A Dynamic Modeling and Tracking Control Method for Adaptive Wire Placement and Compaction Mechanism

Abstract

This invention discloses a dynamic modeling and tracking control method for an adaptive wire-laying and compaction mechanism, belonging to the technical field of specific model calculation systems. The method includes the following steps: S1: Establishing a kinematic model of the adaptive wire-laying and compaction mechanism; S2: Establishing a workpiece surface model and solving for the coordinates of the tangent points and positions of the driving and driven wheels with the ground; S3: Solving for the relationship between the reaction forces and external forces of each support based on the force balance equations and moment balance equations of each rod; S4: Establishing a dynamic model of the driving device; S5: Performing error analysis and optimization to ensure that the main pressure is within the fluctuation range. This invention can ensure a constant roller output pressure when laying steeply varied surface structures, avoiding forming defects caused by uneven pressure.

Description

Technical Field

[0001] This invention relates to the field of digital data processing technology, and in particular to an adaptive method for dynamic modeling and tracking control of a wire-laying and compaction mechanism. Background Technology

[0002] Carbon fiber reinforced resin matrix composites are widely used in aerospace and defense equipment due to their excellent mechanical properties, such as specific strength and specific stiffness being four and eight times that of steel, respectively.

[0003] In aerospace, automotive manufacturing, and other fields, the manufacture of high-performance structural components often requires high-precision, low-damage forming processes. Automated fiber placement technology, as an advanced manufacturing process, is widely used because it can efficiently lay up fiber materials.

[0004] While existing wire-laying and compaction mechanisms for complex, abruptly curved surface structures in China can be designed to match the curvature variations of the surface to meet the adaptive placement and forming requirements of such structures and multiple material specifications, the lack of corresponding control methods leads to abrupt pressure changes during actual placement due to sudden curvature shifts, affecting the mechanical properties of the final parts.

[0005] Traditional fiber-laying and compaction mechanisms struggle to maintain constant pressure, leading to molding defects and impacting product quality. Therefore, those skilled in the art urgently need an algorithmic control method capable of meeting the demands for high-precision pressure control. Summary of the Invention

[0006] The purpose of this invention is to provide a dynamic modeling and tracking control method for an adaptive wire-laying and compacting mechanism. Addressing the issue of pressure abrupt changes due to curvature abrupt changes in the adaptive wire-laying and compacting mechanism under normal operating conditions, the structure of the adaptive wire-laying and compacting mechanism under normal operating conditions is reasonably simplified. Then, a dynamic model of the entire system is established based on the Newton-Euler method. Finally, based on the dynamic model of the adaptive wire-laying and compacting mechanism, a reasonable control algorithm is established to ensure that the roller outputs constant pressure when laying steeply variable surface structures, avoiding forming defects caused by uneven pressure.

[0007] To achieve the above objectives, this invention provides an adaptive filament placement and compaction mechanism dynamic modeling and tracking control method, comprising the following steps:

[0008] S1: Establish the kinematic model of the adaptive wire-laying and compaction mechanism;

[0009] S2: Establish a ground model and solve for the coordinates of the tangent points and positions of the driving wheel, driven wheel, and ground.

[0010] S3: Based on the force balance equations and moment balance equations of each rod, solve for the relationship between the reaction forces of each support and the external forces;

[0011] S4: Establish the dynamic model of the drive device;

[0012] S5: Perform error analysis and optimization to ensure that the main pressure is within the fluctuation range.

[0013] Preferably, in S1, the adaptive fiber laying and compaction mechanism is simplified. The simplified mechanism includes rod zero, rod one, rod two, and rod three. The middle part of rod one is hinged to rod zero. Rod two and rod three are arranged crosswise. One end of rod two is hinged to one end of rod one, and the other end of rod two is rotatably connected to a driven wheel. One end of rod three is hinged to the other end of rod one, and the other end of rod three is rotatably connected to a driving wheel. The middle sections of rod two and rod three are respectively rotatably connected and slidably connected to rod zero.

[0014] Preferably, in S1, the simplified mechanism is modeled. First, a base coordinate system is established, and then coordinate systems are established on link zero, link one, link two, and link three respectively, thereby determining the correspondence between each link; based on each different h0 and the angle of link one... Find the angular relationships between link 1 and link 2, and between link 1 and link 3 at each time point; where, h 0 From point A to x 0 Vertical distance, angle For rod one and x 1 The included angle of the axes; based on the angular relationship, determine the angular velocity, angular acceleration, velocity, acceleration of the origin of the coordinate system for rod zero, rod one, rod two, and rod three, and the acceleration at the center of mass positions of rod zero, rod one, rod two, and rod three.

[0015] Preferably, the origin of the base coordinate system is the center of points D and E; the origin of the coordinate system of rod zero is point A; the origin of the coordinate system of rod one is point A; the origin of the coordinate system of rod two is point C; the origin of the coordinate system of rod three is point B; the origin of the coordinate system of the driving wheel is point G; and the origin of the coordinate system of the driven wheel is F.

[0016] The center of mass of link one and link zero is point A, the center of mass of link two and the driven wheel is point F, and the center of mass of link three and the driving wheel is point G.

[0017] Preferably, in S1, the inertial forces of each rod are calculated according to Newton's second law:

[0018] (1);

[0019] in, For the firsti +1 rod at the i Inertial forces in the +1 rod coordinate system For the first i +1 rod's center of mass is in the... i In the +1 rod coordinate system, relative to the first i The acceleration of each rod, For the first i +1 rod mass;

[0020] Using Euler's equations, the inertial moments of each rod can finally be calculated:

[0021] (2);

[0022] in, For the first i +1 rod at the i +1 rod coordinate system inertial torque, It is the first i +1 moment of inertia of the rod relative to its center of mass. It is the first i +1 rod at the i +1 angular acceleration in the rod coordinate system It is the first i +1 rod at the i Angular velocity in the +1 rod coordinate system.

[0023] Preferably, in S2, a ground coordinate system is established, and the equations of the ground model are also the equations of the workpiece surface. The equations of the workpiece surface are:

[0024] (3);

[0025] Based on the equations of the workpiece surface and the established kinematic relationships, determine the positional relationship of the driving wheel in the ground coordinate system at any given moment:

[0026] (4);

[0027] in, The position of the driving wheel in the ground coordinate system. Let be the horizontal component of the velocity of the driving wheel relative to the ground coordinate system at time t. The velocity of the entire workpiece in the ground coordinate system is x Component of direction;

[0028] Based on the constraints between the driving wheel and the ground, the position of the contact point between the driving wheel and the ground at each position is determined using Newton's iteration method, and the position of the tangent angle between the driving wheel and the ground is also calculated.

[0029] (5);

[0030] in, It is the contact angle between the drive wheel and the ground. The driving wheel in the base coordinate system x Coordinates of direction;

[0031] Determine the vertical component of the position of the active wheel in the base coordinate system. :

[0032] (6);

[0033] in, This represents the vertical component of the position of the base coordinate system relative to the ground coordinate system. The radius of the driving wheel;

[0034] Similarly, the positional relationship of the passive wheel in the ground coordinate system can be obtained:

[0035] (7);

[0036] in, For the passive wheel t The horizontal component of the velocity relative to the ground coordinate system at each moment is determined. Based on the constraints between the driven wheel and the ground, the position of the contact point between the driven wheel and the ground at each position is solved using Newton's iteration method, and the position of the tangent angle between the driven wheel and the ground is also calculated.

[0037] (8);

[0038] in, It is the contact angle between the driven wheel and the ground. The passive wheel in the base coordinate system x Coordinates of direction;

[0039] Based on this, determine the vertical component of the position of the passive wheel on the base coordinate system. :

[0040] (9);

[0041] in, The radius of the driven wheel is determined by... h 1 and h 2 Inverse solution of parameters from various angles.

[0042] Preferably, in S3, the required driving force for each rod is calculated based on the force balance equations of each rod:

[0043] (10);

[0044] in, For the first i The driving force required for each link For the first i The rotation matrix from the +1th rod to the i-th rod. For the first i +1 lever required driving force For the first i The inertial force of the rod, for i The external force acting on the rod;

[0045] Calculate the required driving torque for each link based on the torque balance equations for each link: (11);

[0046] in, Representing the i The required driving torque for the rod For the first i The moment of inertia of the rod, For the first i +1 driving torque required Representing the i The position of the rod's center of mass relative to its coordinate system. for i The origin of the coordinate system for rod +1 is at i The position of the rod in the coordinate system. The point of application of the external force is at i Position in rod coordinate system for w coordinate system to i Rotation matrix of rod coordinate system.

[0047] Since the driving torque on links two and three is zero, the torque balance equation is obtained:

[0048] (12);

[0049] (13);

[0050] Since the driving torque of rod one is zero, the torque balance equation is obtained:

[0051] (14);

[0052] Since the driving force of rod zero is zero, the force balance equation of rod one is obtained:

[0053] (15);

[0054] in, Let the support reaction force be the force acting on rod two at point D. Let E be the support reaction force acting on rod three at point E. Let F be the support reaction force experienced by rod 2 at point F, i.e., at the driven wheel. The support reaction force experienced by rod three at point G, i.e., at the driving wheel; ~ It is related to the parameters of each link and its kinematic parameters, the contact angle and position coordinates of the driving or driven wheel with the ground. ~ The specific values ​​are obtained by solving the established ground equations and the angular relationships between the rods. Therefore, at each moment... ~ All are known quantities;

[0055] Substitute formulas (12), (13), and (14) into formula (15) to obtain the answer. and The relationship between them:

[0056] (16);

[0057] Similarly, find and The relationship between them:

[0058] (17);

[0059] in, 、 Both are the slopes of the equation. 、 All of these are fixed values ​​in the equation.

[0060] Preferably, in S4, the dynamic model of the drive device is the dynamic model of the cylinder. The size is provided by the cylinder, and the cylinder is modeled dynamically:

[0061] (18);

[0062] in, The total mass of the piston, rod, and fiber placement head in the vertical direction. It is the viscous damping coefficient, which is the proportionality coefficient between the damping force generated by viscosity and the velocity. The upper surface area of ​​the piston. The lower surface area of ​​the piston. Frictional force or any disturbance force acting at the end along the y-axis. This refers to the pressure exerted on the upper surface of the piston. This represents the pressure exerted on the lower surface of the piston.

[0063] Preferably, in S5, the constraint optimization problem is transformed into an unconstrained optimization problem by introducing a logarithmic barrier function to handle the constraints;

[0064] Solve for the obstacle function:

[0065] (19);

[0066] in, The pressure provided to the drive wheel The required constant pressure is determined by finding the minimum value of the error solution function. Simultaneously, due to the instantaneous response of the cylinder, the sudden change in the instantaneous force that the cylinder can provide is limited, satisfying the nonlinear inequality:

[0067] , (20);

[0068] in, For the device in The pressure provided by the active wheel at this moment For the device in The pressure provided by the active wheel at this moment The minimum sudden change in force provided by the instantaneous rated energy of the cylinder;

[0069] Based on satisfying the inequality equations, find the value at each time step. The value ensures nonlinearity. error The function takes the minimum value.

[0070] The advantages and positive effects of the adaptive wire-laying and compaction mechanism dynamic modeling and tracking control method described in this invention are:

[0071] 1. An auxiliary control method based on the dynamic model of an adaptive wire placement and compaction mechanism is designed to meet the manufacturing requirements of high-precision, low-damage forming of high-performance structural parts with complex steep deformation surface characteristics. An automatic algorithm control system is designed to adapt to the constant pressure requirement in the automatic wire placement process.

[0072] 2. An error optimization method based on the obstacle function method is used to find a loading scheme that minimizes pressure error while satisfying the maximum output constraint of the cylinder, thereby achieving precise control of the entire mechanism to control the output of the entire mechanism to maintain constant pressure and meet the requirement of constant pressure during automatic laying.

[0073] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0074] Figure 1This is a flowchart of an adaptive wire-laying and compaction mechanism dynamic modeling and tracking control method according to the present invention;

[0075] Figure 2 This is a schematic diagram of the adaptive fiber placement and compaction mechanism of the present invention;

[0076] Figure 3 This is a simplified structural diagram of the adaptive fiber placement and compaction mechanism of the present invention;

[0077] Figure 4 This is a diagram showing the annotations of each rod in the adaptive wire-laying and compaction mechanism of the present invention;

[0078] Figure 5 This is a schematic diagram showing the coordinate system positions of each rod in this invention;

[0079] Figure 6 This is a schematic diagram of the location of the ground coordinate system of the present invention;

[0080] Figure 7 This is a schematic diagram of the support reaction force experienced by the adaptive wire laying and compaction mechanism of the present invention at a certain position;

[0081] Figure 8 This is a comparison diagram of the magnitude of the contact force on the drive wheel calculated by the Adams simulation software under a certain working condition for the adaptive wire laying and compaction mechanism of the present invention.

[0082] Figure 9 This is a comparison diagram of the magnitude of the contact force on the passive wheel calculated by the Adams simulation software under a certain working condition for the adaptive wire laying and compaction mechanism of the present invention.

[0083] Figure 10 This is a comparison diagram showing the magnitude of the contact force experienced by the adaptive wire laying and compaction mechanism of the present invention under a certain working condition, using an error optimization scheme and an unoptimized drive wheel.

[0084] Figure Labels

[0085] 1. Zero lever; 2. One lever; 3. Two levers; 4. Three levers; 5. Driving wheel; 6. Driven wheel. Detailed Implementation

[0086] In the description of this invention, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product is in use. They are used only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. In the description of this invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," and "connect" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0087] In this application, unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. In case of any inconsistency, the meaning set forth in this specification or derived from the content described herein shall prevail. Furthermore, the terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit the scope of this application.

[0088] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0089] like Figure 1 As shown, an adaptive wire-laying and compaction mechanism dynamic modeling and tracking control method includes the following steps:

[0090] S1: Establish the kinematic model of the adaptive wire laying and compaction mechanism.

[0091] S2: Establish a ground model and solve for the coordinates of the tangent points and positions of the driving wheel 5, the driven wheel 6, and the ground.

[0092] S3: Based on the force balance equations and moment balance equations of each rod, solve for the relationship between the reaction forces of each support and the external forces.

[0093] S4: Establish the dynamic model of the drive device.

[0094] S5: Perform error analysis and optimization to ensure that the main pressure is within the fluctuation range.

[0095] like Figure 2 As shown, Figure 2 This is an adaptive wire placement and compaction mechanism. In S1, the adaptive wire placement and compaction mechanism is simplified. The simplified mechanism is as follows: Figure 3As shown, it includes rod 1, rod 2, rod 3, and rod 4. The middle part of rod 2 is hinged to rod 1. Rods 3 and 4 are arranged intersectingly. One end of rod 3 is hinged to one end of rod 2, and the other end of rod 3 is rotatably connected to a driven wheel 6. One end of rod 4 is hinged to the other end of rod 2, and the other end of rod 4 is rotatably connected to a driving wheel 5. The middle sections of rods 3 and 4 are rotatably and slidably connected to rod 1, respectively.

[0096] like Figure 4 As shown, links 1, 2, 3, and 4 are simplified. The driving wheel 5 is fixedly connected to link 4, and the driven wheel 6 is fixedly connected to link 3. The positions of the centers of mass are also simplified. The center of mass of links 2 and 1 is point A. The center of mass of links 3 and 6 is point F. The center of mass of links 4 and 5 is point G.

[0097] like Figure 5 As shown, in S1, the simplified mechanism is modeled. First, a base coordinate system is established, and then coordinate systems are established on links 01, 12, 3, and 4 respectively, thus determining the correspondence between each link. Based on the fundamental kinematic formulas and each different... h 0 By finding the angles between rod 1 and 2, we can determine the angular relationships between rod 1 and 2 and between rod 2 and 3 at each moment. Based on these angular relationships, we can determine the angular velocity, angular acceleration, velocity, acceleration, and the acceleration at the center of mass of rods 01, 12, 3, and 4. h 0 From point A to x 0 Vertical distance, angle For rod 1 and 2 x The included angle of axis 1.

[0098] The origin of the base coordinate system is located at the center of points D and E. x 0 The axis is set horizontally. y 0 The axis is set vertically through point A. The origin of the coordinate system for rod zero 1 is point A, and the coordinate system for rod zero 1... z Axis 1 is along the direction of rod zero 1. x Axis 1 is perpendicular to rod zero 1. The origin of the coordinate system for rod one 2 is point A. x 2. Axis 2 is along the direction of rod 12. y The second axis is perpendicular to rod 2. The origin of the coordinate system for rod 3 is point C. x The 4th axis is along the direction of rod 2, 3. y The fourth axis is perpendicular to rod 2 (3). The origin of the coordinate system for rod 3 (4) is point B. xThe 3rd axis is along the direction of rod 3, 4. y 3 The axis is perpendicular to rod 3 (4). The origin of the coordinate system for the driving wheel (5) is point G. x Axis 5 is along the direction of rod 3, 4. y Axis 5 is perpendicular to rod 3 (4). The origin of the coordinate system for the driven wheel (6) is F. x Axis 6 is along the direction of rod 2, 3. y Axis 6 is perpendicular to rod 2, 3.

[0099] In S1, the inertial forces of each rod are calculated according to Newton's second law:

[0100] (1);

[0101] in, For the first i +1 rod at the i Inertial forces in the +1 rod coordinate system For the first i +1 rod's center of mass is in the... i In the +1 rod coordinate system, relative to the first i The acceleration of each rod, For the first i +1 rod mass.

[0102] Using Euler's equations, the inertial moments of each rod can finally be calculated:

[0103] (2);

[0104] in, For the first i +1 link in the i +1 rod coordinate system inertial torque, It is the first i +1 moment of inertia of the rod relative to its center of mass. It is the first i +1 rod at the i +1 angular acceleration in the rod coordinate system It is the first i +1 rod at the i Angular velocity in the +1 rod coordinate system.

[0105] like Figure 6 As shown. In S2, a ground model is established, and the equation of the ground model is also the equation of the workpiece surface. The equation of the workpiece surface curve is determined by laser scanning. The equation of the workpiece surface is:

[0106] (3);

[0107] in, xThe coordinates of the working face are in the horizontal direction. y These are the coordinates perpendicular to the working surface. Furthermore, the coordinates of the tangent point need to be calculated using formulas to determine the location of the final force-bearing point.

[0108] Based on the equations of the workpiece surface and the established kinematic relationships, the positional relationship of the driving wheel 5 in the ground coordinate system at any given time is determined:

[0109] (4);

[0110] in, The position of drive wheel 5 in the ground coordinate system. For the active wheel 5 in t The horizontal component of the velocity relative to the ground coordinate system at a given moment. The velocity of the entire workpiece in the ground coordinate system is x The directional component.

[0111] like Figure 7 As shown, based on the constraints of the driving wheel 5 and the ground, the position of the contact point between the driving wheel 5 and the ground at each position is solved using Newton's iteration method, and the position of the tangent angle between the driving wheel 5 and the ground is also determined:

[0112] (5);

[0113] in, It is the contact angle between the drive wheel 5 and the ground. It is the driving wheel 5 in the base coordinate system x The coordinates in the 0 direction.

[0114] Determine the vertical component of the position of the driving wheel 5 to the base coordinate system. :

[0115] (6);

[0116] in, The vertical component of the position of the base coordinate system relative to the ground coordinate system; The radius of the drive wheel 5.

[0117] Similarly, the positional relationship of the passive wheel 6 in the ground coordinate system can be obtained:

[0118] (7);

[0119] in, For passive wheel 6 in t The horizontal component of the velocity relative to the ground coordinate system at a given moment. The velocity of the entire workpiece in the ground coordinate system is xThe directional component. Similarly, based on the constraints of the driven wheel 6 and the ground, the position of the contact point between the driven wheel 6 and the ground at each position is solved using Newton's iteration method, and the position of the tangent angle between the driven wheel 6 and the ground is also determined:

[0120] (8);

[0121] in, It is the contact angle between the passive wheel 6 and the ground. It is the passive wheel 6 in the base coordinate system x The coordinates in the 0 direction.

[0122] Determine the vertical component of the position of the passive wheel 6 to the base coordinate system. :

[0123] (9);

[0124] in, The radius of the passive wheel 6 is determined by... h 1 and h 2 Inverse solution of parameters from various angles.

[0125] In S3, the required driving force for each rod is calculated based on the force balance equations of each rod:

[0126] (10);

[0127] in, For the first i The driving force required for each link For the first i +1 stroke to the i The rotation matrix of the rod, For the first i +1 lever required driving force For the first i The inertial force of the rod, for i The external force acting on the rod. Specifically, pay special attention to determining the sign of the force based on its direction.

[0128] Calculate the required driving torque for each link based on the torque balance equations for each link: (11);

[0129] in, Representing the i The required driving torque for the rod For the first i The moment of inertia of the rod, For the first i +1 driving torque required Representing the i The position of the rod's center of mass relative to its coordinate system. for i The origin of the coordinate system for rod +1 is at i The position of the rod in the coordinate system. The point of application of the external force is at i Position in rod coordinate system for w coordinate system ( w 1 coordinate system or w (2 coordinate system) to i Rotation matrix of rod coordinate system.

[0130] Specifically, establish at point E. w 1. Coordinate system x w1 The axis is along the direction of rod 34. y w1 The axis is perpendicular to the direction of rod 3. Establish a point at D. w 2 coordinate system x w2 The axis is along the direction of rod 2, 3. y w2 The axis is perpendicular to the direction of rod 2 (3). Special attention should be paid to determining the sign based on the direction of the force and torque.

[0131] Since the driving torque on links 2 (3) and 3 (4) is zero, the torque balance equation is obtained:

[0132] (12);

[0133] (13);

[0134] Since the driving torque of rod 2 is zero, the torque balance equation is obtained:

[0135] (14);

[0136] Since the driving force of rod 1 is zero, the force balance equation of rod 2 is obtained:

[0137] (15);

[0138] in, Let the support reaction force be the force acting on rod 23 at point D. Let E be the support reaction force experienced by rod 3 at point E. Let be the support reaction force experienced by rod 2 at point F, i.e., at the passive wheel 6. Let 4 be the support reaction force of lever 3 at point G, i.e., at the driving wheel 5.

[0139] ~ It is related to the parameters and kinematic parameters of each rod, the contact angle and position coordinates of the driving wheel 5 or the driven wheel 6 with the ground. ~ The specific values ​​are obtained by solving the established ground equations and the angular relationships between the rods. Therefore, at each moment... ~ All of these are known quantities.

[0140] Substituting formulas (12), (13), and (14) into formula (15) yields the result. and The relationship between them:

[0141] (16);

[0142] Similarly, find and The relationship between them:

[0143] (17);

[0144] in, 、 Both are the slopes of the equation. 、 All of these are fixed values ​​in the equation.

[0145] In S4, the dynamic model of the drive unit is the dynamic model of the cylinder. The size is provided by the cylinder, which requires dynamic modeling of the cylinder:

[0146] (18);

[0147] in, The total mass of the piston, rod, and fiber placement head in the vertical direction. It is the viscous damping coefficient, which is the proportionality coefficient between the damping force generated by viscosity and the velocity. The upper surface area of ​​the piston. The lower surface area of ​​the piston. This refers to the frictional force or any disturbance force acting along the y-axis at the end. This refers to the pressure exerted on the upper surface of the piston. This represents the pressure exerted on the lower surface of the piston.

[0148] In S5, based on the obstacle function method, the constraint optimization problem is transformed into a series of unconstrained optimization problems by introducing a logarithmic obstacle function to handle constraints, thereby obtaining the optimal control scheme.

[0149] First, we need to solve for the barrier function:

[0150] (19);

[0151] in, The pressure provided to the active wheel 5 The required constant pressure is determined by finding the minimum value of the error solution function. Simultaneously, due to the instantaneous response of the cylinder, the sudden change in the instantaneous force that the cylinder can provide is limited, satisfying the nonlinear inequality:

[0152] , (20);

[0153] in, For the device in The pressure provided by the active wheel 5 at this moment For the device in The pressure provided by the active wheel 5 at this moment The minimum sudden change in force provided by the instantaneous rated energy of the cylinder.

[0154] We need to find the condition at each time step, while satisfying the inequality equations. The value ensures nonlinearity. error The function takes the minimum value.

[0155] Example 1

[0156] First, it is necessary to establish a workpiece surface coordinate system, i.e., a ground coordinate system, such as... Figure 6 As shown, the functional relationship of the workpiece surface is obtained as follows:

[0157] (twenty one);

[0158] Under the constraint that the ground equation (21) is tangent to the driving wheel 5 and the driven wheel 6, the coordinates of the tangency point can be found by using Newton's iteration method, and the coordinates of the tangency point at each time step can be solved. h 1 and h 2 By considering the magnitude relationship, we can further solve for the values ​​of each kinematic parameter at each moment. Substituting the obtained parameters into the dynamic formulas (16) and (17), we can obtain the values ​​of each kinematic parameter at each moment. and , The relationship between them.

[0159] To verify the correctness of the model, let With a constant N of 500 N at every time step, the error between the dynamic model and the Adams simulation results is compared, and the results are as follows: Figure 8 , Figure 9 As shown.

[0160] For the driving wheel 5, its maximum error under this condition error max If the value is less than 50N, within a reasonable range, the reliability of the dynamic model can be considered relatively high.

[0161] Based on this, the barrier function method is used to introduce the barrier function, i.e., formula (19), and the minimum sudden change value of the cylinder is required. =18N. Under the above conditions, guarantee... Its size is constant at 389N. Figure 10 The image shows the results before and after error optimization. The size comparison chart shows that after error optimization... Constant.

[0162] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method of adaptive tow placement compaction mechanism dynamics modeling tracking control, characterized in that, The method comprises the following steps: S1: a kinematic model of the adaptive fiber placement and compaction mechanism is established; S2: a ground model is established, and coordinates and position coordinates of the contact points of the driving wheel and the passive wheel with the ground are solved; the equation of the ground model is the equation of the workpiece surface, and the position of the contact points of the driving wheel and the passive wheel with the ground and the position of the tangent angle of the driving wheel and the passive wheel with the ground are solved by the Newton iteration method; S3: according to the force balance equation and the moment balance equation of each rod, the relationship between each support reaction force and external force is solved; the driving force and the driving moment required by each rod are calculated through the inertia force and the inertia moment of each rod solved by the Newton-Euler method; S4: a dynamic model of the driving device is established, which describes the relationship between the driving force provided by the cylinder and the total mass of the piston, the rod and the fiber placement head in the vertical direction, the viscous damping coefficient, the upper and lower surface area of the piston, the friction force or any disturbance force acting on the end, and the pressure received by the upper and lower surfaces of the piston; S5: error analysis and optimization are performed to ensure that the main pressure is within the fluctuation range; In S1, the adaptive fiber placement and compaction mechanism is simplified, and the simplified mechanism comprises rod zero, rod one, rod two and rod three, the middle part of the rod one is hinged to the rod zero, the rod two and the rod three are cross arranged, one end of the rod two is hinged to one end of the rod one, the other end of the rod two is rotatably connected with the passive wheel, one end of the rod three is hinged to the other end of the rod one, the other end of the rod three is rotatably connected with the driving wheel, and the middle segments of the rod two and the rod three are rotatably and slidably connected to the rod zero; According to the angle relationship, the angular velocity, angular acceleration, velocity, acceleration of the coordinate system origins of the rod zero, the rod one, the rod two and the rod three, and the acceleration at the mass center positions of the rod zero, the rod one, the rod two and the rod three are determined; In S5, the constraint optimization problem is converted into an unconstrained optimization problem by introducing an obstacle function to process the constraint; The obstacle function is solved as follows: ； wherein, is the pressure provided by the master cylinder at the moment, is the constant pressure required to be maintained, determined by finding the minimum of the error function, while due to the instantaneous response of the cylinder, the instantaneous force that the cylinder can provide is limited, satisfying the nonlinear inequality: ， ； wherein is the pressure provided by the device at is the pressure provided by the device at is the minimum value of the force provided by the instantaneous power rating of the cylinder On the basis of satisfying inequality equation, the value of each time is found , which ensures the minimum value of nonlinear error function.

2. The method of claim 1, wherein: In S1, the simplified mechanism is modeled, first, the base coordinate system is established, and the coordinate systems are established on the rod zero, rod one, rod two and rod three respectively, so as to determine the corresponding relationship of each rod; according to each different h0 and the angle of rod one , the corresponding angle relationship of rod one and rod two, rod one and rod three at each moment is obtained; wherein, h 0 is the vertical distance from point A to x 0 axis, the angle is the included angle between rod one and x 1 axis, and point A is the origin of the coordinate system of rod zero.

3. The method of claim 2, wherein: The origin of the base coordinate system is at the center position of the points D and E; the origin of the coordinate system of the rod zero is the point A; the origin of the coordinate system of the rod one is the point A; the origin of the coordinate system of the rod two is the point C; the origin of the coordinate system of the rod three is the point B; the origin of the coordinate system of the driving wheel is the point G; and the origin of the coordinate system of the passive wheel is the point F; The mass centers of the rod one and the rod zero are both the point A, the mass centers of the rod two and the passive wheel are both the point F, and the mass centers of the rod three and the driving wheel are both the point G.

4. The method of claim 3, wherein: In S1, the inertia forces of the rods are obtained according to the Newton's second law: ； （1） in, For the first i +1 rod at the i Inertial forces in the +1 rod coordinate system For the first i +1 rod's center of mass is in the... i In the +1 rod coordinate system, relative to the first i The acceleration of each rod, For the first i +1 rod mass; Through the Euler equation, the inertia moments of the rods are finally obtained: ；（2） wherein, is the mass of the i +1st link, i is the moment of inertia of the +1st link about its center of mass, i is the moment of inertia of the +1st link about the i +1st link coordinate system, i is the angular acceleration of the +1st link about the i +1st link coordinate system, i is the angular velocity of the +1st link about the +1st link coordinate system.

5. The method of claim 4, wherein: In S2, a ground coordinate system is established, and the equation of the ground model is also the equation of the workpiece surface, which is as follows: ；（3） wherein x is a coordinate in the horizontal direction of the working face, y is a coordinate in the vertical direction of the working face According to the equation of the workpiece surface and the established kinematic relationship, the position relationship of the driving wheel in the ground coordinate system at any time is determined: ；（4） wherein, is the position of the active wheel in the ground coordinate system, is the component of the velocity of the active wheel in the horizontal direction at time t with respect to the ground coordinate system, is the component of the velocity of the entire workpiece in the ground coordinate in the x direction; According to the constraint condition of the driving wheel and the ground, the position of the contact point of the driving wheel with the ground at each position is solved by the Newton iteration method, and the position of the tangent angle of the driving wheel with the ground is also solved: ；（5） in, It is the contact angle between the drive wheel and the ground. The driving wheel in the base coordinate system x Coordinates of direction; determining the component of the position of the driving wheel to the base coordinate system in the vertical direction : ；（6） wherein is a component of the position of the base coordinate system relative to the ground coordinate system in the vertical direction, is the radius of the drive wheel; Similarly, the position relationship of the passive wheel in the ground coordinate system is obtained as follows: ；（7） in, For the passive wheel t The horizontal component of the velocity relative to the ground coordinate system at each moment is determined. Based on the constraints between the driven wheel and the ground, the position of the contact point between the driven wheel and the ground at each position is solved using Newton's iteration method, and the position of the tangent angle between the driven wheel and the ground is also calculated. ；（8） in, It is the contact angle between the driven wheel and the ground. The passive wheel in the base coordinate system x The coordinates in the 0 direction; On this basis, the position of the passive wheel to the base coordinate system in the vertical direction is determined : ；（9） wherein R is the radius of the passive wheel, by h 1 and h 2 inverse solve for each angular quantity.

6. The method of claim 5, wherein: In S3, the driving force required by each rod is calculated according to the force balance equation of each rod: ； （10） wherein, the driving force required for the first i link, the driving force required for the first i +1 link, i the rotation matrix of the first +1 link, i the driving force required for the first +1 link, i the inertial force of the first +1 link, i the external force on the first +1 link. According to the moment balance equation of each rod, the driving moment required by each rod is calculated: ；（11） wherein, represents the first i the driving torque required for the rod, represents the first i the moment of inertia of the rod, represents the first i the driving torque required for the rod, represents the first i the position of the center of mass of the rod relative to its coordinate system, represents the first i the position of the origin of the coordinate system of the +1 rod in the coordinate system of the first i rod, represents the position of the point of action of the external force in the coordinate system of the first i rod, represents the w coordinate system to the rotation matrix of the coordinate system of the first i rod; Since the driving torque of rod two and rod three is zero, the torque balance equation is obtained: ；（12） ；（13） Since the driving torque of rod one is zero, the torque balance equation is obtained: ；（14） Since the driving force of rod zero is zero, the force balance equation of rod one is obtained: ；（15） wherein, is the reaction force of the second link at point D, is the reaction force of the third link at point E, is the reaction force of the second link at point F, i.e. the passive wheel, is the reaction force of the third link at point G, i.e. the driving wheel; are related to the parameters of each link and its kinematic parameters, the contact angle and position coordinates of the driving wheel or the passive wheel with the ground, are obtained by solving the established ground equation and the angle relationship between each link, and thus are known quantities.​​​ The relationships between the variables are given by equations (12), (13), and (14) and (15) and between the variables: ；（16） The same reasoning applies to finding The relationship between and ；（17） wherein 、 are slopes of the equations, 、 are fixed values of the equations.

7. The method of claim 6, wherein: In S4, the drive dynamics model is the dynamics model of the cylinder, The size of the cylinder is provided by the dynamics model of the cylinder, ；（18） wherein, Mtot is the total mass of the piston, the rod and the fiber placement head in the vertical direction, Cvis is the viscous damping coefficient, i.e. the proportionality coefficient between the damping force and the velocity due to viscous action; Aup is the upper surface area of the piston, Aup is the upper surface area of the piston, Fy is the friction force or any disturbing force acting on the end along the y axis, Pup is the pressure to which the upper surface of the piston is subjected, Pup is the pressure to which the upper surface of the piston is subjected,

Images