Multi-band vibration active suppression method for high-speed heavy-load multi-degree-of-freedom forming equipment

Abstract

The invention relates to a multi-band vibration active suppression method for high-speed heavy-load multi-degree-of-freedom forming equipment, and the method comprises the following steps: S1, adding a hydraulic rod on an original structure of the high-speed heavy-load multi-degree-of-freedom forming equipment, and building an elastodynamic model considering the deformation of a connecting rod and the damping of the hydraulic rod; s2, analyzing a multi-band vibration generation mechanism of the forming equipment according to the kinetic model; and S3, according to a multi-frequency-band vibration generation mechanism, hydraulic pressure is actively adjusted to reduce fluctuation of connecting rod force so as to suppress low-frequency-band vibration, and meanwhile, damping of a hydraulic system is increased to suppress high-frequency-band vibration. According to the method, an elastic dynamic model of the forming equipment is established, and a multi-band vibration generation mechanism of the elastic dynamic model is disclosed; the invention provides a multi-band vibration active suppression method for high-speed heavy-load multi-degree-of-freedom forming equipment. The method has important application prospects in the field of vibration suppression under the heavy-load high-speed working condition.

Description

Technical Field

[0001] The present invention relates to the field of vibration suppression of multi - degree - of - freedom forming equipment, and more specifically, to a multi - band vibration active suppression method for high - speed heavy - load multi - degree - of - freedom forming equipment. Background Art

[0002] In the application of heavy - load high - speed multi - degree - of - freedom forming equipment, due to the combined action of high - speed motion and large load, vibration problems have seriously affected the dynamic accuracy and working stability of the system. Especially the interaction between high - frequency vibration and low - frequency vibration, traditional vibration suppression strategies usually focus on the control of a single frequency band, ignoring the complex effects brought by the coupling of multi - band vibrations. Therefore, how to achieve efficient vibration suppression under heavy - load high - speed conditions has become a key technical problem in improving the performance of forming equipment and ensuring machining accuracy. At present, there have been some research results on the vibration suppression of multi - degree - of - freedom forming equipment. However, most of the existing vibration suppression methods focus on the suppression of single - band vibration, such as reducing the amplitude of high - frequency or low - frequency vibration by optimizing structural stiffness, configuring dampers or using active suppression techniques. But these methods often fail to effectively cope with the coupling effect of multi - band vibrations. During the high - speed forming process, high - frequency vibration is usually caused by the dynamic response of the transmission system or internal friction, while low - frequency vibration is closely related to factors such as the flexible deformation of the mechanical structure, external load and support system. These two types of vibrations interact during the operation of multi - degree - of - freedom forming equipment, making it difficult for traditional suppression methods to solve multi - band vibration problems simultaneously. Traditional vibration suppression methods are limited to dealing only with high - frequency vibration generated by multi - degree - of - freedom forming equipment under high - speed conditions or low - frequency vibration generated under heavy - load conditions, unable to effectively cope with the coupling effect of multi - band vibrations and difficult to solve high - and low - frequency vibration problems simultaneously. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a multi - band vibration active suppression method for high - speed heavy - load multi - degree - of - freedom forming equipment, which can solve the multi - band vibration problem of high - speed heavy - load multi - degree - of - freedom forming equipment.

[0004] The technical solution adopted by the present invention to solve its technical problem is to construct a multi - band vibration active suppression method for high - speed heavy - load multi - degree - of - freedom forming equipment, including the following steps:

[0005] S1. Install hydraulic rods on the original structure of the high - speed heavy - load multi - degree - of - freedom forming equipment, and establish an elastic dynamics model considering the deformation of its connecting rods and the damping of the hydraulic rods;

[0006] S2. Analyze the generation mechanism of multi - band vibration of the forming equipment according to the dynamics model;

[0007] S3. According to the generation mechanism of multi-band vibration, actively adjust the hydraulic pressure to reduce the fluctuation of the connecting rod force to suppress the vibration in the low-frequency band. At the same time, increase the damping of the hydraulic system to suppress the vibration in the high-frequency band.

[0008] According to the above scheme, the elastic dynamics model established in step S1 is:

[0009]

[0010] In the formula, the deformation amount of the connecting rod along the rod direction is defined as The driving torque of the driving roller is defined as The load applied to the moving platform is defined as W p , W p =[w p1 , w p2 , w p3 , w p4 , w p5 , w p6 T ; G R is the gravity of the driving roller, represents the constraint reaction force of the driving roller, is the constraint reaction force received by the spherical pair on the connecting rod, represents the position vectors of points A1, A2, A3 relative to points C1, C2, C3 at the midpoint in the coordinate system S A , and it can be expressed as I R represents the inertia matrix of the driving roller; represents the coordinate transformation matrix from the coordinate system to the coordinate system S A , represents the coordinate transformation matrix from the coordinate system to the coordinate system S A ; G l1 and G l2 are the gravities of the upper and lower parts of the connecting rod respectively, represents the constraint reaction force received by the lower spherical pair of the connecting rod; represents the coordinate transformation matrix from the coordinate system to the coordinate system S A , represents the coordinate transformation matrix from the coordinate system to the coordinate system S A , is the damping force of the hydraulic rod.

[0011] According to the above scheme, the constraint equation of the elastic dynamics model in step S1 is expressed as:

[0012] ​

[0013] According to the above solution, in step S2, the multi-band vibration generation mechanism of the multi-degree-of-freedom forming equipment is as follows: for the low-frequency band of 0-50 Hz, the vibration of the forming equipment is caused by the insufficient stiffness of the mechanical system of the forming equipment; for the high-frequency band of 100 Hz-200 Hz, the vibration of the forming equipment is caused by the insufficient internal damping of the mechanical system of the 3RSS / S forming equipment.

[0014] According to the above solution, in step S3, a set of hydraulic pressures is determined through the optimization model to minimize the root mean square (RMS) value of the connecting rod force. Combining with the elastic dynamics model, the relationship between the connecting rod force, the hydraulic pressure, and the moving platform load is as follows

[0015]

[0016] where J l and J h respectively represent the force Jacobian matrices of the connecting rod and the hydraulic rod.

[0017] According to the above solution, the force Jacobian matrices J l and J h of the connecting rod and the hydraulic rod are calculated by the following formula:

[0018]

[0019] The value range of the hydraulic pressure is:

[0020] According to the above solution, the optimization objective of minimizing the root mean square (RMS) value of the connecting rod force is as follows:

[0021]

[0022] where RMS represents the root mean square value of the connecting rod force .

[0023] Implementing the multi-band vibration active suppression method for the high-speed heavy-duty multi-degree-of-freedom forming equipment of the present invention has the following beneficial effects:

[0024] The present invention establishes an elastic dynamics model of the forming equipment, reveals its multi-band vibration generation mechanism, and proposes a multi-band vibration active suppression method for the high-speed heavy-duty multi-degree-of-freedom forming equipment. Compared with before optimization, the vibration in the low-frequency band of the forming equipment is reduced by 50%, and the vibration in the high-frequency band is reduced by 82.8%. The method of the present invention has an important application prospect in the field of vibration suppression under heavy-duty high-speed working conditions. Description of the Drawings

[0025] The present invention will be further described below in conjunction with the accompanying drawings and embodiments. In the drawings:

[0026] Figure 1 is a schematic diagram of the basic structure of the 3RSS / S forming equipment;

[0027] Figure 2 is a schematic diagram of the pose relationship and dynamic model of the 3RSS / S forming equipment;

[0028] Figure 3 is a force analysis diagram of the driving roller;

[0029] Figure 4 is a force analysis diagram of the connecting rod;

[0030] Figure 5 is a force analysis diagram of the moving platform;

[0031] Figure 6 is the connecting rod force and the frequency spectrum diagram under different hydraulic pressure conditions;

[0032] Figure 7 is a comparison schematic diagram of the maximum connecting rod force and low-frequency vibration of different connecting rods under different hydraulic pressure conditions;

[0033] Figure 8 is the connecting rod force and its frequency spectrum diagram under different damping;

[0034] Figure 9 is a comparison schematic diagram of the maximum connecting rod force and high-frequency vibration of each connecting rod under different damping;

[0035] Figure 10 is the optimized hydraulic pressure curve;

[0036] Figure 11 is the angular error and frequency spectrum diagram under the action of the multi-band vibration active force and damping collaborative suppression method of the high-speed heavy-load multi-degree-of-freedom forming equipment;

[0037] Figure 12 is a schematic diagram of the low-frequency and high-frequency errors under the action of the multi-band vibration active force and damping collaborative suppression method of the high-speed heavy-load multi-degree-of-freedom forming equipment. Specific Embodiments

[0038] For a clearer understanding of the technical features, objectives, and effects of the present invention, the specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0039] S1 Taking the developed 3RSS / S forming equipment as an example, a hydraulic rod is installed on its original structure, and an elastic dynamics model considering the deformation of its connecting rod and the damping of the hydraulic rod is established;

[0040] The pose relationship and elastic dynamics model of the 3RSS / S forming equipment considering the hydraulic rod are asFigure 2 As shown, it can be seen from the figure that the connecting rod is equivalent to two identical mass blocks, which are connected by a spring and a damper, and the hydraulic rod is equivalent to a damper. The deformation of the connecting rod along the rod direction is defined as The driving torque of the driving roller is defined as The load applied to the moving platform is defined as W p , which can be expressed as W p =[w p1 ,w p2 ,w p3 ,w p4 ,w p5 ,w p6 T .

[0041] Figure 3 The force analysis of the driving roller part is given, and the dynamic equation of the driving roller part can be expressed as:

[0042]

[0043] In the formula, G R is the gravity acting on the driving roller, which can be expressed as G R =m R g. represents the constraint reaction force acting on the driving roller, which can be expressed as The constraint reaction force on the spherical pair of the connecting rod, which can be expressed as represents the position vectors of points A1, A2, A3 relative to points C1, C2, C3 at the midpoint in the coordinate system S A , which can be expressed as I R represents the inertia matrix of the driving roller. The driving roller can be equivalent to a cylinder with a radius of r R and a height of l R , then I R can be expressed as,

[0044]

[0045] In the formula, m r is the mass of the driving roller.

[0046] represents the coordinate transformation matrix from the coordinate system to the coordinate system S A , which can be expressed as,

[0047]

[0048] In the formula, R RA ​Represents a coordinate system to the coordinate system S A The rotation matrix, which can be expressed as

[0049]

[0050] where represents the rotation angle about the z A -axis between the two coordinate systems. T RA represents the origin offset from the coordinate system to the coordinate system S A which can be expressed as

[0051] represents the coordinate transformation matrix from the coordinate system to the coordinate system S A which can be expressed as

[0052]

[0053] where R l1A represents the rotation matrix from the coordinate system to the coordinate system S A which can be expressed as

[0054]

[0055] where is the rotation angle about the x A -axis between the two coordinate systems, is the rotation angle about the y A -axis between the two coordinate systems, is the rotation angle about the z A -axis between the two coordinate systems. T l1A represents the origin offset from the coordinate system to the coordinate system S A which can be expressed as

[0056]

[0057] Figure 4 The force analysis of the connecting rod is given. The dynamic equations of the upper and lower parts of the connecting rod can be expressed as:

[0058]

[0059] where G l1 and G l2 are the gravitational forces on the upper and lower parts of the connecting rod respectively, represents the constraint reaction force on the lower spherical pair of the connecting rod, which can be expressed as and respectively represent the elastic force and damping force of the connecting rod, which can be expressed as:

[0060]

[0061] In the formula, K and D respectively represent the stiffness and damping of the connecting rod, which can be expressed as:

[0062]

[0063] In the formula, E represents the Young's modulus of the material, χ l and λ l represent the linear damping coefficients based on the Rayleigh damping model. can be calculated by the following formula:

[0064]

[0065] and respectively represent the pose vectors of the upper and lower mass parts of the connecting rod, which can be expressed as, and I l1 and I l2 respectively represent the inertia matrices of the upper and lower mass parts of the connecting rod. The upper and lower parts of the connecting rod can both be equivalent to a cylinder with a radius of r L , and a height of l L , then I l1 and I l2 can be calculated by the following formula,

[0066]

[0067] The masses of the upper and lower parts of the connecting rod are respectively defined as m l1 and m l2 , then there is m l1 = m l2 = m L . represents the coordinate transformation matrix from coordinate system to coordinate system S A , which can be expressed as,

[0068]

[0069] In the formula, R l2A represents the rotation matrix from coordinate system to coordinate system S A , which can be expressed as,

[0070]

[0071] In the formula, is the rotation angle about the x A -axis between two coordinate systems, is the rotation angle about the y A -axis between two coordinate systems, is the rotation angle about the z A -axis between two coordinate systems. T l2A represents the origin offset from the coordinate system to the coordinate system S A , and it can be expressed as,

[0072] Figure 5 The force analysis of the moving platform is given, and the dynamic equation of the moving platform can be expressed as:

[0073]

[0074] In the formula, G p is the gravity acting on the moving platform, and it can be expressed as G p = m p g. represents the constraint reaction force on the intermediate spherical joint in S B , and it can be expressed as r p represents the position vector of the action point of the load force on the coordinate system S B . represents the position vector of the center of the lower spherical pair of the hydraulic rod in the coordinate system S B . I p represents the inertia matrix of the driving roller, and the driving roller can be equivalent to a cylinder with a radius of r p and a height of l p , then I p can be expressed as,

[0075]

[0076] In the formula, m p is the mass of the moving platform.

[0077] represents the coordinate transformation matrix from the coordinate system to the coordinate system S A , and it can be expressed as,

[0078]

[0079] In the formula, R hA represents the rotation matrix from the coordinate system to the coordinate system S A , and it can be expressed as,

[0080]

[0081] In the formula, is the rotation angle about the x A -axis between two coordinate systems, is the rotation angle about the y A -axis between two coordinate systems, is the rotation angle about the z A -axis between two coordinate systems. T hA represents the origin offset of the coordinate system to the coordinate system S A , which can be expressed as, represents the eccentric angles of the center points E1, E2, E3 of the lower spherical pairs of the hydraulic rods relative to the center of the coordinate system S B . is the damping force of the hydraulic rod, which can be expressed as,

[0082]

[0083] In the formula, D h represents the damping coefficient of the hydraulic rod, D h = χ h m h . m h is the mass of the hydraulic rod. represents the pose vector of the centroid of the hydraulic rod, which can be calculated by the following formula,

[0084]

[0085] In the formula, represents the position vector of the center of the lower spherical pair of the hydraulic rod in the coordinate system S A .

[0086] In summary, the dynamic model of the 3RSS / S forming equipment can be expressed as,

[0087]

[0088] The constraint equation can be expressed as,

[0089]

[0090] S2 Analyze the generation mechanism of the multi-band vibration of the 3RSS / S forming equipment according to the dynamic model

[0091] Based on the dynamic model of the 3RSS / S forming equipment, we will now delve into the multi-band vibration generation mechanism of the 3RSS / S forming equipment. By analyzing various dynamic factors within the model, we will reveal the root causes of its vibration generation, explore potential vibration suppression methods, and provide theoretical support for further optimizing the performance of the multi-degree-of-freedom forming equipment.

[0092] Figure 7 The magnitudes of the link forces with and without hydraulic pressure and their spectrograms are given. As Figure 7 shown in Fig. a, Fig. b and Figure 8 Fig. a, the waveforms of the force curves of the three links are the same, only with a phase difference. Meanwhile, with the introduction of hydraulic pressure, the maximum link force decreases from 103 kN to 57 kN, a reduction of 45%. From Figure 9 Fig. a, Figure 9 Fig. b and Figure 10 it can be seen that the amplitude of the low-frequency band (0 - 50 Hz) vibration of the link force (the peak of the low-frequency band vibration appears at 0 Hz, so here it refers to the amplitude at 0 Hz) decreases from 52 kN to 29 kN, a reduction of 44%. This indicates that the generation of the low-frequency band vibration of the 3RSS / S forming equipment is related to the introduction of hydraulic pressure in the system, and the purpose of increasing the hydraulic pressure is to reduce the fluctuation of the link force, thereby improving the stiffness of the mechanical system of the 3RSS / S forming equipment, and effectively suppressing the low-frequency band vibration. Therefore, the low-frequency band vibration of the 3RSS / S forming equipment is caused by the insufficient stiffness of the mechanical system of the 3RSS / S forming equipment.

[0093] Figure 8 and Figure 9 respectively give the link forces and their spectrograms under different damping, as well as the comparison of the maximum link forces of different links under different damping. It can be observed that the force curves of the three links show the same waveform in the forward and reverse directions, only with different phases. When the damping is 0, the range of the force magnitude is -51.6 kN to 103 kN. In addition, it can be seen from the figure that as the damping of the hydraulic link increases, the magnitude of the link force gradually decreases. The maximum link force decreases from 103 kN when the damping is 0 to 78.6 kN when the damping is 9.2. Meanwhile, from the spectrograms ( Figure 8 Figs. b, d, f), it can be seen that as the damping increases, the high-frequency band (100 Hz - 200 Hz) vibration of the link force gradually decreases. It drops from 9 kN when the damping is 0 to 0.68 kN when the damping is 9.2, and the amplitude of the high-frequency band vibration decreases significantly (the peak of the high-frequency band vibration appears at 165 Hz, so here it refers to the amplitude at 165 Hz). This indicates that when the damping of the mechanical system of the 3RSS / S forming equipment is low, the high-frequency band vibration of the 3RSS / S forming equipment becomes more obvious.

[0094] Therefore, based on the above analysis, the multi-frequency vibration generation mechanism of the 3RSS / S multi-degree-of-freedom forming equipment can be obtained as follows: for the low-frequency band (0 - 50 Hz), the vibration of the 3RSS / S forming equipment is caused by the insufficient stiffness of the mechanical system of the 3RSS / S forming equipment; at the same time, for the high-frequency band (100 Hz - 200 Hz), the vibration of the 3RSS / S forming equipment is caused by the insufficient internal damping of the mechanical system of the 3RSS / S forming equipment.

[0095] According to the generation mechanism of the multi-frequency vibration of the 3RSS / S forming equipment, S3 proposes a method for collaborative suppression of multi-frequency vibration active force and damping for a high-speed heavy-duty multi-degree-of-freedom forming equipment, that is, by actively adjusting the hydraulic pressure to reduce the fluctuation of the connecting rod force to suppress the vibration in the low-frequency band, and at the same time, by increasing the damping of the hydraulic system to suppress the vibration in the high-frequency band.

[0096] Based on the vibration generation mechanism outlined above, that is, the low-frequency vibration is attributed to the insufficient stiffness of the mechanical system, and the high-frequency vibration is caused by the insufficient system damping inside the mechanical system. To solve these problems, a method for collaborative suppression of multi-frequency vibration active force and damping for a high-speed heavy-duty multi-degree-of-freedom forming equipment is proposed. This method aims to actively adjust the force and damping characteristics in the mechanical system, thereby reducing the impact of vibration and improving the overall performance, accuracy, and stability of the 3RSS / S forming equipment. On the one hand, this method adds a hydraulic rod device to the original mechanical structure and actively adjusts the hydraulic pressure to reduce the fluctuation of the connecting rod force, thereby increasing the stiffness of the mechanical system to suppress the vibration in the low-frequency band. To achieve this goal, an optimization model is proposed, aiming to determine a set of hydraulic pressures to minimize the fluctuation of the connecting rod force, that is, to minimize the root mean square (RMS) value of the connecting rod force. Based on this, combined with the 3RSS-S dynamic model mentioned above, the relationship between the connecting rod force, hydraulic pressure, and moving platform load can be obtained as follows:

[0097]

[0098] In the formula, J l and J h respectively represent the force Jacobian matrices of the connecting rod and the hydraulic rod, which can be calculated by the following formula,

[0099]

[0100] The hydraulic pressure is related to the structural parameters of the hydraulic rod and the flow rate of the hydraulic system. It is not infinite but bounded. The value of the hydraulic pressure is taken within the following range: Therefore, a set of constraint conditions can be obtained as follows:

[0101]

[0102] As can be seen from the above constraint equations, if the hydraulic link is allowed to bear a greater force, the link force will decrease accordingly. When the link force decreases to zero, the fluctuation of the link force reaches the minimum. This can be quantified by the root mean square (RMS) value of the link force. In other words, at each moment, a set of optimal hydraulic pressures is determined to minimize the RMS value of the link force. Therefore, the following optimization objective can be proposed:

[0103]

[0104] where RMS represents the link force of the root mean square value. Figure 10 The optimized hydraulic pressure curve is given.

[0105] On the other hand, as described in S2, the vibration in the high-frequency band of the 3RSS / S forming equipment is mainly caused by the insufficient internal damping of the mechanical system. To solve this problem, the proposed multi-band vibration active force and damping collaborative suppression method for high-speed heavy-load multi-degree-of-freedom forming equipment compensates for the insufficient internal damping of the mechanical system by increasing the damping of the hydraulic system, thereby reducing the amplitude of vibration in the high-frequency band and improving the dynamic stability of the 3RSS / S forming equipment.

[0106] The present invention also provides a specific embodiment as follows:

[0107] First, according to the structural schematic diagram of the 3RSS / S forming equipment (as Figure 1 shown). The pose of the moving platform is obtained:

[0108]

[0109] where l i represents the direction vector of the i-th link, l g represents the length of the link, represents the deformation amount of the i-th link along the rod direction. represents the coordinate transformation matrix from coordinate system S B to coordinate system S A . and respectively represent the position vectors of the upper and lower spherical joint centers on the link in coordinate systems S A and S B , and they can be expressed as

[0110]

[0111] where and respectively represent points B1, B2, B3 and C1, C2, C3 relative to coordinate systems S B and S AEccentric angle of the origin Indicates the eccentric angles of points A1, A2, A3 relative to C1, C2, C3, r B and r C respectively represent the polar radii of points B1, B2, B3 and C1, C2, C3. r AC Indicates the distances between points A1, A2, A3 and C1, C2, C3.

[0112] Coordinate transformation matrix can be calculated by the following formula

[0113]

[0114] In the formula, R BA is the rotation matrix from coordinate system S B to coordinate system S A and it can be expressed as

[0115]

[0116] In the formula, c represents cosine and s represents sine.

[0117] T BA represents the offset of the origin of coordinate system S B relative to the origin of coordinate system S A and it can be expressed as

[0118] T BA =[0, 0, h g T (31)

[0119] In the formula, h g represents the distance between the origin of coordinate system S B at the initial position and the origin of coordinate system S A The pose of the moving platform can be obtained through formula (27) and the relationship with the driving angular velocity ω of the 3RSS / S forming equipment

[0120]

[0121] In the formula

[0122]

[0123] Table 1 gives the structural parameters of the 3RSS / S forming equipment. Substituting these parameters into formula (32) can calculate the pose of the moving platform

[0124] Table 1 Structural parameters of the 3RSS / S forming equipment.

[0125] ​

[0126] Subsequently, the dynamic model of the 3RSS / S forming equipment was derived, and the multi-frequency vibration generation mechanism was revealed. Based on this, an active force and damping suppression method for multi-frequency vibration of high-speed heavy-duty multi-degree-of-freedom forming equipment was proposed. On the one hand, this method actively adjusts the hydraulic pressure by adding a hydraulic rod device to the original mechanical structure to reduce the fluctuation of the connecting rod force, thereby improving the stiffness of the mechanical system to suppress the vibration in the low-frequency band. To achieve this goal, an optimization model was proposed to determine a set of hydraulic pressures to minimize the fluctuation of the connecting rod force, that is, to minimize the root mean square (RMS) value of the connecting rod force. On the other hand, the vibration in the high-frequency band of the 3RSS / S forming equipment is mainly caused by insufficient internal damping of the mechanical system. To solve this problem, the proposed method compensates for the insufficient internal damping of the mechanical system by increasing the damping of the hydraulic system, thereby reducing the amplitude of the vibration in the high-frequency band and improving the dynamic stability of the 3RSS / S forming equipment. Finally, according to this method, the multi-frequency vibration errors of the moving platform before and after optimization were compared (0 Hz for the low-frequency band and 165 Hz for the high-frequency band). The simulation results (such as Figure 11 、 Figure 12 ) show that under this method, the low-frequency band error in the alpha direction decreases from 0.74 mrad to 0.39 mrad, a reduction of 47.3%, while the high-frequency band error decreases from 0.066 mrad to 0.017 mrad, a reduction of 74%. In the beta direction, the low-frequency band error decreases from 0.75 mrad to 0.4 mrad, a reduction of 46.7%, while the high-frequency band error decreases from 0.073 mrad to 0.013 mrad, a reduction of 82%. In the gamma direction, the low-frequency band error decreases from 1.9 mrad to 0.95 mrad, a reduction of 50%, while the high-frequency band error decreases from 0.7 mrad to 0.12 mrad, a reduction of 82.8%. This result shows that the proposed active force and damping suppression method for multi-frequency vibration of high-speed heavy-duty multi-degree-of-freedom forming equipment can effectively reduce the vibration of the 3RSS / S forming equipment.

[0127] The embodiments of the present invention have been described above in conjunction with the accompanying drawings. However, the present invention is not limited to the above specific embodiments. The above specific embodiments are merely illustrative and not restrictive. Under the inspiration of the present invention, those of ordinary skill in the art can also make many forms without departing from the spirit and scope protected by the claims of the present invention. These all fall within the protection scope of the present invention.

Claims

1. A multi-band vibration active suppression method for a high-speed heavy-load multi-degree-of-freedom forming equipment, characterized in that, Including the following steps: S1. Install a hydraulic rod on the original structure of the high-speed heavy-duty multi-degree-of-freedom forming equipment, and establish an elastic dynamics model considering the deformation of its connecting rod and the damping of the hydraulic rod; S2. Analyze the generation mechanism of the multi-band vibration of the forming equipment according to the dynamics model; S3. According to the generation mechanism of the multi-band vibration, by actively adjusting the hydraulic pressure to reduce the fluctuation of the connecting rod force to suppress the low-frequency band vibration, and at the same time, by increasing the damping of the hydraulic system to suppress the high-frequency band vibration.

2. The multi-band vibration active suppression method for a high-speed heavy-load multi-degree-of-freedom forming equipment according to claim 1, characterized in that, The elastic dynamics model established in step S1 is: In the formula, the deformation of the connecting rod along the rod direction is defined as The driving torque of the driving roller is defined as The load applied to the moving platform is defined as W p , W p =[w p1 , w p2 , w p3 , w p4 , w p5 , w p6 T ;​ G R is the gravity force acting on the driving roller, represents the reaction force of the constraint on the driving roller, is the reaction force of the constraint on the spherical pair of the connecting rod, represents the position vectors of the midpoints A1, A2, A3 of the coordinate system S A relative to the points C1, C2, C3, which can be expressed as I R represents the inertia matrix of the driving roller; represents the coordinate system to the coordinate system S A coordinate transformation matrix, T Sl1SA represents the coordinate system to the coordinate system S A coordinate transformation matrix; G l1 and G l2 are respectively the gravity forces acting on the upper and lower parts of the connecting rod, represents the reaction force of the constraint on the lower spherical pair of the connecting rod; represents the coordinate system to the coordinate system S A coordinate transformation matrix, represents the coordinate system to the coordinate system S A coordinate transformation matrix, is the damping force of the hydraulic rod.

3. The multi-band vibration active suppression method for high-speed heavy-duty multi-degree-of-freedom forming equipment according to claim 2, wherein, The constraint equation of the elastic dynamics model in step S1 is expressed as:

4. The multi-band vibration active suppression method for high-speed heavy-load multi-degree-of-freedom forming equipment according to claim 1, wherein, In step S2, the generation mechanism of the multi-band vibration of the multi-degree-of-freedom forming equipment is as follows: for the low-frequency band of 0 - 50 Hz, the vibration of the forming equipment is caused by the insufficient stiffness of the mechanical system of the forming equipment; for the high-frequency band of 100 Hz - 200 Hz, the vibration of the forming equipment is caused by the insufficient internal damping of the 3RSS / S forming equipment mechanical system.

5. The multi-band vibration active suppression method for high-speed heavy-load multi-degree-of-freedom forming equipment according to claim 3, wherein, In step S3, a set of hydraulic pressures is determined through optimizing the model to minimize the root mean square (RMS) value of the connecting rod force. Combining with the elastic dynamics model, the relationship among the connecting rod force, the hydraulic pressure and the moving platform load is as follows where J l and J h respectively represent the force Jacobian matrices of the connecting rod and the hydraulic rod.

6. The multi-band vibration active suppression method for high-speed heavy-load multi-degree-of-freedom forming equipment according to claim 5, characterized in that Force Jacobian matrices J of the connecting rod and the hydraulic rod l and J h are calculated by the following formula: Hydraulic pressure The value ranges from:

7. The multi-band vibration active suppression method for a high-speed heavy-load multi-degree-of-freedom forming equipment according to claim 6, wherein The optimization objective of minimizing the root mean square (RMS) value of the connecting rod force is as follows: wherein, RMS represents the connecting rod force and is the root mean square value thereof.

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