CN114654952B - A method for constructing a vibration reduction system model for vehicles without pneumatic tires - Google Patents

Abstract

The present invention provides a method for constructing a vibration reduction system model of a pneumatic tire-free vehicle, specifically, constructing a dynamic model of a pneumatic tire-hybrid electromagnetic active suspension vibration reduction system, wherein the radial stiffness of the pneumatic tire involved in a dynamic differential equation corresponding to the dynamic model is designed based on a nonlinear fitting model of the radial stiffness of the pneumatic tire, and experiments verify that the dynamic model of the pneumatic tire-hybrid electromagnetic active suspension vibration reduction system has high accuracy. The construction method of the present invention is simple, and provides a theoretical basis for dynamic control of pneumatic tire-free vehicles.

Description

A method for constructing a vibration reduction system model for vehicles without pneumatic tires

Technical Field

The invention belongs to the technical field of pneumatic tire-free vehicles, and in particular relates to a method for constructing a vibration reduction system model of a pneumatic tire-free vehicle.

Background technique

The vehicle vibration reduction system can reduce the impact of uneven road surface on the vehicle body, accelerate the attenuation of frame and body vibration, and thus improve the driving stability of the vehicle. Tires are the only part of the vehicle connected to the road, supporting the vehicle, buffering impact, transmitting driving force and braking force, and have the performance of comfort, durability, low rolling resistance and safety, and are one of the key parts of the vehicle vibration reduction system.

With the advancement of science and technology, the market has higher and higher requirements for tires, especially the safety performance of tires. Traditional pneumatic tires cannot have very high safety performance due to their own characteristics, while airless tires can break through this limitation and have very high explosion-proof and puncture-proof safety performance. In addition, they have the advantages of durability, easy processing, and economy. Airless tires have broad market prospects; however, since airless tires do not rely on air pressure to achieve buffering and vibration reduction performance, their buffering and vibration reduction effects are relatively poor, and compared with traditional pneumatic tires, airless tires are generally bulky, have relatively large radial stiffness, and have relatively large elastic hysteresis; at the same time, the nonlinear region of the radial stiffness of traditional pneumatic tires is relatively small and can be regarded as linear, while the nonlinear region of airless tires is large, and their dynamic models are complex and difficult to construct, making it difficult to conduct control research on them.

The passive suspension of a vehicle cannot adapt to the complex and changeable external environment due to its fixed parameters, and the semi-active suspension cannot provide sufficient control force due to its own limitations. The active suspension can break through the limitations due to the introduction of the actuator and provide sufficient control force for the new vibration reduction system of the airless tire-active suspension. The hybrid electromagnetic actuator and the linear electromagnetic actuator are both commonly used actuators for active suspension. However, compared with the linear electromagnetic actuator, the hybrid electromagnetic actuator has many advantages. On the one hand, even when the linear motor or the power supply system fails, the hybrid electromagnetic actuator can still work in a passive form, with high reliability, which improves the safety of passenger cars equipped with airless tires. On the other hand, the damper in the hybrid electromagnetic active suspension can share part of the force required to adjust the damping (or part of the passive force related to the suspension speed), and the system energy consumption is relatively small. The hybrid electromagnetic actuator can provide better dynamic control while also performing certain energy recovery. Therefore, the hybrid electromagnetic actuator is more suitable for use in vehicles equipped with airless tires.

At present, most scholars at home and abroad focus on the material application and structural design of airless tires, and rarely study the vertical mechanical model of airless tires. Although the new vibration reduction system that couples hybrid active suspension with airless tires has good vibration reduction performance, the system is more complex and its dynamic model construction method is rarely reported. Therefore, the current research on dynamic control of airless tire vehicles lacks relevant theoretical references, and the promotion and application of airless tire vehicles urgently needs new technical methods.

Summary of the invention

In view of this, the present invention provides a method for constructing a vibration reduction system model of a pneumatic tire-free vehicle. The established model has high accuracy and a simple method, which provides a theoretical basis for the dynamic control of the pneumatic tire-free vehicle.

The present invention achieves the above technical objectives through the following technical means.

A method for constructing a vibration reduction system model of a pneumatic tire-free vehicle is specifically: constructing a dynamic model of a pneumatic tire-hybrid electromagnetic active suspension vibration reduction system, and the dynamic differential equation corresponding to the dynamic model is:

The radial stiffness k _u of the pneumatic-free tire satisfies the following radial stiffness nonlinear fitting model:

The radial stiffness nonlinear fitting model is obtained by obtaining the first-order derivative of the vertical displacement x of the air-free tire using the vertical force piecewise polynomial fitting model of the air-free tire;

The vertical force piecewise polynomial fitting model of the airless tire is:

Where: _ms is the sprung mass, _mu is the unsprung mass, is the vertical acceleration of the sprung mass, _ks is the spring stiffness, zs _is the vertical displacement of the sprung mass, _zu is the vertical displacement of the unsprung mass, /> is the vertical velocity of the sprung mass, /> is the vertical velocity of the unsprung mass, is the vertical acceleration of the unsprung mass, _cs is the damping coefficient, _csky is the ceiling damping coefficient, u is the motor power, _zr is the random road excitation input, _ku is the tire radial stiffness, _z0 is the static load radius of the airless tire when the vehicle is statically loaded, x is the vertical displacement of the airless tire obtained from the test, _y25 is the 25th data point of the vertical displacement of the airless tire, and _yN is the Nth data point of the vertical displacement of the airless tire.

According to a further technical solution, the vertical force piecewise polynomial fitting model of the airless tire is obtained by using the 25th data point in the test data to perform nonlinear fitting and linear fitting on the relationship between the vertical load at the center of the airless tire and the vertical displacement of the airless tire obtained in the test.

According to a further technical solution, the 25th data point in the test data is determined by selecting a data point whose determination coefficient R-square is not less than 99.95% and whose evaluation index δ is the smallest.

Further technical solution, the Wherein, F ₁ ' is the first-order derivative of the fitted nonlinear polynomial to the vertical displacement, F ₂ ' is the first-order derivative of the fitted linear polynomial to the vertical displacement, and y _M * is the M*th data point of the vertical displacement of the airless tire.

A further technical solution is that the vertical displacement x=n*L0', L0' is the average value of the vertical displacement change L0 of the tire each time the handwheel feeds one circle in multiple groups of tests, n is the number of feeding circles, and n≥1; the L0=(L1+L2)/(m-1), L1 is the initial distance between the top edge of the first gantry bracket and the top edge of the second gantry bracket, L2 is the terminal distance between the top edge of the first gantry bracket and the top edge of the second gantry bracket, and m is the total number of tests in a certain group of tests.

According to a further technical solution, the air-free tire-hybrid electromagnetic active suspension vibration reduction system is formed by coupling the air-free tire with the hybrid electromagnetic active suspension.

The beneficial effects of the present invention are as follows: the present invention first constructs a nonlinear fitting model of the radial stiffness of a pneumatic-free tire, designs the radial stiffness of the pneumatic-free tire based on the nonlinear fitting model of the radial stiffness of the pneumatic-free tire, thereby determining the dynamic model of the pneumatic-free tire-hybrid electromagnetic active suspension vibration reduction system, and experiments verify that the dynamic model of the pneumatic-free tire-hybrid electromagnetic active suspension vibration reduction system has high accuracy, and the construction method of the present invention is simple, which provides a theoretical basis for the subsequent dynamic control of pneumatic-free tire vehicles.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic diagram of a pneumatic tire-hybrid electromagnetic active suspension vibration reduction system model according to the present invention;

FIG2 is a flow chart of the vertical mechanical modeling method of the airless tire according to the present invention;

FIG3 is a data diagram of test results of the airless tire of the present invention;

FIG4 is a diagram showing the coefficient of determination R-square of the inflation-free vertical mechanical nonlinear fitting model of the present invention;

FIG5 is a comparison diagram of the δ values of the optional segmentation points of the vertical mechanical nonlinear fitting model of the pneumatic-free tire of the present invention;

FIG6( a ) is a fitting diagram of the nonlinear part of the vertical load at the center of the airless tire of the present invention;

FIG6( b ) is a fitting diagram of the linear part of the vertical load at the center of the airless tire of the present invention;

FIG7 is a diagram of a dynamic model of the pneumatic-free tire-hybrid electromagnetic active suspension vibration reduction system of the present invention;

FIG8( a ) is a vehicle body acceleration response diagram of the pneumatic tire-hybrid electromagnetic active suspension vibration reduction system of the present invention;

FIG8( b ) is a suspension dynamic deflection response diagram of the pneumatic tire-hybrid electromagnetic active suspension vibration reduction system of the present invention;

FIG8( c ) is a tire dynamic load response diagram of the air-free tire-hybrid electromagnetic active suspension vibration reduction system of the present invention;

Among them: 1- hybrid electromagnetic active suspension, 2- sprung mass, 3- elastic element, 4- hydraulic shock absorber, 5- linear motor, 6- unsprung mass, 7- air-free tire.

Detailed ways

The present invention is further described below in conjunction with the accompanying drawings and specific embodiments, but the protection scope of the present invention is not limited thereto.

As shown in FIG1 , the pneumatic tire-hybrid electromagnetic active suspension vibration reduction system of the pneumatic tire-free vehicle of the present invention comprises a hybrid electromagnetic active suspension 1 and a pneumatic tire 7; the hybrid electromagnetic active suspension 1 comprises an elastic element 3, a hydraulic shock absorber 4 and a linear motor 5, which can withstand and transmit vertical loads, isolate higher frequency vibrations transmitted to the vehicle body due to uneven road surface, attenuate vertical vibrations of the vehicle, and absorb vibration energy at the same time, and the elastic element 3, the hydraulic shock absorber 4 and the linear motor 5 are respectively fixedly connected at both ends between the sprung mass 2 and the unsprung mass 6; the pneumatic tire 7 is a pneumatic safety tire with vertical mechanical nonlinearity, which is coupled with the hybrid electromagnetic active suspension 1 to constitute a pneumatic tire-hybrid electromagnetic active suspension vibration reduction system.

A method for constructing a vibration reduction system model of a pneumatic tire-free vehicle includes vertical mechanical modeling of the pneumatic tire-free vehicle and construction of a dynamics model of the vibration reduction system of the pneumatic tire-free vehicle.

As shown in FIG2 , the vertical mechanical modeling of the airless tire specifically includes the following steps:

S1. Obtain radial stiffness characteristic data of a pneumatic-free tire by test method. The radial stiffness characteristic data of a pneumatic-free tire includes the vertical load at the center of the tire and the corresponding vertical displacement.

The radial stiffness test of the airless tire was carried out using the multifunctional test bench for tire mechanical properties built in the laboratory, using the following test scheme:

S1.1, assemble the airless tire onto the tire mounting shaft of the test bench, calibrate the tire slip angle to zero using the slip angle adjustment mechanism, adjust the vertical position of the tire mounting shaft, use the cardboard inspection method to determine the contact between the tire and the test platform, use the load sensor signal when the tire is just in contact with the test platform as the initial load for zero calibration, and record the initial distance L1 between the top edge of the first gantry support and the top edge of the second gantry support of the test bench at this time;

S1.2, use the compression feed hand wheel to manually apply one turn of feed each time to gradually load the airless tire, and read and record the vertical load size at the center of the airless tire displayed on the signal display at this time;

S1.3, repeat the operation of S1.2 until the deformation of the airless tire has no obvious change, then end this group of tests, and record the end distance L2 between the top edge of the first gantry support and the top edge of the second gantry support, as well as the total number of tests m (including the initial value) of this group of tests;

S1.4, release the vertical load applied to the airless tire and leave it to stand for at least 2 hours to allow the tire to return to its initial state;

S1.5. Repeat the operations of S1.1, S1.2 and S1.3. Calculate the change in the vertical displacement L0 of the tire each time the handwheel is fed one circle in each group of tests by the formula L0=(L1+L2)/(m-1). Taking into account the non-technical errors in the test, take the average value of the three groups of tests as the test result L0', and you can get the radial stiffness characteristic data of the airless tire, that is, the vertical load at the center and the corresponding vertical displacement x=n*L0', where n is the number of feed circles and n≥1.

S2, constructing a nonlinear fitting model for radial stiffness of airless tires

By observing and analyzing the test data of vertical load and vertical displacement at the center of the airless tire shown in Figure 3, it can be seen that the vertical load at the center of the airless tire increases nonlinearly first and then linearly with the increase of the vertical displacement of the tire. Taking the segmentation point as the dividing point, it is divided into two parts, nonlinear and linear. The specific position of the segmentation point needs to be found through the following steps, and the experimental test data is divided into two parts, front and back, based on the segmentation point, and nonlinear fitting and linear fitting are performed respectively.

S2.1, observe and analyze Figure 3. The data before the 22nd point show obvious nonlinearity and the data after the 28th point show obvious linearity. Therefore, determine the interval range of the segmentation points and select the endpoint values N ₁ and N ₂ as 22 and 28.

S2.2, the segmentation points are respectively taken as data points 22, 23, 24, 25, 26, 27, 28 within the interval selected by S2.1. Taking the segmentation points as the dividing points, all the test data are divided into two parts, namely, nonlinear data points and linear data points. The vertical load _F1 at the center of the tire which presents a nonlinear relationship with the vertical displacement x of the airless tire and the vertical load _F2 at the center of the tire which presents a linear relationship with the vertical displacement x of the airless tire are respectively fitted with the segmented polynomials shown in formula (1). The values of the highest degree n of the nonlinear polynomial are tried to be 2, 3, and 4. It is found that when n is 2, the fitting effect is good. Considering the complexity of the polynomial model and the fitting effect, the highest degree n of the nonlinear polynomial is selected to be 2.

Where: _F1 is the vertical load at the center of the tire that presents a nonlinear relationship with the vertical displacement x of the airless tire, n is the highest order of the nonlinear polynomial, _pi is the coefficient of the nonlinear polynomial, _N1 and _N2 are the endpoint values of the interval where the segmentation point is located, M ^* is the optional position in the interval where the segmentation point is located, _F2 is the vertical load at the center of the tire that presents a linear relationship with the vertical displacement x of the airless tire, _q1 and _q0 are the coefficients of the linear polynomial, x is the vertical displacement of the airless tire obtained from the test, _y1 is the first data point of the vertical displacement of the airless tire, is the M*th data point of the vertical displacement of the airless tire, and y _N is the Nth data point of the vertical displacement of the airless tire.

S2.3, all the data obtained from the test are divided into nonlinear part and linear part with the segmentation points as breakpoints, and the airless tire load segmentation fitting as shown in formula (2) is performed respectively, and the fitting determination coefficient R-square is recorded, as shown in FIG4, and then the size of R-square and 99.95% is judged, and finally the data points 22, 23, 24, and 25 with the determination coefficient R-square not less than 99.95% are selected to narrow the optional range of segmentation points;

Among them: A, B, C are nonlinear polynomial coefficients, K, D are linear polynomial coefficients.

S2.4, set the evaluation index δ (such as formula (3)), calculate the δ value of the segmentation points (22, 23, 24, 25) obtained in S2.3, as shown in Figure 5, the δ value comparison chart of the segmentation points of the segmentation polynomial fitting model (in order to better analyze the δ value change trend, Figure 5 shows the segmentation points of all data points 22, 23, 24, 25, 26, 27, 28 in the interval selected by S2.1). As shown in Figure 5, when M is 26, the δ value is the minimum value of 0.33%, but when M is greater than 25, the R-square value of the linear part in the segmentation polynomial model is lower than 99.95%, which does not meet the requirements of S2.3. The segmentation point δ value with the second minimum value 25 (the 25th data point) is selected as the final segmentation point M;

Wherein: F ₁ 'is the first-order derivative of the fitted nonlinear polynomial to the vertical displacement, and F ₂ 'is the first-order derivative of the fitted linear polynomial to the vertical displacement.

S2.5, based on the selected segment point M as the 25th data point, all the data are subjected to nonlinear fitting and linear fitting respectively, as shown in Figures 6(a) and (b), and a piecewise polynomial as shown in formula (4) is fitted, which is the piecewise polynomial fitting model of the vertical force of the airless tire.

Wherein: _y25 is the 25th data point of the vertical displacement of the airless tire, and _yN is the Nth data point of the vertical displacement of the airless tire.

The vertical force piecewise polynomial fitting model of the airless tire obtained in S2.5 is used to obtain the first-order derivative of the vertical displacement x of the airless tire to obtain the nonlinear fitting model of the radial stiffness of the airless tire as shown in formula (5).

A method for constructing a vibration reduction system model of a pneumatic tire-free vehicle, wherein the vibration reduction system is formed by coupling a pneumatic tire 7 with a hybrid electromagnetic active suspension 1. When the radial stiffness k _u of the pneumatic tire is substituted into the dynamic model of the pneumatic tire-hybrid electromagnetic active suspension vibration reduction system, it is slightly different from formula (5), as shown in formula (6):

Among them, _zu - _zr is the dynamic displacement of the pneumatic tire, and _z0 is the static load radius of the pneumatic tire when the vehicle is statically loaded.

FIG7 is a diagram of the dynamic model of the air-free tire-hybrid electromagnetic active suspension vibration reduction system. Furthermore, the dynamic differential equation of the air-free tire-hybrid electromagnetic active suspension vibration reduction system is established as shown in formula (7). The active control strategy adopts the skyhook control strategy.

Among them, _ms is the sprung mass, _mu is the unsprung mass, is the vertical acceleration of the sprung mass, _ks is the spring stiffness, zs _is the vertical displacement of the sprung mass, _zu is the vertical displacement of the unsprung mass, /> is the vertical velocity of the sprung mass, /> is the vertical velocity of the unsprung mass, is the vertical acceleration of the unsprung mass, _cs is the damping coefficient, _csky is the ceiling damping coefficient, _ku is the radial stiffness of the tire; u is the motor force, specifically the ceiling damping force; _zr is the random road excitation input, which is simulated by filtered white noise as shown in formula (8); frequency _f0 = _vn00 , v is the vehicle speed, which is 10 m/s, the lower limit cutoff spatial frequency _n00 = 0.011 m ^-1 ; the standard spatial frequency _n0 = 0.1 m ^-1 ; _Gq ( _n0 ) is the road roughness coefficient, which is 64× ^{10-6 m3} (level b); w(t) is the random Gaussian filtered white noise.

Table 1 Structural parameters of hybrid electromagnetic active suspension

According to the above formulas (7) and (8), combined with the data in Table 1, a new vibration reduction system model of a two-degree-of-freedom 1/4 airless tire-hybrid electromagnetic active suspension is built in MATLAB/Simulink, and the vehicle dynamic performance evaluation index response diagrams (body acceleration, suspension dynamic deflection, tire dynamic load, respectively) of the system are obtained by simulation as shown in Figures 8(a), (b), and (c). The response diagrams are analyzed respectively. The body acceleration response range is -2 to 2m/ ^s2 , and the root mean square value is 0.6398m/ ^s2 . The suspension dynamic deflection response range is -0.015 to 0.015m, and the root mean square value is 0.0055m. The tire dynamic load range is -2000 to 2000N, and the root mean square value is 769.2316N. Although the body acceleration response and tire dynamic load response are both increased compared with traditional conventional pneumatic tires, the radial stiffness of the airless tire is increased compared with conventional tires, so the result is normal. Therefore, the construction method of the vibration reduction system model of the airless tire vehicle is practical and correct.

The embodiments are preferred implementations of the present invention, but the present invention is not limited to the above-mentioned implementations. Any obvious improvements, substitutions or modifications that can be made by those skilled in the art without departing from the essential content of the present invention belong to the protection scope of the present invention.

Claims (6)

1. A method for constructing a vibration reduction system model of a pneumatic tire-free vehicle, characterized in that: a dynamic model of a pneumatic tire-hybrid electromagnetic active suspension vibration reduction system is constructed, and the dynamic differential equation corresponding to the dynamic model is: The radial stiffness k _u of the pneumatic-free tire satisfies the following radial stiffness nonlinear fitting model: The radial stiffness nonlinear fitting model is obtained by obtaining the first-order derivative of the vertical displacement x of the air-free tire using the vertical force piecewise polynomial fitting model of the air-free tire; The vertical force piecewise polynomial fitting model of the airless tire is: Where: _ms is the sprung mass, _mu is the unsprung mass, is the vertical acceleration of the sprung mass, _ks is the spring stiffness, zs _is the vertical displacement of the sprung mass, _zu is the vertical displacement of the unsprung mass, /> is the vertical velocity of the sprung mass, /> is the vertical velocity of the unsprung mass, /> is the vertical acceleration of the unsprung mass, _cs is the damping coefficient, _csky is the ceiling damping coefficient, u is the motor power, _zr is the random road excitation input, _ku is the tire radial stiffness, _z0 is the static load radius of the airless tire when the vehicle is statically loaded, x is the vertical displacement of the airless tire obtained from the test, _y25 is the 25th data point of the vertical displacement of the airless tire, and _yN is the Nth data point of the vertical displacement of the airless tire. 2. The method for constructing a vibration reduction system model of a vehicle with an airless tire according to claim 1 is characterized in that the vertical force piecewise polynomial fitting model of the airless tire is obtained in the following way: using the 25th data point in the test data to perform nonlinear fitting and linear fitting on the relationship between the vertical load at the center of the airless tire obtained in the test and the vertical displacement of the airless tire, respectively. 3. The method for constructing a vibration reduction system model of a pneumatic tire-free vehicle according to claim 2 is characterized in that the 25th data point in the test data is determined by selecting a data point with a determination coefficient R-square not less than 99.95% and a minimum evaluation index δ. 4. The method for constructing a vibration reduction system model of a pneumatic tire-free vehicle according to claim 1, characterized in that Wherein, F ₁ ' is the first-order derivative of the fitted nonlinear polynomial to the vertical displacement, F ₂ ' is the first-order derivative of the fitted linear polynomial to the vertical displacement, and y _M* is the M*th data point of the vertical displacement of the airless tire. 5. The method for constructing a vibration reduction system model of a pneumatic tire-free vehicle according to claim 1 is characterized in that the vertical displacement x=n*L0', L0' is the average value of the tire vertical displacement change L0 for each handwheel feed of one circle in multiple groups of tests, n is the number of feed circles, and n≥1; the L0=(L1+L2)/(m-1), L1 is the initial distance between the top edge of the first gantry bracket and the top edge of the second gantry bracket, L2 is the terminal distance between the top edge of the first gantry bracket and the top edge of the second gantry bracket, and m is the total number of tests in a certain group of tests. 6. The method for constructing a vibration reduction system model of a pneumatic tire vehicle according to claim 1, characterized in that the pneumatic tire-hybrid electromagnetic active suspension vibration reduction system is formed by coupling a pneumatic tire with a hybrid electromagnetic active suspension.