Overturning Dynamics Modeling and Characterization Method of Heavy Vehicles under Strong Loads

Abstract

The present invention discloses a method for modeling the overturning dynamics of heavy vehicles under strong loads, comprising the following steps: S1. Respectively establish an inertial coordinate system O-XYZ, a sprung mass coordinate system O s -X s Y s Z s and an unsprung mass coordinate system O x -X x Y x Z x ; S2. Before the tires leave the ground, calculate the vertical deformation δ xti of each tire, the vertical deformation δ sti of each suspension, and calculate the vertical displacement Δz os of the sprung mass center; S3. After the tires leave the ground, calculate the relative position change δ xli of each tire and the deformation δ sli of each suspension, and calculate the vertical displacement Δz osl of the sprung mass and the vertical displacement z xl of the unsprung mass; S4. Calculate the total potential energy V, the total dissipative energy E, and the total kinetic energy T of the vehicle before the tires leave the ground; S5. Calculate the total potential energy V1, the total dissipative energy E1, and the total kinetic energy T1 of the vehicle after the tires leave the ground; S6. Obtain the dynamic model of the vehicle's overturning motion before the tires leave the ground and the dynamic model of the vehicle's overturning motion after the tires leave the ground.

Description

Technical Field

[0001] The present invention belongs to the technical field of heavy vehicle machinery, and particularly relates to a method for modeling and characterizing the overturning dynamics of heavy vehicles under strong loads. Background Art

[0002] Heavy vehicles are large engineering machinery loading and transportation platforms, characterized by large structural dimensions and high center of mass. This makes such vehicles not only vulnerable to the influence of loads such as strong winds in conventional working environments, but also susceptible to the action of shock waves in mission environments, resulting in certain lateral displacement and roll, and even overturning phenomena, which have a great impact on the stability and use safety of the vehicles.

[0003] Currently, the research on vehicle stability mainly focuses on the study of steering rollover stability. Relevant research scholars have established various vehicle rollover dynamics models for different rollover conditions and vehicle types, such as the roll plane model, yaw-roll model, yaw-roll-vertical motion model, multi-body dynamics model, etc. However, due to the prerequisite of the above rollover models that all tires remain in contact with the ground and the lifting of one side of the tires is defined as the critical rollover point of the vehicle, it is impossible to explain the phenomenon that the lifting of one side of the wheels may not cause rollover. In order to study the rollover characteristics after one-sided tire lifting, Mashadi et al. divided the rollover process of the vehicle into two stages before and after one-sided tire lifting, and established an automobile rollover dynamics model respectively; He Linxuan studied the stability characteristics of SUV models before and after tire lifting on this basis, and proposed the vehicle Figure 1 rollover process division curve shown as follows. The vehicle rollover process is divided into three stages: 1) The vehicle tires remain in contact with the ground without lifting, the sprung mass rolls around the roll center, the loads on both sides of the tires change, and the unsprung mass also undergoes a small amount of roll; 2) One side of the unsprung mass is pulled away from the ground, causing one side of the tires to lift off the ground, and the roll motion of the whole vehicle starts to rotate around the ground contact point of the tire on the non-lifted side; 3) The vehicle's center of mass crosses the longitudinal axis of the ground contact point of the tire on the non-lifted side, and the vehicle's gravity accelerates the rollover motion of the vehicle.

[0004] Different from the current research on vehicle rollover during steering, the anti-overturning stability of vehicles mainly studies the lateral translation and rolling motions of vehicles under external loads, and after the external loads disappear, relying on the restoring moment of structures such as suspensions, the vehicle body returns to the static equilibrium position. At present, the research on the anti-overturning characteristics of vehicles under external loads mainly focuses on the influence of strong wind loads on the driving stability of vehicles on bridges. Guo et al. introduced an independent lateral degree of freedom at the contact point between the bridge deck and the tires to analyze the lateral slip of the vehicle relative to the bridge deck; Rocchi et al. measured the average aerodynamic coefficient of large trailers when passing through local areas of bridge towers and used the multi-body dynamics model method to analyze the driving safety problems of large trailers; Chen Ning et al. established a dynamic analysis model for four-axle trailers and two-axle vehicles based on the principle of virtual work and proposed using the dynamic stability equilibrium method to evaluate the rollover driving safety of vehicles according to the rollover accident judgment criterion. Summary of the Invention

[0005] The purpose of the present invention is to overcome the deficiencies of the prior art and provide a method for modeling and characterizing the overturning dynamics of heavy vehicles under strong loads.

[0006] The first object of the present invention is to provide a method for modeling the overturning dynamics of heavy vehicles under strong loads, including the following steps:

[0007] S1. Respectively establish an inertial coordinate system O-XYZ, a sprung mass coordinate system O s -X s Y s Z s and an unsprung mass coordinate system O x -X x Y x Z x ;

[0008] S2. Before the tires leave the ground, based on the coordinate systems established in step S1, calculate the vertical deformation δ xti of each tire. According to the calculated vertical deformation δ xti of each tire, calculate the vertical deformation δ sti of each suspension, and calculate the vertical displacement Δz os of the sprung mass center;

[0009] S3. After the tires leave the ground, based on the inertial coordinate system O-XYZ established in step S1, calculate the relative position change δ xli of each tire. According to the calculated relative position change δ xli of each tire, calculate the deformation δ sli of each suspension, and calculate the vertical displacement Δz osl of the sprung mass and the vertical displacement z xl of the unsprung mass;

[0010] S4. Based on the vertical deformation δ of each tire obtained in step S2 xti , the vertical deformation δ of each suspension sti and the vertical displacement Δz of the sprung mass center os calculate the total potential energy V1, total dissipated energy E1 and total kinetic energy T of the vehicle before the tire leaves the ground;

[0011] S5. Based on the relative position change δ of each tire obtained in step S3 xli , the deformation δ of each suspension sli , the vertical displacement Δz of the sprung mass osl and the vertical displacement z of the unsprung mass xl calculate the total potential energy V2, total dissipated energy E2 and total kinetic energy T of the vehicle after the tire leaves the ground;

[0012] S6. Calculate the generalized force F of the vehicle Q . Based on the generalized force F Q , the total potential energy V1, total dissipated energy E1 and total kinetic energy T of the vehicle before the tire leaves the ground obtained in step S4 or based on the generalized force F Q , the total potential energy V2, total dissipated energy E2 and total kinetic energy T of the vehicle after the tire leaves the ground obtained in step S5, respectively obtain the dynamic model of the vehicle's overturning motion before the tire leaves the ground and the dynamic model of the vehicle's overturning motion after the tire leaves the ground, and finally obtain the dynamic model of the vehicle's overturning motion;

[0013] The dynamic model of the vehicle's overturning motion is as follows:

[0014]

[0015] where V is V1 or V2, E is E1 or E2, V1 is the total potential energy of the vehicle before the tire leaves the ground, V2 is the total potential energy of the vehicle after the tire leaves the ground, E1 is the total dissipated energy of the vehicle before the tire leaves the ground, E2 is the total dissipated energy of the vehicle after the tire leaves the ground, T is the total kinetic energy of the vehicle, q j is the generalized coordinate in the inertial coordinate system, F Q is the generalized force of the vehicle, and when V is V1, E is E1, and when V is V2, E is E2.

[0016] Preferably, step S2 specifically includes the following steps:

[0017] S21. Before the tire leaves the ground, based on the coordinate systems established in step S1, assume that the position vector of each tire relative to point O x is P xti . Then when the roll angle of the unsprung mass is and the pitch angle is θ x , after the deformation of each tire, relative to O xThe position vector P of the point xTi for:

[0018]

[0019] In the formula, and R θ are direction cosine matrices, P xti Before the tire leaves the ground, each tire is relative to O x The position vector of the point;

[0020] The vertical deformation of each tire is xti for:

[0021] δ xti =|(P xTi -P xti )|

[0022] Where P xti Before the tire leaves the ground, each tire is relative to O x The position vector of the point; P xTi is the deformation of each tire relative to O x The position vector of the point;

[0023] S22, the position vector P of each suspension relative to the roll center RC point in the inertial coordinate system Rsti , the position vector P of each suspension relative to the pitch center EC after deformation sTi and the position vector P of each suspension relative to the pitch center EC before deformation sEi Calculate them separately, and then according to the position vector P sTi and P sEi And the vertical deformation of each tire obtained in step S2 xti The vertical deformation of each suspension is calculated as sti And the vertical displacement of the sprung mass center Δz os Perform calculations.

[0024] Preferably, step S3 specifically comprises the following steps:

[0025] S31, after the tire leaves the ground, based on the inertial coordinate system O-XYZ established in step S1, the position vectors of the center of mass of each tire and the unsprung mass relative to the rotation position R in the inertial coordinate system are respectively P xli and P oxl , when the unsprung mass roll angle is and the pitch angle is θ x When the position vector P of the center of mass of each tire and the unsprung mass relative to the position R is calculated, xLi and P oxL ;

[0026] S32. Based on the position vector P obtained in step S31 xli and P xLi , calculate the relative position change δ of each tire xli , and based on the position vector P obtained in step S31 oxl and P oxL , calculate the vertical displacement Z of the unsprung mass xl ;

[0027] S33. Let the position vectors of each suspension position and the center of mass of the sprung mass relative to the relative rotation position R in the inertial coordinate system be P sli and P osl , when the roll angle of the sprung mass is and the pitch angle is θ s , calculate the position vectors P sLi and P osL of each suspension and the center of mass of the sprung mass relative to the position of R;

[0028] S34. Based on the position vectors P sli and P sLi obtained in step S33 and the relative position change δ of each tire obtained in step S32 xli , calculate the deformation δ of each suspension sli , and based on the position vectors P osl and P osL obtained in step S33 and the vertical displacement Z of the unsprung mass obtained in step S32 xl , calculate the vertical displacement Δz of the sprung mass osl .

[0029] The second object of the present invention is to provide a method for characterizing the anti-overturning ability of a heavy vehicle under strong loads, including the following steps:

[0030] (1) According to the obtained dynamic model of the vehicle's overturning motion, determine that the indexes that can characterize the anti-overturning stability ability of the vehicle are the coefficient matrix U of the difficulty degree of the vehicle's own resistance to overturning motion and the safe overturning range φ of the vehicle;

[0031] (2) Take the logarithmic function normalization of the elements u corresponding to each generalized coordinate q in the coefficient matrix U determined in step (1) to obtain:

[0032] u * = log b u

[0033] where b is the base corresponding to u;

[0034] (3) Take the linear normalization of the safe overturning range φ determined in step (1) to obtain:

[0035] φ * = (φ - φ min ) / (φ max - φ min )

[0036] Wherein, φ max and φ min are the maximum and minimum values of φ respectively;

[0037] (3) Connect the u * obtained in step (2) and the φ * obtained in step S3 in series to obtain the anti-overturning stability ability of the vehicle The calculation formula is as follows:

[0038]

[0039] Wherein, u * is the normalized value of element u, and φ * is the normalized value of the safety overturning range φ.

[0040] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0041] (1) Aiming at the overturning motion state of heavy vehicles under the action of strong explosion shock wave loads, according to the motion evolution law before and after the vehicle leaves the ground, a 9-degree-of-freedom overturning dynamics model of heavy vehicles in two stages before and after the tires leave the ground under strong load action is established based on Lagrange's equation. Through experimental comparison, it is found that compared with the experimental measurement, the comparison error of the lateral displacement and yaw angle in the model calculation results is within 10%; the calculated overturning angle of 92° in the first experiment is consistent with the "rollover" state of the experimental vehicle, and the calculated overturning angle of 446° in the second experiment is consistent with the "rollover after flipping" state of the experimental vehicle, verifying the credibility of the model;

[0042] (2) Based on the dynamic model, the influence relationship of the overturning motion is analyzed, and a method for comprehensively characterizing the anti-overturning stability ability of the vehicle by using the difficulty of the vehicle's own resistance to the overturning motion and the vehicle's safety overturning range with a series relationship is proposed, providing a basis for the evaluation of the anti-overturning stability ability of heavy vehicles. Description of the Drawings

[0043] Figure 1 is a schematic diagram of the vehicle's overturning process when leaving the ground;

[0044] Figure 2 is a schematic diagram of the vehicle's rolling motion;

[0045] Figure 3 is a schematic diagram of the vehicle's pitching motion;

[0046] Figure 4 Schematic diagram of the vehicle's overturning motion after the tire leaves the ground

[0047] Figure 5 Schematic diagram of the roll motion after the wheel leaves the ground

[0048] Figure 6 Flow chart of the dynamic model calculation provided by the present invention

[0049] Figure 7 Dynamic pressure damage test diagram carried out in the existing literature

[0050] Among them, Figure 7 (a) is the test of Dongfeng heavy truck; Figure 7 (b) is the double - vehicle test of Dongfeng heavy truck and pick - up truck; Figure 7 (c) is the blast wave simulation device;

[0051] Figure 8 Longitudinal and lateral displacement curve graph

[0052] Figure 9 Yaw angle curve graph

[0053] Figure 10 Overturning angle curve graph

[0054] Figure 11 Vehicle overturning state diagram

[0055] Figure 12 Diagram for characterizing the anti - overturning stability ability of the vehicle Detailed implementation manners

[0056] Hereinafter, exemplary embodiments of the present disclosure will be described in more detail with reference to the accompanying drawings. Although the exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided so that the present disclosure can be more thoroughly understood and the scope of the present disclosure can be fully conveyed to those skilled in the art.

[0057] The overturning motion of a heavy vehicle under strong loads is mainly divided into two stages: First, when the tire has not left the ground, the sprung mass sways around the roll and pitch centers and the unsprung mass rotates slightly around the unsprung mass center of gravity, as well as the translational motion of the whole vehicle in space; Then, after the tire leaves the ground, while the sprung mass and the unsprung mass rotate relative to each other, they together perform a spatial rotation motion around the tire support position that has not left the ground. To facilitate the establishment of the overturning dynamics model of the heavy vehicle, the present invention makes the following assumptions:

[0058] a. During the action of strong loads, the vehicle is completely stationary, and the braking system is fully functional, and there are no motion phenomena such as tire rolling;

[0059] b. The sprung mass and unsprung mass are symmetric about the longitudinal axis of the vehicle;

[0060] c. Ignoring the flexible deformation of the vehicle body, not considering the deformation phenomena such as vehicle body torsion and bending;

[0061] d. Due to the large cornering stiffness, longitudinal slip stiffness and aligning stiffness of special tires under heavy load conditions, ignoring the influence of tire slip and cornering deformation;

[0062] e. Ignoring the position transfer of the roll center and pitch center during the movement;

[0063] f. In the stage after the wheel leaves the ground, regarding the tire system as a rigid body and temporarily not considering the influence of tire blowout on vehicle overturning.

[0064] Based on the above premises and assumptions, taking the longitudinal displacement x, lateral displacement y, yaw angle γ of the whole vehicle; the roll angle pitch angle θ s and vertical displacement z s ; the roll angle of the unsprung mass pitch angle θ x and vertical displacement z x as degrees of freedom, the present invention establishes a 9-degree-of-freedom overturning dynamics model for heavy vehicles, and the method for modeling the overturning dynamics of heavy vehicles under strong loads includes the following steps:

[0065] S1. According to the characteristics of vehicle overturning motion, the schematic diagrams of vehicle roll and pitch motions are decomposed as shown in Figure 2 and Figure 3 respectively. Then, an inertial coordinate system O-XYZ, a sprung mass coordinate system O s -X s Y s Z s and an unsprung mass coordinate system O x -X x Y x Z x are established. The established inertial coordinate system O-XYZ is fixed at the space O, X is the vehicle axis direction, Y is the vehicle lateral direction, and Z is the vertically upward direction; the origin O s -X s Y s Z s of the sprung mass coordinate system coincides with the sprung mass center position; the origin O s of the unsprung mass coordinate system O x -X x Y x Z x coincides with the unsprung mass center position; xCoincide with the unsprung mass center position. Suppose a resultant force vector F of strong load acts on point K of the vehicle, and the absolute position vector of point K relative to the origin O of the inertial coordinate system is L;

[0066] S2. Before the tire leaves the ground, based on the coordinate systems established in step S1, calculate the vertical deformation δ of each tire xti , and based on the calculated vertical deformation δ of each tire xti calculate the vertical deformation δ of each suspension sti , and calculate the vertical displacement Δz of the sprung mass os , which specifically includes the following steps:

[0067] S21. Before the tire leaves the ground, the main movement of the unsprung mass in all directions is caused by the vertical deformation of the tire. Based on the coordinate systems established in step S1, assume that the position vector of each tire relative to point O x is P xti . According to the position conversion relationship, when the roll angle of the unsprung mass is and the pitch angle is θ x , the position vector P x of each tire relative to point O xTi after deformation is:

[0068]

[0069] In the formula, and R θ are both direction cosine matrices, and P xti is the position vector of each tire relative to point O x before the tire leaves the ground;

[0070] and R θ are in the specific forms of:

[0071]

[0072] Then the vertical deformation δ of each tire xti is:

[0073] δ xti =|(P xTi -P xti )|

[0074] In the formula, P xti is the position vector of each tire relative to point O x before the tire leaves the ground; P xTi is the position vector of each tire relative to point O x after deformation;

[0075] S22. Calculate the position vector P of each suspension relative to the roll center RC point in the inertial coordinate system Rsti , the position vector P of each suspension relative to the pitch center EC point after deformation sTi and the position vector P of each suspension relative to the pitch center EC point before deformation sEi respectively. Then, based on the position vectors P sTi and P sEi and the vertical deformation δ of each tire obtained in step S2 xti , calculate the vertical deformation δ of each suspension sti , and calculate the vertical displacement Δz of the sprung mass center os . The calculation formulas for P Rsti , P sTi and P sEi are as follows:

[0076] P Rsti = P sti + P RC

[0077]

[0078] P sEi = P sti + P RC + P Ec

[0079] In the formula, P Rsti is the position vector of each suspension relative to the roll center RC point in the inertial coordinate system, P sti is the position vector of each suspension relative to point O S which is P sti , P sTi is the position vector of each suspension relative to the pitch center EC point after deformation when the sprung mass roll angle is and the pitch angle is θ s , P RC is the position vector of point O S relative to the roll center RC point in the inertial coordinate system, and P EC is the position vector of the RC point relative to the pitch center EC point in the inertial coordinate system;

[0080] Then the vertical deformation δ of each suspension sti is:

[0081] δ sti = |(P sTi - P sEi )| - δ xti

[0082] In the formula, δ xti is the vertical deformation of each tire;

[0083] The vertical displacement of the sprung mass center is composed of the translational displacement of the sprung mass in the vertical direction and the rotational displacements caused by pitching and rolling, i.e.:

[0084]

[0085] P RCS = P RC + P EC

[0086] In the formula, P RCS is the position vector of the sprung mass center O S point relative to the roll center RC point in the inertial coordinate system; P os is the position vector of the sprung mass center O S point relative to the roll center RC point in the inertial coordinate system;

[0087] Then the vertical displacement Δz of the sprung mass center os is:

[0088] Δz os = (P os - P RCS )| z + z s + z x

[0089] In the formula, P RCS is the position vector of the sprung mass center O S point relative to the roll center RC point in the inertial coordinate system, P OS is the position vector of the sprung mass center O S point relative to the roll center RC point in the inertial coordinate system, z s is the vertical displacement of the sprung mass, z x is the vertical displacement of the unsprung mass.

[0090] S3. After the tire leaves the ground, based on the inertial coordinate system O-XYZ established in step S1, calculate the relative position change δ xli of each tire, and according to the calculated relative position change δ xli of each tire, calculate the deformation δ sli of each suspension, and calculate the vertical displacement Δz osl of the sprung mass and the vertical displacement Z xl of the unsprung mass, which specifically includes the following steps:

[0091] S31. After the tire leaves the ground, based on the inertial coordinate system O-XYZ established in step S1, set the position vectors of each tire and the unsprung mass center relative to the relative rotation position R in the inertial coordinate system as Pxli and P oxl , when the unsprung mass roll angle is and the pitch angle is θ x , the position vectors P xLi and P oxL , P xLi and P oxL of each tire and the unsprung mass centroid relative to the R position are calculated as follows:

[0092]

[0093]

[0094] In the formula, R θx and are the direction cosine matrices relative to the R position respectively;

[0095] S32. According to the position vectors P xli and P xLi obtained in step S31, the relative position change δ xli of each tire is calculated, and according to the position vectors P oxl and P oxL obtained in step S31, the vertical displacement Z xl of the unsprung mass is calculated. The calculation formulas for the relative position change δ xli of each tire and the vertical displacement Z xl of the unsprung mass are as follows respectively:

[0096] δ xli =|(P xLi -P xli )|

[0097] z xl =|(P oxL -P oxl ) z |+z x ;

[0098] S33. Let the position vectors of each suspension position and the sprung mass centroid relative to the rotation position R in the inertial coordinate system be P sli and P osl respectively. When the sprung mass roll angle is and the pitch angle is θ s , the position vectors P sLi and P osL of each suspension and the sprung mass centroid relative to the R position are calculated. The calculation formulas for the position vectors P sLi and P osL are as follows respectively:

[0099]

[0100]

[0101] Wherein, R θx is ;

[0102] S34. The position vectors P sli and P sLi obtained according to step S33, and the relative position change δ xli of each tire obtained in step S32 are used to calculate the deformation δ sli of each suspension, and according to the position vectors P osl and P osL obtained in step S33 and the vertical displacement Z xl of the unsprung mass obtained in step S32, the vertical displacement Δz osl of the sprung mass is calculated. The calculation formulas for the deformation δ sli of each suspension and the vertical displacement Δz osl of the sprung mass are respectively as follows:

[0103] δ sli =|(P sLi -P sli )|-δ xli

[0104] Δz osl =|(P osL -P osl ) z |+z xl

[0105] Wherein, z xl is the vertical displacement of the unsprung mass;

[0106] S4. According to the vertical deformation δ xti of each tire, the vertical deformation δ sti of each suspension, and the vertical displacement Δz os of the sprung mass center obtained in step S2, the total potential energy V1, total dissipated energy E1, and total kinetic energy T of the vehicle before the tire leaves the ground are calculated. The calculation formulas for the total potential energy V1, total dissipated energy E1, and total kinetic energy T of the vehicle before the tire leaves the ground are as follows:

[0107]

[0108]

[0109] V ms =m s gΔz os

[0110] V mx = m x gz x

[0111] Wherein, V t , V s , V ms , V mx are respectively the elastic potential energy of the tire system, the elastic potential energy of the suspension system, the gravitational potential energy of the sprung mass, and the gravitational potential energy of the unsprung mass; k t , k si are respectively the stiffness coefficients of the tire and the suspension;

[0112] The total potential energy V1 of the system is:

[0113] V = V t + V s + V ms + V mx

[0114] The dissipated energy of the system is presented by the damping force generated by the deformation of the suspension and the tire. That is:

[0115]

[0116]

[0117] Wherein, E t , c t are respectively the dissipated energy and the damping coefficient of the tire; E s , c si are respectively the dissipated energy and the damping coefficient of the suspension;

[0118] The total dissipated energy E1 of the system is:

[0119] E = E t + E s

[0120] The kinetic energy of the system consists of the rotation and translation of each mass, that is:

[0121]

[0122]

[0123]

[0124] Wherein, T m , T ms , T mx are respectively the kinetic energy of the vehicle mass, the kinetic energy of the sprung mass, and the kinetic energy of the unsprung mass; m is the vehicle mass, J z , J sx , J sy , Jxx and J xy are the moment of inertia of the whole vehicle about the z-axis, the moments of inertia of the sprung mass about the x-axis and y-axis, and the moments of inertia of the unsprung mass about the x-axis and y-axis, respectively.

[0125] The total kinetic energy T of the system is:

[0126] T = T m + T ms + T mx ;

[0127] S5. According to the relative position changes δ xli of each tire obtained in step S3, the suspension deformations δ sli , the vertical displacement Δz of the sprung mass, and the vertical displacement Z of the unsprung mass osl calculate the total potential energy V2, the total dissipated energy E2, and the total kinetic energy T of the vehicle after the tire leaves the ground; xl Different from conventional vehicles, due to their large structural dimensions, heavy vehicles are prone to the phenomenon of non-simultaneous tire lift-off. Coupled with the random distribution of the strong load application positions, the vehicle is also prone to the phenomenon of non-simultaneous lift-off on the same side, which is different from the conventional rollover dynamics. Therefore, in the working condition after the tire leaves the ground, the overturning motion of the heavy vehicle rotates around the instantaneous center where the relative rotational speed is zero. The schematic diagrams of the vehicle overturning motion after the tire leaves the ground are respectively as

[0128] shown in Figure 4 and Figure 5 .

[0129] Assume that at the instant when the wheel leaves the ground: the rotational speed vector of the tire leaving the ground in the inertial coordinate system is ω0, the rotational speed vector of the unsprung mass center O x point is ω mx , and the rotational speed vector of the sprung mass center O s point is ω ms . Based on the assumption c that the flexible deformation of the vehicle body is ignored, according to the spatial geometric relationship, there are two cases for the instantaneous center position determined by the rotational speed vectors ω0, ω mx and ω ms :

[0130] a. The three planes perpendicular to ω0, ω mx and ω ms intersect at a point R w , that is, the vehicle rotates around the R w point after the tire leaves the ground;

[0131] b. The three planes perpendicular to ω0, ω mx and ω ms intersect at an axis R τ , that is, the vehicle rotates around the R τ axis after the tire leaves the ground;

[0132] Assume that after the tire leaves the ground, the vehicle rotates around the R position (R w / R τ ). The calculation formulas for the system kinetic energy and the generalized force are the same as those before the tire leaves the ground. Based on the assumption f, the system potential energy mainly consists of the elastic potential energy of the suspension system, the gravitational potential energy of the sprung mass, and the gravitational potential energy of the unsprung mass; the dissipated energy is composed of the dissipated energy of the suspension damping force, that is:

[0133]

[0134] V msl =m s gΔz osl

[0135] V mxl =m x gz xl

[0136]

[0137] In the formula, V sl , V msl , V mxl , E sl are the elastic potential energy of the suspension system, the gravitational potential energy of the sprung mass, the gravitational potential energy of the unsprung mass, and the suspension dissipated energy respectively after the tire leaves the ground; δ sli is the deformation of each suspension; Δz osl , Z xl are the vertical displacements of the sprung mass and the unsprung mass respectively;

[0138] Then the calculation formulas for the total potential energy V2 and the total dissipated energy E2 of the vehicle after the tire leaves the ground are:

[0139] V2 = V sl +V msl +V mxl

[0140] E2 = E sl ;

[0141] S6. Calculate the generalized force F Q According to the generalized force F Q The total potential energy V1, the total dissipated energy E1, and the total kinetic energy T of the vehicle before the tire leaves the ground obtained in step S4 or according to the generalized force F Q The total potential energy V2, the total dissipated energy E2, and the total kinetic energy T of the vehicle after the tire leaves the ground obtained in step S5 are used to obtain the dynamic model of the vehicle's overturning motion before the tire leaves the ground and the dynamic model of the vehicle's overturning motion after the tire leaves the ground respectively, and finally the dynamic model of the vehicle's overturning motion is obtained;

[0142] The non-conservative force system of the system is the resultant force F of the strong load and the ground friction force f. According to the principle of virtual work, the generalized force F of the system is established. Q It is:

[0143] ∑δW j = F·δr j + f·δr j

[0144]

[0145] In the formula, ∑δW j is the total virtual work of the system, δr j is the generalized virtual displacement, q j is the generalized coordinate in the inertial coordinate system;

[0146] The calculation formula of the generalized force F of the vehicle before and after the tire leaves the ground is the same; Q The dynamic model of the vehicle rollover motion described is:

[0147] The dynamic model of the vehicle rollover motion described is:

[0148]

[0149] In the formula, V is V1 or V2, E is E1 or E2, V1 is the total potential energy of the vehicle before the tire leaves the ground, V2 is the total potential energy of the vehicle after the tire leaves the ground, E1 is the total dissipated energy of the vehicle before the tire leaves the ground, E2 is the total dissipated energy of the vehicle after the tire leaves the ground, T is the total kinetic energy of the vehicle, q j is the generalized coordinate in the inertial coordinate system, F Q is the generalized force of the vehicle, and when V is V1, E is E l When V is V2, E is E2.

[0150] The boundary conditions of the dynamic model of the vehicle rollover motion provided by the embodiments of the present invention mainly include three: initial input quantity, state judgment quantity, and suspension stroke judgment quantity.

[0151] a. The initial input quantity of the model is the resultant force vector F of the strong load and its absolute position vector L acting on the vehicle body position in the inertial coordinate system, as well as the relevant parameters of the vehicle;

[0152] b. The state judgment quantity of the model is the state quantity for judging that the model enters the stage after the wheel leaves the ground from the stage where the wheel does not leave the ground. The key to judging the two stages of vehicle rollover in this article is the appearance of the tire phenomenon of leaving the ground, that is:

[0153] Making F zi = 0.

[0154] Among them, F zi is the vertical force of the tire at position i, F ziIt can be obtained according to the vehicle state balance equation.

[0155] c. The suspension stroke judgment quantity of the model is to check whether the suspension system is stretched / compressed in place during the vehicle rollover process. When the suspension is stretched / compressed in place at a certain position, there will be no relative movement between the sprung mass and the unsprung mass at that position, that is:

[0156] When δ si ≤δ s min or δ s max ≤δ sj , δ si =δ s min / δ s max .

[0157] Among them, δ si is the suspension deformation, and δ s min , δ s max are the extreme values of suspension deformation respectively. Based on this, the calculation process of the vehicle rollover dynamics model under strong load is established as Figure 6 shown;

[0158] 1. Verify the dynamics model provided by the embodiments of the present invention below

[0159] 1.1 Test introduction

[0160] As Figure 7 shown, the literature "Wang Shihe, Ren Huiqi, Zhou Songbai, etc. Experimental research and analysis on anti-impact damage of military vehicles [C] / / Proceedings of the 16th National Symposium on Shock Waves and Shock Tubes, Luoyang, China, 2014(07): 707-712" and the literature "

[17] Ren Huiqi, Huang Kui, Wu Xiangyun, etc. Research progress on the damage of ground targets by air shock wave dynamic pressure [J]. Defense Engineering, 2021, 43(01): 1-9" reported that the Institute of Defense Engineering of the Academy of Military Sciences conducted three dynamic pressure damage test studies on Dongfeng trucks and pickups using a large-scale explosion wave simulation device, which is the same as the research content of the present invention, and its test data can be used as a model comparison for this research.

[0161] Among them, the data of the Dongfeng truck used in the test are shown in Table 1 below, and the measured pressure and acting position at the outlet end of the large-scale explosion wave simulation device in the two independent (the third is a two-vehicle test) dynamic pressure damage tests of the Dongfeng truck are shown in Table 2 below.

[0162] Table 1 Data of the Dongfeng truck used in the test

[0163]

[0164] Table 2 Initial data of the dynamic pressure damage test

[0165]

[0166] 1.2 Model Validation

[0167] Input the vehicle parameters and shock wave action parameters used in the test as initial parameters into the vehicle rollover dynamics model, and calculate the longitudinal and lateral displacements of the whole vehicle, the yaw angle of the whole vehicle, and the roll angle of the unsprung mass under the action of the test shock wave as Figures 8 to 10 shown.

[0168] Compare the Figures 8 - 10 results with the test data as shown in Table 3.

[0169] Table 3 Comparison between Model Calculation Results and Test Data

[0170]

[0171] It can be seen from Table 3 that: compared with the two test data, the comparison errors of the lateral displacement and yaw angle are within 10%; the calculated roll angle of 92° in the first test is consistent with the roll state "rollover" of the test vehicle, and the calculated roll angle of 446° in the second test is consistent with the roll state "rollover after flipping" of the test vehicle; therefore, the accuracy of the model is credible.

[0172] The embodiment of the present invention also provides a method for characterizing the anti-rollover ability of heavy vehicles under strong loads, which specifically includes the following steps:

[0173] (1) According to the obtained dynamics model of vehicle rollover motion, determine the indicators that can characterize the anti-rollover stability ability of the vehicle as the coefficient matrix U of the difficulty degree of the vehicle's own resistance to rollover motion and the safe rollover range φ of the vehicle, specifically:

[0174] By deforming the obtained dynamics model of vehicle rollover motion, we can get:

[0175]

[0176] For the two terms on the left side of the above equation, and are respectively the differential of the partial differential of kinetic energy with respect to the generalized velocity with respect to time and the partial differential of kinetic energy with respect to the generalized coordinate, that is, the generalized inertial force, which is the mechanical characterization of the motion during vehicle rollover; for the three terms on the right side of the equation, F Q is the generalized active force, which is the excitation for generating motion during vehicle rollover; and are respectively the partial differential of potential energy with respect to the generalized coordinate and the partial differential of dissipated energy with respect to the generalized velocity, that is, the generalized anti-rollover force, which is the resistance to motion during vehicle rollover. If we let:

[0177]

[0178]

[0179] Then there is:

[0180] F T = F Q - F k

[0181] In the formula, F T is the generalized inertial force, and F k is the generalized anti-overturning force.

[0182] From the vehicle overturning motion process, it can be seen that the parameters that can characterize the vehicle overturning motion state are mainly: the longitudinal displacement x of the whole vehicle, the lateral displacement y of the whole vehicle, the yaw angle γ of the whole vehicle, the roll angle of the unsprung mass and the pitch angle θ x of the unsprung mass. x, y, and γ characterize the translational motion of the vehicle, θ x characterizes the flipping motion of the vehicle, and together they constitute the vehicle overturning motion under strong load. Then the formula F T = F Q - F k can be transformed into:

[0183]

[0184] In the formula, U is the coefficient matrix,

[0185] For the translational motion parameters, there is

[0186]

[0187] Then, when the strong load force is certain, the main factor affecting the translational motion during the vehicle overturning process is the translational mass matrix M py , and the main factors affecting the flipping motion during the vehicle overturning process are the flipping stiffness matrix M fz -1 K and the flipping damping matrix M fz -1 C. Obviously, M py , M fz -1 K, M fz -1 c are the vehicle's own structural parameters, independent of the strong load acting parameters, belonging to the vehicle's inherent properties, and being the slope of the overturning motion curve. Then they can be used to characterize the difficulty of the vehicle's own resistance to overturning motion.

[0188] According to the influence of the maximum overturning angle on the vehicle body during the vehicle overturning process, the vehicle overturning process can be divided into three states: no overturning and safe recovery, no overturning but damaged during recovery, and overturning, as Figure 11 shown.

[0189] According to the relationship of rotational torque, we have:

[0190]

[0191]

[0192] In the formula, I A is the safety recovery impulse matrix, M fz is the rollover mass matrix, φ is the initial recovery angle (including pitch and roll states), L G is the gravitational torque, and L c is the recovery drag torque.

[0193] The ultimate rollover angle of the vehicle in the safe recovery state can be determined. Obviously, the ultimate rollover angle in the safe recovery state is an inherent parameter of the vehicle itself and is independent of the strong load of the external action. This parameter can be used to characterize the safe rollover range of the vehicle.

[0194] In summary, the anti-rollover stability ability of the vehicle mainly includes two aspects. On the one hand, it is the coefficient matrix U of the difficulty degree of the vehicle itself to resist the rollover movement; on the other hand, it is the safe rollover range φ of the vehicle. The two together form the anti-rollover stability ability of the vehicle. The main structural parameters of the existing Type A, Type B, and Type C vehicles are shown in Table 4 below. Substituting them into the dynamic model of the vehicle rollover movement provided by the embodiment of the present invention to calculate the rollover movement characteristics as Figure 12 shown.

[0195] Table 4 Main structural parameters of three types of vehicles

[0196]

[0197] From Figure 12 it can be seen that: the safe rollover ranges of Type A and Type B vehicles are the same, both being 70°. However, Type A vehicle has a greater stiffness than Type B vehicle and is easier to resist the rollover movement. Therefore, the rollover speed of Type A vehicle is slower than that of Type B vehicle. Then, the anti-rollover ability of Type A vehicle is higher than that of Type B vehicle; when comparing Type A and Type C vehicles, the difficulty degrees of resisting the rollover movement are the same, that is, the rollover speeds are equal. However, Type A vehicle has a larger safe rollover range than Type C vehicle. Then, the anti-rollover ability of Type A vehicle is also higher than that of Type C vehicle. But for Type B and Type C vehicles, dimensionless normalization processing needs to be carried out.

[0198] (2) Take the logarithm function normalization of the elements u corresponding to each generalized coordinate q in the coefficient matrix U determined in step (1) to obtain:

[0199] u * = log b u

[0200] In the formula, b is the base corresponding to u;

[0201] (3) For the safe tipping range φ determined in step (1), since the extreme values are defined within the range of [0, π / 2], linear normalization is performed to obtain:

[0202] φ * =(φ - φ min ) / (φ max - φ min )

[0203] where φ max and φ min are the maximum and minimum values of φ respectively;

[0204] (3) Since the elements u of the coefficient matrix corresponding to each generalized coordinate q and the safe tipping range φ are independent of each other, and their influence on the vehicle tipping motion is in a series structure, multiply the u * obtained in step (2) and the φ * obtained in step S3 to obtain the anti-tipping stability ability of the vehicle The calculation formula of is as follows:

[0205]

[0206] where u * is the normalized value of element u, and φ * is the normalized value of the safe tipping range φ.

[0207] Calculate the anti-tipping abilities of types A, B, and C The values are shown in Table 5 below.

[0208] Table 5 Anti-tipping ability values of three types of vehicles

[0209]

[0210] As can be seen from Table 5: The anti-pitching tipping abilities of each type of vehicle are higher than the anti-roll tipping abilities. The anti-pitching / roll tipping abilities are type A vehicle, type B vehicle, and type C vehicle in sequence. Among them, although the anti-tipping ability values of types B and C are relatively close, numerical presentation can still be obtained through the characterization calculation method. This characterization calculation method provides an important data basis for the next vehicle anti-tipping ability evaluation work.

[0211] In summary, the embodiment of the present invention establishes a 9-degree-of-freedom heavy vehicle tipping dynamics model based on the Lagrange equation, verifies the credibility of the model by combining relevant tests, and discusses and studies the characterization method of the vehicle anti-tipping stability ability, and obtains the following conclusions:

[0212] 1) From the tipping dynamics model before and after the tire leaves the ground, it can be seen that the anti-tipping stability ability of heavy vehicles under strong loads is related to the vehicle's structural parameters, suspension parameters, and tire parameters. From the vehicle tipping dynamics equation, the sprung mass and unsprung mass, each moment of inertia, as well as the stiffness coefficients and damping coefficients of the suspension and tires are the main positive influencing parameters;

[0213] 2) Through experimental comparison, it is found that compared with the experimental measurements, the calculation results of the model: the comparison error of the lateral displacement and yaw angle is within 10%; the calculated tipping angle of 92° in the first experiment is consistent with the "rollover" tipping state of the experimental vehicle, and the calculated tipping angle of 446° in the second experiment is consistent with the "rollover after flipping" tipping state of the experimental vehicle, verifying the credibility of the model;

[0214] 3) Based on the Lagrangian equation of vehicle tipping dynamics, it is proposed that the characterization of the vehicle's anti-tipping stability ability should include the difficulty of the vehicle's own resistance to tipping motion and the safe tipping range of the vehicle. The two together form the vehicle's anti-tipping stability ability, providing a basis for the evaluation of the anti-tipping stability ability of heavy vehicles.

[0215] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and its equivalent technologies, the present invention is also intended to include these changes and modifications.

Claims

1. A method for modeling the overturning dynamics of heavy vehicles under strong loads, characterized in that, It includes the following steps: S1. Establish an inertial coordinate system O-XYZ, a sprung mass coordinate system O s -X s Y s Z s and an unsprung mass coordinate system O x -X x Y x Z x ; S2. Before the tire leaves the ground, based on the coordinate systems established in step S1, calculate the vertical deformation δ of each tire xti , and based on the calculated vertical deformation δ of each tire xti calculate the vertical deformation δ of each suspension sti , and calculate the vertical displacement Δz of the sprung mass center 0s ; S3. After the tire leaves the ground, based on the inertial coordinate system O-XYZ established in step S1, calculate the relative position change δ of each tire xli , and based on the calculated relative position change δ of each tire xli calculate the deformation of each suspension δ sli , and calculate the vertical displacement Δz of the sprung mass osl and the vertical displacement Z of the unsprung mass xl ; S4. Calculate the total potential energy v1, total dissipated energy E xti and total kinetic energy T of the vehicle before the tire leaves the ground based on the vertical deformation δ sti of each tire, the vertical deformation δ 0s of each suspension, and the vertical displacement Δz l of the sprung mass center; S5. Calculate the total potential energy V2, total dissipated energy E2, and total kinetic energy T of the vehicle after the tire leaves the ground based on the relative position change δ of each tire, the deformation amount δ of each suspension, the vertical displacement Δz of the sprung mass, and the vertical displacement Z of the unsprung mass obtained in step S3. xli and the deformation amount δ of each suspension sli the vertical displacement Δz of the sprung mass osl and the vertical displacement Z of the unsprung mass xl Calculate the total potential energy V2, total dissipated energy E2, and total kinetic energy T of the vehicle after the tire leaves the ground; S6. Calculate the generalized force F of the vehicle Q , according to the generalized force F Q , the total potential energy V1, total dissipated energy E of the vehicle before the tire leaves the ground obtained in step S4 l and the total kinetic energy T, or according to the generalized force F Q , the total potential energy V2, total dissipated energy E2 and total kinetic energy T of the vehicle after the tire leaves the ground obtained in step S5, respectively obtain the dynamic model of the vehicle's overturning motion before the tire leaves the ground and the dynamic model of the vehicle's overturning motion after the tire leaves the ground, and finally obtain the dynamic model of the vehicle's overturning motion; The dynamic model of the vehicle's overturning motion is: Wherein, V is V1 or V2, E is E1 or E2, V1 is the total potential energy of the vehicle before the tire leaves the ground, V2 is the total potential energy of the vehicle after the tire leaves the ground, E1 is the total dissipative energy of the vehicle before the tire leaves the ground, E2 is the total dissipative energy of the vehicle after the tire leaves the ground, T is the total kinetic energy of the vehicle, q j is the generalized coordinate in the inertial coordinate system, F Q is the generalized force of the vehicle, and when V is V1, E is E1, and when V is V2, E is E2.

2. The heavy vehicle rollover dynamics modeling method under strong loads according to claim 1, wherein Step S2 specifically includes the following steps: S21. Before the tire leaves the ground, based on the coordinate systems established in step S1, assuming the position vector of each tire relative to point O x is P xti , then when the unsprung mass roll angle is and the pitch angle is θ x , the position vector P x of each tire relative to point O xTi after deformation is: In the formula, and R θ are both direction cosine matrices, and P xti is the position vector of each tire relative to point O x before the tire leaves the ground; Then the vertical deformation δ of each tire xti is as follows: δ xti = |(P xTi - P xti )| where, P xti is the position vector of each tire relative to point O x before the tire leaves the ground; P xTi is the position vector of each tire relative to point O x after deformation; S22. Calculate the position vector P of each suspension relative to the roll center RC point in the inertial coordinate system Rsti , the position vector P of each suspension relative to the pitch center EC point after deformation sTi and the position vector P of each suspension relative to the pitch center EC point before deformation sEi respectively. Then, based on the position vectors P sTi and P sEi and the vertical deformation δ of each tire obtained in step S2 xti calculate the vertical deformation δ of each suspension sti , and calculate the vertical displacement Δz of the sprung mass center 0S .

3. The heavy vehicle rollover dynamics modeling method under strong loads as described in claim 1, characterized in that, Step S3 specifically includes the following steps: S31. After the tire leaves the ground, based on the inertial coordinate system O-XYZ established in step S1, let the position vectors of the centers of mass of each tire and the unsprung mass relative to the rotational position R in the inertial coordinate system be P xli and P oxl . When the roll angle of the unsprung mass is and the pitch angle is θ x , calculate the position vectors P xLi and P oxL of each tire and the center of mass of the unsprung mass relative to the position of R S32. Based on the position vector P obtained in step S31 xli and P xLi , calculate the relative position change δ of each tire xli , and based on the position vector P obtained in step S31 oxl and P oxL , calculate the vertical displacement Z of the unsprung mass xl ; S33. Let the position vectors of each suspension position and the center of mass of the sprung mass relative to the rotational position R in the inertial coordinate system be P sli and P osl . When the roll angle of the sprung mass is and the pitch angle is θ s , the position vectors P sLi and P osL of each suspension and the center of mass of the sprung mass relative to the position of R are calculated; S34. The position vector P obtained according to step S33 sli and P sLi and the relative position change δ of each tire obtained in step S32 xli , calculate the suspension deformation δ sli , and according to the position vector P osl and P osL obtained in step S33 and the vertical displacement Z of the unsprung mass obtained in step S32 xl , calculate the vertical displacement Δz of the sprung mass osl .

4. A method for characterizing the anti-overturning ability of heavy vehicles under strong loads, characterized in that, It includes the following steps: (1) According to the dynamic model of the vehicle's overturning motion obtained in Claim 1, determine that the indicators that can characterize the anti-overturning stability ability of the vehicle are the coefficient matrix U of the difficulty degree of the vehicle's own resistance to overturning motion and the safe overturning range φ of the vehicle; (2) Take the logarithmic function normalization of the elements u corresponding to each generalized coordinate q in the coefficient matrix U determined in step (1) to obtain: u * = log b u In the formula, b is the base corresponding to u; (3) Take the linear normalization of the safe overturning range φ determined in step (1) to obtain: φ * = (φ - φ min ) / (φ max - φ min ) where φ max and φ min are the maximum and minimum values of φ, respectively; (3) Connect the \(u\) obtained in step (2) * and the \(\varphi\) obtained in step S3 * in series to obtain the anti-overturning stability ability of the vehicle The calculation formula is as follows: where u * is the normalized value of element u, and φ * is the normalized value of the safe tipping range φ.

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