CN114654952B - Construction method of vibration reduction system model of inflation-free tire vehicle - Google Patents
Construction method of vibration reduction system model of inflation-free tire vehicle Download PDFInfo
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- B60G17/00—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load
- B60G17/015—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load the regulating means comprising electric or electronic elements
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Abstract
The invention provides a method for constructing a vibration damping system model of a non-pneumatic tire vehicle, in particular to a method for constructing a dynamic model of a vibration damping system of a non-pneumatic tire-hybrid electromagnetic active suspension, wherein radial stiffness of the non-pneumatic tire involved in a dynamic differential equation corresponding to the dynamic model is designed based on a non-linear fitting model of radial stiffness of the non-pneumatic tire, and the accuracy of the dynamic model of the vibration damping system of the non-pneumatic tire-hybrid electromagnetic active suspension is verified by a test.
Description
Technical Field
The invention belongs to the technical field of inflation-free tire vehicles, and particularly relates to a construction method of a vibration reduction system model of an inflation-free tire vehicle.
Background
The vehicle vibration damping system can slow down the impact on the vehicle body caused by uneven road surface, and accelerate the damping of the vibration of the vehicle frame and the vehicle body, thereby improving the running stability of the vehicle. The tire is the only part of the vehicle connected with the road surface, plays roles in supporting an automobile, buffering impact, transmitting driving force and braking force, has the performances of comfort, durability, low rolling resistance, safety and the like, and is one of key parts of a vehicle vibration reduction system.
With the progress of science and technology, the market demand for tires is higher and higher, and particularly the safety performance of the tires is more and more emphasized, the traditional pneumatic tires cannot have very high safety performance due to the limitation of the characteristics, but the inflation-free tires can break through the limitation, have very high explosion-proof and puncture-proof safety performance, and further have the advantages of durability, easiness in processing, economy and the like, and the inflation-free tires have wide market prospects; however, since the inflation-free tire is not a tire realizing cushioning vibration damping performance by means of air pressure, the cushioning vibration damping effect is poor, and compared with the conventional inflation tire, the inflation-free tire is generally heavier, has larger radial rigidity and larger elastic hysteresis; meanwhile, the traditional pneumatic tire has small radial stiffness nonlinear region which can be regarded as linear, and the inflation-free tire has large nonlinear region, so that a dynamic model is complex, the model is difficult to construct, and further, the control research on the dynamic model is difficult.
The passive suspension of the vehicle cannot adapt to complex and changeable external environments due to the fixed parameters, and the semi-active suspension cannot provide enough control force due to the limitation of self-setting; the active suspension can break through the limitation due to the introduction of the actuator, and provides enough control force for the novel vibration damping system of the inflation-free tire-active suspension, and the hybrid electromagnetic actuator and the linear electromagnetic actuator are all actuators commonly used for the active suspension; however, the hybrid electromagnetic actuator has many advantages over the linear electromagnetic actuator, 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 mode, so that the reliability is high, the safety of assembling the inflation-free tire passenger vehicle is improved, on the other hand, the damper in the hybrid electromagnetic active suspension can share the acting force required by part of damping adjustment (or the part related to the suspension speed is acted on with force), and the energy consumption of the system is relatively small; the hybrid electromagnetic actuator can provide better dynamic control and can also perform certain energy recovery, so that the hybrid electromagnetic actuator is more suitable for being applied to a vehicle assembled with a inflation-free tire.
At present, most of domestic and foreign scholars focus on the material application and structural design of the inflation-free tire, the vertical mechanical model of the inflation-free tire is researched, and a novel vibration reduction system for coupling the hybrid active suspension and the inflation-free tire is more complex in vibration reduction performance, and the dynamic model construction method is more recently reported, so that the dynamics control research of the current inflation-free tire vehicle lacks related theoretical references, and the popularization and application of the inflation-free tire vehicle are in urgent need for a new technical method.
Disclosure of Invention
In view of the above, the invention provides a method for constructing a vibration damping system model of a inflation-free tire vehicle, which has high precision and simple method and provides a theoretical basis for dynamic control of the inflation-free tire vehicle.
The present invention achieves the above technical object by the following means.
A construction method of a vibration damping system model of a inflation-free tire vehicle specifically comprises the following steps: a dynamic model of the inflation-free tire-hybrid electromagnetic active suspension vibration reduction system is constructed, and a dynamic differential equation corresponding to the dynamic model is as follows:
radial stiffness k of inflation-free tire u The following radial stiffness nonlinear fitting model is satisfied:
the radial stiffness nonlinear fitting model is obtained by obtaining a first derivative of vertical displacement x of the inflation-free tire by a vertical force piecewise polynomial fitting model of the inflation-free tire;
the vertical force segmentation polynomial fitting model of the inflation-free tire is as follows:
wherein: m is m s For sprung mass, m u In the form of an unsprung mass,for vertical acceleration of sprung mass, k s For spring rate, z s Vertical displacement of sprung mass, z u Vertical displacement of unsprung mass->For the vertical velocity of the sprung mass, +.>For the vertical velocity of the unsprung mass,for vertical acceleration of unsprung mass, c s C is the damping coefficient sky For the damping coefficient of the canopy, u is motor power, z r For random road surface excitation input, k u For radial stiffness of tyre, z 0 The static load radius of the inflation-free tire during static load of the vehicle is that x is the vertical displacement of the inflation-free tire obtained by the test, y 25 25 th data point for vertical displacement of inflation-free tire, y N The nth data point is displaced vertically to avoid inflation of the tire.
According to a further technical scheme, the vertical force segmentation polynomial fitting model of the inflation-free tire is obtained by the following steps: and respectively performing nonlinear fitting and linear fitting on the relationship between the vertical load at the center of the tested inflation-free tire and the vertical displacement of the inflation-free tire by using the 25 th data point in the test data.
In a further technical scheme, the 25 th data point in the test data is determined by selecting the data point with the determination coefficient R-square not lower than 99.95% and the minimum evaluation index delta.
Further technical proposal thatWherein F is 1 ' first derivative of fitted nonlinear polynomial to vertical displacement, F 2 ' first derivative of fitted linear polynomial with respect to vertical displacement, y M * Data points M x for the vertical displacement of the inflation-free tire.
According to a further technical scheme, the vertical displacement x=n×l0', wherein L0' is an average value of tire vertical displacement variation L0 of one circle of hand wheel feeding in a plurality of groups of tests, n is the number of circles of feeding, and n is more than or equal to 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 termination 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 scheme, the inflation-free tire-hybrid electromagnetic active suspension vibration reduction system is formed by coupling an inflation-free tire with a hybrid electromagnetic active suspension.
The beneficial effects of the invention are as follows: the invention firstly builds a non-linear fitting model of radial stiffness of the inflation-free tire, designs the radial stiffness of the inflation-free tire based on the non-linear fitting model of radial stiffness of the inflation-free tire, thereby determining a dynamic model of the inflation-free tire-hybrid electromagnetic active suspension vibration damping system, and has higher accuracy of the dynamic model of the inflation-free tire-hybrid electromagnetic active suspension vibration damping system through test verification.
Drawings
FIG. 1 is a schematic diagram of a model of a non-pneumatic tire-hybrid electromagnetic active suspension vibration reduction system according to the present invention;
FIG. 2 is a flow chart of a method of vertical mechanical modeling of a non-pneumatic tire according to the present invention;
FIG. 3 is a graph of test results data for a non-pneumatic tire according to the present invention;
FIG. 4 is a graph of the determination coefficients R-square of the inflation-free vertical mechanical nonlinear fitting model of the present invention;
FIG. 5 is a graph comparing delta values of optional segment points of a non-linear fit model of a non-pneumatic tire vertical mechanics according to the present invention;
FIG. 6 (a) is a fitted view of a vertical load nonlinear section at the center of a non-pneumatic tire according to the present invention;
FIG. 6 (b) is a fitted view of the vertical load linear portion at the center of the non-pneumatic tire according to the present invention;
FIG. 7 is a dynamic model of a non-pneumatic tire-hybrid electromagnetic active suspension damping system according to the present invention;
FIG. 8 (a) is a graph of the vehicle body acceleration response of the non-pneumatic tire-hybrid electromagnetic active suspension vibration reduction system of the present invention;
FIG. 8 (b) is a graph of the dynamic deflection response of the suspension of the non-pneumatic tire-hybrid electromagnetic active suspension damping system of the present invention;
FIG. 8 (c) is a graph of the dynamic tire load response of the non-pneumatic tire-hybrid electromagnetic active suspension vibration reduction system of the present invention;
wherein: 1-hybrid electromagnetic active suspension, 2-sprung mass, 3-elastic element, 4-hydraulic damper, 5-linear motor, 6-unsprung mass, 7-inflation-free tire.
Detailed Description
The invention will be further described with reference to the drawings and the specific embodiments, but the scope of the invention is not limited thereto.
As shown in fig. 1, the inflation-free tire-hybrid electromagnetic active suspension vibration damping system of the inflation-free tire vehicle of the present invention includes a hybrid electromagnetic active suspension 1 and an inflation-free tire 7; the hybrid electromagnetic active suspension 1 comprises an elastic element 3, a hydraulic damper 4 and a linear motor 5, can bear and transmit vertical load, isolate higher-frequency vibration transmitted to a vehicle body due to uneven road surface, attenuate vertical vibration of the vehicle, absorb vibration energy at the same time, and respectively and fixedly connect two ends of the elastic element 3, the hydraulic damper 4 and the linear motor 5 between a sprung mass 2 and an unsprung mass 6; the inflation-free tire 7 is a vertical mechanical nonlinear inflation-free safety tire, and is coupled with the hybrid electromagnetic active suspension 1 to form a inflation-free tire-hybrid electromagnetic active suspension vibration reduction system.
A method for constructing a vibration reduction system model of a non-pneumatic tire vehicle comprises non-pneumatic tire vertical mechanical modeling and dynamic model construction of the vibration reduction system of the non-pneumatic tire vehicle.
As shown in fig. 2, the vertical mechanical modeling of the inflation-free tire specifically comprises the following steps:
s1, acquiring radial stiffness characteristic data of the inflation-free tire by a test method, wherein the radial stiffness characteristic data of the inflation-free tire comprise vertical loads at the center of the tire and corresponding vertical displacements
The multifunctional test bench for the mechanical properties of the tire constructed in a laboratory is used for carrying out radial stiffness test on the inflation-free tire, and the following test scheme is adopted:
s1.1, assembling a inflation-free tire on a tire mounting shaft of a test bench, zeroing the tire side deflection angle through a side deflection angle adjusting mechanism, adjusting the vertical position of the tire mounting shaft, judging the contact condition of the tire and a test platform by using a card paper inspection method, zeroing by taking a load sensor signal when the tire just contacts the test platform as an initial load, and recording the initial distance L1 between the top edges of a first gantry bracket and a second gantry bracket of the test bench at the moment;
s1.2, manually applying a circle of feeding amount each time through a compression amount feeding hand wheel, gradually loading the inflation-free tire, and reading and recording the vertical load at the center of the inflation-free tire displayed by a signal display at the moment;
s1.3, repeating the operation of S1.2 until the deformation amount of the inflation-free tire is not changed obviously, ending the test set, and recording the termination distance L2 between the top edge of the first gantry bracket and the top edge of the second gantry bracket at the moment, and the total test times m (including an initial value) of the test set;
s1.4, releasing the vertical load applied to the inflation-free tire, and standing for at least 2 hours to restore the tire to be tested to an initial state;
s1.5, repeating the operations of S1.1, S1.2 and S1.3, calculating the vertical displacement variable quantity L0 of the tire fed by the hand wheel for one circle in each group of tests through the formula L0= (L1+L2)/(m-1), taking the average value of 3 groups of tests as a test result L0' in consideration of the non-technical errors in the tests, and obtaining radial stiffness characteristic data of the inflation-free tire, wherein the vertical load at the center and the corresponding vertical displacement x=n are the fed circles, and n is more than or equal to 1.
S2, constructing a radial stiffness nonlinear fitting model of the inflation-free tire
By observing and analyzing the vertical load and vertical displacement test data at the center of the inflation-free tire shown in fig. 3, the phenomenon that the vertical load at the center of the inflation-free tire increases firstly in a nonlinear manner and then in a linear manner along with the increase of the vertical displacement of the tire can be seen, the phenomenon that the vertical load at the center of the inflation-free tire takes a piecewise point as a demarcation point is divided into two parts of nonlinearity and linearity, the piecewise point is specifically located, the following steps are needed to search, and the experimental test data are divided into a front part and a rear part based on the piecewise point, and nonlinear fitting and linear fitting are respectively carried out.
S2.1, observing and analyzing FIG. 3, the data before the 22 nd point shows obvious nonlinearity and the data after the 28 th point shows obvious linearity, thus determining the range of the interval where the segmentation point is located and selecting the endpoint value N thereof 1 、N 2 22 and 28.
S2.2, the segmentation points are respectively taken as data points 22, 23, 24, 25, 26, 27 and 28 in the interval range selected in S2.1, the segmentation points are taken as demarcation points, all data obtained by the test are divided into a nonlinear data point and a linear data point front and back parts, and the vertical load F at the center of the tire which shows nonlinear relation with the vertical displacement x of the inflation-free tire 1 Vertical load F at the center of the tire in linear relation to vertical displacement x of the inflation-free tire 2 Respectively performing piecewise polynomial fitting as shown in formula (1); the numerical value of the highest degree n of the nonlinear polynomial is 2, 3 and 4, when n is found to be 2, the fitting effect is good, the complexity degree and the fitting effect of the polynomial model are comprehensively considered, and the highest degree n of the nonlinear polynomial is selected to be 2;
wherein: f (F) 1 Is the vertical load at the center of the tire which shows nonlinear relation with the vertical displacement x of the inflation-free tire, n is the highest degree of nonlinear polynomial, p i Is a nonlinear polynomial coefficient, N 1 、N 2 For the end point value of the interval where the segmentation point is located, M * For optional position in the interval of the segmentation point, F 2 Is the vertical load at the center of the tire in linear relation with the vertical displacement x of the inflation-free tire, q 1 、q 0 Is a linear polynomial coefficient, x is the vertical displacement of the inflation-free tire obtained by the test, y 1 To move the first data point vertically from the pneumatic tire,data point M x and data point y for vertical displacement of inflation-free tyre N The nth data point is displaced vertically to avoid inflation of the tire.
S2.3, dividing all data obtained by the test into a nonlinear part and a linear part by taking a segmentation point as a breakpoint, respectively carrying out the segmentation fitting of the load of the inflation-free tire as shown in a formula (2), recording a determination coefficient R-square of the fitting, judging the sizes of the R-square and 99.95%, and finally selecting data points 22, 23, 24 and 25 with the determination coefficient R-square not lower than 99.95%, so as to narrow the optional range of the segmentation point;
wherein: A. b, C is a nonlinear polynomial coefficient and K, D is a linear polynomial coefficient.
S2.4, setting an evaluation index delta (such as a formula (3)), calculating delta values of the segmentation points (22, 23, 24 and 25) obtained in S2.3, such as a delta value comparison chart of alternative segmentation points of the segmentation polynomial fitting model of FIG. 5 (for better analysis of delta value change trend, FIG. 5 shows that the segmentation points are all data points 22, 23, 24, 25, 26 and 27 and 28 within a range selected by S2.1), such as FIG. 5, although the delta value is the minimum value of 0.33% when M is 26, when M is more than 25, linear part R-square value of the segmentation polynomial model is lower than 99.95%, the requirement of S2.3 is not met, and a segmentation point delta value sub-small value point 25 (25 th data point) is selected as a final segmentation point M;
wherein: f (F) 1 ' is the first derivative of the fitted nonlinear polynomial with respect to vertical displacement, F 2 ' is the first derivative of the fitted linear polynomial with respect to vertical displacement.
S2.5, according to the 25 th data point of the selected segmentation point M, respectively performing nonlinear fitting and linear fitting on all data, and fitting a segmentation polynomial shown in a formula (4) as shown in fig. 6 (a) and (b), namely, a inflation-free tire vertical force segmentation polynomial fitting model.
Wherein: y is 25 25 th data point for vertical displacement of inflation-free tire, y N The nth data point is displaced vertically to avoid inflation of the tire.
And (3) obtaining a first derivative of the vertical force piecewise polynomial fitting model of the inflation-free tire obtained in the step (S2.5) on the vertical displacement x of the inflation-free tire, and obtaining the radial stiffness nonlinear fitting model of the inflation-free tire as shown in a formula (5).
A construction method of a vibration reduction system model of a inflation-free tire vehicle comprises the steps that the vibration reduction system is formed by coupling an inflation-free tire 7 with a hybrid electromagnetic active suspension 1, and the radial rigidity k of the inflation-free tire is calculated u When substituted into a dynamic model of a non-pneumatic tire-hybrid electromagnetic active suspension vibration reduction system, the dynamic model is slightly different from the formula (5), as shown in the formula (6):
wherein z is u -z r Is the dynamic displacement, z of the inflation-free tyre 0 Is the static load radius of the inflation-free tyre when the vehicle is in static load.
Fig. 7 is a diagram of a dynamic model of a non-pneumatic tire-hybrid electromagnetic active suspension vibration reduction system, and further, a dynamic differential equation of the non-pneumatic tire-hybrid electromagnetic active suspension vibration reduction system is established as shown in formula (7), and an active control strategy adopts a zenith control strategy.
Wherein m is s For sprung mass, m u In the form of an unsprung mass,for vertical acceleration of sprung mass, k s For spring rate, z s Vertical displacement of sprung mass, z u Vertical displacement of unsprung mass->For the vertical velocity of the sprung mass, +.>For the vertical velocity of the unsprung mass,for vertical acceleration of unsprung mass, c s C is the damping coefficient sky Is the damping coefficient, k of the canopy u Is the radial stiffness of the tire; u is motor power, specifically ceiling damping force; z r For random pavement excitation input, performing simulation as shown in a formula (8) by using filtering white noise; frequency f 0 ＝vn 00 V is the running speed of the vehicle, 10m/s is taken, and the lower limit cutoff spatial frequency n 00 ＝0.011m -1 The method comprises the steps of carrying out a first treatment on the surface of the Standard spatial frequency n 0 ＝0.1m -1 ；G q (n 0 ) For road surface unevenness coefficient, 64×10 is taken -6 m 3 (stage b); w (t) is random Gaussian filtered white noise.
Table 1 structural parameters of hybrid electromagnetic active suspension
According to the formulas (7) and (8), combining the data of table 1, building a novel vibration reduction system model of the two-degree-of-freedom 1/4 inflation-free tire-hybrid electromagnetic active suspension in MATLAB/Simulink, and obtaining the vehicle dynamics performance evaluation of the system as shown in fig. 8 (a), (b) and (c) through simulationPrice index (vehicle body acceleration, suspension dynamic deflection and tyre dynamic load) response diagram; respectively analyzing the response graphs, wherein the response range of the acceleration of the vehicle body is-2 m/s 2 Root mean square value of 0.6398m/s 2 The dynamic deflection response range of the suspension is-0.015 m, the root mean square value is 0.0055m, the dynamic load range of the tire is-2000N, and the root mean square value is 769.2316N; although both the vehicle body acceleration response and the tire dynamic load response are increased as compared with the conventional pneumatic tire, the result is also normal because the radial rigidity of the inflation-free tire is increased as compared with the conventional tire, and thus the construction method of the inflation-free tire vehicle vibration damping system model is realistic and correct.
The examples are preferred embodiments of the present invention, but the present invention is not limited to the above-described embodiments, and any obvious modifications, substitutions or variations that can be made by one skilled in the art without departing from the spirit of the present invention are within the scope of the present invention.
Claims (6)
1. A construction method of a vibration damping system model of a inflation-free tire vehicle is characterized by comprising the following steps of: a dynamic model of the inflation-free tire-hybrid electromagnetic active suspension vibration reduction system is constructed, and a dynamic differential equation corresponding to the dynamic model is as follows:
radial stiffness k of inflation-free tire u The following radial stiffness nonlinear fitting model is satisfied:
the radial stiffness nonlinear fitting model is obtained by obtaining a first derivative of vertical displacement x of the inflation-free tire by a vertical force piecewise polynomial fitting model of the inflation-free tire;
the vertical force segmentation polynomial fitting model of the inflation-free tire is as follows:
wherein: m is m s For sprung mass, m u In the form of an unsprung mass,for vertical acceleration of sprung mass, k s For spring rate, z s Vertical displacement of sprung mass, z u Vertical displacement of unsprung mass->For the vertical velocity of the sprung mass, +.>For unsprung mass vertical velocity, +.>For vertical acceleration of unsprung mass, c s C is the damping coefficient sky For the damping coefficient of the canopy, u is motor power, z r For random road surface excitation input, k u For radial stiffness of tyre, z 0 The static load radius of the inflation-free tire during static load of the vehicle is that x is the vertical displacement of the inflation-free tire obtained by the test, y 25 25 th data point for vertical displacement of inflation-free tire, y N The nth data point is displaced vertically to avoid inflation of the tire.
2. The method of constructing a model of a vibration reduction system for a non-pneumatic tire vehicle of claim 1, wherein the vertical force piecewise polynomial fitting model of the non-pneumatic tire is obtained by: and respectively performing nonlinear fitting and linear fitting on the relationship between the vertical load at the center of the tested inflation-free tire and the vertical displacement of the inflation-free tire by using the 25 th data point in the test data.
3. The method of constructing a model of a vibration reduction system for a vehicle having a free pneumatic tire according to claim 2, wherein the 25 th data point in the test data is determined by selecting a data point having a determination coefficient R-square of not less than 99.95% and having the smallest evaluation index δ.
4. The method for constructing a vibration reduction system model of a tire-free vehicle according to claim 1, wherein the following is performedWherein F is 1 ' first derivative of fitted nonlinear polynomial to vertical displacement, F 2 ' first derivative of fitted linear polynomial with respect to vertical displacement, y M* Data points M x for the vertical displacement of the inflation-free tire.
5. The method for constructing a vibration damping system model of a non-pneumatic tire vehicle according to claim 1, wherein the vertical displacement x=n×l0', L0' is an average value of the tire vertical displacement variation L0 of one turn of each hand wheel feed in a plurality of sets of tests, n is the number of turns of feed, and n is not less than 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 termination 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 of constructing a model of a non-pneumatic tire vehicle vibration reduction system according to claim 1, wherein the non-pneumatic tire-hybrid electromagnetic active suspension vibration reduction system is formed by coupling a non-pneumatic tire with a hybrid electromagnetic active suspension.
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