parameter to be identified, vertical load F _z, normal load F _z0, slip angle of tire α, tyre side tilt angle gamma be the input quantity of model, the inclined stable state aligning torque M of tyre side canting _zfor the output quantity of model, all the other parameters are model intermediate variable.

6. tyre side canting according to claim 1 inclined stable state aligning torque characteristic semiempirical modeling method, is characterized in that: specifically comprise the following steps:

The first step: be arranged on tire mechanical property testing platform by test request by needing the tire of the inclined steady-state characteristic model of establishment side canting, complete stable state mechanical property testing under the inclined operating mode of tyre side canting, record test figure, test figure at least comprises tyre side tilt angle gamma, side drift angle α, vertical load F _z, tire rolling speed V _r, side force F _yand aligning torque M _z, normal load F _z0determine by the load index of 0.8 times, load index can obtain from the specifications and models of tire;

Second step: the tyre side inclination angle adopting curve fitting technique to obtain from the first step, side drift angle, vertical load and side force test figure, identification obtains Wheel slip side force F _{y α}and effective side drift angle α _e, by effective side drift angle α _ecalculate Wheel slip and return positive arm of force D _x, and then obtain lateral deviation side force aligning torque M _{z α};

3rd step: the tyre side inclination angle adopting curve fitting technique to obtain from the first step, side drift angle, vertical load and aligning torque test figure, identification obtains all parameter m to be determined in tyre side canting inclined stable state aligning torque model ₁₁, m ₁₂, m ₁₃, m ₁₄, m ₁₅, m ₁₆, m ₁₇, m ₁₈, set up the inclination lateral deviation stable state aligning torque characteristic model of this tire.

7. the step of tyre side canting according to claim 6 inclined stable state aligning torque characteristic semiempirical modeling method, is characterized in that: described curve fitting technique can adopt least square method, genetic algorithm etc.