Method for calculating static overturning limit angle of bowing and twisting tractor

Abstract

The invention provides a method for calculating a static overturning limit angle of a bowing and twisting tractor, and aims to accurately evaluate the static stability of the bowing and twisting tractor in a complex posture. The core of the method is to construct a three-dimensional virtual simulation model of bowing and twisting degrees of freedom, and to set a target attitude of any combination. The gradient angle of the tractor reaching the overturning critical state is determined by simulating the iteration increasing process of a cross slope or a longitudinal slope and combining real-time geometric judgment on the position relation between front, rear and whole vehicle mass center projections and corresponding supporting polygons according to specific cross slope and longitudinal slope instability triggering conditions. The method provided by the invention can quantitatively calculate the static stability limit of the tractor in a complex attitude.

Description

Technical Field

[0001] The invention belongs to the technical field of vehicle stability analysis, and in particular relates to a method for calculating the static overturning limit angle of a waist-bending and twisting tractor. Background Art

[0002] Twisting and bending tractors are widely used in agriculture, forestry, and other fields due to their superior terrain adaptability. However, when operating on uneven or sloping terrain, these tractors face significant challenges with lateral and longitudinal rollover stability, which can directly impact the driver's life. Static stability is a fundamental metric for evaluating tractor safety performance, especially at low speeds or when stationary. A tractor's ability to resist lateral (side-to-side roll) and longitudinal (fore-and-aft pitch) rollover is crucial.

[0003] Traditional tractor static stability analysis methods often rely on the projection of the vehicle's center of mass. Stability is assessed by determining whether the projection of the vehicle's center of mass falls within the support polygon formed by the wheel contact points. These methods are somewhat applicable to conventional tractors, which can be simplified to consist of a front axle and a chassis. However, articulated tractors with a twisting mechanism typically have a more complex articulation system, allowing not only for bending (relative rotation about a vertical axis) but also twisting (relative torsion about a longitudinal axis). For tractors with both bending and twisting freedom, the relative postures of the front and rear chassis are extremely diverse, resulting in an extremely complex and variable position of the tractor's overall center of gravity, the geometry of the support polygon, and its relationship to the projection of the center of mass. Therefore, the field currently lacks an effective method that fully considers the coupled effects of bending and twisting and accurately calculates the static tipping limit angle of tractors with bending and twisting in these complex postures. This, to a certain extent, hinders the more refined safety design and assessment of these tractors. To address this technical gap, the present invention proposes a method for calculating the static overturning limit angle of a twisting tractor. Through simplified modeling and systematic iterative analysis, the method aims to effectively determine the static stability boundary of such tractors in complex postures. Summary of the Invention

[0004] The purpose of the present invention is to overcome the technical difficulty in the prior art in accurately quantifying the influence of complex coupling postures on the overturning limit angle of an articulated tractor with both bending and twisting functions when conducting static stability analysis on the articulated tractor. This method constructs a three-dimensional virtual simulation model that can accurately reflect the tractor's geometric parameters, mass distribution, and bending and twisting kinematic characteristics, combines the simulation of posture changes under different ground slope conditions, and uses centroid projection and stability polygon criteria for iterative analysis, aiming to calculate the maximum allowable static transverse and longitudinal slope inclination angles of a bending and twisting tractor under any given combination of bending and twisting angles. The present invention aims to provide a quantitative and reliable analysis tool and technical support for the safety design of bending and twisting tractors and the definition of safe operating range.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] The actual bending and twisting tractor is simplified to establish a virtual simulation model; the virtual simulation model is initialized and various body parameters of the tractor are set; the bending angle and twisting angle to be calculated are loaded and used as input to adjust the posture of the virtual simulation model; after initializing the transverse and longitudinal slope angles to 0°, the transverse and longitudinal slope angles are increased respectively; according to the angle changes, whether the projections of the front body center of mass, the rear body center of mass and the overall center of mass exceed the corresponding stability support boundary, and whether the instability condition is met is evaluated; the transverse and longitudinal slope angles when the projections of the front body center of mass, the rear body center of mass and the overall center of mass exceed the boundary line of the stable area are recorded as the limit stability angle; the limit stability angle data is output to reflect the overturning limit angle of the tractor under the given bending angle and twisting angle. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] Figure 1 It is a flow chart of the method for calculating the static overturning limit angle of a tractor with a bent and twisted waist.

[0008] Figure 2 It is a schematic diagram of the simplified structure of the bending and twisting tractor.

[0009] Figure 3 It is a three-dimensional schematic diagram of the reference posture of the bending and twisting tractor model when it is placed horizontally without bending and twisting angles.

[0010] Figure 4 This is a schematic diagram of the three-dimensional posture of the model of the bending and twisting tractor when the front and rear bending angles are 20° and the front and rear twisting angles are 7.5°.

[0011] Figure 5 It is a three-dimensional schematic diagram of the bending and twisting tractor reaching a lateral static overturning critical angle of 38° when the front and rear bending angles are 20° and the front and rear twisting angles are 7.5°.

[0012] Figure 6 It is a three-dimensional schematic diagram of the bending and twisting tractor reaching a longitudinal static overturning critical angle of 43.9° when the front and rear bending angles are 20° and the front and rear twisting angles are 7.5°.

[0013] Figure 7 It is a three-dimensional surface diagram showing the change of the ultimate transverse slope angle of the bending and twisting tractor vehicle with the bending angle and twisting angle.

[0014] Figure 8 It is a three-dimensional surface diagram showing the change of the ultimate longitudinal slope angle of the bending and twisting tractor vehicle with the bending angle and twisting angle. DETAILED DESCRIPTION

[0015] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and examples. The various embodiments listed in the present invention are only used to illustrate the present invention and are not intended to limit the scope of the present invention. Any obvious modifications or changes made to the present invention do not depart from the spirit and scope of the present invention.

[0016] A method for calculating the static overturning limit angle of a tractor with a bent and twisted waist comprises the following steps:

[0017] S10, simplifying the actual bending and twisting tractor to establish a virtual simulation model;

[0018] S20, initializing the virtual simulation model and setting various body parameters of the tractor;

[0019] S30, loading the waist bending angle and waist twisting angle to be calculated, and using them as input to adjust the posture of the virtual simulation model;

[0020] S40, after initializing the transverse slope and longitudinal slope angles to 0°, respectively increase the transverse slope and longitudinal slope angles;

[0021] S50. Calculate, based on the angle change, whether the projections of the front vehicle center of mass, the rear vehicle center of mass, and the overall center of mass exceed corresponding stability support boundaries, and assess whether an instability condition is met;

[0022] S60. Record the transverse slope and longitudinal slope angles when the projections of the front vehicle body center of mass, the rear vehicle body center of mass, and the overall center of mass exceed the boundary line of the stable area as the ultimate stability angle;

[0023] S70: Outputting the limit stability angle data, reflecting the limit overturning angle of the tractor under the given bending angle and twisting angle.

[0024] Preferably, the step S10 further includes:

[0025] S11. Analyze the physical structure of the target bending and twisting tractor, identifying and extracting the key structural components that primarily influence static stability, including the front and rear bodies, articulated joints, and the four front and rear wheels. Simplify these components to a structure that adequately reflects the primary mass distribution and geometric characteristics of the vehicle.

[0026] S12. Determine the key parameters that characterize the static stability of the tractor, including at least: the mass of the front body, the mass of the rear body, the three-dimensional coordinates of the center of mass of the front body, the three-dimensional coordinates of the center of mass of the rear body, the three-dimensional coordinates of the articulation point, and the reference three-dimensional coordinates of the contact points of each wheel.

[0027] S13. Establish a virtual geometric and physical model of the tractor in a three-dimensional Cartesian coordinate system. The model at least includes: rigid body units representing the front and rear bodies, and assigns corresponding mass and center of mass position attributes to them. Define the spatial position of the hinge point as the pivot point connecting the front and rear bodies. The hinge point is set in the model to allow relative rotation around the vertical axis, i.e., bending motion, and relative rotation around the longitudinal axis, i.e., twisting motion, between the front and rear bodies, while constraining the relative translation between the two and the relative rotation around the lateral axis; define the ground reference point of each wheel, which together constitute the support base surface for stability assessment.

[0028] S14. The defined model geometry information and physical parameters are stored in digital form as a basis for subsequent calculations, wherein the geometry information includes the three-dimensional coordinates of each key point, and the physical parameters include the mass and center of mass position of each main component.

[0029] Preferably, the step S20 further includes:

[0030] S21. Based on actual measurement data or design specifications for a specific tractor model, assign specific values ​​to key parameters in the virtual simulation model established in S10, such as the front and rear vehicle body masses, the three-dimensional coordinates of the front and rear vehicle body centers of mass, the three-dimensional coordinates of the articulation points, and the reference ground coordinates of each wheel. Specific parameter values ​​are as follows: The tractor wheelbase is 1500 mm, and the front and rear wheel tracks are both 1150 mm. The reference position of the articulation point is set above the tractor's longitudinal and transverse centerlines, at a reference height of 450 mm from the ground. The front vehicle body mass is 1550 kg, and its center of mass reference position is located on the tractor's longitudinal centerline, 650 mm forward of the articulation point, and 700 mm above the ground. The rear vehicle body mass is 650 kg, and its center of mass reference position is also located on the tractor's longitudinal centerline, 650 mm behind the articulation point, and 700 mm above the ground.

[0031] S22. Set the initial spatial posture of the model, which is usually a horizontal static state, that is, assume that the bending and twisting tractor is placed on an ideal horizontal ground, and the bending angle, twisting angle, transverse slope angle and longitudinal slope angle are all 0°.

[0032] S23, initializing the key angle variables used to describe the tractor posture and environmental status, that is, setting the initial bending angle, twisting angle, transverse slope angle and longitudinal slope angle to 0°.

[0033] Preferably, the step S30 further includes:

[0034] S31. Set the target posture parameters required for overturning limit angle calculation, and specify the bending rotation angle around the vertical axis and the twisting rotation angle around the longitudinal axis that the front and rear vehicle bodies need to perform relative to the initial state.

[0035] S32. Based on the set target bending angle, the front and rear bodies in the virtual model are subjected to corresponding rotational transformations around the vertical axis, i.e., the Z axis, with the hinge point as a reference, so as to achieve a relative angle in the horizontal plane corresponding to the target bending angle between the two.

[0036] S33. Based on the set target twisting angle, the front and rear bodies in the virtual model are subjected to corresponding rotational transformations around the longitudinal axis, i.e., the X-axis, with the hinge point as a reference, so as to achieve a relative twisting posture between the two corresponding to the target twisting angle.

[0037] S34. Update the real-time three-dimensional coordinates p′ of the model wheel contact point and the front / rear center of mass based on the bending and twisting transformations applied in S32 and S33. Determine the equivalent rotation axis unit vector u, i.e., the unit vector [0,0,1] for Z-axis rotation and the unit vector [1,0,0] for X-axis rotation, and confirm the rotation angle θ entered in S31. Use the Rodriguez formula to calculate the required rotation matrix R(u,θ)

[0038] R(u,θ)=I+sin(θ)K+(1-cos(θ))K 2

[0039] Where I is the 3x3 identity matrix, K is the matrix u=[u x ,u y ,u z ] T The skew-symmetric matrix formed is:

[0040]

[0041] The rotation matrix R corresponding to S32 and S33 is obtained by matrix multiplication 折腰 With R 扭腰 Combined, we get the net rotation matrix R that describes the overall posture adjustment net :

[0042] R net =R 折腰 R 扭腰

[0043] Assume that the coordinate of the hinge point is a, and the coordinate of any key point before rotation is p. Then the new coordinate p′ after rotation is obtained by multiplying the vector (pa) of the point relative to the hinge point by the transpose of the net rotation matrix. Then add the resulting vector back to the hinge point coordinates to get:

[0044]

[0045] That is, the real-time three-dimensional coordinates p′ of the model wheel contact point and the front / rear vehicle center of mass under the target posture parameters.

[0046] Preferably, the step S40 further includes:

[0047] S41. Determine the strategy for increasing the slope in this simulation. One of the following methods can be used: keep the longitudinal slope angle at zero and only gradually increase the transverse slope angle; keep the transverse slope angle at zero and only gradually increase the longitudinal slope angle; gradually increase the transverse slope angle at a preset constant longitudinal slope angle; gradually increase the longitudinal slope angle at a preset constant transverse slope angle.

[0048] S42. Setting the variables of the transverse slope angle and longitudinal slope angle used to simulate the ground inclination to the desired initial values.

[0049] S43, start the iterative process, and perform the following operations in each iterative step: increase the slope angle of the direction selected in step S41 by 0.5°; based on the current accumulated total values ​​of the transverse slope angle and longitudinal slope angle, apply a corresponding global rotation transformation to the entire tractor virtual model including the front and rear bodies, which is intended to simulate the posture of the entire tractor on the inclined ground; update the accumulated rotation state and recalculate the corresponding net rotation matrix R net , and apply the coordinate transformation formula defined in step S34 Updates the real-time 3D coordinates of all key points in the model.

[0050] Preferably, the step S50 further includes:

[0051] S51, obtain the center of mass p of the front vehicle under the current slope angle and fixed bending and twisting angles fcg and the center of mass of the rear vehicle p rcg Real-time three-dimensional coordinates;

[0052] S52, based on the front vehicle mass m f , rear vehicle mass m r And the coordinates of the center of mass of the front and rear vehicles obtained in S51, calculate the comprehensive center of mass p of the vehicle ocg The real-time three-dimensional coordinates of are calculated as follows:

[0053]

[0054] S53, determine p fcg 、p rcg 、p ocg Two-dimensional projection point P on the horizontal reference plane fcg 、P rcg 、P ocg ; And define the stability support polygon area, including the front support polygon composed of the horizontal projection of the front wheel real-time contact point and the horizontal projection of the hinge point, which is usually a triangle; the rear support polygon composed of the horizontal projection of the rear wheel real-time contact point and the horizontal projection of the hinge point, which is usually a triangle; and the overall support polygon composed of the horizontal projection of the real-time contact points of all four wheels, which is usually a quadrilateral. Each polygon is composed of its vertices P0, P1, ..., P n-1 (P i =(x i ,y i ),P n =P0) are defined in sequence;

[0055] S54, using the geometric inclusion relationship judgment algorithm based on vector cross product, by each directed edge P of the polygon i P i+1 Calculate its intersection with the vector (where P is the projection point to be tested (p x ,p y ))'s two-dimensional cross product C i :

[0056] C i =(x i+1 -x i )(p y -y i )-(y i+1 -y i )(p x -x i )

[0057] Judge all C i (For i=0 to n-1) whether the signs are the same, that is, both are non-negative or both are non-positive, check respectively: the projection point P of the center of mass of the front vehicle fcg Whether it is located within or on the boundary of the aforementioned front support triangle; the projection point P of the rear body centroid rcg Whether it is located within or on the boundary of the aforementioned rear support triangle; and the projection point P of the vehicle's integrated center of mass ocg Whether it is located within or on the boundary of the aforementioned overall supporting quadrilateral;

[0058] S55. Based on the results of all three geometric inclusion relationship checks in S54, the current overall stability state of the tractor is determined, and a stability state flag is generated accordingly: if and only if all three centroid projection points fall within or on the boundary of their respective supporting polygons, the state flag is assigned a value indicating "stable"; otherwise, the state flag is assigned a value indicating "unstable." "Unstable" indicates that at least one geometric stability condition is not met, providing preliminary criteria for determining whether the overturning limit has been reached in subsequent steps.

[0059] Preferably, the step S60 further includes:

[0060] S61 . During the slope angle iteration process of S40 , continuously monitor the stability status flag outputted by S50 .

[0061] S62. If the current strategy is to increase the cross slope angle only or to increase it mainly based on the cross slope, then when the stability state flag of S55 indicates "instability" for the first time, it is determined that a critical instability condition has been reached;

[0062] If the current strategy is to only increase the longitudinal slope angle or to increase it mainly based on the longitudinal slope, the critical instability condition is determined to be reached only when the stability status flag of S55 indicates "instability" and the instability is caused by the projection point of the vehicle's integrated center of mass exceeding the overall support quadrilateral area.

[0063] S63. When S62 determines that the critical instability condition is reached, record the slope angle value of the current iteration step, which is the value of the horizontal slope angle or longitudinal slope angle that is increasing in S40. This value is defined as the ultimate stability angle under the specific bending angle and twisting angle set in S30, also known as the static overturning limit angle.

[0064] S64. After recording the ultimate stability angle, stop the slope angle iteration process in the current direction, i.e., the transverse slope direction or the longitudinal slope direction.

[0065] S65. This method may further include: after completing the single-direction test of the transverse slope or longitudinal slope, resetting the slope angle and selecting the untested transverse slope or longitudinal slope direction, repeating the limit angle iterative calculation process to determine the corresponding limit stability angle, thereby obtaining more comprehensive stability information.

[0066] Preferably, the step S70 further includes:

[0067] S71 . Obtain the limit stability angle value recorded in S60 and corresponding to the specific waist bending angle and waist twisting angle input in S30 .

[0068] S72. Outputting the calculated limit stability angle data. The output may include: directly displaying the numerical result; generating a data table containing the input attitude angle and the corresponding limit slope angle; or providing data for drawing a static stability boundary diagram.

[0069] S73. It is clearly stated that the output limit angle is calculated based on the specific input combination of bending angle and twisting angle, reflecting the static overturning critical slope of the bending and twisting tractor under the specific working condition.

Claims

1. A method for calculating the static tipping limit angle of a tractor with a bent and twisted waist, comprising the following steps: S10, simplifying the actual bending and twisting tractor to establish a virtual simulation model; S20, initializing the virtual simulation model and setting various body parameters of the tractor; S30, loading the waist bending angle and waist twisting angle to be calculated, and using them as input to adjust the posture of the virtual simulation model; S40, after initializing the transverse slope and longitudinal slope angles to 0°, respectively increase the transverse slope and longitudinal slope angles; S50. Calculate, based on the angle change, whether the projections of the front vehicle center of mass, the rear vehicle center of mass, and the overall center of mass exceed corresponding stability support boundaries, and assess whether an instability condition is met. S60. Record the transverse slope and longitudinal slope angles when the projections of the front vehicle body center of mass, the rear vehicle body center of mass, and the overall center of mass exceed the boundary line of the stable area as the ultimate stability angle; S70: Outputting the limit stability angle data, reflecting the limit overturning angle of the tractor under the given bending angle and twisting angle.

2. The calculation method according to claim 1, characterized in that The step S10 further includes: S11. Analyze the physical structure of the target bending and twisting tractor, identify and extract the key structural components that have a major impact on static stability, including the front and rear bodies, articulated mechanisms, and the four front and rear wheels, and simplify them into a simplified structure that sufficiently reflects the main mass distribution and geometric characteristics of the vehicle; S12. Determine key parameters characterizing the static stability of the tractor, including at least: the mass of the front vehicle body, the mass of the rear vehicle body, the three-dimensional coordinates of the center of mass of the front vehicle body, the three-dimensional coordinates of the center of mass of the rear vehicle body, the three-dimensional coordinates of the articulation point, and the reference three-dimensional coordinates of the contact points of each wheel; S13. Establish a virtual geometric and physical model of the tractor in a three-dimensional Cartesian coordinate system, the model comprising at least: rigid body elements representing the front and rear bodies, and assigning corresponding mass and center of mass position attributes to each element; defining the spatial position of a hinge point as the pivot point connecting the front and rear bodies, the hinge point being configured in the model to allow relative rotation about a vertical axis, i.e., bending motion, and about a longitudinal axis, i.e., twisting motion, between the front and rear bodies, while constraining relative translation and relative rotation about a lateral axis; and defining a ground reference point for each wheel, such that these points together constitute a support base for stability assessment. S14. The defined model geometry information and physical parameters are stored in digital form as a basis for subsequent calculations, wherein the geometry information includes the three-dimensional coordinates of each key point, and the physical parameters include the mass and center of mass position of each main component.

3. The calculation method according to claim 2, characterized in that The step S20 further includes: S21. Assign specific values ​​to key parameters in the virtual simulation model established in S10, such as the front and rear vehicle body masses, the three-dimensional coordinates of the front and rear vehicle body centers of mass, the three-dimensional coordinates of the articulation points, and the reference ground coordinates of each wheel, based on actual measurement data or design specifications of the specific tractor model; S22, setting the initial spatial posture of the model to a horizontal static state, where the bending angle, twisting angle, horizontal slope angle, and vertical slope angle are all 0°; S23, initializing the key angle variables used to describe the tractor posture and environmental status, that is, setting the initial bending angle, twisting angle, transverse slope angle and longitudinal slope angle to 0°.

4. The calculation method according to claim 3, characterized in that The step S30 further includes: S31, setting target posture parameters for overturning limit angle calculation, respectively specifying the bending rotation angle around the vertical axis and the twisting rotation angle around the longitudinal axis that the front and rear vehicle bodies need to perform relative to the initial state; S32. Based on the set target bending angle, a corresponding rotation transformation around the vertical axis, i.e., the Z axis, is applied to the front and rear bodies in the virtual model with the hinge point as a reference, so as to achieve a relative angle in the horizontal plane corresponding to the target bending angle. S33, based on the set target twist angle, applying corresponding rotational transformations around the longitudinal axis, i.e., the X-axis, to the front and rear bodies of the virtual model with the hinge point as a reference, so as to achieve a relative twisting posture corresponding to the target twist angle between the front and rear bodies; S34. Based on the bending and twisting transformations applied in S32 and S33, update the real-time three-dimensional coordinates p′ of the model wheel contact point and the front / rear vehicle center of mass, determine their equivalent rotation axis unit vector u, i.e., the unit vector [0,0,1] corresponding to the Z-axis rotation; the unit vector [1,0,0] corresponding to the X-axis rotation, and confirm the rotation angle θ input in S31; and use the Rodriguez formula to calculate the required rotation matrix R(u,θ). The rotation matrix R corresponding to S32 and S33 is obtained by matrix multiplication 折腰 With R 扭腰 Combined, we get the net rotation matrix R that describes the overall posture adjustment net : R net =R 折腰 R 扭腰 。 5. The calculation method according to claim 1, characterized in that The step S40 further includes: S41. Determine a strategy for increasing the slope in this simulation. One of the following methods may be used: keep the longitudinal slope angle at zero and gradually increase only the transverse slope angle; keep the transverse slope angle at zero and gradually increase only the longitudinal slope angle; or gradually increase the transverse slope angle at a preset constant longitudinal slope angle; or gradually increase the longitudinal slope angle at a preset constant transverse slope angle; S42, setting the variables of the transverse slope angle and longitudinal slope angle used to simulate the ground inclination to the desired initial values; S43, start the iterative process, and perform the following operations in each iterative step: increase the slope angle of the direction selected in step S41 by 0.5°; based on the current accumulated total values ​​of the transverse slope angle and longitudinal slope angle, apply a corresponding global rotation transformation to the entire tractor virtual model including the front and rear bodies, which is intended to simulate the posture of the entire tractor on the inclined ground; update the accumulated rotation state and recalculate the corresponding net rotation matrix R net , update the real-time 3D coordinates of all key points in the model.

6. The calculation method according to claim 4, characterized in that The step S50 further includes: S51, obtain the center of mass p of the front vehicle under the current slope angle and fixed bending and twisting angles fcg and the center of mass of the rear vehicle p rcg Real-time three-dimensional coordinates; S52, based on the front vehicle mass m f , rear vehicle mass m r And the coordinates of the center of mass of the front and rear vehicles obtained in S51, calculate the comprehensive center of mass p of the vehicle ocg Real-time three-dimensional coordinates; S53. Determine p fcg 、p rcg 、p ocg Two-dimensional projection point P on the horizontal reference plane fcg 、P rcg 、P ocg ; And define the stability support polygon area, including the front triangular support polygon formed by the horizontal projection of the front wheel real-time contact point and the horizontal projection of the hinge point; the rear triangular support polygon formed by the horizontal projection of the rear wheel real-time contact point and the horizontal projection of the hinge point; and the overall support polygon of a quadrilateral formed by the horizontal projection of the real-time contact points of all four wheels, each polygon is composed of its vertices P0, P1, ..., P n-1 (P i =(x i ,y i ),P n =P0) are defined in sequence; S54, using the geometric inclusion relationship judgment algorithm based on vector cross product, by each directed edge P of the polygon i P i+1 Calculate the two-dimensional cross product C with the vector i : C i =(x i+1 -x i )(p y -y i )-(y i+1 -y i )(p x -x i ), Judge all C i Check whether the signs are the same, that is, both are non-negative or both are non-positive: the projection point P of the center of mass of the front vehicle fcg Whether it is located inside or on the boundary of the front support triangle; the projection point P of the rear body center of mass rcg Whether it is located inside or on the boundary of the rear support triangle; and the projection point P of the vehicle's integrated center of mass ocg Whether it is located inside or on the boundary of the overall supporting quadrilateral; S55. Based on the results of all three geometric inclusion relationship checks in S54, determine the current overall stability state of the tractor, and generate a stability state flag accordingly: if and only if all three centroid projection points fall within or on the boundaries of their respective corresponding supporting polygons, assign the state flag a value indicating "stable", otherwise assign it a value indicating "instability".

7. The calculation method according to claim 6, characterized in that: The step S60 further includes: S61. During the slope angle iteration process of S40, continuously monitor the stability status flag output by S50; S62. If the current strategy is to increase the cross slope angle only or to increase the cross slope as the main factor, when the stability state flag of S55 indicates "instability" for the first time, it is determined that the critical instability condition has been reached; If the current strategy is to increase the longitudinal slope angle only or to increase it primarily based on the longitudinal slope, the critical instability condition is determined to have been reached only when the S55 stability status flag indicates "instability" and the instability is caused by the projection of the vehicle's integrated center of mass exceeding the overall support quadrilateral area; S63. When S62 determines that a critical instability condition is reached, the slope angle value of the current iteration step is recorded. The slope angle value is defined as the ultimate stability angle under the set specific bending angle and twisting angle, also known as the static overturning limit angle. S64. After recording the ultimate stability angle, stop the slope angle iteration process in the current direction, i.e., the transverse slope direction or the longitudinal slope direction; S65. After completing the single-direction test of the transverse slope or longitudinal slope, reset the slope angle and select the untested transverse slope or longitudinal slope direction, and repeat the limit angle iterative calculation process to determine the corresponding limit stability angle, thereby obtaining more comprehensive stability information.

8. The calculation method according to claim 7, characterized in that: The step S70 further includes: S71, obtaining the limit stability angle value recorded in S60 and corresponding to the specific waist bending angle and waist twisting angle input in S30; S72, outputting the calculated ultimate stability angle data; S73. It is clearly stated that the output limit angle is calculated based on the specific input combination of bending angle and twisting angle, reflecting the static overturning critical slope of the bending and twisting tractor.

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