Rigid-flexible coupling dynamic modeling method and device for height adjustment of paddy field leveler

Abstract

The application relates to a rigid-flexible coupling dynamic modeling method and device for height adjustment of a paddy field leveler. W O W Y W And a generalized coordinate system X1O1Y1; according to the vibration theory of an Euler Bernoulli beam, a transverse vibration mode function of the flexible beam under boundary conditions is obtained; according to the two-dimensional world coordinate system X W O W Y W , the generalized coordinate system X1O1Y1 and the transverse vibration mode function of the flexible beam, kinetic energy and potential energy of the flexible beam system are calculated; the force of the force equivalent spring exerted by the height cylinder for controlling the height movement of the leveler on the flexible beam is calculated to obtain the driving torque of the hydraulic cylinder of the flexible beam; the kinetic energy, the potential energy and the driving torque of the flexible beam system are substituted into the Lagrange equation, and the Lagrange equation is discretized by using the assumed mode method to obtain a transverse displacement function of an arbitrary point on the flexible beam changing with time when the height of the flat blade is adjusted. The method can accurately perform kinematic modeling on the flexible beam.

Description

Technical Field

[0001] This application relates to the field of dynamic modeling technology for graders, and in particular to a rigid-flexible coupling dynamic modeling method and device for elevation adjustment of paddy field graders. Background Technology

[0002] Because the working environment of a paddy field grader is in mud, the machine's posture changes irregularly as it travels through the mud, making the control and adjustment of the shovel more difficult. Leveling the shovel, in particular, introduces many interferences. During operation, if the flexible beam vibrates significantly, it greatly affects the shovel's leveling effect, severely impacting the flatness of the paddy field. Insufficient flatness not only hinders sowing and transplanting but also leads to low freshwater utilization efficiency, irrigation waste, and a serious impact on rice yield. Therefore, it is necessary to construct an accurate dynamic model for the flexible beam connected to the shovel in the grader. Chen Junmei et al. (Chen Junmei, Zhao Zuoxi, Chen Jiaqi, Yu Long, Ye Juan. Nonlinear horizontal control system of laser grader for paddy fields[J]. Transactions of the Chinese Society for Agricultural Machinery, 2014, 45(07):79-84) simplified and established a model of the leveling system of the grader, but the simplification could not reflect the true dynamic characteristics of the grader. Chen Jiaqi et al. (Chen Jiaqi, Zhao Zuoxi, Shi Lei, Ke Xinrong, Wu Zhiwei, Liu Xiong. Dynamic modeling of leveling system of laser grader for paddy fields[J]. Transactions of the Chinese Society of Agricultural Engineering, 2015, 31(07):18-23) modeled the dynamics of the leveling system of laser grader for paddy fields, but did not treat the suspension device as a flexible component, and it was a multi-rigid-body dynamic model, so the results were not very accurate.

[0003] Previous research methods treated the flexible beam connecting the grader and the shovel, as well as the two connecting rods, as rigid components. However, the actual properties of the three components (left connecting rod, right connecting rod, and flexible beam) are flexible, which affects the accuracy of the research results and fails to accurately reflect the mechanical vibration characteristics of the flexible beam. Therefore, an accurate dynamic model of the flexible beam is urgently needed. Summary of the Invention

[0004] Therefore, it is necessary to provide a rigid-flexible coupling dynamic modeling method and device for the elevation adjustment of paddy field graders that can accurately reflect the mechanical vibration characteristics of flexible beams, in order to address the above-mentioned technical problems.

[0005] A rigid-flexible coupled dynamic modeling method for elevation adjustment of paddy field graders, the method comprising:

[0006] The hinge point of the flexible beam in the three-point suspension mechanism of the grader is taken as the origin of the world coordinate system. and the origin of the moving coordinate system The straight line containing the axis when the cross-sectional axis of the flexible beam is parallel to the ground is taken as... , to be perpendicular to and the straight line on the ground is To obtain a two-dimensional world coordinate system Taking the straight line containing the axis of the flexible beam's cross-section as... , to be perpendicular to And with A straight line in the plane is Establish a generalized coordinate system ;

[0007] Based on the vibration theory of Euler-Bernoulli beams, the transverse vibration mode function of the flexible beam under boundary conditions is obtained;

[0008] According to the two-dimensional world coordinate system Generalized coordinate system Given the transverse vibration mode function of the flexible beam, calculate the kinetic and potential energy of the flexible beam system;

[0009] The force exerted by the elevation cylinder controlling the elevation movement of the grader on the flexible beam is equivalent to the force applied by the spring, and the driving torque of the hydraulic cylinder of the flexible beam is calculated.

[0010] Substituting the kinetic energy, potential energy, and driving torque of the flexible beam system into the Lagrange equation, and using the assumed modal method to discretize the Lagrange equation, we obtain the lateral displacement function of any point on the flexible beam as time changes when the height of the flat-bottomed shovel is adjusted.

[0011] In one embodiment, obtaining the transverse vibration mode function of the flexible beam under boundary conditions based on the vibration theory of Euler-Bernoulli beams includes: obtaining the mode shape function based on the vibration theory of Euler-Bernoulli flexible beams. The calculation formula is:

[0012] ;

[0013] in, , To simplify the formula design, and without other meanings, ρ is the mass density, S is the cross-sectional area, E is the elastic modulus of the material, I is the moment of inertia of the cross section about the neutral axis, ω is the natural frequency, A, B, C, and D are constants, the values ​​of A, B, C, and D are determined according to the boundary conditions of the flexible beam, and x is the coordinate of any point on the flexible beam; then the transverse vibration mode function of the flexible beam is: Where u(x, t) is the lateral displacement function. Let q(t) be the mode shape function, q(t) be the modal coordinates, and t be the time.

[0014] In one embodiment, the method based on a two-dimensional world coordinate system Generalized coordinate system Given the transverse vibration mode function of the flexible beam, calculate the kinetic and potential energy of the flexible beam system, including: in the coordinate system and When the coordinate systems coincide, the position of the flexible beam at this moment is defined as the initial position. At this point, the kinetic and potential energy of the flexible beam structure are both zero. As the grader moves along the elevation, the flexible beam generates kinetic and potential energy. In the coordinate system, Let's consider a point before the flexible beam deforms, with coordinates as follows: After the flexible beam deforms, Transform to Location, coordinates are , exist The position vector in the coordinate system is:

[0015]

[0016] in, This is the coordinate transformation matrix. for coordinate system and The angle between the X-axis and the coordinate system, u is coordinate transformation matrix for:

[0017]

[0018] The formula for calculating the kinetic energy T1 of a flexible beam is as follows:

[0019]

[0020] Kinetic energy of the concentrated mass at the end of the flexible beam for:

[0021]

[0022] Where m is the concentrated mass at the end of the flexible beam. For the concentrated mass at the end of the flexible beam The position vector in the coordinate system, where L is the length of the flexible beam, and u is... The formula for calculating the total kinetic energy T is: During the operation of the elevation cylinder controlling the elevation movement of the grader, the elastic potential energy and gravitational potential energy of the flexible beam change with the movement. During the movement of the flexible beam, due to its deformation and change in position and height, the total potential energy includes the strain energy stored during deformation and the gravitational potential energy. Therefore, the strain energy of the flexible beam... The calculation formula is:

[0023] Based on the initial position of the flexible beam, the potential energy of the flexible beam structure is zero. The change in gravitational potential energy of the concentrated mass at the end of the flexible beam and the mass of the flexible beam is equal to the gravitational potential energy of the flexible beam. The formula for calculating the change in gravitational potential energy U of the concentrated mass at the end of the flexible beam and the mass of the flexible beam is expressed as:

[0024] in, Let be the mass of the flexible beam, and e be a unit vector along the direction of gravity; then the formula for calculating the total potential energy V is: .

[0025] In one embodiment, the calculation of the driving torque of the hydraulic cylinder of the flexible beam by elevating the force exerted by the elevation cylinder controlling the elevation movement of the grader on the flexible beam is equivalent to the force applied by a spring. This includes: the driving device for elevation movement is an elevation cylinder, and b and h are the hinge points between the elevation hydraulic cylinder push rod and the flexible beam. The horizontal and vertical coordinates are used to derive the displacement vector of the hydraulic push rod's extension and retraction from its geometric position. for:

[0026]

[0027] in, , displacement vector Components of displacement along the x and y axes for coordinate system and The angle between the X-axis and the coordinate system; then the force F exerted by the elevation cylinder controlling the elevation movement of the grader on the flexible beam is equivalent to the force F applied by the spring. The formula for calculating the force F applied by the equivalent spring is:

[0028]

[0029] in, , The force F applied by the equivalent spring has its x and y axis components. Hydraulic stiffness, hydraulic stiffness The calculation formula is:

[0030]

[0031] in, The elastic modulus of hydraulic oil. Let V be the piston area, V be the original volume of the hydraulic cylinder, and V be the elastic modulus of the hydraulic oil. The range of values ​​is Based on the force F applied by the equivalent spring, the driving torque of the hydraulic cylinder of the flexible beam is... The calculation formula is: .

[0032] In one embodiment, substituting the kinetic energy, potential energy, and driving torque of the flexible beam system into the Lagrange equation, and discretizing the Lagrange equation using the assumed modal method to obtain the lateral displacement function of any point on the flexible beam as the height of the flat-bottomed shovel is adjusted, includes: the assumed modal method is a discretization method for continuous systems, which uses a linear combination of a finite number of known modal functions to approximate the system response; according to the assumed modal method, the lateral displacement function... Represented as:

[0033]

[0034] in, Let i be the basis function of the i-th mode. Let be the coordinates of the i-th modal, where i represents the i-th discretized system, and Satisfies the following orthogonality relation:

[0035]

[0036] According to the orthogonality relation, then Discretized as:

[0037]

[0038] in, , For the purpose of simplifying the formula design, this has no other meaning. for ;

[0039] Will Discretized as:

[0040]

[0041] in, for ; to transfer the elastic potential energy of the flexible beam Discretized as:

[0042]

[0043] in, For generalized stiffness, The Lagrange equation is:

[0044]

[0045] Where q is q(t), T is the total kinetic energy, V is the total potential energy, t is time, and θ is the coordinate system of X1O1Y1 and X. W O W Y WThe angle between the X-axis and the coordinate system; substituting the formulas for calculating total kinetic energy T, total potential energy V, and driving torque τ into the Lagrange equation, we obtain the dynamic equation of the flexible beam during the elevation movement of the leveling shovel:

[0046]

[0047] The coordinates of the i-th mode are obtained by solving the dynamic equations of the flexible beam. And substitute the lateral displacement function determined according to the assumed modal method. We obtain a functional expression for the lateral displacement x of any point on the flexible beam with time t when the height of the shovel is adjusted.

[0048] A rigid-flexible coupled dynamic modeling device for elevation adjustment of a paddy field grader, the device comprising:

[0049] The coordinate system establishment module is used to establish the origin of the world coordinate system based on the hinge point of the flexible beam in the three-point suspension mechanism of the grader. and the origin of the moving coordinate system The straight line containing the axis when the cross-sectional axis of the flexible beam is parallel to the ground is taken as... , to be perpendicular to and the straight line on the ground is To obtain a two-dimensional world coordinate system Let X1 be the straight line containing the axis of the flexible beam's cross-section, and let X1 be a line perpendicular to X1 and parallel to the axis of the flexible beam's cross-section. Let Y1 be the straight line in the plane, and establish a generalized coordinate system. ;

[0050] The transverse vibration mode function calculation module is used to obtain the transverse vibration mode function of a flexible beam under boundary conditions based on the vibration theory of Euler-Bernoulli beams.

[0051] The kinetic potential energy calculation module is used to calculate based on a two-dimensional world coordinate system. Generalized coordinate system Given the transverse vibration mode function of the flexible beam, calculate the kinetic and potential energy of the flexible beam system;

[0052] The driving torque calculation module is used to calculate the driving torque of the hydraulic cylinder of the flexible beam by equating the force exerted by the elevation cylinder controlling the elevation movement of the grader on the flexible beam with the force applied by the spring.

[0053] The lateral displacement function calculation module is used to substitute the kinetic energy, potential energy, and driving torque of the flexible beam system into the Lagrange equation, and to discretize the Lagrange equation using the assumed modal method to obtain the lateral displacement function of any point on the flexible beam as time changes when the height of the flat-bottomed shovel is adjusted.

[0054] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program performing the following steps:

[0055] The hinge point of the flexible beam in the three-point suspension mechanism of the grader is taken as the origin of the world coordinate system. and the origin of the moving coordinate system The straight line containing the axis when the cross-sectional axis of the flexible beam is parallel to the ground is taken as... , to be perpendicular to and the straight line on the ground is To obtain a two-dimensional world coordinate system Taking the straight line containing the axis of the flexible beam's cross-section as... , to be perpendicular to And with A straight line in the plane is Establish a generalized coordinate system ;

[0056] Based on the vibration theory of Euler-Bernoulli beams, the transverse vibration mode function of the flexible beam under boundary conditions is obtained;

[0057] According to the two-dimensional world coordinate system Generalized coordinate system Given the transverse vibration mode function of the flexible beam, calculate the kinetic and potential energy of the flexible beam system;

[0058] The force exerted by the elevation cylinder controlling the elevation movement of the grader on the flexible beam is equivalent to the force applied by the spring, and the driving torque of the hydraulic cylinder of the flexible beam is calculated.

[0059] Substituting the kinetic energy, potential energy, and driving torque of the flexible beam system into the Lagrange equation, and using the assumed modal method to discretize the Lagrange equation, we obtain the lateral displacement function of any point on the flexible beam as time changes when the height of the flat-bottomed shovel is adjusted.

[0060] A computer-readable storage medium having a computer program stored thereon, the computer program performing the following steps when executed by a processor:

[0061] The hinge point of the flexible beam in the three-point suspension mechanism of the grader is taken as the origin of the world coordinate system. and the origin of the moving coordinate system The straight line containing the axis when the cross-sectional axis of the flexible beam is parallel to the ground is taken as... , to be perpendicular to and the straight line on the ground is To obtain a two-dimensional world coordinate system Taking the straight line containing the axis of the flexible beam's cross-section as... , to be perpendicular to And with A straight line in the plane is Establish a generalized coordinate system ;

[0062] Based on the vibration theory of Euler-Bernoulli beams, the transverse vibration mode function of the flexible beam under boundary conditions is obtained;

[0063] According to the two-dimensional world coordinate system Generalized coordinate system Given the transverse vibration mode function of the flexible beam, calculate the kinetic and potential energy of the flexible beam system;

[0064] The force exerted by the elevation cylinder controlling the elevation movement of the grader on the flexible beam is equivalent to the force applied by the spring, and the driving torque of the hydraulic cylinder of the flexible beam is calculated.

[0065] By substituting the kinetic energy, potential energy, and driving torque of the flexible beam system into the Lagrange equation and discretizing the Lagrange equation using the assumed modal method, the lateral displacement function of any point on the flexible beam as a function of time during the height adjustment of the flat-bottomed shovel is obtained. The aforementioned rigid-flexible coupling dynamic modeling method and device for the elevation adjustment of a paddy field grader simplifies the grader model, conveniently and quickly obtaining the dynamic model of the grader's elevation movement process, and can obtain a functional expression for the lateral displacement of any point on the flexible beam as the time changes during the flat-bottomed shovel height adjustment. Simultaneously, the influence of the flexible body on the mechanism's dynamics is considered, making the obtained model more accurate and better predicting the trajectory of the flat-bottomed shovel, facilitating the optimization of the grader's mechanical structure and control design. The method described in this application has guiding significance for the dynamic modeling of other hydraulically driven agricultural machinery. Attached Figure Description

[0066] Figure 1 This is an application environment diagram of the rigid-flexible coupling dynamics modeling method for elevation adjustment of a paddy field grader in one embodiment.

[0067] Figure 2 This is a flowchart illustrating the rigid-flexible coupling dynamics modeling method for elevation adjustment of a paddy field grader in one embodiment.

[0068] Figure 3 This is a schematic diagram of the coordinate system position of the flexible beam in one embodiment;

[0069] Figure 4 This is a vector diagram showing the position of the hydraulic cylinder of the elevation cylinder in one embodiment;

[0070] Figure 5 This is a structural block diagram of a rigid-flexible coupling dynamics modeling device for elevation adjustment of a paddy field grader in one embodiment.

[0071] Figure 6 This is an internal structural diagram of a computer device in one embodiment;

[0072] Figure 7 This is a comparison diagram of the lateral displacement calculated by the rigid-flexible coupling dynamic modeling method using a paddy field grader for elevation adjustment at a point on a flexible beam in a specific embodiment, and the actual measured lateral displacement.

[0073] Attached diagram labels: 1. Elevation cylinder; 2. Left connecting rod; 3. Leveling shovel; 4. Horizontal cylinder; 5. Mounting bracket; 6. Flexible beam; 7. Right connecting rod. Detailed Implementation

[0074] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0075] The rigid-flexible coupling dynamic modeling method for elevation adjustment of paddy field graders provided in this application can be applied to, for example... Figure 1 In the application environment shown, a bench is used instead of the vehicle body. The three-point suspension mechanism, intermediate mounting platform, and leveling shovel 3 are removed from the vehicle body and installed on the bench. The deformation of the left link 2 and right link 7 of the three-point suspension mechanism is negligible compared to the flexible beam 6, so the three-point suspension is simplified to the flexible beam 6, the elevation cylinder 1 is regarded as an equivalent spring, and the implement and intermediate mounting platform are regarded as rigid bodies. In this application, the elevation cylinder 1 is a hydraulic cylinder. The three-point suspension mechanism includes the left link 2, right link 7, and flexible beam 6. In one embodiment, such as Figure 2 As shown, a rigid-flexible coupling dynamic modeling method for elevation adjustment of paddy field graders is provided, including the following steps:

[0076] S110, based on the hinge point of the flexible beam in the three-point suspension mechanism of the grader as the origin of the world coordinate system. and the origin of the moving coordinate system The straight line containing the axis when the cross-sectional axis of the flexible beam is parallel to the ground is taken as... , to be perpendicular to and the straight line on the ground is To obtain a two-dimensional world coordinate system Taking the straight line containing the axis of the flexible beam's cross-section as... , to be perpendicular to And with A straight line in the plane is Establish a generalized coordinate system .

[0077] Among them, such as Figure 1 As shown, a two-dimensional world coordinate system is illustrated. and generalized coordinate system When the cross-sectional axis of the flexible beam is parallel to the ground, the two-dimensional world coordinate system and generalized coordinate system coincide.

[0078] S120, based on the vibration theory of Euler-Bernoulli beams, obtains the transverse vibration mode function of the flexible beam under boundary conditions.

[0079] The working principle of the grader's elevation adjustment is as follows: Before the grader starts working, a reference plane is set. When the grader is working in an uneven paddy field, the laser receiver on the mounting frame 5 controls the elevation reversing valve to retract or extend the elevation cylinder 1 according to the change of the plane, thereby achieving the purpose of lowering or raising the height of the grader. According to the structure and boundary conditions of the flexible beam 6 of the paddy field grader, the length of the flexible beam is much greater than its cross-sectional height, which conforms to the structural characteristics of an Euler Bernoulli beam.

[0080] Based on Euler's Bernoulli beam theory, the following assumptions are made regarding beams:

[0081] 1. The principal axes of inertia of all sections of the beam lie in the same plane;

[0082] 2. The beam undergoes transverse vibration in this plane, and the main deformation is bending deformation;

[0083] 3. When the vibration frequency is low, the effects of shaft rotational inertia and shear deformation are ignored;

[0084] 4. When a beam undergoes bending deformation, it will also have a slight displacement in the axial direction. Under small deformation conditions, the elongation deformation of the beam along its axial direction is a high-order infinitesimal quantity compared with the lateral displacement. Therefore, its axial deformation is not considered when modeling.

[0085] S130, according to the two-dimensional world coordinate system Generalized coordinate system Given the transverse vibration mode function of the flexible beam, calculate the kinetic and potential energy of the flexible beam system.

[0086] S140 calculates the driving torque of the hydraulic cylinder of the flexible beam by equating the force exerted by the elevation cylinder controlling the elevation movement of the grader on the flexible beam with the force applied by the spring.

[0087] S150, by substituting the kinetic energy, potential energy and driving torque of the flexible beam system into the Lagrange equation, and using the assumed modal method to discretize the Lagrange equation, the lateral displacement function of any point on the flexible beam as a function of time is obtained when the height of the flat-bottomed shovel is adjusted.

[0088] In the aforementioned rigid-flexible coupling dynamic modeling method for elevation adjustment of a paddy field grader, the grader model is simplified to quickly and easily obtain the dynamic model of the grader's elevation movement process. Furthermore, a functional expression for the lateral displacement of any point on the flexible beam over time during grader height adjustment can be obtained. Simultaneously, the influence of the flexible body on the mechanism's dynamics is considered, making the obtained model more accurate and better predicting the trajectory of the grader's movement, thus facilitating the optimization of the grader's mechanical structure and control design. The method described in this application provides guidance for the dynamic modeling of other hydraulically driven agricultural machinery. In one embodiment, obtaining the lateral vibration mode function of the flexible beam under boundary conditions based on Euler-Bernoulli beam vibration theory includes: obtaining the mode shape function based on Euler-Bernoulli flexible beam vibration theory. The calculation formula is:

[0089] in, , To simplify the formula design, and without other meanings, ρ is the mass density, S is the cross-sectional area, E is the elastic modulus of the material, I is the moment of inertia of the cross section about the neutral axis, ω is the natural frequency, A, B, C, and D are constants, the values ​​of A, B, C, and D are determined according to the boundary conditions of the flexible beam, and x is the coordinate of any point on the flexible beam; then the transverse vibration mode function of the flexible beam is: Where u(x, t) is the lateral displacement function. Let q(t) be the mode shape function, q(t) be the modal coordinates, and t be the time.

[0090] In one embodiment, such as Figure 3 As shown, the two-dimensional world coordinate system Generalized coordinate system Given the transverse vibration mode function of the flexible beam, calculate the kinetic and potential energy of the flexible beam system, including: in the coordinate system and When the coordinate systems coincide, the position of the flexible beam at this moment is defined as the initial position. At this point, the kinetic and potential energy of the flexible beam structure are both zero. As the grader moves along the elevation, the flexible beam generates kinetic and potential energy. In the coordinate system, Let's consider a point before the flexible beam deforms, with coordinates as follows: After the flexible beam deforms, Transform to Location, coordinates are , exist The position vector in the coordinate system is:

[0091]

[0092] in, This is the coordinate transformation matrix. for coordinate system and The angle between the X-axis and the coordinate system, u is coordinate transformation matrix for:

[0093]

[0094] The formula for calculating the kinetic energy T1 of a flexible beam is as follows:

[0095]

[0096] Kinetic energy of the concentrated mass at the end of the flexible beam for:

[0097]

[0098] Where m is the concentrated mass at the end of the flexible beam. For the concentrated mass at the end of the flexible beam The position vector in the coordinate system, where L is the length of the flexible beam, and u is... The formula for calculating the total kinetic energy T is: During the operation of the elevation cylinder controlling the elevation movement of the grader, the elastic potential energy and gravitational potential energy of the flexible beam change with the movement. During the movement of the flexible beam, due to its deformation and change in position and height, the total potential energy includes the strain energy stored during deformation and the gravitational potential energy. Therefore, the strain energy of the flexible beam... The calculation formula is:

[0099]

[0100] Based on the initial position of the flexible beam, the potential energy of the flexible beam structure is zero. The change in gravitational potential energy of the concentrated mass at the end of the flexible beam and the mass of the flexible beam is equal to the gravitational potential energy of the flexible beam. The formula for calculating the change in gravitational potential energy U of the concentrated mass at the end of the flexible beam and the mass of the flexible beam is expressed as:

[0101]

[0102] in, Let be the mass of the flexible beam, and e be a unit vector along the direction of gravity; then the formula for calculating the total potential energy V is: .

[0103] In one embodiment, such as Figure 4 As shown, the force exerted by the elevation cylinder controlling the elevation movement of the grader on the flexible beam is equivalent to the force applied by a spring, and the driving torque of the hydraulic cylinder of the flexible beam is calculated. This includes: the driving device for elevation movement is an elevation cylinder, and b and h are the hinge points between the elevation hydraulic cylinder push rod and the flexible beam. The horizontal and vertical coordinates are used to derive the displacement vector of the hydraulic push rod's extension and retraction from its geometric position. for:

[0104]

[0105] in, , displacement vector Components of displacement along the x and y axes for coordinate system and The angle between the X-axis and the coordinate system; then the force F exerted by the elevation cylinder controlling the elevation movement of the grader on the flexible beam is equivalent to the force F applied by the spring. The formula for calculating the force F applied by the equivalent spring is:

[0106]

[0107] in, , The force F applied by the equivalent spring has its x and y axis components. Hydraulic stiffness, hydraulic stiffness The calculation formula is:

[0108]

[0109] in, The elastic modulus of hydraulic oil. Let V be the piston area, V be the original volume of the hydraulic cylinder, and V be the elastic modulus of the hydraulic oil. The range of values ​​is Based on the force F applied by the equivalent spring, the driving torque of the hydraulic cylinder of the flexible beam is... The calculation formula is: .

[0110] In one embodiment, substituting the kinetic energy, potential energy, and driving torque of the flexible beam system into the Lagrange equation, and discretizing the Lagrange equation using the assumed modal method to obtain the lateral displacement function of any point on the flexible beam as the height of the flat-bottomed shovel is adjusted, includes: the assumed modal method is a discretization method for continuous systems, which uses a linear combination of a finite number of known modal functions to approximate the system response; according to the assumed modal method, the lateral displacement function... Represented as:

[0111]

[0112] in, Let i be the basis function of the i-th mode. Let be the coordinates of the i-th modal, where i represents the i-th discretized system, and Satisfies the following orthogonality relation:

[0113]

[0114] Here, according to the formula contained in T1 ,Will Substitution get When i=j, The value is ,but ;

[0115] According to the orthogonality relation, then Discretized as:

[0116]

[0117] in, , For the purpose of simplifying the formula design, this has no other meaning. for ;

[0118] Will Discretized as:

[0119]

[0120] in, for ; to transfer the elastic potential energy of the flexible beam Discretized as:

[0121]

[0122] in, For generalized stiffness, The Lagrange equation is:

[0123]

[0124] Where q is q(t), T is the total kinetic energy, V is the total potential energy, t is time, and θ is the coordinate system of X1O1Y1 and X. W O W Y W The angle between the X-axis and the coordinate system; substituting the formulas for calculating total kinetic energy T, total potential energy V, and driving torque τ into the Lagrange equation, we obtain the dynamic equation of the flexible beam during the elevation movement of the leveling shovel:

[0125]

[0126] The coordinates of the i-th mode are obtained by solving the dynamic equations of the flexible beam. And substitute the lateral displacement function determined according to the assumed modal method. We obtain a functional expression for the lateral displacement x of any point on the flexible beam with time t when the height of the shovel is adjusted.

[0127] In a specific embodiment, the implementation process of a rigid-flexible coupling dynamic modeling method for elevation adjustment of a paddy field grader is as follows:

[0128] The hinge point of the flexible beam in the three-point suspension mechanism of the grader is taken as the origin of the world coordinate system. and the origin of the moving coordinate system The straight line containing the axis when the cross-sectional axis of the flexible beam is parallel to the ground is taken as... , to be perpendicular to and the straight line on the ground is To obtain a two-dimensional world coordinate system Let X1 be the straight line containing the axis of the flexible beam's cross-section, and let X1 be a line perpendicular to X1 and parallel to the axis of the flexible beam's cross-section. Let Y1 be the straight line in the plane, and establish a generalized coordinate system. ;

[0129] The transverse vibration mode function of the flexible beam is: ;in, It is a lateral displacement function. For modal shape functions, Let x be the modal coordinate, x be the coordinate of any point on the flexible beam, and t be time.

[0130] Based on Euler-Bernoulli's vibration theory of flexible beams, the modal shape functions are obtained. The calculation formula is:

[0131]

[0132] in, , To simplify the formula design, and without other meanings, ρ is the mass density, S is the cross-sectional area, E is the elastic modulus of the material, I is the moment of inertia of the cross section about the neutral axis, ω is the natural frequency, and A, B, C, and D are constants. The values ​​of A, B, C, and D are determined according to the boundary conditions of the flexible beam.

[0133] In coordinate system and When the coordinate systems coincide, the position of the flexible beam at this moment is defined as the initial position. At this point, the kinetic and potential energy of the flexible beam structure are both zero. As the grader moves along the elevation, the flexible beam generates kinetic and potential energy. In the coordinate system, Let's consider a point before the flexible beam deforms, with coordinates as follows: After the flexible beam deforms, Transform to Location, coordinates are , exist The position vector in the coordinate system is:

[0134]

[0135] in, This is the coordinate transformation matrix. for coordinate system and The angle between the X-axis and the coordinate system, u is coordinate transformation matrix for:

[0136]

[0137] The formula for calculating the kinetic energy T1 of a flexible beam is as follows:

[0138] Kinetic energy of the concentrated mass at the end of the flexible beam for:

[0139]

[0140] Where m is the concentrated mass at the end of the flexible beam. For the concentrated mass at the end of the flexible beam The position vector in the coordinate system, where L is the length of the flexible beam, and u is... ;

[0141] The formula for calculating the total kinetic energy T is:

[0142] ;

[0143] During the operation of the elevation cylinder controlling the elevation movement of the grader, the elastic potential energy and gravitational potential energy of the flexible beam change with the movement. During the movement of the flexible beam, due to its deformation and change in position and height, the potential energy includes the strain energy stored during deformation and the gravitational potential energy. Therefore, the formula for calculating the elastic potential energy V1 of the flexible beam is:

[0144]

[0145] Based on the initial position of the flexible beam, the potential energy of the flexible beam structure is zero. The change in gravitational potential energy of the concentrated mass at the end of the flexible beam and the mass of the flexible beam is equal to the gravitational potential energy of the flexible beam. The change in gravitational potential energy caused by the elastic deformation of the flexible beam usually has a very small impact and can be ignored. The formula for calculating the change in gravitational potential energy U of the concentrated mass at the end of the flexible beam and the mass of the flexible beam is:

[0146]

[0147] in, Let be the mass of the flexible beam, and e be a unit vector along the direction of gravity;

[0148] The formula for calculating the total potential energy V is: .

[0149] The driving device for elevation motion is an elevation hydraulic cylinder (assuming no friction inside the cylinder, no oil leakage, and no pressure drop, and ignoring the effect of beam deformation on the extension and retraction of the hydraulic push rod), where b and h are the hinge points between the elevation hydraulic cylinder push rod and the flexible beam. The horizontal and vertical coordinates are used to derive the displacement vector of the hydraulic push rod's extension and retraction from its geometric position. for:

[0150]

[0151] in, , displacement vector Components of displacement along the x and y axes

[0152] The formula for calculating the force F applied by the equivalent spring is:

[0153]

[0154] in, , The force F applied by the equivalent spring has its x and y axis components. Hydraulic stiffness, hydraulic stiffness The calculation formula is:

[0155]

[0156] in, The elastic modulus of hydraulic oil. Let V be the piston area, V be the original volume of the hydraulic cylinder, and V be the elastic modulus of the hydraulic oil. The range of values ​​is The determining factors are the amount of gas dissolved in the hydraulic oil and the working pressure. When the gas content is low and the pressure is high, the elastic modulus of the hydraulic oil is high. For large quantities, the elastic modulus of hydraulic oil is generally taken. The value is 7000×10 5 N / m 2 The driving torque of the hydraulic cylinder of the flexible beam The calculation formula is: .

[0157] The assumed modal method is a discretization method for continuous systems. It approximates the system response by using a linear combination of a finite number of known modal functions. According to the assumed modal method, the transverse displacement function... Represented as:

[0158]

[0159] in, Let i be the basis function of the i-th mode. Let be the coordinates of the i-th modal, where i represents the i-th discretized system, and Satisfies the following orthogonality relation:

[0160]

[0161] According to the orthogonality relation, then Discretized as:

[0162]

[0163] in, , For the purpose of simplifying the formula design, this has no other meaning. for ;

[0164] Will Discretized as:

[0165]

[0166] in, for ;

[0167] The elastic potential energy of the flexible beam Discretized as:

[0168]

[0169] in, For generalized stiffness, ;

[0170] The Lagrange equation is:

[0171]

[0172] Where q is q(t), T is the total kinetic energy, V is the total potential energy, t is time, and θ is the coordinate system of X1O1Y1 and X. W O W Y W The angle between the X-axis and the coordinate system;

[0173] Substituting the formulas for calculating total kinetic energy T, total potential energy V, and driving torque τ into the Lagrange equation, we obtain the dynamic equation of the flexible beam during the elevation movement of the leveling shovel:

[0174]

[0175] Solving the dynamic equations of the flexible beam And substitute the lateral displacement function determined according to the assumed modal method. We obtain a functional expression for the lateral displacement x of any point on the flexible beam with time t when the height of the shovel is adjusted.

[0176] It should be understood that, although Figure 2 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 2 At least some of the steps in the process may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but may be executed at different times. The execution order of these steps or stages is not necessarily sequential, but may be executed in turn or alternately with other steps or at least some of the steps or stages in other steps.

[0177] In one embodiment, such as Figure 5 As shown, a rigid-flexible coupled dynamic modeling device for elevation adjustment of a paddy field grader is provided, comprising:

[0178] The coordinate system establishment module 210 is used to establish the origin of the world coordinate system based on the hinge point of the flexible beam in the three-point suspension mechanism of the grader. and the origin of the moving coordinate system The straight line containing the axis when the cross-sectional axis of the flexible beam is parallel to the ground is taken as... , to be perpendicular to and the straight line on the ground is To obtain a two-dimensional world coordinate system Taking the straight line containing the axis of the flexible beam's cross-section as... , to be perpendicular to And with A straight line in the plane is Establish a generalized coordinate system ;

[0179] The transverse vibration mode function calculation module 220 is used to obtain the transverse vibration mode function of the flexible beam under boundary conditions based on the vibration theory of Euler-Bernoulli beams.

[0180] The kinetic potential energy calculation module 230 is used to calculate based on a two-dimensional world coordinate system. Generalized coordinate system Given the transverse vibration mode function of the flexible beam, calculate the kinetic and potential energy of the flexible beam system;

[0181] The driving torque calculation module 240 is used to calculate the driving torque of the hydraulic cylinder of the flexible beam by converting the force exerted by the elevation cylinder controlling the elevation movement of the grader on the flexible beam into the force applied by the equivalent spring.

[0182] The lateral displacement function calculation module 250 is used to substitute the kinetic energy, potential energy, and driving torque of the flexible beam system into the Lagrange equation, and to discretize the Lagrange equation using the assumed modal method to obtain the lateral displacement function of any point on the flexible beam as a function of time during the height adjustment of the flat-bottomed shovel. In one embodiment, obtaining the lateral vibration mode function of the flexible beam under boundary conditions based on the vibration theory of Euler Bernoulli beams includes: obtaining the mode shape function based on the vibration theory of Euler Bernoulli flexible beams. The calculation formula is:

[0183]

[0184] in, , To simplify the formula design, and without other meanings, ρ is the mass density, S is the cross-sectional area, E is the elastic modulus of the material, I is the moment of inertia of the cross section about the neutral axis, ω is the natural frequency, A, B, C, and D are constants, the values ​​of A, B, C, and D are determined according to the boundary conditions of the flexible beam, and x is the coordinate of any point on the flexible beam; then the transverse vibration mode function of the flexible beam is: Where u(x, t) is the lateral displacement function. Let q(t) be the mode shape function, q(t) be the modal coordinates, and t be the time.

[0185] In one embodiment, such as Figure 3 As shown, the two-dimensional world coordinate system Generalized coordinate system Given the transverse vibration mode function of the flexible beam, calculate the kinetic and potential energy of the flexible beam system, including: in the coordinate system and When the coordinate systems coincide, the position of the flexible beam at this moment is defined as the initial position. At this point, the kinetic and potential energy of the flexible beam structure are both zero. As the grader moves along the elevation, the flexible beam generates kinetic and potential energy. In the coordinate system, p1 is a point on the flexible beam before deformation, with coordinates of After the flexible beam deforms, position p1 changes to position p2, with coordinates as follows: p2 in coordinate system The position vector in is:

[0186]

[0187] in, This is the coordinate transformation matrix. for coordinate system and The angle between the X-axis and the coordinate system, u is coordinate transformation matrix for:

[0188]

[0189] The formula for calculating the kinetic energy T1 of a flexible beam is as follows:

[0190]

[0191] Kinetic energy of the concentrated mass at the end of the flexible beam for:

[0192]

[0193] Where m is the concentrated mass at the end of the flexible beam. For the concentrated mass at the end of the flexible beam The position vector in the coordinate system, where L is the length of the flexible beam, and u is... The formula for calculating the total kinetic energy T is: During the operation of the elevation cylinder controlling the elevation movement of the grader, the elastic potential energy and gravitational potential energy of the flexible beam change with the movement. During the movement of the flexible beam, due to its deformation and change in position and height, the total potential energy includes the strain energy stored during deformation and the gravitational potential energy. Therefore, the strain energy of the flexible beam... The calculation formula is:

[0194]

[0195] Based on the initial position of the flexible beam, the potential energy of the flexible beam structure is zero. The change in gravitational potential energy of the concentrated mass at the end of the flexible beam and the mass of the flexible beam is equal to the gravitational potential energy of the flexible beam. The formula for calculating the change in gravitational potential energy U of the concentrated mass at the end of the flexible beam and the mass of the flexible beam is expressed as:

[0196]

[0197] in, Let be the mass of the flexible beam, and e be a unit vector along the direction of gravity; then the formula for calculating the total potential energy V is: .

[0198] In one embodiment, such as Figure 4 As shown, the force exerted by the elevation cylinder controlling the elevation movement of the grader on the flexible beam is equivalent to the force applied by a spring, and the driving torque of the hydraulic cylinder of the flexible beam is calculated. This includes: the driving device for elevation movement is an elevation cylinder, and b and h are the hinge points between the elevation hydraulic cylinder push rod and the flexible beam. The horizontal and vertical coordinates are used to derive the displacement vector of the hydraulic push rod's extension and retraction from its geometric position. for:

[0199]

[0200] in, , displacement vector For the components of displacement along the x and y axes, the force exerted by the elevation cylinder controlling the elevation movement of the grader on the flexible beam is equivalent to the force F applied by the spring. The formula for calculating the force F applied by the equivalent spring is:

[0201]

[0202] in, , The force F applied by the equivalent spring has its x and y axis components. Hydraulic stiffness, hydraulic stiffness The calculation formula is:

[0203]

[0204] in, The elastic modulus of hydraulic oil. Let V be the piston area, V be the original volume of the hydraulic cylinder, and V be the elastic modulus of the hydraulic oil. The range of values ​​is Based on the force F applied by the equivalent spring, the driving torque of the hydraulic cylinder of the flexible beam is... The calculation formula is: .

[0205] In one embodiment, substituting the kinetic energy, potential energy, and driving torque of the flexible beam system into the Lagrange equation, and discretizing the Lagrange equation using the assumed modal method to obtain the lateral displacement function of any point on the flexible beam as the height of the flat-bottomed shovel is adjusted, includes: the assumed modal method is a discretization method for continuous systems, which uses a linear combination of a finite number of known modal functions to approximate the system response; according to the assumed modal method, the lateral displacement function... Represented as:

[0206]

[0207] in, Let i be the basis function of the i-th mode. Let be the coordinates of the i-th modal, where i represents the i-th discretized system, and Satisfies the following orthogonality relation:

[0208]

[0209] According to the orthogonality relation, then Discretized as:

[0210]

[0211] in, , For the purpose of simplifying the formula design, this has no other meaning. for ;

[0212] Will Discretized as:

[0213]

[0214] in, for ; to transfer the elastic potential energy of the flexible beam Discretized as:

[0215]

[0216] in, For generalized stiffness, ;

[0217] The Lagrange equation is:

[0218]

[0219] Where q is q(t), T is the total kinetic energy, V is the total potential energy, t is time, and θ is the coordinate system of X1O1Y1 and X. W O W Y W The angle between the X-axis and the coordinate system;

[0220] Substituting the formulas for calculating total kinetic energy T, total potential energy V, and driving torque τ into the Lagrange equation, we obtain the dynamic equation of the flexible beam during the elevation movement of the leveling shovel:

[0221]

[0222] Solving the dynamic equations of the flexible beam And substitute the lateral displacement function determined according to the assumed modal method. We obtain a functional expression for the lateral displacement x of any point on the flexible beam with time t when the height of the shovel is adjusted.

[0223] In one embodiment, the paddy field grader platform used in this application, based on actual measurement and calculation, has an arm length L = 0.86m and a cross-sectional area of... ,density elastic modulus end quality Moment of inertia Piston area Hydraulic cylinder volume The horizontal and vertical coordinates of the hinge point B0 between the hydraulic cylinder push rod and the flexible beam are b=0.18m and h=0.062m. Using MATLAB's rigid-flexible coupling dynamic modeling method for elevation adjustment of a paddy field grader, numerical analysis was performed on the dynamic equation of the flexible beam during the elevation movement of the grader and the functional expression of the lateral displacement x of any point on the flexible beam with time t during grader height adjustment. The simulation results of the displacement of a point on the grader in the Z direction under the working condition of the hydraulic cylinder piston length from 80cm to its maximum stroke and then from the maximum stroke to the minimum stroke are shown below. Figure 7 As shown by the dashed line. Using a binocular high-speed camera, under the same working conditions, the displacement of the same point on the leveling shovel in the Z direction is measured, as shown. Figure 7 As shown by the solid line. The simulation results are compared with the measurement results, and the comparison results are as follows. Figure 7 As shown, the results indicate that the model accurately describes the elevation motion of the grader.

[0224] Specific limitations regarding the rigid-flexible coupling dynamics modeling device for elevation adjustment of paddy field graders can be found in the limitations of the rigid-flexible coupling dynamics modeling method for elevation adjustment of paddy field graders mentioned above, and will not be repeated here. Each module in the aforementioned rigid-flexible coupling dynamics modeling device for elevation adjustment of paddy field graders can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0225] In one embodiment, a computer device is provided, which may be a server, and its internal structure diagram may be as follows: Figure 6 As shown, the computer device includes a processor, memory, and network interface connected via a system bus. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The database stores parameter data of the flexible beam of the grader. The network interface communicates with external terminals via a network connection. When the computer program is executed by the processor, it implements a rigid-flexible coupling dynamic modeling method for elevation adjustment of a paddy field grader.

[0226] Those skilled in the art will understand that Figure 6The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0227] In one embodiment, a computer device is also provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above method embodiments.

[0228] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon that, when executed by a processor, implements the steps in the above method embodiments.

[0229] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the methods described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0230] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0231] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A rigid-flexible coupling dynamic modeling method for elevation adjustment of a paddy field grader, characterized in that, The method includes: using the hinge point of the flexible beam in the three-point suspension mechanism of the grader as the origin of the world coordinate system. and the origin of the moving coordinate system The straight line containing the axis when the cross-sectional axis of the flexible beam is parallel to the ground is taken as... , to be perpendicular to and the straight line on the ground is To obtain a two-dimensional world coordinate system Taking the straight line containing the axis of the flexible beam's cross-section as... , to be perpendicular to And with A straight line in the plane is Establish a generalized coordinate system ; Based on the vibration theory of Euler-Bernoulli beams, the transverse vibration mode function of the flexible beam under boundary conditions is obtained; According to the two-dimensional world coordinate system Generalized coordinate system Given the transverse vibration mode function of the flexible beam, calculate the kinetic and potential energy of the flexible beam system; The force exerted by the elevation cylinder controlling the elevation movement of the grader on the flexible beam is equivalent to the force applied by the spring, and the driving torque of the hydraulic cylinder of the flexible beam is calculated. Substituting the kinetic energy, potential energy, and driving torque of the flexible beam system into the Lagrange equation, and using the assumed modal method to discretize the Lagrange equation, we obtain the lateral displacement function of any point on the flexible beam as time changes when the height of the flat-bottomed shovel is adjusted. The calculation of the driving torque of the hydraulic cylinder of the flexible beam, which is equivalent to the force applied by the spring to the force exerted by the elevation cylinder controlling the elevation movement of the grader, includes: The driving device for elevation motion is an elevation hydraulic cylinder, and b and h are the hinge points between the elevation hydraulic cylinder push rod and the flexible beam. The horizontal and vertical coordinates are used to derive the displacement vector of the hydraulic push rod's extension and retraction from its geometric position. for: in, , displacement vector Components of displacement along the x and y axes for coordinate system and The angle between the X-axis and the coordinate system; The force exerted by the elevation cylinder controlling the elevation movement of the grader on the flexible beam is equivalent to the force F applied by the spring. The formula for calculating the force F applied by the equivalent spring is as follows: in, , The force F applied by the equivalent spring has its x and y axis components. Hydraulic stiffness, hydraulic stiffness The calculation formula is: in, The elastic modulus of hydraulic oil. Let V be the piston area, V be the original volume of the hydraulic cylinder, and V be the elastic modulus of the hydraulic oil. The range of values ​​is ; Based on the force F applied by the equivalent spring, the driving torque of the hydraulic cylinder of the flexible beam is... The calculation formula is: .

2. The method according to claim 1, characterized in that, The process of obtaining the transverse vibration mode function of the flexible beam under boundary conditions based on the vibration theory of Euler-Bernoulli beams includes: obtaining the mode mode function based on the vibration theory of Euler-Bernoulli flexible beams. The calculation formula is: in, , To simplify the formula design, it has no other meaning. ρ is the mass density, S is the cross-sectional area, E is the elastic modulus of the material, I is the moment of inertia of the cross section about the neutral axis, ω is the natural frequency, A, B, C, and D are constants, the values ​​of A, B, C, and D are determined according to the boundary conditions of the flexible beam, and x is the coordinate of any point on the flexible beam. The transverse vibration mode function of the flexible beam is: Where u(x, t) is the lateral displacement function. Let q(t) be the mode shape function, q(t) be the modal coordinates, and t be the time.

3. The method according to claim 2, characterized in that, According to the two-dimensional world coordinate system Generalized coordinate system Given the transverse vibration mode function of the flexible beam, calculate the kinetic and potential energy of the flexible beam system, including: In coordinate system and When the coordinate systems coincide, the position of the flexible beam at this moment is defined as the initial position. At this point, the kinetic and potential energy of the flexible beam structure are both zero. As the grader moves along the elevation, the flexible beam generates kinetic and potential energy. In the coordinate system, Let's consider a point before the flexible beam deforms, with coordinates as follows: After the flexible beam deforms, Transform to Location, coordinates are , exist The position vector in the coordinate system is: in, This is the coordinate transformation matrix. for coordinate system and The angle between the X-axis and the coordinate system, u is coordinate transformation matrix for: The formula for calculating the kinetic energy T1 of a flexible beam is as follows: Kinetic energy of the concentrated mass at the end of the flexible beam for: Where m is the concentrated mass at the end of the flexible beam. For the concentrated mass at the end of the flexible beam The position vector in the coordinate system, where L is the length of the flexible beam, and u is... ; The formula for calculating the total kinetic energy T is: ; During the operation of the elevation cylinder controlling the elevation movement of the grader, the elastic potential energy and gravitational potential energy of the flexible beam change with the movement. During the movement of the flexible beam, due to its deformation and change in position and height, the total potential energy includes the strain energy stored during deformation and the gravitational potential energy. Therefore, the strain energy of the flexible beam... The calculation formula is: Based on the initial position of the flexible beam, the potential energy of the flexible beam structure is zero. The change in gravitational potential energy of the concentrated mass at the end of the flexible beam and the mass of the flexible beam is equal to the gravitational potential energy of the flexible beam. The formula for calculating the change in gravitational potential energy U of the concentrated mass at the end of the flexible beam and the mass of the flexible beam is expressed as: in, Let be the mass of the flexible beam, and e be a unit vector along the direction of gravity; The formula for calculating the total potential energy V is: .

4. The method according to claim 1, characterized in that, The process involves substituting the kinetic energy, potential energy, and driving torque of the flexible beam system into the Lagrange equation, and then discretizing the Lagrange equation using the assumed modal method to obtain the lateral displacement function of any point on the flexible beam as the height of the flat-bottomed shovel is adjusted. This includes: the assumed modal method is a discretization method for continuous systems, which approximates the system response using a linear combination of a finite number of known modal functions. According to the assumed modal method, the lateral displacement function... Represented as: in, Let i be the basis function of the i-th mode. Let be the coordinates of the i-th modal, where i represents the i-th discretized system, and Satisfies the following orthogonality relation: According to the orthogonality relation, then Discretized as: in, , For the purpose of simplifying the formula design, this has no other meaning. for ; Will Discretized as: in, for ; The elastic potential energy of the flexible beam Discretized as: in, For generalized stiffness, ; The Lagrange equation is: Where q is q(t), T is the total kinetic energy, V is the total potential energy, t is time, and θ is the coordinate system of X1O1Y1 and X. W O W Y W The angle between the X-axis and the coordinate system; Substituting the formulas for calculating total kinetic energy T, total potential energy V, and driving torque τ into the Lagrange equation, we obtain the dynamic equation of the flexible beam during the elevation movement of the leveling shovel: The coordinates of the i-th mode are obtained by solving the dynamic equations of the flexible beam. And substitute the lateral displacement function determined according to the assumed modal method. We obtain a functional expression for the lateral displacement x of any point on the flexible beam with time t when the height of the shovel is adjusted.

5. A rigid-flexible coupling dynamic modeling device for the elevation adjustment of a paddy field grader, applied to the rigid-flexible coupling dynamic modeling method for elevation adjustment of a paddy field grader as described in claim 1, characterized in that, The device includes: The coordinate system establishment module is used to establish the origin of the world coordinate system based on the hinge point of the flexible beam in the three-point suspension mechanism of the grader. and the origin of the moving coordinate system The straight line containing the axis when the cross-sectional axis of the flexible beam is parallel to the ground is taken as... , to be perpendicular to and the straight line on the ground is To obtain a two-dimensional world coordinate system Let X1 be the straight line containing the axis of the flexible beam's cross-section, and let X1 be a line perpendicular to X1 and parallel to the axis of the flexible beam's cross-section. Let Y1 be the straight line in the plane, and establish a generalized coordinate system. ; The transverse vibration mode function calculation module is used to obtain the transverse vibration mode function of a flexible beam under boundary conditions based on the vibration theory of Euler-Bernoulli beams. The kinetic potential energy calculation module is used to calculate based on a two-dimensional world coordinate system. Generalized coordinate system Given the transverse vibration mode function of the flexible beam, calculate the kinetic and potential energy of the flexible beam system; The driving torque calculation module is used to calculate the driving torque of the hydraulic cylinder of the flexible beam by equating the force exerted by the elevation cylinder controlling the elevation movement of the grader on the flexible beam with the force applied by the spring. The lateral displacement function calculation module is used to substitute the kinetic energy, potential energy, and driving torque of the flexible beam system into the Lagrange equation, and to discretize the Lagrange equation using the assumed modal method to obtain the lateral displacement function of any point on the flexible beam as time changes when the height of the flat-bottomed shovel is adjusted.

6. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 4.

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