A method for calculating dynamic stability limit of a tractor with folded and twisted waist

Abstract

This invention proposes a method for calculating the dynamic stability limit of articulated tractors under cross slope conditions, aiming to accurately assess the lateral stability of articulated tractors under complex terrain and dynamic operating conditions. This method first obtains parameters such as the tractor's geometry, mass, and dynamic acceleration; then, a spatial attitude model is established based on the rear body, transforming the articulation and torsional axes in the local coordinate system of the rear body to the global space, and causing the front body to move relative to the spatial articulation and torsional axes; the spatial coordinates of the four wheel points, articulation points, and centers of mass are calculated, constructing a four-wheel horizontal projection support quadrilateral, and obtaining the dynamic equivalent projection points based on longitudinal and lateral accelerations; by determining the positional relationship of the projection points relative to the left and right rollover boundaries, the critical stability angle of the cross slope is determined. This invention can be used to assess the lateral rollover risk of articulated tractors under different articulation, torsional, terrain undulation, and acceleration / deceleration conditions.

Description

Technical Field

[0001] This invention belongs to the technical field of vehicle stability analysis and agricultural equipment safety assessment, specifically relating to a method for calculating the dynamic stability limit of a folding and twisting tractor on a cross slope. Background Technology

[0002] Articulated tractors, with their small turning radius and strong adaptability to complex terrain, are widely used in agriculture, forestry, hilly and mountainous operations, and special engineering scenarios. Furthermore, articulated tractors, equipped with folding steering and twisting steering functions, can improve wheel contact with uneven ground through the relative rotation and torsion between the front and rear bodies, thereby enhancing vehicle passability and terrain adaptability. However, on slopes, undulating terrain, or when turning, the stability issues of these vehicles become more prominent, especially the risk of lateral rollover on cross slopes, which directly affects vehicle operational safety and driver safety.

[0003] Existing stability analysis methods typically rely on the positional relationship between the center of mass projection and the supporting polygon. This means evaluating tractor stability by determining whether the projected center of mass is located within the support area formed by the wheel contact points. While this method is suitable for traditional tractors, for articulated folding and twisting tractors, there is not only folding and turning motion around the vertical axis between the front and rear bodies, but also relative twisting motion around the longitudinal axis. Furthermore, the folding and twisting axes typically change spatially with the vehicle's attitude, rather than remaining fixed in the global coordinate system. Therefore, directly using traditional planar vehicle models or simple Euler angle stacking methods can easily lead to problems such as inconsistent articulation points between the front and rear bodies, distorted wheel positions, errors in center of mass calculation, and inaccurate support boundary construction.

[0004] Furthermore, tractors are often not completely stationary during actual operation, but rather experience longitudinal acceleration, braking, turning, and complex dynamic conditions. In these situations, the static centroid projection method alone is insufficient to reflect the impact of inertia on the vehicle's cross-slope stability. Especially when the bending angle, twisting angle, terrain height, and acceleration all change simultaneously, the dynamic projection positions of the front, rear, and overall vehicle centroids can all change significantly, causing the vehicle's cross-slope stability limit to exhibit complex nonlinear characteristics. Therefore, current technology still lacks a method that can simultaneously consider the constraints of the bending and twisting spatial mechanism, terrain height input, and dynamic acceleration effects, and effectively calculate the cross-slope stability limit of articulated bending and twisting tractors.

[0005] To address the aforementioned issues, this invention proposes a method for calculating the dynamic stability limit of a hinged and twisted tractor on a cross slope. By establishing the rear vehicle body reference posture, spatial mechanism axis transformation, solving the relative motion of the front vehicle body, inversely solving the terrain height of the four wheels, constructing the four-wheel projection support domain, and performing a dynamic equivalent projection calculation process, this method enables quantitative analysis of the cross slope stability limit of an articulated hinged and twisted tractor under complex postures and dynamic working conditions. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of existing stability analysis methods for articulated articulated and torsional tractors in complex terrain and dynamic operations. These shortcomings include insufficient expression of constraints on the articulation and torsional spatial mechanisms, inaccurate calculation of the relative attitude of the front and rear vehicles, disconnect between the four-wheel terrain height and vehicle attitude solutions, and the impact of dynamic acceleration on cross-slope stability. This invention proposes a dynamic cross-slope stability limit calculation method for articulated articulated and torsional tractors that considers the constraints of the articulation and torsional spatial mechanisms. This method integrates the rear vehicle's spatial attitude, the spatial transformation of the articulation and torsional axes, the relative motion of the front vehicle, the inverse solution of the four-wheel terrain height, the construction of the four-wheel projected support domain, and the dynamic equivalent projection into the stability calculation process. While maintaining the shared articulation points and rigid geometric constraints of the vehicle bodies, it quantitatively calculates the cross-slope stability limit under different articulation angles, torsional angles, terrain heights, and dynamic acceleration conditions. This provides a basis for the safety assessment, structural parameter optimization, and control strategy design of articulated articulated and torsional tractors on slopes.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] This invention proposes a method for calculating the dynamic stability limit of articulated articulated tractors under cross slope conditions, aiming to accurately assess the lateral stability of articulated tractors under complex terrain and dynamic operating conditions. The method first obtains the tractor's geometric parameters, mass parameters, center of mass parameters, articulation angle, twist angle, four-wheel terrain height, and dynamic acceleration parameters. A spatial attitude model is established based on the rear vehicle body, transforming the articulation and twist axes in the local coordinate system of the rear vehicle body to the global space, and causing the front vehicle body to move relative to the spatial articulation and twist axes. The spatial coordinates of the four wheel points, articulation points, and centers of mass are calculated, constructing a four-wheel horizontal projection support quadrilateral, and obtaining the dynamic equivalent projection points based on longitudinal and lateral accelerations. By determining the positional relationship of the projection points relative to the left and right rollover boundaries, the critical stability angle of the cross slope is determined. This invention can be used to assess the lateral rollover risk of articulated tractors under different articulation, twist, terrain undulation, and acceleration / deceleration conditions. Attached Figure Description

[0009] Figure 1 This is a flowchart of a method for calculating the dynamic stability limit of a tractor with a bendable and twisted cross slope.

[0010] Figure 2This is a simplified three-dimensional geometric model of a tractor with a hinged and twisted waist.

[0011] Figure 3 This is a schematic diagram of the initial state for determining cross slope stability when the tractor's bending angle is 30° and its twisting angle is 8°.

[0012] Figure 4 This is a schematic diagram of the limit state for judging cross slope stability when the tractor's bending angle is 30° and its twisting angle is 8°.

[0013] Figure 5 This is a schematic diagram of a typical posture caused by a change in the height of a single wheel, resulting in a twisted waist.

[0014] Figure 6 This is a diagram showing the cross slope stability results caused by the change in the height of a single wheel leading to the twisting of the waist.

[0015] Figure 7 This is a schematic diagram of typical postures under general terrain conditions;

[0016] Figure 8 This is a diagram showing the cross slope stability under typical terrain conditions. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. The embodiments listed herein are merely illustrative and not intended to limit the scope of the invention. Any obvious modifications or alterations made to this invention do not depart from the spirit and scope of the invention.

[0018] A method for calculating the dynamic stability limit of a tractor with a bendable and twisting profile on a cross slope includes the following steps:

[0019] S10. Establish a tractor stability analysis model that includes the geometric parameters, mass parameters, center of mass parameters, bend angle parameters, twist angle parameters, terrain height parameters, and dynamic acceleration parameters of the articulated tractor. Configure attitude solution parameters, geometric verification parameters, and stability judgment parameters. Construct a three-dimensional attitude calculation scene for the articulated tractor based on the input working conditions. Figure 2 As shown, the actual folding and twisting tractor is simplified into a three-dimensional geometric model consisting of a front body, a rear body, hinge points, four wheel points, and a center of mass. Figure 2 The top part represents the actual vehicle structure and its articulation areas, while the middle part extracts the support relationships between the front and rear vehicle bodies and wheel points through "simplification." Figure 2 Further extraction of the front vehicle's center of gravity from the lower part Rear vehicle body weight center The simplified process retains key factors such as the shared hinge points between the front and rear vehicle bodies, the relative motion of bending and twisting, wheel support, and the position of the center of gravity, providing a geometric basis for subsequent attitude solutions and cross slope stability calculations.

[0020] S20. Using the rear vehicle body as the reference vehicle body, establish a spatial attitude model, transform the waist-folding axis and waist-twisting axis defined in the local mechanism coordinate system of the rear vehicle body to the global spatial coordinate system, and make the front vehicle body move relative to the mechanism axis in the global spatial coordinate system.

[0021] S30. Based on the shared hinge point constraint of the front and rear vehicle bodies, solve the pose of the front vehicle body in the global spatial coordinate system, and calculate the spatial coordinates of the front left wheel, front right wheel, rear left wheel, rear right wheel, hinge point, center of mass of the front vehicle body, center of mass of the rear vehicle body and center of mass of the whole vehicle.

[0022] S40. Solve the spatial attitude of the tractor based on the terrain height. Under normal terrain conditions, the rear roll angle, rear pitch angle, rear vertical position and relative waist angle of the front and rear bodies are taken as unknowns. Solve the overall vehicle attitude that satisfies the four-wheel terrain height constraint.

[0023] S50. Perform geometric consistency verification on the attitude solution results, and construct a supporting quadrilateral based on the projection of the four wheel points onto the horizontal plane to obtain the static projection points of the center of mass of the front body, rear body, and the entire vehicle; Figure 3 It can be seen that in the initial posture with a waist-bending angle of 30° and a waist-twisting angle of 8°, , , , The horizontal projections of the four wheel points form a supporting quadrilateral. This represents the initial positional relationship of each projection point relative to the four wheel support boundaries before the cross slope angle increases. (See figure.) , , These represent the front body, rear body, and center of gravity of the vehicle, respectively. , , Indicates the corresponding static projection point; , , Represents the dynamic equivalent projection point.

[0024] S60. Based on the longitudinal acceleration and lateral acceleration, the static projection point of the centroid is dynamically equivalently corrected to obtain the dynamic equivalent projection points of the front body, the rear body, and the whole vehicle.

[0025] S70. Calculate the critical cross slope angle when the dynamic equivalent projection point reaches the corresponding rollover boundary along the left and right cross slope directions, respectively. Use the cross slope angle when any stable object among the front, rear, and entire vehicles reaches the rollover boundary first as the comprehensive cross slope stability limit output. Combined with... Figure 4 It can be seen that as the cross slope angle increases, the static projection points and dynamic equivalent projection points of each centroid will move towards the overturn boundary along the cross slope direction. (The figures marked with apostrophes are shown in the diagram.) , , This represents the static projection point after the change in cross slope. , , This represents the dynamic equivalent projection point after the cross slope changes. When any projection point first reaches the left or right overturn boundary, the corresponding stable object is considered to have reached the critical state of the cross slope, and the comprehensive cross slope stability limit is determined accordingly.

[0026] Preferably, step S10 further includes:

[0027] S11. Define the base points of the articulated folding and twisting tractor, including the articulation points. Front left wheel point Front right wheel point Rear left wheel point and rear right wheel point The set of basic points can be represented as:

[0028]

[0029] in, This represents the set of key points of the tractor; Indicates the hinge point; , , , These represent the wheel points of the front left wheel, front right wheel, rear left wheel, and rear right wheel, respectively. This set serves as the fundamental computational object for the tractor's geometric link, used to subsequently solve for the wheel point spatial coordinates, hinge point consistency, and the four-wheel projected support quadrilateral.

[0030] S12. Define the tractor's mass and center of gravity parameters, including the front body mass, rear body mass, and front body center of gravity. Rear vehicle body weight center and vehicle center of gravity The vehicle's center of gravity is obtained by weighted calculation of the center of gravity of the front and rear vehicle bodies and their corresponding masses; the vehicle's center of gravity can be expressed as:

[0031]

[0032] in, Indicates the vehicle's center of gravity; Indicates the center of gravity of the vehicle in front; Indicates the center of gravity of the rear vehicle; Indicates the mass of the front vehicle body; This represents the mass of the rear vehicle body. The above formula calculates the overall center of gravity of the vehicle based on the masses of the front and rear vehicle bodies and their center of gravity positions, providing a projection object for the vehicle stability criterion.

[0033] S13. Define the tractor's geometric parameters. The tractor's geometric parameters include the position of the front wheel relative to the hinge point, the position of the rear wheel relative to the hinge point, the front wheel track, the rear wheel track, the hinge point height, the local coordinates of the front body's center of gravity, and the local coordinates of the rear body's center of gravity.

[0034] The set of geometric parameters for a tractor can be represented as:

[0035]

[0036] in, Represents the set of geometric parameters of a tractor; , This indicates the positions of the front left and front right wheels in the local coordinate system of the front vehicle body; , This indicates the positions of the left and right rear wheels in the local coordinate system of the rear vehicle body; and These represent the positions of the articulation points in the local coordinate systems of the front and rear vehicle bodies, respectively. and These represent the positions of the center of mass of the front and rear vehicles in their respective local coordinate systems. The tractor geometric parameter set is used to initialize the geometric model of the articulated, folding, and torsional tractor, and to provide basic data for rigid body transformation, wheel point calculation, and geometric consistency verification.

[0037] S14. Define attitude and mechanism angle parameters, including the bend angle. Relative torsional angle between front and rear vehicle bodies Rear body roll angle Rear vehicle pitch angle and the vertical position of the rear vehicle body ;

[0038] The set of attitude variables can be represented as:

[0039]

[0040] in, Represents the set of attitude variables; Indicates the bend angle; Indicates the relative torsional angle between the front and rear vehicle bodies; Indicates the roll angle of the rear vehicle body; Indicates the rear vehicle's pitch angle; This represents the vertical position of the rear vehicle body. The set of attitude variables describes the spatial attitude of the rear vehicle body and the relative motion of the front and rear vehicle bodies, and is the core unknown or input quantity for solving the tractor's three-dimensional geometric state.

[0041] S15. Define terrain input parameters, including the ground height of the front left wheel. Front right wheel ground height Rear left wheel ground height and the ground height of the rear right wheel ;

[0042] The terrain height vector can be represented as:

[0043]

[0044] in, This represents the four-wheel terrain height input vector; , , , These represent the terrain heights corresponding to the front left wheel, front right wheel, rear left wheel, and rear right wheel, respectively. The height input vector is the target height used as the inverse solution for the four-wheel height, which is used to solve for the rear vehicle posture and the relative twist angle between the front and rear vehicles while satisfying the terrain constraints.

[0045] S16. Define dynamic operating parameters, including longitudinal acceleration. lateral acceleration Longitudinal acceleration to gravity ratio The ratio of lateral acceleration to gravity ;

[0046] The dynamic acceleration parameters can be expressed as:

[0047]

[0048] in, Represents a set of dynamic operating condition parameters; Indicates the longitudinal acceleration of the tractor; This indicates the lateral acceleration of the tractor; Represents gravitational acceleration; and These represent the longitudinal and lateral acceleration-to-gravity ratios, respectively. The purpose of the dynamic operating condition parameter set is to calculate the dynamic equivalent projection points, which characterize the impact of acceleration, braking, turning, and combined dynamic operating conditions on the tractor's stability margin.

[0049] S17. Define stability criteria parameters, including the supporting quadrilateral formed by the horizontal projections of the four wheels. Left side boundary Right side boundary Critical stability angle of left cross slope Right cross slope critical stability angle And the comprehensive criterion of cross slope stability angle .

[0050] The comprehensive criterion for cross slope stability can be expressed as:

[0051]

[0052] in, Indicates the cross slope stability angle as a comprehensive criterion; Indicates the front vehicle body's cross slope stability angle; Indicates the rear vehicle body's cross slope stability angle; This represents the vehicle's cross slope stability angle. The above formula unifies the three stable objects—the front body, the rear body, and the entire vehicle—within the same safety evaluation framework. As long as any object reaches the rollover boundary first, the critical angle corresponding to that object is taken as the comprehensive stability limit.

[0053] Preferably, step S20 further includes:

[0054] S21. The local coordinate system of the rear vehicle body is used as the definition reference for the mechanism axes. The bending axis is defined as the vertical steering axis in the local mechanism coordinate system of the rear vehicle body, and the twisting axis is defined as the longitudinal torsion axis in the local mechanism coordinate system of the rear vehicle body. This definition method allows the bending axis and twisting axis to change spatially synchronously with the attitude of the subsequent vehicle body, rather than being fixed in the global coordinate system.

[0055] Establish local mechanism axes for the rear vehicle body, and then transform them into global spatial mechanism axes using the rear vehicle body rotation matrix. The local mechanism axes can be represented as follows:

[0056]

[0057] in, Indicates the direction of the folding axis in the local coordinate system of the rear vehicle body; Indicates the direction of the torsional axis in the local coordinate system of the rear vehicle body; superscript This indicates that the vector is defined in the local coordinate system of the rear vehicle body.

[0058] S22. The spatial position, roll angle, pitch angle and yaw angle of the rear vehicle body are used to establish the homogeneous transformation matrix of the rear vehicle body, which is used to describe the rigid body transformation relationship from the local coordinate system of the rear vehicle body to the global spatial coordinate system.

[0059] The homogeneous transformation matrix of the rear vehicle body can be expressed as:

[0060]

[0061] in, This represents the homogeneous transformation matrix from the local coordinate system to the global coordinate system of the rear vehicle body; This represents the rotation matrix of the rear vehicle body; This represents the translation vector of the rear vehicle body.

[0062] The rear vehicle body rotation matrix can be represented as:

[0063]

[0064] in, , , These represent rotation matrices about the x-axis, y-axis, and z-axis, respectively. , , These represent the roll angle, pitch angle, and yaw angle of the rear vehicle body, respectively. The above formulas generate a spatial rigid body transformation matrix from the rear vehicle body attitude, providing a basis for the global coordinate calculation of wheel points, center of mass, and mechanism axes.

[0065] S23. Using the homogeneous transformation matrix of the rear vehicle body, transform the folding axis and twisting axis in the local coordinate system of the rear vehicle body into the spatial folding axis and spatial twisting axis in the global spatial coordinate system.

[0066] The axis of a spatial mechanism can be represented as:

[0067]

[0068] in, Represents the bent axis in the global spatial coordinate system; Represents the torsion axis in the global spatial coordinate system; This represents the rotation matrix of the rear vehicle body. The purpose is to ensure that the bending and twisting axes are not fixed global axes, but rather change synchronously with the already calculated posture of the rear vehicle body, thus conforming to the real spatial mechanism relationship of the bending and twisting tractor.

[0069] S24. The front vehicle body first performs a bending steering motion around the spatial bending axis, and then moves around the spatial torsion axis updated by the bending motion. The rotation process can be represented by axis angle rotation.

[0070] The Rodrigues rotation matrix corresponding to the axis angle can be expressed as:

[0071]

[0072] in, Indicates about the unit axis Rotation angle The rotation matrix; Indicates the direction of the rotation axis; This indicates the rotation angle. The rotation relationship of the front vehicle body can be expressed as:

[0073]

[0074] in, This represents the rotation matrix of the front vehicle body; Indicates the spatial fold axis; This indicates the spatial twisting axis that is updated after a bending motion. Indicates the bend angle; This represents the relative torsional angle between the front and rear vehicle bodies. The formula for the rotation relationship of the front vehicle body is used to generate the spatial attitude of the front vehicle body under the combined effects of bending and torsional angles, avoiding the simplification of the front vehicle body attitude as a superposition of several global Euler angles.

[0075] S25. During the relative motion of the front and rear vehicle bodies, the front and rear vehicle bodies share the same hinge point, and the wheelbase, the distance from the hinge point to each wheel point, and the rigid structural dimensions of the vehicle body remain unchanged. These constraints ensure that the tractor remains a geometrically continuous articulated, bent-waist, and torsional rigid body system throughout the attitude solution process.

[0076] Preferably, step S30 further includes:

[0077] S31. Subsequent homogeneous transformation matrix of the vehicle body, calculate the wheel point of the rear left wheel. Rear right wheel point Rear vehicle body weight center and hinge points Coordinates in the global coordinate system;

[0078] The global coordinates of any local point on the rear of the vehicle can be represented as:

[0079]

[0080] in, Indicates the first The coordinates of a point in the global coordinate system; This indicates the coordinates of the point in the local coordinate system of the rear vehicle body; This represents the rotation matrix of the rear vehicle body; This represents the translation vector of the rear vehicle body. The global coordinate formula is used to transform the rear vehicle body wheel points, rear vehicle body centroid, and hinge points from the local coordinate system to the global spatial coordinate system.

[0081] S32, based on the spatial folding axis, spatial twisting axis, and folding angle. and waist angle The spatial rotational relationship between the front vehicle body and the rear vehicle body is calculated. This process ensures that the bending and twisting movements of the front vehicle body relative to the rear vehicle body are performed around the axis of the real space mechanism.

[0082] S33. Based on the shared hinge point constraint of the front and rear vehicle bodies, solve the translation vector of the front vehicle body in the global spatial coordinate system so that the local hinge point of the front vehicle body coincides with the global hinge point of the rear vehicle body.

[0083] The translation vector of the front vehicle body can be expressed as:

[0084]

[0085] in, This represents the translation vector of the front vehicle body in the global coordinate system; Indicates the coordinates of hinge point A in the global coordinate system; This represents the rotation matrix of the front vehicle body; This represents the coordinates of hinge point A in the local coordinate system of the front vehicle body. The shared hinge point constraint determines the translation of the front vehicle body, rather than arbitrarily specifying its position, thus avoiding the problem of separation between the front and rear vehicle hinge points.

[0086] S34. Based on the spatial pose of the front vehicle body, calculate the wheel point of the front left wheel. Front right wheel point and the body weight of the car in front Coordinates in the global coordinate system;

[0087] The global coordinates of any local point on the front of the vehicle can be represented as:

[0088]

[0089] in, Indicates the first The coordinates of each front vehicle body point in the global coordinate system; This indicates the coordinates of the point in the local coordinate system of the front vehicle body; This represents the rotation matrix of the front vehicle body; This represents the translation vector of the front vehicle body. The formula calculates the three-dimensional spatial position of the front wheel hub and the center of mass of the front vehicle body, providing data for subsequent calculations of the four-wheel height residuals, support domain, and projection points.

[0090] S35. Based on the front vehicle mass, rear vehicle mass, and front vehicle center of gravity... and the weight of the car behind Calculate the vehicle's center of gravity Coordinates in the global coordinate system.

[0091] Preferably, step S40 further includes:

[0092] S41. Under three-point contact conditions, select three of the four wheel points as contact wheel points, and then determine the roll angle of the vehicle body. Rear vehicle pitch angle and the vertical position of the rear vehicle body As an unknown quantity, establish the residual between the actual height of the three contact wheel points and the target terrain height;

[0093] The unknowns in a three-point contact working condition can be expressed as:

[0094]

[0095] The residual under three-point contact conditions can be expressed as:

[0096]

[0097] in, This represents the unknowns in the attitude solution for a three-point contact working condition; This represents the height of the three contact wheel points calculated from the current tractor posture; This indicates the target terrain height corresponding to the three contact wheel points; This represents the height residual at three points. The three-wheel contact condition is transformed into a nonlinear residual equation, which is used to solve for the rear vehicle attitude.

[0098] S42. Perform finite difference processing on the residuals of the three-point contact condition, construct the Jacobian matrix, and use the least squares iterative method to update the rear vehicle roll angle, rear vehicle pitch angle and rear vehicle vertical position until the contact height residuals meet the preset tolerance.

[0099] The finite difference Jacobian matrix can be expressed as:

[0100]

[0101] in, Represents the Jacobian matrix of the first... List; and They represent the first The residuals after positive and negative disturbances of an unknown quantity; This represents a finite difference perturbation.

[0102] The least squares update can be expressed as:

[0103]

[0104] in, This represents the update amount of the variable to be solved; Represents the Jacobian matrix; This represents the current residual vector. The rear vehicle attitude under contact constraints is solved iteratively until the height of the three contact wheel points matches the target terrain height.

[0105] S43. Under normal four-wheel terrain conditions, the rear vehicle roll angle Rear vehicle pitch angle Vertical position of the rear vehicle body relative waist angle between the front and rear vehicle bodies As an unknown quantity, establish the actual height of the four wheel points and... , , and The residuals between;

[0106] The unknown quantities of the four-wheel height inverse solution can be expressed as:

[0107]

[0108] The residual height of the four wheels can be expressed as:

[0109]

[0110] in, This represents the unknown quantity in the inverse solution of the four-wheel height; , , , This indicates the actual height of the four wheel points in the current posture; , , , This indicates the target terrain height corresponding to the four wheel points; This represents the four-wheel height residual vector. The four-wheel height input under general terrain is transformed into an inverse attitude problem, while simultaneously solving for the rear vehicle attitude and the relative torsional angle between the front and rear vehicles.

[0111] S44. Perform finite difference processing on the four-wheel height residuals to construct a four-dimensional Jacobian matrix, and use the least squares iterative method to solve for the rear vehicle attitude and the relative torsional angle between the front and rear vehicles that satisfy the four-wheel terrain height constraints. ;

[0112] S45. When the inverse solution of the four-wheel height fails to converge, the geometric error exceeds the preset threshold, or the relative torsional angle between the front and rear vehicle bodies is not reached... If the current attitude point exceeds the range allowed by the mechanism, it will be marked as an invalid stability calculation point.

[0113] Preferably, step S50 further includes:

[0114] S51. Perform a hinge point consistency check on the attitude solution results to determine whether the hinge points of the front and rear vehicle bodies coincide in the global spatial coordinate system.

[0115] The hinge point consistency error can be expressed as:

[0116]

[0117] in, Indicates the consistency error of the hinge point; This represents the global coordinates of the articulation point calculated from the front vehicle body. This represents the global coordinates of the articulation point calculated from the rear vehicle body. The consistency error is calculated to check whether the front and rear vehicle bodies satisfy the shared articulation point constraint. If the error exceeds the threshold, it indicates that the tractor's geometric link is not valid.

[0118] S52. Perform rigid body geometric constraint verification on the attitude solution results to determine whether the front wheel track, rear wheel track, distance from the hinge point to the front wheel point, and distance from the hinge point to the rear wheel point remain at the design values.

[0119] To ensure that the rigid body structure is not stretched, compressed, or destroyed after a change in attitude, the distance constraint error between any two points can be expressed as:

[0120]

[0121] in, Indicates distance constraint error; and This represents the coordinates of two geometric points in the global coordinate system. This indicates the design distance between two points.

[0122] S53. Perform rotation matrix orthogonality check on the attitude solution results to determine whether the rotation matrices of the front and rear vehicle bodies satisfy the rigid body rotation matrix conditions.

[0123] The orthogonality condition of rotation matrices can be expressed as:

[0124]

[0125] in, Represents the rotation matrix; Represents the identity matrix; This represents the determinant of a rotation matrix.

[0126] S54. Move the front left wheel to the wheel position. Front right wheel point Rear left wheel point and rear right wheel point Projected onto a horizontal plane, a four-wheel-supported quadrilateral is constructed based on the horizontal projection of the four wheel points. ;

[0127] The quadrilateral formed by the supporting boundaries can be represented as:

[0128]

[0129] in, This represents the supporting quadrilateral formed by the horizontal projection of four wheels; Represents the convex hull operation; , , , These represent the projection points of the four wheel points onto the horizontal plane.

[0130] S55, center of gravity of the front vehicle Rear vehicle body weight center and vehicle center of gravity Projecting them onto the horizontal plane respectively, we obtain the static projection point of the center of mass of the front vehicle. Static projection point of the rear vehicle's center of mass and the static projection point of the vehicle's center of gravity ;

[0131] Converting the three-dimensional centroid position into a stability criterion point on the horizontal plane, the static projection point can be represented as:

[0132]

[0133] in, Represents the static centroid projection point of a stable object; and These represent the horizontal coordinates of the object's centroid in the global coordinate system.

[0134] S56. The three-point contact condition is only used to reverse-engineer the tractor's spatial attitude; stability determination still uses the support quadrilateral formed by the horizontal projection of the four wheels. Instead of using the triangle formed by the three-point contact condition as the boundary for determining cross slope stability, this approach avoids reducing the tractor's support domain due to the three-point fixed attitude, making the stability calculation results more consistent with the actual geometric boundaries of the four-wheel tractor.

[0135] Depend on Figure 5 It can be seen that when the height of a single wheel point changes, the front and rear vehicles will form relative twisting postures in different directions around the hinge area. Figure 5 The four sub-graphs in the middle represent the working conditions of varying wheel heights for the front right, front left, rear right, and rear left wheels, respectively. , , , The diagram represents four wheel points. Solid lines indicate the connection between the vehicle body and the articulation points, dashed lines represent the ground projection, and dotted lines indicate the lifting direction of the wheel points. Changes in the height of a single wheel simultaneously alter the vehicle's spatial attitude and the shape of its support domain. Therefore, it is necessary to introduce four-wheel height constraints and relative torsional angles in the attitude solution.

[0136] Depend on Figure 6 It can be seen that, under the condition that the vehicle twists due to the change in the height of a single wheel, this embodiment can calculate the cross slope stability angle under different combinations of bending angle and twisting angle. Figure 6 The four sub-graphs correspond to the changing wheel heights of the right front, left front, right rear, and left rear wheels, respectively. Solid lines represent static stability results, while dashed lines represent stability results under combined braking and turning dynamic conditions. The yaw angle, torsional angle, and dynamic acceleration all affect the vehicle's cross-slope stability limit, and the stability results under dynamic conditions differ significantly from the static results.

[0137] Preferably, step S60 further includes:

[0138] S61, former center of gravity Rear vehicle body weight center and vehicle center of gravity Take any centroid in the coordinate system as a stable object, and read the centroid coordinates of that stable object in the global coordinate system;

[0139] The centroid coordinates of a stable object can be represented as:

[0140]

[0141] in, Indicates the centroid of the currently stable object; , , These represent the vertical, horizontal, and lateral coordinates of the centroid in the global coordinate system, respectively.

[0142] S62, Based on longitudinal acceleration and lateral acceleration The static projection point of the stable object is offset along the equivalent direction of the inertial force to obtain the corresponding dynamic equivalent projection point.

[0143] The inertial effect caused by the dynamic acceleration of the tractor is equivalent to the horizontal displacement of the center of mass projection point. Based on the static support domain, dynamic stability is determined. The dynamic equivalent projection point can be expressed as:

[0144]

[0145] in, Represents the dynamic equivalent projection point; , , Represents the centroid coordinates of a stable object; Indicates longitudinal acceleration; Indicates lateral acceleration; It represents the acceleration due to gravity.

[0146] S63, Regarding the weight center of the vehicle in front Perform dynamic equivalent corrections to obtain the dynamic projection point of the center of mass of the front vehicle. ;

[0147] The dynamic projection point of the front vehicle body can be represented as:

[0148]

[0149] in, This represents the dynamic projection point of the center of mass of the preceding vehicle. , , This indicates the coordinates of the center of mass of the preceding vehicle.

[0150] S64, Regarding the rear vehicle's center of gravity Perform dynamic equivalent corrections to obtain the dynamic projection point of the rear vehicle's center of mass. ;

[0151] The dynamic projection point of the rear vehicle body can be represented as:

[0152]

[0153] in, This represents the dynamic projection point of the rear vehicle's center of mass; , , This indicates the coordinates of the center of mass of the rear vehicle.

[0154] S65, Regarding the vehicle's center of gravity Perform dynamic equivalent correction to obtain the dynamic projection point of the vehicle's center of gravity. ;

[0155] The dynamic projection points of the whole vehicle can be represented as:

[0156]

[0157] in, This represents the dynamic projection point of the vehicle's center of gravity. , , This represents the coordinates of the vehicle's center of gravity.

[0158] S66, the dynamic equivalent projection point, is used to characterize the influence of tractor inertia on cross slope stability under longitudinal acceleration, braking, lateral turning, and combined braking and turning conditions. and When there is longitudinal or lateral acceleration, the dynamic equivalent projection point degenerates into the static centroid projection point; when there is longitudinal or lateral acceleration, the dynamic equivalent projection point shifts relative to the static projection point to reflect the change in stability margin under dynamic conditions.

[0159] Preferably, step S70 further includes:

[0160] S71, support the quadrilateral with four wheels. The center is formed by the front left wheel point. and rear left wheel point The resulting boundary is defined as the left-side flip boundary. The front right wheel point and rear right wheel point The resulting boundary is defined as the right-side overhang boundary. ;

[0161] The transverse slope instability boundaries are defined as the left and right boundaries of the tractor, without considering whether the tractor's front or rear direction crosses the boundary. The left and right overturning boundaries can be represented as follows:

[0162]

[0163] in, Indicates the left-side flip boundary; Indicates the right-side boundary; The line connecting the horizontal projection points of the front left wheel and the rear left wheel; This represents the line connecting the horizontal projection points of the front right wheel and the rear right wheel.

[0164] S72, Dynamic projection point of the center of gravity of the front vehicle Calculate the distance from the left transverse slope to the left overturn boundary. The critical stability angle at that time and the right overturn boundary along the right cross slope direction The critical stability angle at that time is determined, and the smaller of the two values ​​is taken as the front vehicle body cross slope stability angle. ;

[0165] The front body cross slope stability angle can be expressed as:

[0166]

[0167] in, Indicates the front vehicle body's cross slope stability angle; This indicates the critical angle at which the dynamic projection point of the front vehicle body reaches the left overturn boundary along the left cross slope direction; This indicates the critical angle at which the dynamic projection point of the front vehicle body reaches the right overturn boundary along the right cross slope direction.

[0168] S73, Dynamic projection point of the rear vehicle's center of gravity Calculate the distance from the left transverse slope to the left overturn boundary. The critical stability angle at that time and the right overturn boundary along the right cross slope direction The critical stability angle at that time is determined, and the smaller of the two values ​​is taken as the rear vehicle body cross slope stability angle. ;

[0169] The rear vehicle's cross slope stability angle can be expressed as:

[0170]

[0171] in, Indicates the rear vehicle body's cross slope stability angle; This indicates the critical angle at which the dynamic projection point of the rear vehicle body reaches the left overturning boundary along the left cross slope direction. It represents the critical angle at which the dynamic projection point of the rear vehicle body reaches the right overturn boundary along the right cross slope direction.

[0172] S74, Dynamic projection point of the vehicle's center of gravity Calculate the distance from the left transverse slope to the left overturn boundary. The critical stability angle at that time and the right overturn boundary along the right cross slope direction The critical stability angle at that time is determined, and the smaller of the two values ​​is taken as the overall vehicle cross slope stability angle. ;

[0173] The vehicle's cross slope stability angle can be expressed as:

[0174]

[0175] in, Indicates the vehicle's cross slope stability angle; This represents the critical angle at which the dynamic projection point of the entire vehicle reaches the left overturn boundary along the left transverse slope direction. It represents the critical angle at which the dynamic projection point of the whole vehicle reaches the right overturn boundary along the right cross slope direction.

[0176] S75, previous vehicle body cross slope stability angle Rear vehicle cross slope stability angle and the vehicle's cross slope stability angle The minimum value in the range is used as the comprehensive criterion for cross slope stability angle. ;

[0177] The comprehensive criterion for cross slope stability can be expressed as:

[0178]

[0179] in, This represents the cross slope stability angle as a comprehensive criterion. The above formula implements the safety assessment logic that "any stable object that first reaches the rollover boundary is judged as having comprehensive instability."

[0180] S76, Output different bend angles Twist angle The system takes terrain height input and dynamic acceleration conditions as input, and generates visualizations of the static and dynamic cross slope stability angles. Output results may include attitude solution results, four-wheel spatial coordinates, hinge point coordinates, centroid coordinates, support quadrilateral, dynamic projection points, left cross slope critical angle, right cross slope critical angle, and overall cross slope stability angle.

[0181] Figure 7 The diagram illustrates typical terrain conditions, including flat ground, different heights of the two wheels on the left, diagonal undulations, and uneven heights of the four wheels. , , , The diagram represents four wheel points. Solid lines indicate the connection between the vehicle body and the articulation points, dashed lines represent the ground projection, and dotted lines indicate the direction of height change. Different wheel point height inputs will cause different vehicle spatial attitudes, therefore, it is necessary to inversely solve the vehicle attitude and relative torsional angle by analyzing the residuals of the four wheel heights.

[0182] Depend on Figure 8 As can be seen, this embodiment can output two-dimensional results showing the variation of the cross slope stability angle with the bend angle under different general terrain conditions. Figure 8The four sub-plots correspond to flat ground baseline, diagonal undulation, different wheel heights on one side, and unequal wheel heights, respectively. Solid lines represent static conditions, while dashed lines represent dynamic conditions involving braking and turning. Different terrain inputs and dynamic accelerations will change the vehicle's cross slope stability limit, which can be used for stability evaluation and safety operation parameter setting in complex terrain.

Claims

1. A method for calculating the dynamic stability limit of a tractor with a bendable and twisting profile on a cross slope, characterized in that, Includes the following steps: S10. Establish a tractor stability analysis model that includes the geometric parameters, mass parameters, bending angle parameters, twisting angle parameters, dynamic acceleration parameters, and terrain height parameters of the tractor's location. Configure attitude solution parameters, geometric verification parameters, and stability judgment parameters. Construct a three-dimensional attitude calculation scene for the articulated tractor based on the input working conditions. S20. Using the rear vehicle body as the reference vehicle body, establish a spatial attitude model, transform the waist-folding axis and waist-twisting axis defined in the local mechanism coordinate system of the rear vehicle body to the global spatial coordinate system, and make the front vehicle body move relative to the mechanism axis in the global spatial coordinate system. S30. Based on the shared hinge point constraint of the front and rear vehicle bodies, solve the pose of the front vehicle body in the global spatial coordinate system, and calculate the spatial coordinates of the front left wheel, front right wheel, rear left wheel, rear right wheel, hinge point, center of mass of the front vehicle body, center of mass of the rear vehicle body and center of mass of the whole vehicle. S40. Solve the spatial attitude of the tractor based on the terrain height. Under normal terrain conditions, the rear roll angle, rear pitch angle, rear vertical position and relative waist angle of the front and rear bodies are taken as unknowns. Solve the overall vehicle attitude that satisfies the four-wheel terrain height constraint. S50. Perform geometric consistency verification on the attitude solution results, and construct a supporting quadrilateral based on the projection of the four wheel points on the horizontal plane to obtain the static projection points of the center of mass of the front body, the rear body and the whole vehicle respectively. S60. Based on the longitudinal acceleration and lateral acceleration, the static projection point of the centroid is dynamically equivalently corrected to obtain the dynamic equivalent projection points of the front body, the rear body, and the whole vehicle. S70. Calculate the critical cross slope angle when the dynamic equivalent projection point reaches the corresponding rollover boundary along the left and right cross slope directions respectively, and use the cross slope angle when any stable object in the front body, rear body and whole vehicle reaches the rollover boundary first as the comprehensive cross slope stability limit output.

2. The method for calculating the dynamic stability limit of the cross slope of a jacking machine according to claim 1, characterized in that, Step S10 also includes: S11. The basic points of the articulated hinged and twisted tractor include the hinge point, the front left wheel point, the front right wheel point, the rear left wheel point, and the rear right wheel point; S12. Tractor mass and center of gravity parameters include front body mass, rear body mass, front body center of gravity, rear body center of gravity and vehicle center of gravity, wherein the vehicle center of gravity is obtained by weighted calculation of the front body center of gravity, the rear body center of gravity and their corresponding masses; S13. Tractor geometric parameters include the position of the front wheel relative to the hinge point, the position of the rear wheel relative to the hinge point, the front and rear wheel track, the hinge point height, the position of the center of gravity of the front vehicle body, and the position of the center of gravity of the rear vehicle body. S14. Attitude and mechanism angle parameters include the bend angle, the relative twist angle between the front and rear vehicle bodies, the roll angle of the rear vehicle body, the pitch angle of the rear vehicle body, and the vertical position of the rear vehicle body. S15. Terrain input parameters include the ground height of the front left wheel, the ground height of the front right wheel, the ground height of the rear left wheel, and the ground height of the rear right wheel; S16. Dynamic operating parameters include longitudinal acceleration, lateral acceleration, longitudinal acceleration-to-gravity ratio, and lateral acceleration-to-gravity ratio; S17. Stability determination parameters include the support quadrilateral formed by the horizontal projection of the four wheels, the left overturning boundary, the right overturning boundary, the critical stability angle of the left cross slope, the critical stability angle of the right cross slope, and the comprehensive criterion cross slope stability angle.

3. The method for calculating the dynamic stability limit of a tractor on a cross slope according to claim 1, characterized in that, Step S20 also includes: S21. Using the local coordinate system of the rear vehicle body as the definition reference for the mechanism axis, the bending axis is defined as the vertical steering axis in the local mechanism coordinate system of the rear vehicle body, and the twisting axis is defined as the longitudinal torsion axis in the local mechanism coordinate system of the rear vehicle body. S22. The spatial position, roll angle, pitch angle and yaw angle of the rear vehicle body are used to establish the homogeneous transformation matrix of the rear vehicle body, which is used to describe the rigid body transformation relationship from the local coordinate system of the rear vehicle body to the global spatial coordinate system. S23. Using the homogeneous transformation matrix of the rear vehicle body, transform the folding axis and twisting axis in the local coordinate system of the rear vehicle body into the spatial folding axis and spatial twisting axis in the global spatial coordinate system. S24. Make the front body first perform a bending steering motion around the spatial bending axis, and then move around the spatial twisting axis after the bending motion. S25. During the relative movement of the front and rear vehicle bodies, the front and rear vehicle bodies share the same hinge point, and the wheel track, the distance from the hinge point to each wheel point, and the rigid structural dimensions of the vehicle body remain unchanged.

4. The method for calculating the dynamic stability limit of a tractor on a cross slope according to claim 3, characterized in that, Step S30 also includes: S31. After the homogeneous transformation matrix of the vehicle body, calculate the coordinates of the rear left wheel point, the rear right wheel point, the rear vehicle body centroid, and the hinge point in the global spatial coordinate system. S32. Calculate the spatial rotational relationship between the front vehicle body and the rear vehicle body based on the spatial folding axis, spatial torsion axis, folding angle, and torsion angle. S33. Based on the shared hinge point constraint between the front and rear vehicle bodies, solve the translation vector of the front vehicle body in the global spatial coordinate system to make the local hinge point of the front vehicle body coincide with the global hinge point of the rear vehicle body. S34. Based on the spatial pose of the front vehicle body, calculate the coordinates of the front left wheel point, the front right wheel point, and the center of mass of the front vehicle body in the global spatial coordinate system. S35. Based on the mass of the front vehicle body, the mass of the rear vehicle body, the center of gravity of the front vehicle body, and the center of gravity of the rear vehicle body, calculate the coordinates of the vehicle's center of gravity in the global spatial coordinate system.

5. The method for calculating the dynamic stability limit of a tractor on a cross slope according to claim 1, characterized in that, Step S40 also includes: S41. Under the three-point contact condition, select three of the four wheel points as contact wheel points, and use the rear vehicle roll angle, rear vehicle pitch angle and rear vehicle vertical position as unknowns to establish the residual between the actual height of the three contact wheel points and the target terrain height. S42. Perform finite difference processing on the residuals of the three-point contact condition, construct the Jacobian matrix, and use the least squares iterative method to update the rear vehicle roll angle, rear vehicle pitch angle and rear vehicle vertical position until the contact height residuals meet the preset tolerance. S43. Under normal terrain conditions, with the rear vehicle roll angle, rear vehicle pitch angle, rear vehicle vertical position and the relative waist angle between the front and rear vehicles as unknowns, establish the residuals between the actual height of the four wheel points and the ground height of the front left wheel, the front right wheel, the rear left wheel and the rear right wheel. S44. Perform finite difference processing on the four-wheel height residuals to construct a four-dimensional Jacobian matrix, and use the least squares iterative method to solve the rear vehicle posture and the relative twist angle between the front and rear vehicles that satisfy the four-wheel terrain height constraints. S45. When the inverse solution of the four-wheel height fails to converge, the geometric error exceeds the preset threshold, or the relative torsional angle between the front and rear vehicle bodies exceeds the allowable range of the mechanism, the current attitude point is marked as an invalid stability calculation point.

6. The method for calculating the dynamic stability limit of a tractor on a cross slope according to claim 5, characterized in that, Step S50 also includes: S51. Perform a hinge point consistency check on the attitude solution results to determine whether the hinge points of the front and rear vehicle bodies coincide in the global spatial coordinate system. S52. Perform rigid body geometric constraint verification on the attitude solution results to determine whether the front wheel track, rear wheel track, distance from the hinge point to the front wheel point, and distance from the hinge point to the rear wheel point remain at the design values. S53. Perform rotation matrix orthogonality check on the attitude solution results to determine whether the rotation matrices of the front and rear vehicle bodies satisfy the rigid body rotation matrix conditions. S54. Project the front left wheel point, front right wheel point, rear left wheel point and rear right wheel point onto the horizontal plane, and construct a four-wheel support quadrilateral based on the horizontal projection of the four wheel points; S55. Project the center of mass of the front vehicle body, the center of mass of the rear vehicle body, and the center of mass of the whole vehicle onto the horizontal plane respectively to obtain the static projection point of the center of mass of the front vehicle body, the static projection point of the center of mass of the rear vehicle body, and the static projection point of the center of mass of the whole vehicle. S56. The three-point contact condition is only used to solve the spatial attitude of the tractor. The stability judgment still uses the support quadrilateral formed by the horizontal projection of the four wheels, instead of using the triangle formed by the three-point contact condition as the boundary for judging the cross slope stability.

7. The method for calculating the dynamic stability limit of a tractor on a cross slope according to claim 1, characterized in that, Step S60 also includes: S61. Take any one of the centroids of the front vehicle body, the rear vehicle body, and the whole vehicle as a stable object, and read the centroid coordinates of the stable object in the global space coordinate system. S62. Based on the longitudinal acceleration and lateral acceleration, the static projection point of the stable object is offset along the equivalent direction of the inertial force to obtain the corresponding dynamic equivalent projection point. S63. Perform dynamic equivalent correction on the center of mass of the front vehicle to obtain the dynamic projection point of the center of mass of the front vehicle. S64. Perform dynamic equivalent correction on the rear vehicle's center of gravity to obtain the dynamic projection point of the rear vehicle's center of gravity. S65. Perform dynamic equivalent correction on the vehicle's center of gravity to obtain the dynamic projection point of the vehicle's center of gravity. S66, the dynamic equivalent projection point is used to characterize the effect of tractor inertia on cross slope stability under longitudinal acceleration, braking, lateral turning, and combined braking and turning conditions.

8. The method for calculating the dynamic stability limit of a tractor on a cross slope according to claim 7, characterized in that, Step S70 also includes: S71. Define the boundary formed by the front left wheel point and the rear left wheel point in the four-wheel support quadrilateral as the left-side flip boundary, and define the boundary formed by the front right wheel point and the rear right wheel point as the right-side flip boundary. S72. For the dynamic projection point of the center of mass of the front vehicle body, calculate the critical stability angle when it reaches the left overturning boundary along the left cross slope direction and the critical stability angle when it reaches the right overturning boundary along the right cross slope direction, and take the smaller value of the two as the cross slope stability angle of the front vehicle body. S73. For the dynamic projection point of the rear vehicle's center of mass, calculate the critical stability angle when it reaches the left overturning boundary along the left cross slope direction and the critical stability angle when it reaches the right overturning boundary along the right cross slope direction, and take the smaller of the two values ​​as the rear vehicle's cross slope stability angle. S74. For the dynamic projection point of the vehicle's center of gravity, calculate the critical stability angle when it reaches the left overturning boundary along the left cross slope direction and the critical stability angle when it reaches the right overturning boundary along the right cross slope direction, and take the smaller value of the two as the vehicle's cross slope stability angle. S75. The minimum value among the front body cross slope stability angle, the rear body cross slope stability angle and the whole vehicle cross slope stability angle is used as the comprehensive criterion for cross slope stability angle. S76. Output the cross slope stability limit results under different bending angles, twisting angles, terrain height inputs and dynamic acceleration conditions, and generate visualizations corresponding to the static cross slope stability angle and dynamic cross slope stability angle.

Images