Methods for controlling the accuracy and stability of multi-degree-of-freedom envelope forming equipment

Abstract

This invention relates to a method for controlling the accuracy and stability of a multi-degree-of-freedom envelope forming equipment. The envelope forming equipment includes a bed, a motor, a planetary reducer, an electric cylinder, a slider, a connecting rod, a ball seat, a swivel head, and a lower die. The control method includes the following steps: S1, motion planning for the multi-degree-of-freedom envelope forming equipment, solving for the displacement of each slider based on the envelope forming motion requirements and the equipment's kinematic model; S2, solving for the force state of the multi-degree-of-freedom envelope forming equipment; S3, solving for the error compensation amount of the multi-degree-of-freedom envelope forming equipment; S4, obtaining the control strategy for the multi-degree-of-freedom envelope forming equipment, achieving precise motion control of the swivel head under time-varying heavy loads. This invention is based on real-time prediction of the force state of the equipment and the dynamic error of the swivel head using connecting rod strain feedback, solving for the real-time driving force and the error compensation amount of the slider, achieving high-precision and high-stability control of the multi-degree-of-freedom envelope forming equipment.

Description

Technical Field

[0001] This invention relates to a control method for multi-degree-of-freedom envelope forming equipment, and more specifically, to a method for controlling the accuracy and stability of multi-degree-of-freedom envelope forming equipment. Background Technology

[0002] Multi-degree-of-freedom envelope forming equipment is used to realize the spatial envelope forming process of parts. This equipment employs a 6-set servo motor-reducer-ball screw drive, and a parallel load-bearing structure of 6 chain ball joints-ball head connecting rods-ball joints. Multiple servo motors are used for coordinated control to achieve the multi-degree-of-freedom spatial envelope forming motion of the mold. This equipment features a large degree of freedom of motion, good flexibility, and strong adaptability, enabling high-performance and high-efficiency forming manufacturing of thin-walled, high-ribbed extreme structures.

[0003] During the spatial envelope forming process, the swing head motion is complex and the forming force is difficult to predict, resulting in poor stability of the control system. At the same time, the forming force of the equipment is large, and the deformation mechanism of the equipment structure is complex, resulting in large dynamic errors, which affect the motion accuracy of the equipment and the forming accuracy of the final product. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method for controlling the accuracy and stability of a multi-degree-of-freedom envelope forming equipment, which can achieve high-precision and high-stability control of the multi-degree-of-freedom envelope forming equipment.

[0005] The technical solution adopted by this invention to solve its technical problem is as follows: A method for controlling the accuracy and stability of a multi-degree-of-freedom envelope forming equipment is constructed. The envelope forming equipment includes a bed, motors, a planetary reducer, an electric cylinder, a slider, connecting rods, a ball seat, a swivel head, and a lower die. Six motors are controlled to rotate, driving the lead screws in the planetary reducer and electric cylinder to rotate. The output end of the electric cylinder drives the slider to reciprocate, causing the connecting rods to perform complex spatial movements. Finally, the six-degree-of-freedom spatial envelope forming motion of the swivel head is achieved through the coordinated action of the six connecting rods. The control method includes the following steps:

[0006] S1. Motion planning for multi-degree-of-freedom envelope forming equipment: The displacement of each slider is solved based on the envelope forming motion requirements of the equipment and the kinematic model of the equipment.

[0007] S2. Solving the stress state of a multi-degree-of-freedom envelope forming equipment;

[0008] S3. Solving for the error compensation of multi-degree-of-freedom envelope forming equipment;

[0009] S4. Obtain the control strategy for the multi-degree-of-freedom envelope forming equipment. Based on the structural characteristics, dynamic model, and error compensation algorithm of the envelope forming equipment, the actual position of the connecting rod strain and the motor encoder is used as feedback quantities. A three-loop collaborative control model of six motor positions, speeds, and currents is established to achieve precise motion control under time-varying heavy loads of the oscillating head.

[0010] According to the above scheme, in step S1, the equipment bed coordinate system is S A (O A -x A y A z A The coordinate system for the equipment's head swing is S. B (O B -x B y B z B A1 to A6 are the center points of the ball joints of the slider on the equipment bed, which are located in coordinate system S. A The coordinates in the middle are:

[0011]

[0012] In the formula, For corresponding point A i The coordinate vector; For corresponding point A i The x and y coordinate components; For corresponding point A i The z-coordinate component, which is the displacement of the slider;

[0013] B1 to B6 are the center points of the ball joint on the swing head of the equipment, which are located in coordinate system S. B The coordinates in the middle are:

[0014]

[0015] In the formula, For the corresponding point B i The coordinate vector; For the corresponding point B i The x, y, and z coordinate components;

[0016] The coordinate transformation relationship between the head and the bed is given according to the motion requirements of the equipment, and is set as follows: The displacement h of each slider is equipped i Solve using the condition that the length of the connecting rod remains constant, that is:

[0017]

[0018] In the formula, The displacement of the slider corresponds to the rotation angle of the motor, which is also the control quantity of the drive system.

[0019] According to the above scheme, in step S2, the lumped mass-spring damping method is used to establish the equipment dynamics equation as follows:

[0020]

[0021] In the formula, This represents the coordinate transformation between the mass element on the i-th slider and the bed. This represents the coordinate transformation between the mass element under the i-th slider and the bed. This represents the coordinate transformation between the mass element on the i-th link and the machine bed. This represents the coordinate transformation between the mass element of the i-th link and the machine bed. For the coordinate transformation between the i-th circumferential mass element on the swing head and the bed, T ck For coordinate transformation between the center mass unit of the oscillating head and the bed; W is the driving force for the i-th slider. l The forming force experienced by the swing head; The constraint force at the connection point between the i-th slider and the electric cylinder is... Let be the constraint force at the connection between the i-th slider and the connecting rod. M represents the constraint force at the connection between the i-th link and the pendulum head; a Let M be the mass of the mass unit on the i-th slider. ak Let M be the mass of the mass unit under the i-th slider. b Let M be the mass of the mass element on the i-th link. bk Let M be the mass of the mass element under the i-th link. c Let M be the mass of the i-th circumferential mass unit of the swing head. ck The mass of the center mass unit of the swing head; Let be the deformation stiffness matrix of the i-th slider. Let be the deformation damping matrix of the i-th slider. Let be the deformation stiffness matrix of the i-th link. Let be the deformation damping matrix of the i-th link. Let be the deformation stiffness matrix of the i-th circular mass element of the swing head. Let be the deformation damping matrix of the i-th circumferential mass element of the swing head; Let be the weight of the mass element on the i-th slider. Let be the gravity of the mass element under the i-th slider. Let be the weight of the mass element on the i-th link. Let be the weight of the mass element under the i-th link. Let G be the gravity of the i-th circumferential mass unit of the swing head. ck The weight of the mass unit at the center of the swing head; Let $\mathbf{i}$ be the rotational speed of the mass on the $i$-th slider, the mass unit on the link, and the circumferential mass unit of the $i$-th pendulum head, respectively. These are the deformation screws of the mass unit under the i-th slider, the mass unit under the connecting rod, and the mass unit at the center of the oscillating head, respectively. for The second derivative, for The first derivative;

[0022] Strain gauges were used to measure the deformation of the six connecting rods, denoted as... According to the above dynamic equation (4), the displacements of the six sliders Equation (3) provides the force state of the equipment, including the external load W. l The driving force of each slider And the coordinate transformation T of the head swing ck The driving force vector F of each slider d Expressed using equation (5):

[0023]

[0024] According to the above scheme, in step S3, the dynamic error of the equipment swing head is calculated according to formula (6):

[0025]

[0026] In the formula, p represents any point on the swing head;

[0027] The overall dynamic error of the oscillating head is calculated using rotational angular deviations in three directions. and translational deviations δ in three directions x ,δ y ,δ z This indicates that the rotation angle deviation and translation deviation are calculated according to equation (7):

[0028]

[0029] S B It is the theoretical coordinate system for head movement, l i Let A be the direction vector of the i-th link. i and B i Theoretically, the center points of the ball joints on the slider and the ball joints on the oscillating head are used; the coordinate system of the oscillating head with dynamic error is set as S. B At this point, the center point of the ball joint on the slider and the center point of the ball joint on the oscillating head are set as A. i ′ and B i Let the direction vector of the i-th link be l. i ′; Deviation vector of the center point of the ball joint on the oscillating head Set as Calculate according to formula (8):

[0030]

[0031] Let the error compensation amount of the i-th slider be... At this moment, the displacement deviation vector of the slider is The actual position of the i-th link, which includes dynamic error, is calculated according to equation (9):

[0032]

[0033] The length of the link remains constant, resulting in the constraint relationship shown in equation (10):

[0034]

[0035] According to equation (10), the error compensation amount of the slider is calculated. Used for real-time error compensation control.

[0036] According to the above scheme, in step S4, the three-loop coordinated control model of the position-speed-current of the six motors is as shown in equation (11):

[0037]

[0038] In the formula, T d The driving torque vector of the 6 motors, δ s For the error compensation amount, g s For the transmission ratio of the drive system, F d ε represents the driving force of the six sliders. e represents the position deviation vector of the six motors in the control system. K pp K is the control parameter matrix for the position loop. vp ,K vi K is the control parameter matrix for the speed loop. ip ,K ii ,K id Here is the control parameter matrix for the current loop. All of the above control parameter matrices are diagonal matrices, and are represented by equation (12):

[0039]

[0040] In the formula, These are the system's control parameters.

[0041] The method for controlling the accuracy and stability of multi-degree-of-freedom envelope forming equipment according to the present invention has the following beneficial effects:

[0042] 1. During the spatial envelope forming process, the swing head motion is complex and the forming force is difficult to predict, resulting in poor stability of the control system. This invention proposes to use a linkage strain feedback strategy to calculate the real-time stress state of the equipment, and then dynamically adjust the driving force. This can effectively address the problem of decreased system stability caused by complex forming forces, and enable the equipment to have good motion reliability under complex forming loads.

[0043] 2. During the spatial envelope forming process, the forming force of the equipment is large, and the deformation mechanism of the equipment structure is complex, resulting in large dynamic errors, which affect the motion accuracy of the equipment and the forming accuracy of the final product. This invention proposes an equipment error compensation algorithm that can calculate the dynamic error of the swing head in real time based on the strain of the connecting rod, and compensate for the deformation error of the swing head in real time by correcting the displacement of the slider. This effectively compensates for the problem of decreased motion accuracy of the equipment caused by dynamic errors, enabling the equipment to have good motion accuracy under complex forming loads, thereby ensuring the forming accuracy of the final product.

[0044] 3. This invention, based on real-time prediction of the stress state and dynamic error of the swing head using linkage strain feedback, solves for the real-time driving force and slider error compensation, achieving high-precision and high-stability control of multi-degree-of-freedom envelope forming equipment. Applying this invention's method for controlling the precision and stability of multi-degree-of-freedom envelope forming equipment enables high-performance and high-efficiency forming manufacturing of thin-walled, high-ribbed extreme structures. Attached Figure Description

[0045] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:

[0046] Figure 1 Schematic diagram of a three-dimensional model of a multi-degree-of-freedom envelope forming equipment;

[0047] Figure 2 Schematic diagram of the motion configuration of a multi-degree-of-freedom envelope forming equipment;

[0048] Figure 3 Schematic diagram of the dynamic error of the swing head of a multi-degree-of-freedom envelope forming equipment;

[0049] Figure 4 Schematic diagram of dynamic error compensation method for swing head of multi-degree-of-freedom envelope forming equipment;

[0050] Figure 5 Schematic diagram of the control system of a multi-degree-of-freedom envelope forming equipment;

[0051] Figure 6 Schematic diagram of the hardware architecture of the control system for a multi-degree-of-freedom envelope forming equipment;

[0052] Figure 7 Results of traditional PID control methods for multi-degree-of-freedom envelope forming equipment;

[0053] Figure 8 Results of an error-free strain feedback control method for multi-degree-of-freedom envelope forming equipment;

[0054] Figure 9 Results of strain feedback-error compensation control for multi-degree-of-freedom envelope forming equipment;

[0055] Figure 10 The motion trajectory of the swing head at different points under different control methods;

[0056] Figure 11 Surface deviations of formed parts under different control methods. Detailed Implementation

[0057] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0058] This invention provides a method for controlling the accuracy and stability of a multi-degree-of-freedom envelope forming equipment. Based on the characteristics of a six-bar parallel configuration where the connecting rods are two-force members, exhibit large deformation, are sensitive to dynamic errors, and are insensitive to strain gauge installation errors, this method proposes a three-loop PID motion control method using stress feedback. The main implementation steps of this method are as follows:

[0059] S1. Mechanical structure of multi-degree-of-freedom envelope forming equipment; multi-degree-of-freedom envelope forming equipment is used to realize the spatial envelope forming process of parts, and its basic structure is as follows: Figure 1 As shown, the system mainly includes a bed, motors, planetary reducers, electric cylinders, sliders, connecting rods, ball seats, a swivel head, and a lower die. Controlling the rotation of six motors drives the lead screws in the reducers and electric cylinders to rotate. The output of the electric cylinders drives the slider to reciprocate, causing the connecting rods to perform complex spatial movements. Ultimately, the coordinated action of the six connecting rods achieves the 6-DOF spatial envelope forming motion of the swivel head. The main challenge in controlling this equipment system is to achieve precise movement of the swivel head under time-varying heavy loads by coordinating the movement of the six motors through the controller and control algorithm.

[0060] S2. Motion planning for multi-degree-of-freedom envelope forming equipment; solving for the displacement of each slider based on the equipment's envelope forming motion requirements and kinematic model. For example... Figure 2 The figure shows the basic motion configuration parameters of the equipment, with the equipment bed coordinate system being S. A (O A -x A y A z A The coordinate system for the equipment's head swing is S. B (O B -x B y B z B A1 to A6 are the center points of the slider ball joints on the equipment bed, which are located in coordinate system S. A The coordinates in the middle are:

[0061]

[0062] In the formula, For corresponding point A i The coordinate vector. For corresponding point A i The x and y coordinate components. For corresponding point Ai The z-coordinate component, which is the displacement of the slider.

[0063] B1 to B6 are the center points of the ball joint on the swing head of the equipment, which are located in coordinate system S. B The coordinates in the middle are:

[0064]

[0065] In the formula, For the corresponding point B i The coordinate vector. For the corresponding point B i The x, y, and z coordinate components.

[0066] The coordinate transformation relationship between the head and the bed is given according to the motion requirements of the equipment, and is set as follows: The displacement h of each slider is equipped i The solution can be obtained by applying the condition that the length of the connecting rod remains constant, i.e.:

[0067]

[0068] In the formula, The displacement of the slider corresponds to the rotation angle of the motor, which is also the control quantity of the drive system.

[0069] S3. Solving the stress state of a multi-degree-of-freedom envelope forming equipment;

[0070] The dynamic equations of the equipment are established using the lumped mass-spring damping method as follows:

[0071]

[0072] In the formula, This represents the coordinate transformation between the mass element on the i-th slider and the bed. This represents the coordinate transformation between the mass element under the i-th slider and the bed. This represents the coordinate transformation between the mass element on the i-th link and the machine bed. This represents the coordinate transformation between the mass element of the i-th link and the machine bed. For the coordinate transformation between the i-th circumferential mass element on the swing head and the bed, T ck This refers to the coordinate transformation between the center mass unit of the oscillating head and the bed. W is the driving force for the i-th slider. l This refers to the forming force experienced by the oscillating head. The constraint force at the connection point between the i-th slider and the electric cylinder is... Let be the constraint force at the connection between the i-th slider and the connecting rod. M represents the constraint force at the connection between the i-th link and the swing head. a Let M be the mass of the mass unit on the i-th slider.ak Let M be the mass of the mass unit under the i-th slider. b Let M be the mass of the mass element on the i-th link. bk Let M be the mass of the mass element under the i-th link. c Let M be the mass of the i-th circumferential mass unit of the swing head. ck The mass of the center mass unit of the swing head. Let be the deformation stiffness matrix of the i-th slider. Let be the deformation damping matrix of the i-th slider. Let be the deformation stiffness matrix of the i-th link. Let be the deformation damping matrix of the i-th link. Let be the deformation stiffness matrix of the i-th circular mass element of the swing head. Let be the deformation damping matrix of the i-th circumferential mass element of the swing head. Let be the weight of the mass element on the i-th slider. Let be the gravity of the mass element under the i-th slider. Let be the weight of the mass element on the i-th link. Let be the weight of the mass element under the i-th link. Let G be the gravity of the i-th circumferential mass unit of the swing head. ck The gravity of the mass unit at the center of the swing head. Let $\mathbf{i}$ be the rotational speed of the mass on the $i$-th slider, the mass unit on the link, and the circumferential mass unit of the $i$-th pendulum head, respectively. These are the deformation spin of the mass of the i-th slider, the mass of the connecting rod, and the mass of the center of the oscillating head, respectively. for The second derivative, for The first differential.

[0073] In this invention, strain gauges are used to measure the deformation of six connecting rods, denoted as... According to the above dynamic equation (4), the displacements of the 6 sliders Equation (3) provides the force state of the equipment, including the external load W. l The driving force of each slider And the coordinate transformation T of the head swing ck Ultimately, the driving force vector F of each slider... d Expressed using equation (5):

[0074]

[0075] S4, Solving for the error compensation of the multi-degree-of-freedom envelope forming equipment; In S3, the coordinate transformation T of the swing head can be calculated based on the displacement of the slider and the strain of the connecting rod. ckTherefore, the dynamic error of the oscillating head can be calculated according to formula (6):

[0076]

[0077] In the formula, p represents any point on the swing head.

[0078] like Figure 3 As shown, the overall dynamic error of the oscillating head is expressed as the rotational angular deviation in three directions. and translational deviations δ in three directions x ,δ y ,δ z This is expressed as follows. The rotation angle deviation and translation deviation can be solved according to equation (7):

[0079]

[0080] like Figure 4 As shown, S B It is the theoretical coordinate system for head movement, l i Let A be the direction vector of the i-th link. i and B i Theoretically, the center points of the ball joints on the slider and the ball joints on the oscillating head are used. The coordinate system of the oscillating head, which has dynamic errors, is denoted as S. B At this point, the center point of the ball joint on the slider and the center point of the ball joint on the oscillating head are set as A. i ′ and B i Let the direction vector of the i-th link be l. i ′。 Deviation vector of the center point of the ball joint on the oscillating head Set as It can be calculated according to formula (8):

[0081]

[0082] Let the error compensation amount of the i-th slider be... At this moment, the displacement deviation vector of the slider is Therefore, the actual position of the i-th link, which includes dynamic error, can be calculated according to equation (9):

[0083]

[0084] The length of the link remains constant, resulting in the constraint relationship shown in equation (10):

[0085]

[0086] According to equation (10), the error compensation amount of the slider can be calculated. This is then used for real-time error compensation control.

[0087] S5. Control strategy for multi-degree-of-freedom envelope forming equipment; Based on the structural characteristics, dynamic model and error compensation algorithm of the above equipment, the actual position of the connecting rod strain and the motor encoder is used as the feedback quantity to establish a three-loop collaborative control model of motor position-speed-current as shown in equation (11):

[0088]

[0089] In the formula, T d The driving torque vector of the 6 motors, δ s For the error compensation amount, g s For the transmission ratio of the drive system, F d ε represents the driving force of the six sliders. e represents the position deviation vector of the six motors in the control system. K pp K is the control parameter matrix for the position loop. vp ,K vi K is the control parameter matrix for the speed loop. ip ,K ii ,K id Here is the control parameter matrix for the current loop. All of the above control parameter matrices are diagonal matrices, and are represented by equation (12):

[0090]

[0091] In the formula, These are the system's control parameters.

[0092] The control block diagram of this control method is shown in Figure 5, and the corresponding hardware architecture is shown in Figure 6. Figure 6 As shown, it includes three subsystems: a motion planning system, a servo control system, and a feedback control system.

[0093] (1) The motion planning system is at the highest level, mainly completed by the host computer and corresponding software system. It is responsible for the motion design and solution of the equipment, that is, to carry out the trajectory planning of the worktable according to the given mold motion and corresponding feed strategy, and then to solve the theoretical motion position of each slider according to the kinematic model of the equipment. Finally, the motion command is transmitted to the servo drive system through the motion control card. Its hardware and software structure includes industrial control computer, motion control card, and motion planning algorithm.

[0094] (2) The servo control system is at the lowest level, mainly implemented by the servo driver. It consists of six independent subsystems that drive the motor to achieve the movement of the equipment. Its basic architecture is a three-loop PID control mode, including a position loop, a speed loop, and a current loop. The inputs to the position loop include the theoretical position of the slider given by the motion planning system, the feedback signal from the position encoder, and the error compensation amount from the feedback control system. The inputs to the speed loop include the theoretical speed of the slider given by the motion planning system and the output of the position loop. The inputs to the current loop include the motor coil current fed back by the Hall sensor on the motor, the output of the speed loop, and the motor driving force calculated by the feedback control system. Its hardware and software structure includes a servo motor, a position encoder, a servo driver, and a three-loop PID servo control algorithm.

[0095] (3) The feedback control system is located in the intermediate layer. The host computer acquisition card collects the actual position values ​​of the equipment encoder and the actual stress values ​​of the strain gauges on the connecting rod. Then, based on the dynamic model, it solves the stress state of the equipment and transmits the driving force of the motor to the current loop of the servo control system. At the same time, it solves the dynamic error of the equipment based on the stress state of the equipment, and then calculates the error compensation amount of each slider according to the error compensation algorithm, and transmits it to the position loop of the servo control system to realize real-time compensation of dynamic error.

[0096] The above method was used to control a multi-degree-of-freedom envelope forming equipment. The equipment's motion configuration parameters are shown in Table 1, its dynamic parameters in Table 2, and its control parameters in Table 3. Strain feedback control without error compensation and strain feedback control with error compensation were implemented. Additionally, traditional PID control was conducted for comparison. The control results under the traditional PID control method are shown in Table 3. Figure 7 As shown, the control results under the strain feedback control method without error compensation are as follows: Figure 8 As shown, the control results under the strain feedback control method with error compensation are as follows: Figure 9 As shown, the motion trajectories of the swing head at different points under different control methods are as follows: Figure 10 As shown, the surface deviation measurement results of the formed parts under different control methods are as follows: Figure 11 As shown in the figure, it can be seen that by adopting the strain feedback control method with error compensation proposed in this patent, the fluctuation of the slider position deviation is significantly reduced, and the slider position deviation is significantly reduced, indicating that the method can effectively control the accuracy and stability of the multi-degree-of-freedom envelope forming equipment.

[0097] Table 1. Kinematic configuration parameters of multi-degree-of-freedom envelope forming equipment

[0098]

[0099] Table 2. Dynamic parameters of the multi-degree-of-freedom envelope forming equipment

[0100]

[0101]

[0102] Table 3. Control System Parameters of Multi-DOF Envelope Forming Equipment

[0103]

[0104]

[0105] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A multi-degree-of-freedom envelope forming equipment precision and stability control method, the envelope forming equipment comprising a bed, a motor, a planetary reducer, an electric cylinder, a sliding block, a connecting rod, a ball seat, a swing head and a lower mold, six motors are controlled to rotate, drive the screw rods in the planetary reducer and the electric cylinder to transport, the output end of the electric cylinder drives the sliding block to move reciprocatingly, the connecting rod makes complex spatial motion, and finally the six-degree-of-freedom spatial envelope forming motion of the swing head is realized through the synergistic action of the six connecting rods; characterized in that, The control method comprises the following steps: S1, multi-degree-of-freedom envelope forming equipment motion planning, solving the displacement of each slider according to the envelope forming motion demand of the equipment and the kinematics model of the equipment; S2, solving the stress state of the multi-degree-of-freedom envelope forming equipment; S3, solving the error compensation amount of the multi-degree-of-freedom envelope forming equipment; S4, obtaining the control strategy of the multi-degree-of-freedom envelope forming equipment, based on the structural characteristics, the dynamics model and the error compensation algorithm of the envelope forming equipment, adopting the actual positions of the connecting rod strain and the motor encoder as feedback quantities, establishing a six-motor position-velocity-current three-loop coordinated control model, and realizing accurate motion control under the condition of time-varying heavy load of swing; In the step S1, the coordinate system of the machine bed is , the coordinate system of the machine head is , is the center point of the ball joint of the sliding block on the machine bed, and the coordinates of the center point in the coordinate system are: （1） wherein is the coordinate vector of the corresponding point ; and are the x and y coordinate components of the corresponding point ; and is the z coordinate component of the corresponding point , i.e. the displacement of the slider. To equip the center point of the ball joint on the swing head, which coordinates in the coordinate system are: （2） wherein is the coordinate vector of the corresponding point ; and is the x, y and z coordinate components of the corresponding point . The coordinate transformation relationship between the swing head and the bed body is given according to the motion requirement of the equipment, and is set as The displacement of each slide of the equipment is solved under the condition that the length of the connecting rod is unchanged, that is: （3） In the formula, is the displacement of the slide, corresponding to the angle of rotation of the motor, i.e. the control variable of the drive system; In the step S4, the six-motor position-velocity-current three-loop coordinated control model is as shown in formula (11): （11） wherein, is the driving torque vector of the 6 motors, is the error compensation amount, is the transmission ratio of the driving system, is the driving force of the 6 sliders; is the position deviation vector of the 6 motors of the control system; is the control parameter matrix of the position loop, is the control parameter matrix of the speed loop, is the control parameter matrix of the current loop, and all of the above control parameter matrices are diagonal matrices, which are expressed by equation (12): （12） In the formulae, Control parameters of the system.

2. The multi-degree-of-freedom envelope-shaping equipment accuracy and stability control method of claim 1, wherein, In the step S2, the concentrated mass-spring damping method is adopted to establish the equipment dynamics equation as follows: （4） wherein, is the coordinate transformation between the upper mass unit of the first slider and the machine bed, is the coordinate transformation between the lower mass unit of the first slider and the machine bed, is the coordinate transformation between the upper mass unit of the first link and the machine bed, is the coordinate transformation between the lower mass unit of the first link and the machine bed, is the coordinate transformation between the first circumferential mass unit of the head and the machine bed, is the coordinate transformation between the central mass unit of the head and the machine bed; is the driving force of the first slider, is the shaping force received by the head; is the constraint force at the connection between the first slider and the electric cylinder, is the constraint force at the connection between the first upper mass unit and the first link, is the constraint force at the connection between the first link and the head; is the mass of the first upper mass unit of the first slider, is the mass of the first lower mass unit of the first slider, is the mass of the first upper mass unit of the first link, is the mass of the first lower mass unit of the first link, is the mass of the first circumferential mass unit of the head, is the mass of the central mass unit of the head; is the deformation stiffness matrix of the first slider, is the deformation damping matrix of the first slider, is the deformation stiffness matrix of the first link, is the deformation damping matrix of the first link, is the deformation stiffness matrix of the first circumferential mass unit of the head, is the deformation damping matrix of the first circumferential mass unit of the head; is the gravity of the first upper mass unit of the first slider, is the gravity of the first The weight of the mass unit under the slider For the first The weight of the mass unit on each link. For the first The weight of the mass unit under the link. For the first time to shake the head The gravity of a circular mass unit The weight of the mass unit at the center of the swing head; The first Mass on the slider, mass unit on the connecting rod, and the first oscillating head. The rotational motion of a circular mass unit The first Deformation screw of the mass unit under the slider, the mass unit under the connecting rod, and the mass unit at the center of the oscillating head; for The second derivative, for The first derivative; The deformation of the six connecting rods is measured by strain gauges, and is set as According to the above dynamic equation (4), the displacement of the six sliders is given by equation (3), so that the force state of the equipment, including the external load , the driving force of each slider and the coordinate transformation of the swing head can be solved. The vector of the driving force of each slider is represented by equation (5): （5）。 3. The multi-degree-of-freedom envelope-shaping equipment accuracy and stability control method of claim 2, wherein, In the step S3, the dynamic error of the equipment swing is calculated according to formula (6): （6） In the formula, denotes an arbitrary point on the swing. The overall dynamic error of the head shake is expressed in terms of 3 rotational angle deviations and 3 translational deviations ; the rotational angle deviations and the translational deviations are solved according to equation (7): （7） is the theoretical motion coordinate system of the swing, is the direction vector of the first link, and is the theoretical center point of the slider spherical hinge and the center point of the upper spherical hinge of the swing; the swing coordinate system with dynamic error is set as , at this time the center point of the slider spherical hinge and the center point of the upper spherical hinge of the swing are set as and , the direction vector of the first link is set as ; the deviation vector of the center point of the upper spherical hinge of the swing is set as and is calculated according to formula (8): （8） Let the first The error compensation amount for each slider is At this point, the displacement deviation vector of the slider is The first one, which includes dynamic error The actual position of each link is calculated according to formula (9): （9） The length of the connecting rod remains unchanged, so there is a constraint relationship as shown in formula (10): （10） According to formula (10), the error compensation amount of the slider is solved for real-time error compensation control.

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