Prestress design optimization method of prestress parallel mechanism

Abstract

The invention relates to a prestress design optimization method for a parallel mechanism of a prestress heavy-load forming robot. The prestress design optimization method comprises the following steps: S1, establishing a kinematics model and a dynamics model of the prestress heavy-load forming robot; s2, according to the heavy-load forming robot dynamic model, active prestress design is achieved by setting the driving force of a sliding block and the output force of a hydraulic rod; the purpose of pre-stress design optimization is to enable the connecting rod to have the maximum dynamic pre-stress, so that the deformation of the connecting rod in the forming process is controlled within an allowable range. According to the method, the principle of a prestress parallel mechanism and a corresponding effective load enhancement mechanism are combined, so that the effective load of the parallel mechanism is increased to the maximum extent, and the time-varying prestress is optimized by maximizing an effective load area. The invention provides a new method for enhancing the effective load of the parallel mechanism, expands the effective load limitation of the existing parallel mechanism, and has important application prospects in light-load and heavy-load parallel mechanisms.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of prestressed parallel mechanism configuration design, more particularly, to a prestressed parallel mechanism prestressed design optimization method. BACKGROUND

[0002] Parallel mechanisms are widely used in handling, picking, processing, welding and forming fields because they can achieve multi-degree-of-freedom (Multi-DoF) motion under certain loads. The maximum torque that can be borne by the end effector of a parallel mechanism is called the effective load, and improving the effective load is of great significance to the robot system. At present, the research contents related to the enhancement of the effective load can be summarized as two methods: parallel mechanism design and optimization. However, the above methods are limited by the strength of the materials of the parallel mechanism itself and the design and optimization methods are not universal. With the increasing demand for lightweight, large overall, extreme structure, high-temperature-resistant and high-load components, there is a demand for parallel mechanisms with greater forming force and higher effective load. The existing parallel mechanisms have small effective load, which leads to poor stability and low motion accuracy of the parallel mechanism. SUMMARY

[0003] The technical problem to be solved by the present application is to provide a prestressed parallel mechanism prestressed design optimization method that can overcome the effective load limitation of existing parallel mechanisms.

[0004] The technical scheme adopted by the present application to solve the technical problem is: a prestressed design optimization method for a prestressed heavy-load forming robot parallel mechanism is constructed, comprising the following steps:

[0005] S1, establishing a kinematics model and a dynamics model of the prestressed heavy-load forming robot;

[0006] S2, according to the dynamics model of the heavy-load forming robot, the driving force of the slider and the output force of the hydraulic rod are set to realize active prestressed design; the purpose of prestressed design optimization is to make the connecting rod have the maximum dynamic prestress, so that the deformation of the connecting rod in the forming process is controlled within the allowable range.

[0007] According to the above scheme, in the step S2, the instantaneous force is regarded as a vector in a high-dimensional space, and the volume of the high-dimensional space is used to quantify the effective load area, that is, the larger the effective load volume, the stronger the carrying capacity of the mechanical system, and the effective load of the parallel mechanism is increased by controlling the value of the prestress.

[0008] According to the above scheme, the heavy-duty forming robot includes a machine tool, a hydraulic rod, a slider, and a six-degree-of-freedom parallel motion mechanism. The parallel motion mechanism includes a moving platform and six independent motion chains, which are suspended on the slider. The independent motion chains include an upper S-joint, a connecting rod, and a lower S-joint connected in sequence.

[0009] According to the above scheme, the method for establishing the kinematic model of the prestressed heavy-duty forming robot includes the following steps:

[0010] Establish coordinate system S0 at the center of the machine tool plane and coordinate system S1 at the end vertex of the tool in the parallel mechanism; the length of each of the six rigid links is l. r All three hydraulic linkages are l h . Angle A is the angle of the slider in coordinate system S0. m Let the upper ball joint center of the rigid link be the position vector. In S0; C n The position vector is the center of the ball joint on the hydraulic rod. In S0; B m For the center of the lower ball joint of the rigid connecting rod, the position vector is... and Located in coordinate systems S1 and S0 respectively; D n The position vector is the center of the lower ball joint of the hydraulic rod. and They are located in coordinate systems S1 and S0 respectively; their position vectors are represented as:

[0011]

[0012] In the formula, It is the distance of the m-th slider. yes Values ​​in three directions, yes Values ​​in three directions, yes Values ​​in three directions, yes Values ​​in three directions; the geometric constraints of a parallel mechanism can be expressed as:

[0013]

[0014] In the formula, q=[α p ,β p ,γ p ,x p ,y p ,z p ] is the motion vector of the platform, p p =[x p ,y p,z p ] represents three positional parameters, θ p =[α p ,β p ,γ p [These are three angular parameters.] Let S1 be the coordinate transformation matrix from S0, and let it be expressed as:

[0015]

[0016] In the formula, R ZYX This is the rotation transformation matrix of ZYX, which is represented as:

[0017]

[0018] In the formula, cγ = cosγ, sγ = sinγ.

[0019] According to the above scheme, the dynamic model of the prestressed heavy-duty forming robot is constructed based on the Lagrangian method, taking into account the deformation of each rigid link, and the rigid-flexible coupling dynamics of the heavy-duty forming robot are established.

[0020] According to the above scheme, the method for the dynamic model of the prestressed heavy-duty forming robot includes:

[0021] Energy equations for each mechanical component of the heavy-duty forming robot are established sequentially. Based on the coupling relationships among these components, a coupled dynamics model of the heavy-duty forming robot is established. By integrating the energy equations for each mechanical component, the overall energy equation of the heavy-duty forming robot's dynamics system is expressed as:

[0022]

[0023] According to the above scheme, the method for the dynamic model of the prestressed heavy-duty forming robot also includes:

[0024] The total energy equation for the heavy-duty forming robot is rewritten using an energy-based Lagrangian function, and is expressed as follows:

[0025]

[0026] According to the above scheme, the dynamic model of the prestressed heavy-duty forming robot is expressed as follows:

[0027]

[0028] In the formula, M(q) is the inertial force matrix. Let G(q) be the Coriolis force and the centrifugal force, and let G(q) be gravity.

[0029] According to the above scheme, in step S2, an additional driving force Δτ is applied to the slider. dAdditional force Δτ of hydraulic rod h Adding them together, the final dynamic equation of the heavy-duty forming robot can be rewritten as:

[0030]

[0031] According to the above scheme, in step S2, the constraints and objectives of the prestressed design optimization are as follows:

[0032] constraint:

[0033] Target: max{V F}=max{F n (w r F r (w) t F t (w) f r f )}.

[0034] The prestressing design optimization method for the prestressed parallel mechanism of the present invention has the following beneficial effects:

[0035] This invention combines the principles of prestressed parallel mechanisms and the corresponding effective load enhancement mechanism to maximize the effective load of the parallel mechanism. A rigid-flexible coupling dynamic model is established based on the Lagrange method, and time-varying prestress is optimized by maximizing the effective load region, resulting in a 1.68-fold increase in the volume of the effective load region and a 1.4-fold increase in the maximum normal load. This invention provides a new method for enhancing the effective load of parallel mechanisms, expanding the existing limitations on the effective load of parallel mechanisms, and has significant application prospects in both lightly and heavily loaded parallel mechanisms. Attached Figure Description

[0036] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:

[0037] Figure 1 This is a schematic diagram illustrating the principle of enhancing the effective load of a prestressed mechanism.

[0038] Figure 2 A kinematic model of the heavy-duty forming robot (Nonapod);

[0039] Figure 3 This is a schematic diagram showing the force and geometric constraints of a heavy-duty forming robot.

[0040] Figure 4 This is a schematic diagram of a multi-degree-of-freedom forming load.

[0041] Figure 5 A schematic diagram of the effective load area of ​​a Nonapod without prestress;

[0042] Figure 6 A schematic diagram of the effective load area of ​​a prestressed Nonapod.

[0043] Figure 7 Schematic diagram of the effective load area volume with and without prestress;

[0044] Figure 8 A schematic diagram for optimizing preload and prestress of connecting rods in a hydraulic system. Detailed Implementation

[0045] 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.

[0046] The prestressing design optimization method of the prestressed parallel mechanism of the present invention includes the following steps:

[0047] S1. Comparative analysis of the principle and effective load enhancement mechanism of prestressed parallel mechanism.

[0048] In mechanical structures, prestressing means inducing stress in a certain part beforehand to increase the rigidity of the mechanical structure itself, reduce vibration and elastic deformation, and enhance its original resistance. For example... Figure 1 (a) is a force balance model of a general planar four-bar linkage, such as Figure 1 As shown in (a). Assume the deformations of the input and output rods are δ1 and δ2, respectively, and the external load is τ. L =[τ Lx ,τ Ly ], τ Lx and τ Ly Let x and y represent the external loads in the x and y directions, respectively. Neglecting structural deformation, the force equilibrium condition of the mechanism is:

[0049]

[0050] In the formula, θ1 and θ2 are the angles between the input rod and the output rod, respectively; l1 and l2 are the lever arms of the input rod and the output rod, respectively; k1, k2 and k L These are coefficients determined by the different cross-sectional shapes, lengths, and materials of the bars. Simplifying equation (1), it can be expressed as:

[0051]

[0052] Since any deformation of a member must satisfy a constraint condition, namely:

[0053]

[0054] Assuming l1>l2, the external load τ in the x-direction... Lx It can be represented as:

[0055]

[0056] In practical applications, due to the continuous changes in instantaneous loads, the effective load of a mechanical system is the collection of all instantaneous loads. However, the scale range of each force element is different. Treating instantaneous force as a vector in a high-dimensional space and using the volume of this high-dimensional space to quantify the effective load region, i.e., the effective load volume V, is a solution. F The larger the volume, the stronger the load-bearing capacity of the mechanical system. Combined with equation (4), the effective load area volume V... F It can be represented as:

[0057]

[0058] Inspired by prestressed structures in the construction field, this paper introduces prestressed structures into parallel mechanisms and establishes a force balance model for these mechanisms. To meet the actual working conditions of parallel mechanisms in heavy-duty forming robots, a hydraulic system (with additional prestress) is introduced into a certain link, and a corresponding force balance model is established, such as... Figure 1 As shown in (b). At this time, the external loads in the x and y directions can be expressed as:

[0059]

[0060] In the formula, θ h τ is the hydraulic angle. Lpx and τ Lpy These are the external loads in the x and y directions under the hydraulic system, respectively. Combined with equation (6), the effective load region volume V... Fp It can be represented as:

[0061]

[0062] To further explain the effective load enhancement mechanism, subtract equation (5) from equation (7), that is:

[0063]

[0064] It is easy to see that the volume of the effective load area increases with the increase of prestress, that is, by reasonably controlling the value of prestress, the effective load of the parallel mechanism can be multiplied.

[0065] S2. Establish the kinematic and dynamic models of the prestressed heavy-duty forming robot (Nonapod).

[0066] (1). Kinematic model of the heavy-duty forming robot (Nonapod)

[0067] Kinematic model of prestressed heavy-duty forming robot (Nonapod) as follows Figure 2As shown, the robot comprises a machine tool, hydraulic rods, a slider, and a six-degree-of-freedom parallel motion mechanism. The parallel motion mechanism includes a moving platform and six independent motion chains suspended on the slider; each chain is connected sequentially by an upper S-joint, a connecting rod, and a lower S-joint, and fixed to the moving platform; finally, the forming tool is fixed to the moving platform. By controlling the hydraulic rod to output appropriate prestress, the six-degree-of-freedom parallel motion mechanism can be pre-deformed, thereby increasing the effective load of the parallel mechanism.

[0068] Establish coordinate system S0 at the center of the machine tool plane, and coordinate system S1 at the end vertex of the tool in the parallel mechanism. The length of each of the six rigid links is l. r All three hydraulic linkages are l h . Angle A is the angle of the slider in coordinate system S0. m (m=1…6) is the center of the upper ball joint of the rigid link, and its position vector is... In S0; C n (n=1…3) represents the center of the ball joint on the hydraulic rod, and its position vector. In S0; B m (m=1…6) represents the center of the lower ball joint of the rigid connecting rod, and its position vector. and Located in coordinate systems S1 and S0 respectively; D n (n=1…3) represents the center of the lower ball joint of the hydraulic rod, and its position vector. and They are located in coordinate systems S1 and S0, respectively. These position vectors can be represented as:

[0069]

[0070] In the formula, It is the distance of the m-th slider (point A) m (radius), yes Values ​​in three directions, yes Values ​​in three directions, yes Values ​​in three directions, yes Values ​​in three directions. The geometric constraints of the parallel mechanism can then be expressed as:

[0071]

[0072] In the formula, q=[α p ,β p ,γ p ,x p ,y p ,zp [ is the platform's motion vector.] p p =[x p ,y p ,z p ] represents three positional parameters. θ p =[α p ,β p ,γ p ] are three angular parameters. Let S1 be the coordinate transformation matrix from S0, which can be represented as:

[0073]

[0074] In the formula, R ZYX This is the rotation transformation matrix of ZYX, which can be represented as:

[0075]

[0076] In the formula, cγ = cosγ, sγ = sinγ, and the calculation methods for the other trigonometric function elements are similar.

[0077] (2). Dynamic model of the heavy-duty forming robot (Nonapod)

[0078] The stress conditions and geometric constraints of heavy-duty forming robots are as follows: Figure 3 As shown, based on the Lagrangian method and considering the deformation of each rigid link, the rigid-flexible coupling dynamics of the heavy-duty forming robot (Nonapod) are established. In the figure, coordinate system S0 is established at the center of the machine tool plane, and coordinate system S1 is established at the end vertex of the tool in the parallel mechanism. Let be the driving force of the m-th slider. τ is the driving force of the nth hydraulic rod. p To combine external forces.

[0079] Based on the Lagrange equation, the energy of the slider can be expressed as:

[0080]

[0081] Assuming that all mechanical parameters of each rigid link are consistent, and considering a single rigid link as having a radius r r Height h r For a cylindrical rigid linkage, the energy equation can be expressed as:

[0082]

[0083] In the formula, Let be the generalized coordinate vector of the m-th rigid link. Let I be the angular velocity of the m-th rigid link. r Let be the inertia tensor of the m-th link. Let k be the deformation of the m-th rigid link. r For the stiffness of the rigid link, the above mechanical parameters can be expressed as follows:

[0084]

[0085] In the formula, E is the elastic modulus of the connecting rod material. Combining equation (15), the total energy equation of the rigid connecting rod can be expressed as:

[0086]

[0087] In the formula, and It can be represented as:

[0088]

[0089] Assuming that all mechanical parameters of each hydraulic rod are consistent, and considering a single hydraulic rod as having a radius r h Height h h For a cylindrical cylinder, the energy equation of the hydraulic rod can be expressed as:

[0090]

[0091] In the formula, Let be the generalized coordinate vector of the nth hydraulic rod. Let I be the angular velocity of the nth hydraulic link. h Let n be the inertia tensor of the nth hydraulic rod. The above mechanical parameters can be expressed as follows:

[0092]

[0093] Combining equation (19), the total energy equation of the hydraulic rod can be expressed as:

[0094]

[0095] In the formula, and It can be represented as:

[0096]

[0097] Consider the platform as having a radius r p Height h p The energy equation for the cylindrical platform can be expressed as:

[0098]

[0099] In the formula, ω Ep I is the angular velocity of the platform. pLet the platform's inertia tensor be the mechanical parameters mentioned above, which can be expressed as follows:

[0100]

[0101] Combining equation (23), the total energy equation of the platform can be expressed as:

[0102]

[0103] In the formula, M p (q p ) and G p (q p This can be represented as:

[0104]

[0105] The stress conditions and geometric constraints of heavy-duty forming robots are as follows: Figure 3 As shown, based on the corresponding dynamic model, nonlinear constraint equations can be established through the coupling relationship between different mechanical parts, that is:

[0106]

[0107] Combining the nonlinear constraint equation established by equation (26) with the distance between the slider and the hydraulic cylinder, and the poses of the connecting rod and the hydraulic rod, the above constraint equations are solved using the pose of the platform. The solution result can be expressed as:

[0108]

[0109] Its first-order difference can be represented by the corresponding Jacobian matrix as follows:

[0110]

[0111] After establishing the energy equations for each mechanical component of the heavy-duty forming robot, a coupled dynamics model of the robot is established based on the coupling relationships between these components. Integrating the energy equations for each mechanical component, the overall energy equation of the heavy-duty forming robot's dynamics system can be expressed as:

[0112]

[0113] Using the energy-based Lagrangian function to rewrite equation (29), the total energy equation of the heavy-duty forming robot can be expressed as:

[0114]

[0115] Combining equations (29) and (30), the final dynamic model of the heavy-duty forming robot can be expressed as:

[0116]

[0117] In the formula, M(q) is the inertial force matrix. Let G(q) be the Coriolis force and the centrifugal force, and let G(q) be gravity.

[0118] S3. Prestressed design and optimization method for heavy-duty forming robot (Nonapod).

[0119] Based on the dynamic model of the heavy-duty forming robot, active prestressing design is achieved by setting the driving force of the slider and the output force of the hydraulic rod. An additional driving force Δτ is applied to the slider. d Additional force Δτ of hydraulic rod h Adding them together, the final dynamic equation of the heavy-duty forming robot can be rewritten as:

[0120]

[0121] Applying force Δτ through the force-adding slider d Additional force Δτ of hydraulic rod h This brings the six-bar linkage to equilibrium. At this point, the initial deformation of a single link can be expressed as:

[0122]

[0123] Due to external force τ p The resulting deformation of the connecting rod can be expressed as:

[0124]

[0125] Therefore, the transformation of the six-free parallel mechanism is Δδ r =δ r -δ r0 Based on the above discussion, the deformation limit of a single connecting rod is [δ]. Lim Furthermore, the deformation of each connecting rod is within the deformation limit, that is:

[0126] |δ r |=|δ r0 +Δδ r |<[δ Lim (34)

[0127] The load applied to the six-free parallel mechanism causes the connecting rod to be compressed (Δδ). r >0), when δ r0 When = 0, 0 < Δδ r <[δ Lim ]; when δ r0 =-[δ Lim When 0 < Δδ r <2[δ Lim The above two cases show that by pre-setting the deformation of the connecting rod to δ...r0 =-δ Lim The load-bearing capacity of the connecting rod can be increased several times over. Furthermore, when the initial deformation of the connecting rod is δ... r0 At that time, the stiffness of the six-free parallel mechanism is k. PKM =τ p / (δ r -δ r0 This indicates that increasing the initial deformation of the connecting rod will increase the stiffness of the six-free parallel mechanism. When δ r0 =δ r At that time, the actual deformation of the connecting rod is Δδ r =δ r -δ r0 =0, meaning the stiffness of the six-free parallel mechanism can be increased indefinitely, thereby greatly improving the motion accuracy of the six-free parallel mechanism.

[0128] To more rationally design and determine the prestress of the parallel mechanism, in the actual forming motion, the tool resembles a simplified circular forming motion, i.e., the tip of the tool remains constant, while another point on the tool axis follows a circular path. The purpose of the prestress design is to maximize the dynamic prestress of the connecting rod, ensuring that the deformation of the connecting rod during the forming process is controlled within allowable limits. Neglecting inertial forces, the force balance between the preloading stage and the actual forming process is as follows:

[0129]

[0130] In the formula, τ h0 For the preload of the hydraulic rod, This represents the deformation caused by prestress on the rigid connecting rod. F represents the actual deformation that occurs during the connecting rod forming process. n The normal force F is the force along the normal direction of the upper surface of the billet. r F is the radial force along the radius of the billet. t r is the tangential force along the tangential direction of the billet. f The forming force radius, such as Figure 4 As shown. Therefore, the prestressing design requirement is to find the preload that causes the connecting rod deformation to reach its limit. Right now Designing the prestress of the connecting rods becomes an optimization problem to ensure that the parallel mechanism can withstand the highest external load under specific motion requirements. The prestress optimization constraint can be expressed as:

[0131] Constraint 1:

[0132] Furthermore, in actual machining and forming processes, the maximum constraint of radial and tangential forces is 15% of the normal force; the point of maximum application is approximately located at the maximum radius of the blank [r]. blankAt 2 / 3 of the distance, there are three remaining constraints:

[0133] Constraint 2:

[0134] The optimization objective is to maximize F n ,F r ,F t ,r f The maximum value is reached. However, these coupling parameters affect the deformation of the parallel mechanism. Furthermore, assuming equal weights for the four parameters, the volume of the effective load region can be calculated. Therefore, the objective of the optimization problem becomes maximizing this volume, i.e., max{V F Combining equations (36) and (37), the optimization problem can be summarized as follows:

[0135] constraint:

[0136] Target: max{V F}=max{F n (w r F r (w) t F t (w) f r f )}.

[0138] Combining the aforementioned novel prestressed parallel mechanism and prestressing design and optimization method, this invention introduces the concept of a prestressed structure. Without altering the mechanical system, prestress is applied to the parallel mechanism to improve the robot's payload capacity, providing a new method to overcome the payload limitations of existing robots. Specific examples of this invention are provided below:

[0139] Based on the principle of prestressed parallel mechanisms and the effective load enhancement mechanism, theoretical calculations and comparative analyses were performed on the normal force, radial force, tangential force, and effective load area of ​​parallel mechanisms with and without prestressing. The calculation results are as follows: Figure 5 , Figure 6 and Figure 7 As shown. The results indicate that without prestress, F n From 7MN to 4.8MN, F t From 1.2MN to 0.95MN, F r From 1.2MN to 0.88MN; with prestress, F n From 10.1MN to 6.3MN, F t Keeping 1.2MN constant, F r Keeping 1.2MN constant, the range of values ​​for normal force, tangential force, and radial force is improved after applying prestress. For example... Figure 7As shown in (a), without prestress, the effective load volume is between 800 and 300; with prestress, the effective load volume is between 1200 and 850, showing a significant increase in effective load volume; simultaneously, as the load radius increases, the rate of increase in effective load volume with prestress is greater; as... Figure 7 As shown in (b), the effective load volume with prestress is approximately 1.68 times higher than that without prestress. Furthermore, Figure 8 (a) and Figure 8 (b) The optimized hydraulic rod pressure and connecting rod prestress are shown respectively. The hydraulic pressure curves output by the three hydraulic rods have the same shape and size, but different phase angles, conforming to the centrally symmetrical distribution of hydraulic rods in parallel mechanisms. The prestress curves of connecting rods 1, 3, and 5 have the same shape and size, as do the prestress curves of connecting rods 2, 4, and 6, conforming to the centrally symmetrical distribution of connecting rods 1, 3, and 5 and connecting rods 2, 4, and 6 in parallel mechanisms. Furthermore, the prestress size of connecting rods 1, 3, and 5 is larger than that of connecting rods 2, 4, and 6, with the maximum prestress of the connecting rods being 280 MPa, which is less than the allowable stress set for the connecting rods. This indicates that using a prestressed structure in parallel mechanisms can significantly improve the forming force and effective load of traditional parallel mechanisms, broadening their application scenarios.

[0140] The advantages of this invention are as follows:

[0141] 1. Inspired by prestressed structures in the construction field, this invention introduces prestressed structures into parallel mechanisms and establishes a force balance model for parallel mechanisms. It analyzes the principle of prestressed parallel mechanisms and the corresponding effective load enhancement mechanism, showing that the effective load of parallel mechanisms can increase exponentially with the increase of prestress.

[0142] 2. Taking the novel heavy-duty forming robot (Nonapod) as an example, this invention establishes its rigid-flexible coupling dynamic model and kinematic model based on the Lagrange method, and proposes a design and optimization method to increase the volume of the effective load area; the dynamic preset hydraulic pressure and the link prestress are optimized, showing that the prestressing mechanism can significantly increase its effective load volume and maximum normal effective load.

[0143] 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 prestressing design optimization method for a parallel mechanism of a prestressed heavy-duty forming robot, characterized in that, Includes the following steps: S1. Establish the kinematic and dynamic models of the prestressed heavy-duty forming robot; S2. Based on the dynamic model of the heavy-duty forming robot, active prestress design is achieved by setting the driving force of the slider and the output force of the hydraulic rod. The purpose of prestress design optimization is to make the connecting rod have the maximum dynamic prestress and to control the deformation of the connecting rod within the allowable range during the forming process.

2. The prestressing design optimization method for the prestressed parallel mechanism according to claim 1, characterized in that, In step S2, the instantaneous force is regarded as a vector in a high-dimensional space and the volume of the high-dimensional space is used to quantify the effective load area. That is, the larger the effective load volume, the stronger the load-bearing capacity of the mechanical system. The effective load of the parallel mechanism is increased by controlling the value of the prestress.

3. The prestressing design optimization method for the prestressed parallel mechanism according to claim 1, characterized in that, The heavy-duty forming robot includes a machine tool, a hydraulic rod, a slider, and a six-degree-of-freedom parallel motion mechanism. The parallel motion mechanism includes a moving platform and six independent motion chains, which are suspended on the slider. Each independent motion chain includes an upper S-joint, a connecting rod, and a lower S-joint connected in sequence.

4. The prestressing design optimization method for the prestressed parallel mechanism according to claim 1, characterized in that, The method for establishing the kinematic model of a prestressed heavy-duty forming robot includes the following steps: Establish coordinate system S0 at the center of the machine tool plane and coordinate system S1 at the end vertex of the tool in the parallel mechanism; the length of each of the six rigid links is l. r All three hydraulic linkages are l h . Angle A is the angle of the slider in coordinate system S0. m Let the upper ball joint center of the rigid link be the position vector. In S0; C n The position vector is the center of the ball joint on the hydraulic rod. In S0; B m For the center of the lower ball joint of the rigid connecting rod, the position vector is... and Located in coordinate systems S1 and S0 respectively; D n The position vector is the center of the lower ball joint of the hydraulic rod. and They are located in coordinate systems S1 and S0 respectively; their position vectors are represented as: In the formula, It is the distance of the m-th slider. yes Values ​​in three directions, yes Values ​​in three directions, yes Values ​​in three directions, yes Values ​​in three directions; the geometric constraints of a parallel mechanism can be expressed as: In the formula, q=[α p ,β p ,γ p ,x p ,y p ,z p ] is the motion vector of the platform, p p =[x p ,y p ,z p ] represents three positional parameters, θ p =[α p ,β p ,γ p [These are three angular parameters.] Let S1 be the coordinate transformation matrix from S0, and let it be expressed as: In the formula, R ZYX This is the rotation transformation matrix of ZYX, which is represented as: In the formula, cγ = cosγ, sγ = sinγ.

5. The prestressing design optimization method for the prestressed parallel mechanism according to claim 1, characterized in that, The dynamic model of the prestressed heavy-duty forming robot is constructed based on the Lagrangian method, taking into account the deformation of each rigid link, and the rigid-flexible coupling dynamics of the heavy-duty forming robot are established.

6. The prestressing design optimization method for the prestressed parallel mechanism according to claim 5, characterized in that, Methods for modeling the dynamics of prestressed heavy-duty forming robots include: Energy equations for each mechanical component of the heavy-duty forming robot are established sequentially. Based on the coupling relationships among these components, a coupled dynamics model of the heavy-duty forming robot is established. By integrating the energy equations for each mechanical component, the overall energy equation of the heavy-duty forming robot's dynamics system is expressed as:

7. The prestressing design optimization method for the prestressed parallel mechanism according to claim 6, characterized in that, The methods for modeling the dynamics of prestressed heavy-duty forming robots also include: The total energy equation for the heavy-duty forming robot is rewritten using an energy-based Lagrangian function, and is expressed as follows:

8. The prestressing design optimization method for the prestressed parallel mechanism according to claim 7, characterized in that, The dynamic model of the prestressed heavy-duty forming robot is expressed as follows: In the formula, M(q) is the inertial force matrix. Let G(q) be the Coriolis force and the centrifugal force, and let G(q) be gravity.

9. The prestressing design optimization method for the prestressed parallel mechanism according to claim 8, characterized in that, In step S2, a driving force Δτ is applied to the slider. d Additional force Δτ of hydraulic rod h Adding them together, the final dynamic equation of the heavy-duty forming robot can be rewritten as:

10. The prestressing design optimization method for the prestressed parallel mechanism according to claim 8, characterized in that, In step S2, the constraints and objectives for prestressed design optimization are as follows: constraint: Target: max{V F }=max{F n (w r F r (w) t F t (w) f r f )}.

Images