Multi-degree-of-freedom envelope forming equipment motion-rigidity collaborative optimization design method

Abstract

The present application relates to a kind of multi-degree-of-freedom envelope forming equipment motion-stiffness collaborative optimization design method, envelope forming equipment adopts six connecting rod parallel configuration, adopts ball head connecting rod and spherical hinge structure to realize the transmission of force and energy, its six branch chain structure is completely same, motor is connected with ball screw through connecting shaft, ball screw and slider spherical hinge solid connection, slider spherical hinge and the upper ball head of ball head connecting rod form spherical pair connection, optimization design method includes the following steps: S1, the kinematic model of multi-degree-of-freedom envelope forming equipment is established;S2, the motion stability condition of multi-degree-of-freedom envelope forming equipment is established;S3, the velocity transmission condition of multi-degree-of-freedom envelope forming equipment is established;S4, the stiffness model of the moving platform of multi-degree-of-freedom envelope forming equipment is established;S5, the motion-stiffness collaborative optimization of multi-degree-of-freedom envelope forming equipment.By the present application, equipment configuration parameters can be optimized and designed, and then provide basis and guidance for high-performance multi-degree-of-freedom envelope forming equipment design and development.

Description

Technical Field

[0001] This invention relates to the field of envelope forming, and more specifically, to a motion-stiffness co-optimization design method for multi-degree-of-freedom envelope forming equipment. Background Technology

[0002] Multi-degree-of-freedom (DOF) envelope forming is a continuous, localized near-net-shape plastic forming process for components. It boasts advantages such as low forming force, good metal flowability, and high forming efficiency, making it a promising candidate for high-performance, high-efficiency, and low-cost manufacturing of thin-walled, high-ribbed components. For this process, a novel configuration of a multi-DOF envelope forming equipment driven by six servo motors and six-link parallel linkages was developed. The complex multi-DOF envelope forming motion is achieved through the coordinated motion of the six servo motors, while the heavy-load requirements of the equipment are met through the parallel coordination of the six links. From a design perspective, using multi-link collaborative support can improve the stiffness of the equipment. However, the configuration parameters of the mechanism have a significant impact on the overall stiffness of the equipment. Therefore, it is necessary to propose a stiffness optimization design method for multi-DOF envelope forming equipment that considers both motion performance and rigidity. This is crucial for achieving high-stiffness design of the equipment and fully utilizing the performance of multi-link collaborative support. Currently, there are no research reports on stiffness optimization design methods for multi-DOF envelope forming equipment. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a motion-stiffness co-optimization design method for multi-degree-of-freedom envelope forming equipment, which can optimize the equipment configuration parameters and thus provide a basis and guidance for the design and development of high-performance multi-degree-of-freedom envelope forming equipment.

[0004] The technical solution adopted by this invention to solve its technical problem is as follows: A motion-stiffness co-optimization design method for a multi-degree-of-freedom envelope forming equipment is constructed. The envelope forming equipment adopts a six-link parallel configuration, driven by a motor and a ball screw. Force and energy transmission are achieved using a ball joint and a ball hinge structure. All six links are identical. The motor is connected to the ball screw via a coupling. The ball screw is fixedly connected to the slider ball hinge. The slider ball hinge forms a spherical joint connection with the upper ball head of the ball joint, and the lower ball head of the ball joint forms a spherical joint connection with the moving platform ball hinge. The optimization design method includes the following steps:

[0005] S1. Establish a kinematic model of a multi-degree-of-freedom envelope forming equipment;

[0006] S2. Establish motion stability conditions for multi-degree-of-freedom envelope forming equipment;

[0007] S3. Establish speed transmission conditions for multi-degree-of-freedom envelope forming equipment;

[0008] S4. Establish the stiffness model of the dynamic platform of the multi-degree-of-freedom envelope forming equipment;

[0009] S5. Co-optimization of motion and stiffness of multi-degree-of-freedom envelope forming equipment.

[0010] According to the above scheme, in step S1, the centers of each ball joint point on the moving platform of the envelope forming equipment are B1, B2, B3, B4, B5, B6, and the centers of each ball joint point on the slider are A1, A2, A3, A4, A5, A6. A coordinate system S is established on the moving platform of the equipment. B (O B -x B y B z B Establish a coordinate system S on the static plane of the equipment. A (O A -x A y A z A );

[0011] B1, B2, B3, B4, B5, B6 are in the moving platform coordinate system S B The position vector in is Determined by equation (1):

[0012]

[0013] In the formula, r B Let be the radius of the plane circle containing points B1, B2, B3, B4, B5, and B6. The central angle of the plane distributed as B1, B2, B3, B4, B5, B6;

[0014] A1, A2, A3, A4, A5, A6 are in the static coordinate system S. A Position vector in Determined by equation (2):

[0015]

[0016] In the formula, r A Let be the radius of the plane circle containing points A1, A2, A3, A4, A5, and A6. The central angles of the plane distributed among A1, A2, A3, A4, A5, and A6. The distance between the six sliders and the stationary plane of the equipment, where each slider slides.

[0017] Through the motion tensor of the moving platform The actual displacements of each slider in the equipment can be obtained by solving equation (3) based on the link vector condition.

[0018]

[0019] In the formula, is the motion tensor of the equipment moving platform, and l is the length of the equipment link;

[0020] Define the vector direction of each link: The direction vector of the central axis of the link is defined as follows: Vector e perpendicular to the axis of the link i1 and the position vectors of B1, B2, B3, B4, B5, B6 The direction vector is defined as e i2 ; and e i1 and e i2 Simultaneously, the vertical direction vector is defined as e. i3 The vectors in each direction are calculated according to equation (4):

[0021]

[0022] According to the above scheme, in step S2, the motion spinor system of the equipment is established, and S is defined. i1 S is the spinor of the slider's movement. i2 ,S i3 ,S i4 Let the ball joint points A1, A2, A3, A4, A5, and A6 on the slider be along the three directions e of the connecting rod. i1 ,e i2 ,e i3 rotational spinor, S i4 ,S i5 Let B1, B2, B3, B4, B5, and B6 be the motion screws of the ball joint points B1, B2, B3, B4, B5, and B6 along the normal and connecting rod directions. Each screw is solved according to equation (5):

[0023]

[0024] In the formula, S is the spinor i1 ,S i2 ,S i3 ,S i4 ,S i5 ,S i6 The corresponding unity spinor, ξ i1 ,ξ i2 ,ξ i3 ,ξ i4 ,ξ i5 ,ξ i6 Let S be the magnitude of each screw, which is also the velocity in that direction; the constraint screw corresponding to each motion position is determined by equation (6), i.e., S. ri :

[0025]

[0026] The kinematic screw relation of the equipment's moving platform is established as shown in equation (7):

[0027]

[0028] In the formula, S p For the motion spinor of the moving platform, multiply both sides of equation (7) by... get:

[0029]

[0030] The relationship between the rotational spin of the moving platform and the various related velocities can be calculated according to equation (9):

[0031] S p =J v [ξ 11 …ξ 61 ] T (9)

[0032] In the formula, J v The motion Jacobi matrix of the equipment platform is expressed as shown in equation (10):

[0033]

[0034] In order for the equipment to move correctly and stably without singularities, the determinant of the Jacobi matrix must be non-zero, that is, the motion constraint condition as shown in equation (11) must be satisfied:

[0035] det(J v )=0 (11).

[0036] According to the above scheme, in step S3, the stable motion of the multi-degree-of-freedom envelope forming equipment must satisfy the condition of equation (12):

[0037]

[0038] In the formula, [v max ] and [a max These are the allowable speeds and accelerations of each joint of the equipment, determined based on the equipment's motion and load levels.

[0039] The inter-chain transmission pressure angle between the components satisfies equation (13):

[0040] α ci =a cos(s ri s i1 / |s ri s i1 |)=a cos(e i1 s i1 )≤[α c (13)

[0041] In the formula, [α c] is the allowable pressure angle of the equipment link, determined based on the equipment's motion and load level. ri ,s i1 For the movement S ri ,S i1 Principal vector;

[0042] Calculate the overall constraint spin of the moving platform according to equation (14):

[0043] S r =S r1 +S r2 +…S r6 (14)

[0044] The intersection vector r of the constrained spinor ro Solve according to equation (15):

[0045]

[0046] In the formula, s r and s r0 The overall constraint spinor S of the moving platform are respectively r The main body and the deputy body;

[0047] The combined transmission pressure angle of the moving platform satisfies equation (16):

[0048] α p =a cos(s r v ro / |s r v ro |)≤[α p (16)

[0049] In the formula, [α p [This refers to the allowable pressure angle of the moving platform of the equipment, determined based on the equipment's motion and load level.]

[0050] According to the above scheme, in step S4, an equipment stiffness screw coordinate system is established. Assuming the instantaneous displacement of the slider remains constant, let the tensile and compressive screw forces acting on points B1, B2, B3, B4, B5, and B6 be S. ia ,S ib ,S ic And the torsional torque spinor is S id ,S ie ,S if According to the spinor theory, the spinors of each deformation are solved according to equation (17):

[0051]

[0052] In the formula, S ia ,S ib S ic ,S id,S ie ,S if For the corresponding force spinor, f is the corresponding unity spinor. ia ,f ib ,f ic ,f id ,f ie ,f if For each screw quantity, the corresponding force or torque amplitude is given.

[0053] Based on the force balance condition of the moving platform, the forming force acting on the moving platform is defined as the force spinor S. w Solve according to equation (18):

[0054]

[0055] In the formula, matrix J k =[J1,J2,J3,J4,J5,J6], and its corresponding subvectors Force matrix f = [f1, f2, f3, f4, f5, f6] T Its corresponding subvector f i =[f ia ,f ib ,f ic ,f id ,f ie ,f if (i = 1…6);

[0056] According to Hooke's law, the relationship between the force vector matrix f and the deformation is as follows:

[0057] f = K q q (19)

[0058] In the formula, q is the deformation vector of the connecting rod along each force spinor direction; K q The comprehensive stiffness matrix of the moving platform is calculated according to equation (20):

[0059]

[0060] In the coordinate system of the connecting rod, by equating the connecting rod to a cylinder, the stiffness matrix K q0 Determined by the radius and length of the connecting rod, it can be calculated using equation (21) according to the linear elasticity theory:

[0061]

[0062] In the formula, d s Where is the cross-sectional diameter of the connecting rod, and E is the elastic modulus of the material;

[0063] The components of the equipment stiffness matrix are obtained through coordinate transformation.

[0064]

[0065] In the formula, I is a 3x3 identity matrix, and A l The matrix transformation caused by the translation of the link's coordinate center is as follows:

[0066]

[0067] Simultaneous deformation spindle S of the moving platform d The deformation vectors q in each direction of the connecting rod are synthesized according to equation (23), that is:

[0068]

[0069] The relationship between the external force screw and the deformation screw of the moving platform can be calculated by substituting equations (23) and (22) into equation (18), resulting in equation (24):

[0070]

[0071] The deformation screw of the moving platform can be obtained from the external force screw, as shown in equation (25):

[0072]

[0073] Suppose there is a point on the moving platform, i.e., coordinate system S B The position vector of a point in the middle is defined according to equation (26):

[0074] r td =[r td cosθ td ,r td sinθ td ,z t (26)

[0075] In the formula, r td Let θ be the radius of the circle containing that point. td The central angle corresponding to that point, z t Let this point be the height relative to the moving platform, and let the rotational twist S of the moving platform be... d The deformation at this point is calculated using equation (27):

[0076]

[0077] In the formula, s d ,s d0 These are the deformable spinor S d The main part and the deputy part.

[0078] According to the above scheme, in step S5, the motion constraints of the equipment are established as shown in equation (28):

[0079]

[0080] Assume the radius of the largest mold is [r] w The maximum height of the upper mold is [z]. t The maximum allowable deformation of the moving platform is [d]. w The equipment design constraints considering the deformation of the moving platform are established as shown in equation (29):

[0081]

[0082] Based on the strength condition of the connecting rod, the stress of the connecting rod is solved according to equation (30):

[0083] σ=[σ 11 ,σ 12 …σ 16 ,σ 21 …σ 26 …σ 66 ]=Eq (30)

[0084] Thus, the strength constraint conditions for the link can be established as shown in equation (31):

[0085]

[0086] In the formula, [σ n ] and [σ t These represent the allowable tensile, compressive, and shear stresses of the connecting rod material, respectively.

[0087] Given the motion tensor at all moments during the equipment forming process Based on the conditions determined by equations (28), (29) and (31), the configuration parameters of the equipment, including rod length l and connecting rod diameter d, can be determined. s The radius of the ball joint distribution on the moving platform is r A The ball joint distribution angle θ of the moving platform A The radius of the static platform ball joint distribution r B The static platform ball joint distribution angle θ B The optimization objective function is shown in equation (32):

[0088] f i =min(η) p ,l,d s ,r A ,r B (32).

[0089] The kinematic-stiffness co-optimization design method for multi-degree-of-freedom envelope forming equipment of the present invention has the following beneficial effects:

[0090] 1. The multi-degree-of-freedom envelope forming equipment of the present invention adopts a new configuration of six servo motors and six-link parallel drive. The complex multi-degree-of-freedom envelope forming motion is realized through the linkage motion of the six servo motors, and the heavy load requirement of the equipment is met through the parallel coordination of the six links.

[0091] 2. The present invention proposes a motion-stiffness co-optimization design method for multi-degree-of-freedom envelope forming equipment, which can find the optimal configuration parameters while taking into account the motion performance of multi-degree-of-freedom envelope forming equipment, so as to give the equipment the maximum mechanical stiffness, thereby significantly improving the load-bearing performance and dynamic stability of the equipment.

[0092] 3. The motion-stiffness co-optimization design method for multi-degree-of-freedom envelope forming equipment proposed in this invention can achieve lightweighting of equipment while ensuring equipment performance, thereby reducing equipment production costs. Attached Figure Description

[0093] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:

[0094] Figure 1 This is a schematic diagram of the branch configuration process of a multi-degree-of-freedom envelope forming equipment;

[0095] Figure 2 This is a schematic diagram of the overall configuration process of a multi-degree-of-freedom envelope forming equipment;

[0096] Figure 3 This is a schematic diagram of the configuration parameters of the motion of a multi-degree-of-freedom envelope forming equipment;

[0097] Figure 4 This is a schematic diagram of the motion and force transmission relationship of a multi-degree-of-freedom envelope forming equipment;

[0098] Figure 5 This is a schematic diagram of the quasi-static stiffness model of a multi-degree-of-freedom envelope forming equipment;

[0099] Figure 6 It is the deformation curve of the connecting rod under different motion parameters of the multi-degree-of-freedom envelope forming equipment;

[0100] Figure 7 This is a schematic diagram of the instantaneous deformation law of the worktable of a multi-degree-of-freedom envelope forming equipment;

[0101] Figure 8 This is a schematic diagram of the overall deformation law of the worktable of a multi-degree-of-freedom envelope forming equipment. Detailed Implementation

[0102] 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.

[0103] This invention relates to a motion-stiffness co-optimization design method for multi-degree-of-freedom envelope forming equipment. This method uses spinor theory and branch deformation coordination conditions to establish the equipment stiffness model. Its basic steps are as follows:

[0104] S1. Configuration Design of Multi-Degree-of-Freedom Enveloping Forming Equipment: To achieve multi-degree-of-freedom spatial envelope forming motion under large forming loads, this equipment adopts a 6-link parallel configuration, driven by a motor and roller screw, and uses ball joints and ball hinges to transfer force and energy. Its 6-branch structure is identical, and the configuration process of the branches is as follows... Figure 1 As shown: The motor is connected to the ball screw via a coupling. The ball screw is fixedly connected to the slider ball joint. The slider ball joint forms a spherical joint with the upper ball joint of the ball joint connecting rod. The lower ball joint of the ball joint connecting rod forms a spherical joint with the moving platform ball joint. The overall mechanism configuration process of the equipment is as follows: Figure 2 As shown, by connecting six identical branch structures to the moving platform at a certain angle, and simultaneously mounting the motors and ball screws on the bed, the multi-degree-of-freedom spatial envelope forming motion of the moving platform can be achieved by controlling the movement of the six motors to move the corresponding sliders up and down.

[0105] S2. Establish a kinematic model of the multi-degree-of-freedom envelope forming equipment; such as... Figure 3 As shown, the centers of the ball joints on the moving platform of the envelope forming equipment are B1, B2, B3, B4, B5, B6, and the centers of the ball joints on the slider are A1, A2, A3, A4, A5, A6. A coordinate system S is established on the moving platform of the equipment. B (O B -x B y B z B Establish a coordinate system S on the static plane of the equipment. A (O A -x A y A z A ).

[0106] Therefore, B1, B2, B3, B4, B5, and B6 are in the moving platform coordinate system S. B The position vector in is Determined by equation (1):

[0107]

[0108] In the formula, r B Let be the radius of the plane circle containing points B1, B2, B3, B4, B5, and B6. The central angle of the plane distributed as B1, B2, B3, B4, B5, B6.

[0109] Furthermore, A1, A2, A3, A4, A5, and A6 are equipped with a static coordinate system S. A Position vector in Determined by equation (2):

[0110]

[0111] In the formula, r A Let be the radius of the plane circle containing points A1, A2, A3, A4, A5, and A6. The central angles of the plane distributed among A1, A2, A3, A4, A5, and A6. The distance between the six sliders and the stationary plane of the equipment.

[0112] Furthermore, through the motion tensor of the moving platform The actual displacements of each slider in the equipment can be obtained by solving equation (3) based on the link vector condition.

[0113]

[0114] In the formula, It is the motion tensor of the moving platform of the equipment, given by the process requirements, and l is the length of the connecting rod of the equipment.

[0115] Therefore, the vector direction of each link can be defined: the direction vector of the central axis of the link is defined as follows: Vector e perpendicular to the axis of the link i1 and the position vectors of B1, B2, B3, B4, B5, B6 The direction vector is defined as e i2 ; and e i1 and e i2 Simultaneously, the vertical direction vector is defined as e. i3 The vectors in each direction are calculated according to equation (4):

[0116]

[0117] S3. Establish motion stability conditions for multi-degree-of-freedom envelope forming equipment; such as... Figure 4 As shown, firstly, the kinematic spinor system of the equipment is established, and S is defined. i1 S is the spinor of the slider's movement. i2 ,S i3 ,S i4 Let the ball joint points A1, A2, A3, A4, A5, and A6 on the slider be along the three directions e of the connecting rod. i1 ,e i2 ,e i3rotational spinor, S i4 ,S i5 Let B1, B2, B3, B4, B5, and B6 be the motion screws of the ball joint points B1, B2, B3, B4, B5, and B6 along the normal and connecting rod directions. Each screw can be solved according to equation (5):

[0118]

[0119] In the formula, S is the spinor i1 ,S i2 ,S i3 ,S i4 ,S i5 ,S i6 The corresponding unity spinor, ξ i1 ,ξ i2 ,ξ i3 ,ξ i4 ,ξ i5 ,ξ i6 Let S be the magnitude of each screw, which is also the velocity in that direction. The constraint screw corresponding to each motion position is determined by equation (6), i.e., S. ri :

[0120]

[0121] Then, the kinematic spinor relationship of the equipment's moving platform is established, as shown in equation (7):

[0122]

[0123] In the formula, S p For the motion spinor of the moving platform, multiply both sides of equation (7) by... available:

[0124]

[0125] The relationship between the rotational spin of the moving platform and the various related velocities can be calculated according to equation (9):

[0126] S p =J v [ξ 11 …ξ 61 ] T (9)

[0127] In the formula, J v The motion Jacobi matrix of the equipment platform is expressed as shown in equation (10):

[0128]

[0129] In order for the equipment to move correctly and stably without singularities, the determinant of the Jacobi matrix must be non-zero, that is, the motion constraint condition as shown in equation (11) must be satisfied:

[0130] det(J v )=0 (11)

[0131] S4. Establish the velocity transmission conditions for the multi-degree-of-freedom envelope forming equipment; the stable motion of the multi-degree-of-freedom envelope forming equipment must satisfy the conditions of equation (12):

[0132]

[0133] In the formula, [v max ] and [a max These are the allowable speeds and accelerations of each joint of the equipment, determined based on the equipment's motion and load levels.

[0134] Furthermore, such as Figure 4 As shown, in order to ensure that the linkages and sliders of the equipment can transmit motion correctly and reasonably, the inter-chain transmission pressure angle between the components should not be too large, that is, satisfying equation (13):

[0135] α ci =a cos(s ri s i1 / |s ri s i1 |)=a cos(e i1 s i1 )≤[α c (13)

[0136] In the formula, [α c ] is the allowable pressure angle of the equipment link, determined based on the equipment's motion and load level. ri ,s i1 For the movement S ri ,S i1 The principal vector.

[0137] To determine the velocity transmission conditions of the moving platform, the overall constraint screw of the moving platform is first solved, and calculated according to equation (14):

[0138] S r =S r1 +S r2 +…S r6 (14)

[0139] The intersection vector r of the constrained spinor ro Solve according to equation (15):

[0140]

[0141] In the formula, sr and s r0 The overall constraint spinor S of the moving platform are respectively r The main part and the deputy part.

[0142] Therefore, in order for the connecting rod and the moving platform to transmit motion correctly, the combined transmission pressure angle of the moving platform should not be too large, that is, it should satisfy equation (16):

[0143] α p =a cos(s r v ro / |s r v ro |)≤[α p (16)

[0144] In the formula, [α p [This refers to the allowable pressure angle of the moving platform of the equipment, determined based on the equipment's motion and load level.]

[0145] S5. Establish a stiffness model for the dynamic platform of the multi-degree-of-freedom envelope forming equipment; establish a stiffness screw coordinate system for the equipment, such as... Figure 5 As shown, assuming the instantaneous displacement of the slider remains constant, let the tensile and compressive rotations acting on points B1, B2, B3, B4, B5, and B6 be S. ia ,S ib ,S ic And the torsional torque spinor is S id ,S ie ,S if According to the spinor theory, the spinors of each deformation can be solved by equation (17):

[0146]

[0147] In the formula, S ia ,S ib S ic ,S id ,S ie ,S if For the corresponding force spinor, f is the corresponding unity spinor. ia ,f ib ,f ic ,f id ,f ie ,f if This represents the force or torque amplitude corresponding to each spinor.

[0148] Based on the force balance condition of the moving platform, the forming force acting on the moving platform is defined as the force spinor S. w The solution can be obtained using equation (18):

[0149]

[0150] In the formula, matrix J k =[J1,J2,J3,J4,J5,J6], and its corresponding subvectors Force matrix f = [f1, f2, f3, f4, f5, f6] T Its corresponding subvector f i =[f ia ,f ib ,f ic ,f id ,f ie ,f if (i = 1…6).

[0151] According to Hooke's law, the relationship between the force vector matrix f and the deformation is as follows:

[0152] f = K q q (19)

[0153] In the formula, q is the deformation vector of the connecting rod along each force spinor direction. K q The comprehensive stiffness matrix of the moving platform is calculated according to equation (20):

[0154]

[0155] In the coordinate system of the connecting rod, by equating the connecting rod to a cylinder, the stiffness matrix K q0 Determined by the radius and length of the connecting rod, such as Figure 5 As shown in (b), the following calculation is performed according to equation (21) based on linear elasticity theory:

[0156]

[0157] In the formula, d s Let be the cross-sectional diameter of the connecting rod, and E be the elastic modulus of the material.

[0158] The components of the equipment stiffness matrix can be obtained through coordinate transformation.

[0159]

[0160] In the formula, I is a 3x3 identity matrix, and A l The matrix transformation caused by the translation of the link's coordinate center is as follows:

[0161]

[0162] Simultaneous deformation spindle S of the moving platform d It can be synthesized from the deformation vectors q in each direction of the connecting rod according to equation (23), that is:

[0163]

[0164] Therefore, the relationship between the external force screw and the deformation screw of the moving platform can be calculated by substituting equations (23) and (22) into equation (18), resulting in equation (24):

[0165]

[0166] The deformation screw of the moving platform can be obtained from the external force screw, as shown in equation (25):

[0167]

[0168] Suppose there is a point on the moving platform, i.e., coordinate system S B The position vector of a point in the middle is defined according to equation (26):

[0169] r td =[r td cosθ td ,r td sinθ td ,z t (26)

[0170] In the formula, r td Let θ be the radius of the circle containing that point. td The central angle corresponding to that point, z t Let this point be the height relative to the moving platform, and let the rotational twist S of the moving platform be... d The deformation at this point can be solved according to equation (27):

[0171]

[0172] In the formula, s d ,s d0 These are the deformable spinor S d The main part and the deputy part.

[0173] S6. Motion-stiffness co-optimization of multi-degree-of-freedom envelope forming equipment; First, based on the motion requirements of the equipment, the motion constraints of the equipment are established as shown in equation (28):

[0174]

[0175] Assume the radius of the largest mold is [r] w The maximum height of the upper mold is [z]. t The maximum allowable deformation of the moving platform is [d]. w Therefore, the equipment design constraints considering the deformation of the moving platform can be established as shown in equation (29):

[0176]

[0177] Furthermore, based on the strength condition of the connecting rod, the stress of the connecting rod is solved according to equation (30):

[0178] σ=[σ 11 ,σ 12 …σ 16 ,σ 21 …σ 26 …σ 66 ]=Eq (30)

[0179] Thus, the strength constraint conditions for the link can be established as shown in equation (31):

[0180]

[0181] In the formula, [σ n ] and [σ t These represent the allowable tensile, compressive, and shear stresses of the connecting rod material, respectively.

[0182] Finally, given the motion tensor at all moments during the equipment forming process. Based on the conditions determined by equations (28), (29) and (31), the configuration parameters of the equipment, including the rod length l and the connecting rod diameter d, can be determined. s The radius of the ball joint distribution on the moving platform is r A The ball joint distribution angle θ of the moving platform A The radius of the static platform ball joint distribution r B The static platform ball joint distribution angle θ B The optimization objective function is shown in equation (32):

[0183] f i =min(η) p ,l,d s ,r A ,r B (32).

[0184] Based on the design constraints given in Table 1, a set of ideal mechanism configuration parameters can be obtained by following the method provided in this invention, as shown in Table 2. Furthermore, the deformation curves of the connecting rod of the multi-degree-of-freedom envelope forming equipment under different motion parameters can be obtained, as shown in Table 2. Figure 6 As shown, the instantaneous deformation law of the worktable of the multi-degree-of-freedom envelope forming equipment under different motion parameters is as follows: Figure 7 As shown, the overall deformation law of the worktable of the multi-degree-of-freedom envelope forming equipment under different motion parameters is as follows: Figure 8 As shown.

[0185] Table 1 Design constraints for multi-DOF envelope forming equipment

[0186]

[0187] Table 2 shows the optimized configuration parameters of the multi-degree-of-freedom envelope forming equipment.

[0188]

[0189]

[0190] 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 motion-stiffness co-optimization design method for a multi-degree-of-freedom envelope forming equipment, wherein the envelope forming equipment adopts a six-link parallel configuration, driven by a motor and a ball screw, and uses a ball joint and ball hinge structure to achieve force and energy transmission. Its six-link structure is identical. The motor is connected to the ball screw via a coupling, the ball screw is fixedly connected to the slider ball hinge, the slider ball hinge forms a spherical joint connection with the upper ball head of the ball joint, and the lower ball head of the ball joint forms a spherical joint connection with the moving platform ball hinge. The method is characterized in that… The optimization design method includes the following steps: S1. Establish a kinematic model of a multi-degree-of-freedom envelope forming equipment; S2. Establish motion stability conditions for multi-degree-of-freedom envelope forming equipment; S3. Establish speed transmission conditions for multi-degree-of-freedom envelope forming equipment; S4. Establish the stiffness model of the dynamic platform of the multi-degree-of-freedom envelope forming equipment; S5. Co-optimization of motion and stiffness of multi-degree-of-freedom envelope forming equipment; In step S1, the center of each ball joint point on the moving platform of the envelope forming equipment is... The center of each ball joint on the slider is Establish a coordinate system on the equipment moving platform Establish a coordinate system on the static plane of the equipment. ; In the coordinate system of the moving platform The position vector in is It is determined by equation (1): （1） In the formula, for The radius of the plane circle where the points are distributed. for The central angle of the plane of distribution; In equipping a static coordinate system Position vector in Determined by equation (2): （2） In the formula, for The radius of the plane circle where the points are distributed. for The central angle of the distributed plane, The distance between the six sliders and the stationary plane of the equipment, where each slider slides. Through the motion tensor of the moving platform The actual displacement of each slider in the equipment can be obtained by solving equation (3) based on the link vector condition. : （3） In the formula, It is the motion tensor of the equipment moving platform. It is the length of the connecting rod; Define the vector direction of each link: The direction vector of the central axis of the link is defined as follows: ; Vector perpendicular to the link axis and Position vector The direction vector is defined as ;and and Simultaneously, the vertical direction vector is defined as... The vectors in each direction are calculated according to equation (4): （4）。 2. The motion-stiffness co-optimization design method for multi-degree-of-freedom envelope forming equipment according to claim 1, characterized in that, In step S2, the motion spinor system of the equipment is established and defined. Let be the spinor of the slider's movement. The ball joint point on the slider Along the three directions of the connecting rod rotational spinor, For the moving platform ball joint point The rotational factors along the normal and connecting rod directions are calculated using equation (5): （5） In the formula, spinor The corresponding unit spinor, Let be the modulus of each spinor, that is, the velocity of motion in that direction; The constraint spinor corresponding to each motion position is determined by equation (6), i.e. : （6） The kinematic screw relation of the equipment's moving platform is established as shown in equation (7): （7） In the formula, For the motion spinor of the moving platform, multiply both sides of equation (7) by... ,get: （8） The relationship between the rotational spin of the moving platform and the various related velocities can be calculated according to equation (9): （9） In the formula, The motion Jacobi matrix of the equipment platform is expressed as shown in equation (10): （10） In order for the equipment to move correctly and stably without singularities, the determinant of the Jacobi matrix must be non-zero, that is, the motion constraint condition as shown in equation (11) must be satisfied: （11）。 3. The motion-stiffness co-optimization design method for multi-degree-of-freedom envelope forming equipment according to claim 2, characterized in that, In step S3, the stable motion of the multi-degree-of-freedom envelope forming equipment must satisfy the condition of equation (12): （12） In the formula, and These are the allowable speeds and accelerations of each joint of the equipment, determined based on the equipment's motion and load levels. The inter-chain transmission pressure angle between the components satisfies equation (13): （13） In the formula, The allowable pressure angle of the equipment link is determined based on the equipment's motion and load level. For sports Principal vector; Calculate the overall constraint spin of the moving platform according to equation (14): （14） Intersection vector of constrained spinors Solve according to equation (15): （15） In the formula, and These are the overall constraint spindles of the moving platform. The main body and the deputy body; The combined transmission pressure angle of the moving platform satisfies equation (16): （16） In the formula, The allowable pressure angle of the moving platform of the equipment, determined based on the equipment's motion and load level.

4. The motion-stiffness co-optimization design method for multi-degree-of-freedom envelope forming equipment according to claim 3, characterized in that, In step S4, a stiffness screw coordinate system for the equipment is established. It is assumed that the instantaneous displacement of the slider remains constant. Let the force acting on... The tensile and compressive rotation at the point is and the torsional torque spinor are According to the spinor theory, the spinors of each deformation are solved according to equation (17): (17) In the formula, For the corresponding force spinor, For the corresponding unit spinor, For each screw quantity, the corresponding force or torque amplitude is given. Based on the force balance condition of the moving platform, the forming force acting on the moving platform of the equipment is defined as the force spinor. Solve according to equation (18): (18) In the formula, the matrix Its corresponding subvector Force matrix Its corresponding subvector ; According to Hooke's law, the force vector matrix The relationship with the amount of deformation is as follows: (19) In the formula, This is the deformation vector of the link along each force spinor direction; The comprehensive stiffness matrix of the moving platform is calculated according to equation (20): (20) In the coordinate system of the connecting rod, by representing the connecting rod as an equivalent cylinder, the stiffness matrix... Determined by the radius and length of the connecting rod, it can be calculated using equation (21) according to the linear elasticity theory: (21) In the formula, Let be the diameter of the connecting rod's cross-section. The elastic modulus of the material; The components of the equipment stiffness matrix are obtained through coordinate transformation. : (22) In the formula, It is a 3x3 identity matrix. The matrix transformation caused by the translation of the link's coordinate center is as follows: ； Simultaneous deformation spin of the moving platform The deformation vectors of the connecting rod in each direction Synthesize according to formula (23), that is: (23) The relationship between the external force screw and the deformation screw of the moving platform can be calculated by substituting equations (23) and (22) into equation (18), resulting in equation (24): (24) The deformation screw of the moving platform can be obtained from the external force screw, as shown in equation (25): (25) Assume a point on the moving platform, i.e., the coordinate system The position vector of a point in the middle is defined according to equation (26): (26) In the formula, The radius of the circle containing that point is... The central angle corresponding to that point. The height of this point relative to the moving platform is determined by the rotational deformation of the moving platform. The deformation at this point is calculated using equation (27): (27) In the formula, Deformed spinor The main part and the deputy part.

5. The motion-stiffness co-optimization design method for multi-degree-of-freedom envelope forming equipment according to claim 4, characterized in that, In step S5, the motion constraints of the equipment are established as shown in equation (28): （28） Assume the radius of the largest mold is The maximum height of the upper mold is The maximum allowable deformation of the moving platform is The equipment design constraints considering the deformation of the moving platform are shown in equation (29): （29） Based on the strength condition of the connecting rod, the stress of the connecting rod is solved according to equation (30): （30） Thus, the strength constraint conditions for the link can be established as shown in equation (31): （31） In the formula, and These are the allowable tensile, compressive, and shear stresses of the connecting rod material, respectively. Given the motion tensor at all moments during the equipment forming process Based on the conditions determined by equations (28), (29) and (31), the configuration parameters of the equipment, including the rod length, can be determined. connecting rod diameter The radius of the ball joint distribution on the moving platform The angle of the ball joint distribution on the moving platform static platform ball joint distribution radius static platform ball joint distribution angle The optimization objective function is shown in equation (32): （32）。

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