CN112287465B - A Real-time Simulation Method for In-Plane Tire Flexible Ring Model - Google Patents
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Abstract
一种面内轮胎柔性环模型实时仿真的实现方法，该方法是建立轮胎柔性环模型，将轮胎带束部分简化成用一系列弹簧单元连接的质量点，胎侧部分和轮胎内的压缩空气简化成弹簧阻尼单元；在带束部分弯曲特性建模时采用一种线性化的表达方式，降低模型的非线性程度，提高模型的计算效率；模型求解过程中结合使用具有二阶收敛速度的牛顿迭代法和具有无条件收敛特性的Newmark方法，使模型解算速度能够满足实时仿真的要求。
A method for realizing real-time simulation of an in-plane tire flexible ring model. The method is to establish a tire flexible ring model, simplify the tire belt part into a mass point connected by a series of spring elements, and simplify the sidewall part and the compressed air in the tire. It is a spring damping element; a linear expression is used in the modeling of the bending characteristics of the belt part, which reduces the nonlinear degree of the model and improves the calculation efficiency of the model; the Newton iteration with the second-order convergence speed is used in the model solution process. method and the Newmark method with unconditional convergence characteristics, so that the model solving speed can meet the requirements of real-time simulation.
Description
Technical Field
The invention relates to a method for realizing real-time simulation of an in-plane tire flexible ring model, and belongs to the technical field of tire flexible ring model modeling.
Background
The tire is the only part of the vehicle contacting with the road surface, transmits the acting force of the road surface to the vehicle, and the performance index of the whole vehicle is closely related to the mechanical property of the tire, so that the vehicle dynamics simulation analysis needs an accurate and efficient tire model.
At present, tire models are classified into the following categories according to different applicable frequency ranges: the method is suitable for a tire steady-state model with the tire motion input frequency lower than 8 Hz; the method is suitable for a tire rigid ring model with the tire motion input frequency lower than 80 Hz; the method is suitable for the tire flexible ring model with the tire motion input frequency higher than 80 Hz; the method is theoretically suitable for the tire finite element model with the tire motion input frequency of any value. The tire steady-state model and the rigid ring model are limited in tire motion input frequency range, the tire finite element model is huge in calculation amount and cannot be used in the whole vehicle dynamics simulation, and therefore the establishment of the tire flexible ring model with high calculation efficiency and high calculation precision is always a research hotspot of the tire model
The modeling method of the tire flexible ring model mainly comprises the following steps: the first is to discretize the tire belt into a series of mass points or concentrated masses connected by spring damping units, the sidewall portions and the compressed air being represented by spring damping units; the second is to represent the tire belt portion by a beam unit, and the sidewalls and compressed air by a spring damping system; and thirdly, simplifying the finite element model of the tire into a layer of composite shell elements. The beam unit and the shell unit are added into the model, so that the calculation consumption is increased, and real-time simulation is difficult to perform, so that the first tire flexible ring model modeling method is more common. In order to enable the tire model to have real-time simulation capability, a reasonable model structure and a rapid solving algorithm are of great importance.
In many documents relating to tire flex-ring models, modeling relating to belt tensile mechanical characteristics and modeling relating to compressed air in the sidewalls and tires are substantially linear, but there is a large room for improvement in modeling of belt bending characteristics and in model solution algorithms. At present, inverse trigonometric functions are introduced into the modeling of the belt bending characteristics, so that the nonlinearity degree of the model is increased, and the calculation efficiency of the model is reduced; in order to avoid the computational consumption caused by modeling of the belt bending characteristics, even without modeling the belt bending characteristics, some researchers do not accurately express the ground contact characteristics of the tire, which is obviously inaccurate. In the aspect of solving the algorithm, some documents adopt ODE solvers carried by commercial software MATLAB, and some documents do not refer to the specific solving algorithm of the model.
As described above, in order to obtain a tire flexible ring model which has high calculation efficiency, high calculation accuracy, and can be simulated in real time, a belt bending characteristic modeling method having a high degree of linearization and a calculation algorithm having high calculation efficiency are required.
Disclosure of Invention
The invention provides a method for realizing real-time simulation of an in-plane tire flexible ring model, and particularly introduces a belt bending characteristic modeling method with high linearization degree in the model and a solving algorithm with high calculation efficiency. The established tire flexible ring model not only has higher precision, but also has real-time simulation capability, and can be used for the complete vehicle dynamics simulation.
A method for realizing real-time simulation of an in-plane tire flexible ring model comprises the following steps:
building a flexible ring model of the tire, simplifying a belt part of the tire into mass points connected by a series of spring units, and simplifying compressed air in a sidewall part and the tire into spring damping units. A linear expression mode is adopted during modeling of the bending characteristic of the beam part, the non-linear degree of the model is reduced, and the calculation efficiency of the model is improved. In the model solving process, a Newton iteration method with second-order convergence speed and a Newmark method with unconditional convergence characteristics are combined, so that the model solving speed can meet the requirement of real-time simulation. The method specifically comprises the following steps:
firstly, dispersing a belt beam part into a plurality of mass points which are uniformly distributed, wherein the belt beam mass points are connected through an extension spring and a bending spring; the mass point and the rim are connected through a series of spring damping units to simulate compressed air in a tire sidewall part and a tire; the tread is discretized into a series of elastic elements for calculating the contact force of the tire with the road surface.
And secondly, the acting force between the mass points, which is received due to the deformation of the bending spring, is subjected to linearization treatment, so that the acting force of the bending spring, which is received by the mass points, is only linearly related to the displacement of the mass points, an inverse trigonometric function with high nonlinear degree is not introduced any more, and the nonlinear degree of belt bending characteristic modeling is reduced.
And thirdly, combining and using a Newton iteration method with second-order convergence speed and a Newmark method with unconditional convergence characteristics in the model resolving process. And converting the model kinetic equation set into a linear equation set by a Newmark method, and then solving the linear equation set by a Newton iteration method.
The invention has the beneficial effects that:
1. the invention has the advantages of high applicable frequency range, accurate calculation and capability of carrying out real-time operation.
2. The invention solves the problem of high nonlinearity of the traditional tire flexible ring model with the restraint bending characteristic modeling, reduces the complexity of the model, and plays an important role in accurate and real-time operation of the model.
3. The invention can carry out the solving algorithm of the real-time operation of the model; the time for solving is saved, and the real-time performance is realized.
Drawings
FIG. 1 is a schematic structural diagram of an in-plane tire flexible ring model built by the present invention.
FIG. 2 is a schematic view of a tread model in the tire model established by the present invention
FIG. 3 is a graphical illustration of bending force linearization.
Detailed Description
A method for realizing real-time simulation of an in-plane tire flexible ring model comprises the following steps:
first, as shown in FIG. 1, the belt portion is discretized into a plurality of uniformly distributed mass points miMass point miConnected by springs in the circumferential and radial directions of the tire, expressing beltsTensile properties of, three adjacent mass points miThe bending characteristic of the belt is expressed by connecting the two through a bending spring, and the mass point miThe rim accommodates compressed air in the tire and the sidewall of the tire via the spring damping units in the circumferential direction and the radial direction of the tire. As shown in fig. 2, the tread is discretized to be evenly distributed at the mass point miAnd the contact force between the tire and the road surface is calculated through the deformation of the spring.
Two, to mass point miThe mass point m is linearized by the acting force of the bending spring deformationiThe applied force of the bending spring is only linearly related to the displacement of the mass point, an inverse trigonometric function with high nonlinear degree is not introduced any more, and the nonlinear degree of belt bending characteristic modeling is reduced.
The structure shown in figure 3, two rigid rods are connected by a bending spring, and when three points ABC respectively generate displacement uk-1ukuk+1In time, according to the calculation method of the prior literature, the point C is subjected to the acting force F of a bending spring due to the change of & lt ABCk+1The calculation formula is as follows:
in the above formula: k is a radical ofbkIs the bending spring rate; thetakAnd thetak-1The included angles between the BC rod and the AB rod and the Z axis are respectively formed; lkThe length of the projection of the BC pole on the Z axis; wherein with respect to thetakThe solution of (2) involves the application of an inverse trigonometric function, increasing the degree of model non-linearity.
The potential energy of the bending spring is derived by applying the clip theorem to obtain the acting force of the bending spring on the point C due to the change of the & lt ABC. Firstly, calculating the displacement u generated when three points of ABC are respectively displacedk-1ukuk+1The calculation formula of the potential energy V of the time bending spring is as follows:
in the above formula: k is a radical ofbkIs the bending spring rate; u. ofk-1、ukAnd uk+1Displacement of points A, B and C, respectively; lk-1And lkThe lengths of the projection of the AB rod and the BC rod on the Z axis respectively
The action force of a bending spring on the C point obtained by applying the clip theorem due to the change of & lt ABC is as follows:
method for calculating bending force of the invention requires thetakSatisfies thetak≈tan(θk) In the process of model simulation, when the number of the mass points reaches a certain value, the requirement of theta is completely metk≈tan(θk)。
And thirdly, combining and using a Newton iteration method with second-order convergence speed and a Newmark method with unconditional convergence characteristics in the model resolving process. And converting the model kinetic equation set into a linear equation set by a Newmark method, and then solving the linear equation set by a Newton iteration method.
The basic assumptions of the Newmark method are as follows:
in the above formula
Respectively representing the displacement state, the speed state and the acceleration state of each mass point in the t moment model;
respectively representing the displacement state, the speed state and the acceleration state of each mass point in the t + delta t moment model; Δ t isThe simulation time is not long; γ and β are parameters of the Newmark method, typically β is 0.25 and γ is 0.5;
expressing the speed state and the acceleration state in the t + delta t moment model as a function of the displacement state in the t + delta t moment model through the known states of all the mass points in the t moment model, so that a motion equation set of the t + delta t moment model is converted into an algebraic equation set, and then the algebraic equation set is solved by a Newton iteration method;
the basic format of the Newton iteration method is as follows
In the above formula xkAnd xk+1The values of the variables in the k-th iteration step and the k + 1-th iteration step equation set, f' (x)k) Jacobian matrix f (x) of the kth iteration step equation setk) Is the value of the kth set of iteration step equations.
Due to the local convergence characteristic of the Newton iteration method, the calculation efficiency of the model, the contact change condition of the model, the rolling speed of the model and the like need to be comprehensively considered when the time step is selected
By the bending force calculation method introduced by the invention, the non-linear degree of the model is reduced, so that the solving algorithm of the invention can be smoothly implemented; the currently common bending force calculation method cannot use the solving algorithm mentioned in the invention due to the highly nonlinear characteristic, and generally adopts Runge-Kutta solving algorithm. Solving 1s simulation, the same computer equipment (CPU: Intel i 59600 kf) and the same compiling software (VS2019), the currently common bending force calculation method and Runge-Kutta solving algorithm need about 13s of calculation time, the bending force calculation method and the solving algorithm introduced in the invention need about 0.65s of calculation time, the solving time is saved, and the method has real-time performance.
Claims (1)
1. A method for realizing real-time simulation of an in-plane tire flexible ring model is characterized by comprising the following steps: the method comprises the following steps:
building a flexible ring model of the tire, simplifying a belted part of the tire into mass points connected by a series of spring units, and simplifying compressed air in a sidewall part and the tire into a spring damping unit; a linear expression mode is adopted during modeling of the bending characteristic of the beam-containing part, so that the non-linear degree of the model is reduced, and the calculation efficiency of the model is improved; in the model solving process, a Newton iteration method with second-order convergence speed and a Newmark method with unconditional convergence characteristics are combined, so that the model solving speed can meet the requirement of real-time simulation;
the method specifically comprises the following steps:
firstly, dispersing a belt beam part into a plurality of mass points which are uniformly distributed, wherein the belt beam mass points are connected through an extension spring and a bending spring; the mass point and the rim are connected through a series of spring damping units to simulate compressed air in a tire sidewall part and a tire; discretizing the tread into a series of elastic elements for calculating the contact force of the tyre with the road surface;
secondly, the acting force between the mass points, which is received due to the deformation of the bending spring, is subjected to linearization treatment, so that the acting force of the bending spring, which is received by the mass points, is only linearly related to the displacement of the mass points, and the nonlinear degree of modeling of the belt bending characteristic is reduced;
combining and using a Newton iteration method with second-order convergence speed and a Newmark method with unconditional convergence characteristics in the model resolving process; converting the model kinetic equation set into a linear equation set by a Newmark method, and then solving the linear equation set by a Newton iteration method;
obtaining the acting force of the bending spring on the point C due to the change of the & lt ABC by applying the card theorem to derive the potential energy of the bending spring; firstly, calculating the displacement u generated when three points of ABC are respectively displacedk-1ukuk+1The calculation formula of the potential energy V of the time bending spring is as follows:
the action force of a bending spring on the C point obtained by applying the clip theorem due to the change of & lt ABC is as follows:
in the above formula: k is a radical ofbkIs the bending spring rate; u. ofk-1、ukAnd uk+1Displacement of points A, B and C, respectively; lk-1And lkThe lengths of the projection of the AB rod and the BC rod on the Z axis respectively
Method of calculating bending force requires θkSatisfies thetak≈tan(θk) In the process of model simulation, when the number of the mass points reaches a certain value, the requirement of theta is completely metk≈tan(θk)；
The Newmark method comprises the following steps:
in the above formula
Respectively representing the displacement state, the speed state and the acceleration state of each mass point in the t moment model;
respectively representing the displacement state, the speed state and the acceleration state of each mass point in the t + delta t moment model; Δ t is the time of the simulation; gamma and beta are parameters of a Newmark method, beta is 0.25, and gamma is 0.5;
expressing the speed state and the acceleration state in the t + delta t moment model as a function of the displacement state in the t + delta t moment model through the known states of all the mass points in the t moment model, so that a motion equation set of the t + delta t moment model is converted into an algebraic equation set, and then the algebraic equation set is solved by a Newton iteration method;
the format of the Newton iteration method is as follows
In the above formula xkAnd xk+1The values of the variables in the k-th iteration step and the k + 1-th iteration step equation set, f' (x)k) Jacobian matrix f (x) of the kth iteration step equation setk) Is the value of the kth set of iteration step equations.
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| CN113239450B (en) * | 2021-03-11 | 2022-12-16 | 华南理工大学 | A multi-objective optimization method for interconnected air suspension based on interval analysis |
| CN115096612B (en) * | 2022-05-31 | 2025-04-01 | 中国第一汽车股份有限公司 | A method for testing tire cornering characteristics under dynamic load |
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