Method and apparatus for low frequency chatter suppression in robotic milling based on joint damper

Abstract

The application belongs to the technical field of milling processing, and discloses a robot milling low-frequency chatter suppression method and equipment based on a joint damper, which comprises the following steps: (1) magnetic circuit analysis is performed based on an equivalent magnetic circuit model of the joint damper to obtain the inner diameter and the outer diameter of a magneto-rheological fluid layer of the joint damper; the joint damper is arranged at a joint of a robot; (2) the relationship between the braking torque of the joint damper and the force at the end of the joint of the robot in the joint space is derived based on the characteristics of a Bingham fluid and static analysis of the robot, and then a relationship diagram between the joint angles of the robot and the vibration suppression effect is analyzed to determine the optimal joint angles of the joints based on the relationship diagram, so that the robot works at the optimal joint angles to suppress the milling low-frequency chatter. The application can effectively improve the anti-vibration capability of the joint of the robot.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field related to milling processing, and more particularly to a robot milling low-frequency chatter suppression method and device based on joint damper. BACKGROUND

[0002] Robot processing has the advantages of high flexibility, large workspace, low cost, and multi-sensor integration, which makes it gradually applied in the field of milling processing. However, the low structural stiffness of the robot causes vibration during processing, and severe chatter often causes irreversible damage to the processing quality, tool life, and even the structure of the robot. The mechanism of robot milling chatter is complex, not only has high-frequency chatter dominated by tool modal similar to regenerative chatter, but also has low-frequency chatter dominated by robot structural modal. Most of the existing robot milling chatter suppression methods follow the vibration suppression strategy of machine tool at the tool end, mainly using intelligent spindle, force control actuator and other end-of-arm chatter suppression devices and their application methods, which can effectively suppress high-frequency chatter. However, robot low-frequency chatter is caused by its low structural stiffness, mainly concentrated in the joints, and the end-of-arm chatter suppression strategy cannot effectively suppress joint vibration.

[0003] For robot low-frequency chatter, existing vibration suppression methods include optimizing robot processing posture, feed direction, etc. to maximize its stiffness, and low-frequency chatter semi-active and active control based on various end effectors. Although these methods consider the characteristics of the robot and have some effect on low-frequency chatter, they limit the flexibility of robot processing to some extent and do not fundamentally enhance the structural stiffness of the robot joint. A few studies have focused on controlling the robot joint motor, but there is a certain time delay between the control command and the motor actuation. This method is only effective at low speed, and most robots do not open their joint motor control authority, so this method is difficult to apply. SUMMARY

[0004] In view of the above defects or improvement needs of the prior art, the present application provides a robot milling low-frequency chatter suppression method and device based on joint damper, which optimizes the geometric parameters of the magnetorheological fluid layer of the joint damper, analyzes the influence of the joint angle on the braking effect, and then selects the best joint angle, thereby effectively improving the anti-vibration ability of the robot joint.

[0005] To achieve the above purpose, according to one aspect of the present application, a robot milling low-frequency chatter suppression method based on joint damper is provided, which comprises the following steps:

[0006] (1) Perform magnetic circuit analysis based on the equivalent magnetic circuit model of the joint damper to obtain the inner diameter and outer diameter of the magnetorheological fluid layer; the joint damper is arranged at the joint of the robot;

[0007] (2) Based on the characteristics of Bingham fluid, the relationship between the braking torque of the joint damper and the force of the robot joint in the joint space is derived, and then the relationship diagram between the joint angle of the robot and the vibration suppression effect is analyzed, and the optimal joint angle of each joint is determined based on the relationship diagram, so that the robot works at the optimal joint angle to suppress the milling low-frequency chatter.

[0008] Further, the magnetic circuit analysis is performed based on the equivalent magnetic circuit model of the joint damper to obtain the coil turns and the rated current value of the joint damper, and then the mapping relationship between the braking torque of the joint damper and the inner diameter and the outer diameter of the magnetorheological fluid layer is derived, so as to determine the inner diameter and the outer diameter of the magnetorheological fluid layer.

[0009] Further, the total magnetic motive force of the excitation coil is analyzed based on the equivalent magnetic circuit model of the joint damper and the thickness of the joint damper, and then the coil turns and the rated current value of the joint damper are determined.

[0010] Further, based on the coil turns and the rated current value of the joint damper, the calculation formula of the braking torque and the calculation formula of the magnetic flux density, the mapping relationship between the braking torque and the outer diameter and the inner diameter of the magnetorheological fluid layer is derived, and then the outer diameter and the inner diameter of the magnetorheological fluid layer are determined.

[0011] Further, based on the characteristics of Bingham fluid, the relationship between the braking torque of the joint damper and the force of the robot joint in the joint space is derived, and the decay rate of the joint force is defined as the joint braking coefficient, and the end braking coefficient is determined based on the joint braking coefficient and the statics analysis of the robot, and then the relationship diagram between the joint angle and the end braking coefficient is obtained, and the optimal joint angle of each joint is determined based on the relationship diagram, so that the robot works at the optimal joint angle to suppress the milling low-frequency chatter.

[0012] Further, the expression of the joint braking coefficient α q,i is as follows:

[0013]

[0014] In the formula, T is the braking torque; M i (t) is the torque acting on the joint.

[0015] Further, the joint braking coefficient is mapped to the end Cartesian space to derive the end braking coefficient A e =[α e,x ,α e,y ,α e,z ,α e,ωx ,α e,ωy ,α e,ωz ], wherein α e,x ,αe,y ,α e,z are respectively braking coefficients of X, Y, Z directions of robot end; e,ωx ,α e,ωy ,α e,ωz are respectively braking coefficients of X, Y, Z rotation directions of robot end.

[0016] Further, the end braking coefficient represents the vibration suppression effect; the end vibration speed and the cutting force in the robot milling process are mapped into the joint space through the Jacobian matrix, and the corresponding formula is:

[0017]

[0018] In the formula, J F (q) is the force Jacobian matrix, q T (q) is the velocity Jacobian matrix, q v =[q v,1 ,q v,2 ,q v,3 ,q v,4 ,q v,5 ,q v,6 ] T represents the vibration speed of each joint, v e =[v e,x ,v e,y ,v e,z ,v e,ωx ,v e,ωy ,v e,ωz ] T represents the vibration speed of the robot end X, Y and Z moving and rotating directions, M(t)=[M1(t),M2(t),M3(t),M4(t),M5(t),M6(t)] T represents the torque of each joint, F(t)=[F x (t),F y (t),F z (t),M x (t),M y (t),M z (t)] T represents the cutting force and torque of the robot end three directions.

[0019] The application also provides a robot milling low-frequency chatter suppression system based on joint damper, which comprises a memory and a processor, the memory stores a computer program, and the processor executes the computer program to execute the robot milling low-frequency chatter suppression method based on joint damper as described above.

[0020] The application further provides a computer readable storage medium, which stores machine executable instructions, and the machine executable instructions, when called and executed by a processor, cause the processor to implement the robot milling low-frequency chatter suppression method based on a joint damper.

[0021] Overall, compared with the prior art, the robot milling low-frequency chatter suppression method and device based on a joint damper provided by the application mainly have the following beneficial effects:

[0022] 1. The joint damper is optimized in terms of the geometry parameters of the magneto-rheological fluid layer, the influence of the joint angle on the braking effect is analyzed, and then the optimal joint angle range is selected, so that the vibration suppression effect of the joint damper is optimized by optimizing the robot posture, the anti-vibration capability of the robot joint is effectively improved, the anti-vibration capability of the robot is improved from the joint, and the processing quality and efficiency of the robot are effectively improved.

[0023] 2. The application derives the relationship between the braking torque of the joint damper and the force on the robot joint end in the joint space, proposes the joint braking coefficient and the end braking coefficient, reveals the mapping relationship between the vibration suppression effect of the joint damper and the robot joint angle, and analyzes the influence of the joint angle on the braking effect on this basis, so that the vibration suppression effect of the joint damper is optimized by optimizing the robot posture.

[0024] 3. The robot works in the optimal joint angle range selected by the method of the application, and the vibration suppression effect is improved by 10.47% relative to the conventional posture.

[0025] 4. The braking torque is related to the size of the magneto-rheological fluid layer and the magnetic flux density, the size w, r1 and r2 of the magneto-rheological fluid layer determines the magnetic flux density in the region, and the three size parameters ultimately determine the braking torque of the joint damper, so that the braking torque range of the joint damper can be increased by optimizing the geometric size of the magneto-rheological fluid layer. BRIEF DESCRIPTION OF DRAWINGS

[0026] Figure 1 is a flowchart of a robot milling low-frequency chatter suppression method based on a joint damper provided by the application;

[0027] Figure 2 is an equivalent magnetic circuit model of the joint damper involved in the application;

[0028] Figure 3 is a yield strength diagram of the magneto-rheological fluid under different magnetic flux densities obtained by the application;

[0029] Figure 4The braking torque of the joint damper under different magnetorheological fluid layer geometries obtained by this invention;

[0030] Figure 5 (a) and (b) in the figure are respectively a cross-sectional view and a three-dimensional schematic diagram of the joint damper involved in the present invention;

[0031] Figure 6 It is a parallel coordinate diagram (X direction) of the braking coefficient at the end of the joint damper;

[0032] Figure 7 It is a parallel coordinate diagram (Y direction) of the braking coefficient at the end of the joint damper;

[0033] Figure 8 It is a parallel coordinate graph showing the mapping relationship between the joint angles and the braking coefficient in the X direction;

[0034] Figure 9 This is a schematic diagram illustrating the setup for an example of vibration suppression in robotic milling.

[0035] Figure 10 (a), (c), (e), (g), (i), and (k) are schematic diagrams of vibration suppression results of a milling robot without joint dampers in different experiments, while (b), (d), (f), (h), (j), and (l) are schematic diagrams of vibration suppression results of a milling robot with joint dampers in different experiments.

[0036] In all the accompanying drawings, the same reference numerals are used to denote the same elements or structures, wherein: 1-stator upper end cover, 2-coil chamber upper end cover, 3-coil chamber lower end cover, 4-stator lower end cover, 5-first rolling bearing, 6-first felt gasket, 7-rotor, 8-second felt gasket, 9-second rolling bearing, 10-circlip ring for hole. Detailed Implementation

[0037] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0038] Please see Figure 1 This invention provides a method for suppressing low-frequency chatter in robot milling based on joint dampers, the method mainly including the following steps:

[0039] Step one, install joint damper at the joint of the robot, and based on the equivalent magnetic circuit model of the joint damper, magnetic circuit analysis is carried out to obtain the coil turns and rated current value of the joint damper, and then the inner diameter and outer diameter of the magneto-rheological fluid layer are derived.

[0040] Among them, the mapping relationship between the braking torque of the joint damper and the inner diameter and outer diameter of the magneto-rheological fluid layer is derived, so as to determine the inner diameter and outer diameter of the magneto-rheological fluid layer.

[0041] The joint damper can provide damping force, and the damping force can be calculated according to the size of the magneto-rheological fluid layer in the joint damper. When there is no external magnetic field, the magneto-rheological fluid shows the characteristics of low viscosity Newtonian fluid, at this time the braking torque of the joint damper only exists weak viscous damping, which can be generally ignored. When the coil is energized, the magneto-rheological fluid shows the Bingham fluid with variable yield strength, and the yield strength is determined by the magnetic field strength, at this time the braking torque T of the joint damper is about the size of the coulomb damping of the structure, which can be expressed as the following expression:

[0042]

[0043] In the formula, τ B is the yield stress generated by the external magnetic field, which is related to the magnetic induction intensity B, w is the width of the magneto-rheological fluid layer, r1 is the inner diameter of the magneto-rheological fluid layer, and r2 is the outer diameter of the magneto-rheological fluid layer. It can be found that the braking torque at this time is related to the size of the magneto-rheological fluid layer and the magnetic flux density. Further, the size of the magneto-rheological fluid layer w, r1 and r2 determines the magnetic flux density in the region, so the three size parameters ultimately determine the braking torque of the joint damper. According to the installation size and assembly requirement of the device, the width of the magneto-rheological fluid layer is set to w=28mm. Further, the braking torque range of the joint damper can be increased by optimizing the geometric size of the magneto-rheological fluid layer.

[0044] The optimization of the magneto-rheological fluid layer mainly includes the following steps:

[0045] Firstly, based on the equivalent magnetic circuit model of the joint damper arranged at the joint of the robot and the calculation formula of the braking torque of the joint damper, the coil turns and rated current of the joint damper are determined.

[0046] Please refer to Figure 2 , where R1 is the coil cavity magnetic resistance, R2 and R3 are air magnetic resistance, R4 is the rotor magnetic resistance, and NI is the magnetic motive force generated by the excitation coil. The calculation expression of the magnetic circuit can be obtained:

[0047] F a = NI = φR a (2)

[0048] Among them, F aTotal magnetic motive force, determined by current I and number of turns N; R a Total magnetic reluctance; φ = BS is total magnetic flux, determined by magnetic flux density B and effective area S.

[0049] Magnetic reluctance R is related to permeability, equivalent length of magnetic circuit L, and effective area S, and is expressed as:

[0050]

[0051] In the formula, μ0=4π×10 -7 T·m / A is vacuum permeability, μ is relative permeability, dimensionless, and related to material properties. In the present embodiment, the manufacturing material of the coil cavity and the rotor of the joint damper is selected to be silicon steel, and the relative permeability is μ = 7000. The magnetic reluctance of each part can be calculated as follows:

[0052]

[0053] In the formula, R1=2.29×10 3 H -1 , R2=R3. The expression of R4 is as follows:

[0054]

[0055] From the above calculation, it can be seen that R1 and R4 are much smaller than R2 and R3, and it can be approximately considered that the air gap width of the magnetorheological fluid layer, i.e., the thickness of the magnetorheological fluid layer, determines the total magnetic reluctance of the magnetic circuit. Considering the manufacturing and assembly precision, the thickness of the magnetorheological layer is usually between 0.25 mm and 2 mm, and at this time, the air gap magnetic reluctance accounts for 85.95% to 97.95% of the total magnetic reluctance of the magnetic circuit. In order to facilitate the optimal design of the parameters of the MRF layer, the total magnetic resistance R a can be approximated as:

[0056]

[0057] Based on the total magnetic motive force of the joint damper and the total magnetic resistance, and the recommended thickness of the magnetorheological fluid layer, the number of turns of the coil of the joint damper and the rated current are determined. Specifically, the relationship between the magnetic flux density of the magnetorheological fluid and the yield stress is as shown in Figure 3 . When the magnetic flux density is about 0.25 T, the yield stress of the magnetorheological fluid is basically saturated. Therefore, B = 0.25 T is preset. Combined with formula (2) and formula (6), and the recommended thickness of the magnetorheological fluid layer (0.25 mm to 2 mm), the total magnetic motive force should be 48.06 Wb·H -1 to 326.79 Wb·H -1 . Considering factors such as leakage and approximation of the total magnetic resistance R a , the total magnetic motive force of the excitation coil is preset to 400 Wb·H -1According to the above, the number of turns of the coil N = 400 and the rated current I = 1A are determined.

[0058] Then, based on the number of turns of the coil and the rated current of the joint damper, the formula for calculating the braking torque, and the formula for calculating the magnetic flux density, the mapping relationship between the braking torque and the outer diameter and the inner diameter of the magnetorheological fluid layer is derived, and then the outer diameter and the inner diameter of the magnetorheological fluid layer are determined.

[0059] Specifically, according to the determined excitation coil parameters, the expression of the magnetic flux density can be obtained by combining formula (2) and formula (6) as follows:

[0060]

[0061] According to formula (1) and formula (7), the mapping relationship between the braking torque and the inner diameter r1 and the outer diameter r2 of the magnetorheological fluid layer can be derived, as shown in formula (8). Figure 4 As can be seen, when r1 and r2 are relatively close, the braking torque of the joint damper increases significantly, and the braking torque increases with the increase of r1 / r2, and then r1 and r2 can be optimized according to the overall size of the joint damper and the required maximum braking torque. In this embodiment, the size of point A is selected for the design of the magnetorheological fluid layer, and the magnetorheological fluid layer is designed with an inner layer radius r1 = 35mm, an outer layer radius r2 = 35.5mm, and a layer width w = 28mm.

[0062] The joint damper after optimization of the geometric size is shown in Figure 5 The joint damper includes a stator upper end cover 1, a coil chamber upper end cover 2, a coil chamber lower end cover 3, a stator lower end cover 4, a first rolling bearing 5, a first felt gasket 6, a rotor 7, a second felt gasket 8, a second rolling bearing 9, and a hole clamp ring 10. The first rolling bearing and the second rolling bearing ensure the coaxial assembly of the stator and the rotor. The coil chamber upper end cover and the coil chamber lower end cover combine to form a coil chamber, in which an excitation coil is installed. The annular gap between the coil chamber and the rotor forms a magnetorheological fluid layer, and the concave groove in the coil chamber forms a horseshoe-shaped structure, which drives the magnetic flux path through the magnetorheological fluid layer to form a loop in the rotor component. The second felt gasket ensures sealing to prevent leakage of the magnetorheological fluid, and the hole clamp ring is used to axially limit the first rolling bearing.

[0063] When the coil is not powered, the magnetorheological fluid without an external magnetic field exhibits the characteristics of a low-viscosity Newtonian fluid, which does not affect the joint movement. When the coil is powered, the magnetorheological fluid under the action of an external magnetic field will instantaneously exhibit the characteristics of a high-viscosity, low-flow Bingham fluid within milliseconds, thereby providing a braking torque to resist joint vibration and enhancing the joint structure.

[0064] Step two, based on the characteristics of Bingham fluid, the relationship between the braking torque of joint damper and the force of robot joint in joint space is derived, and then the relationship between the joint angle of robot and the vibration suppression effect is analyzed to determine the optimal joint angle range of each joint, so that the robot works in the optimal joint angle range to suppress the low-frequency chatter in milling.

[0065] Based on the characteristics of Bingham fluid, the relationship between the braking torque of joint damper and the force of robot joint in joint space is derived, and the decay rate of joint force is defined as the joint damping coefficient, based on which and the statics analysis of robot, the end damping coefficient is determined, and then the relationship between the joint angle and the end damping coefficient is obtained, based on which the optimal joint angle range of each joint is determined, so that the robot works in the optimal joint angle range to suppress the low-frequency chatter in milling.

[0066] Specifically, in the milling process, the end of the robot is subjected to the milling force, and the joint is subjected to the braking torque generated by the joint damper. The embodiment analyzes the influence of joint angle on damping effect, and optimizes the vibration suppression effect of joint damper by optimizing the posture of robot.

[0067] The end vibration speed and the cutting force in the milling process of robot are mapped into joint space through Jacobian matrix, which can be expressed as:

[0068]

[0069] Where J F (q)=J T (q) is the force Jacobian matrix, q v =[q v,1 ,q v,2 ,q v,3 ,q v,4 ,q v,5 ,q v,6 ] T represents the vibration speed of each joint, v e =[v e,x ,v e,y ,v e,z ,v e,ωx ,v e,ωy ,v e,ωz ] T represents the vibration speed of robot end X, Y and Z direction translation and rotation, M(t)=[M1(t),M2(t),M3(t),M4(t),M5(t),M6(t)] T represents the torque of each joint, F(t)=[F x (t),F y (t),F z(t),M x (t),M y (t),M z (t)] T The cutting force and torque in three directions of the robot end.

[0070] Due to the characteristics of Bingham fluid, the joint damper will rotate only when the applied torque reaches its minimum shear stress threshold, otherwise it behaves as an ordinary fluid. Therefore, when the absolute value of the torque acting on the joint |M i (t)| does not exceed the braking torque T, the joint does not vibrate under the action of the joint damper, and the actual joint vibration velocity When the absolute value of the torque acting on the joint |M i (t)| exceeds the braking torque T, the joint damper rotates, and its braking torque is shown in equation (1). The size of the braking torque T is always less than or equal to the size of the torque M i (t) acting on the joint, and the direction is opposite, at this time the equivalent torque acting on the joint is |M i (t)|-T. The decay rate of the force acting on the joint is related to the torque M i (t) acting on the joint and the braking torque T, and the joint braking coefficient a q,i is defined as follows:

[0071]

[0072] Considering the braking effect of the joint damper, the actual joint vibration can be calculated as:

[0073]

[0074] Map the joint braking coefficient to the end Cartesian space to represent the braking effect of the joint damper in each direction: first assume that the joint damper does not consider the braking effect, the robot end vibration velocity is v e =[1,1,1,1,1,1] T , according to equation (8), the joint vibration velocity q v can be expressed as:

[0075] q v,i =i inv,i1 +i inv,i2 +i inv,i3 +i inv,i4 +i inv,i5 +i inv,i6 ,(i=1,2,…,6) (11)

[0076] where j inv,ij is the element in the i-th row and j-th column of matrix J -1 (q).

[0077] According to the robot kinematics equation v e = J(q) q v , the joint vibration velocity is converted to the end Cartesian space, and the robot end vibration velocity is known as v e = [1, 1, 1, 1, 1, 1] T , the equation can be expressed as:

[0078] j i1 q v1 + j i2 q v2 + j i3 q v3 + j i4 q v4 + j i5 q v5 + j i6 q v6 = 1, (i = 1, 2, …, 6) (12)

[0079] where j ij is the element of the i-th row and the j-th column of the matrix J(q).

[0080] Combining equation (11) and equation (12) has:

[0081]

[0082] According to equation (10), the joint vibration velocity under the influence of the joint damper brake can be expressed as:

[0083]

[0084] Considering the robot end vibration velocity under the influence of the joint damper brake , the joint vibration velocity is converted to the end Cartesian space, and the following is obtained:

[0085]

[0086] Taking the expression of the X direction as an example, the robot end vibration velocity can be expressed as:

[0087]

[0088] Combining equation (11) and equation (16) can be obtained:

[0089]

[0090] Finally, multiply equation (17) by 1 on the right, and substitute equation (13) into equation (17) to obtain:

[0091]

[0092] The expression of the vibration velocity of the robot end in the X direction under the influence of the joint damper braking is obtained:

[0093]

[0094] Similarly, the vibration velocity v of the robot end under the influence of the joint damper braking can be expressed as: e

[0095]

[0096] Since the previous assumption v e is a unit matrix, the end braking coefficient A e = [α e,x , α e,y , α e,z , α e,ωx , α e,ωy , α e,ωz ] can finally be expressed as:

[0097]

[0098] It can be obtained from equation (21) that the end braking coefficient (vibration suppression effect) is related to the angle of each joint of the robot. In order to optimize the vibration suppression effect of the joint damper, it is necessary to analyze the vibration suppression effect of the joint damper under different joint configurations and to optimize the posture according to the analysis results.

[0099] Taking the ABB IRB6660 robot as an example, the motion range of each joint is shown in Table 1. Six equidistant angles are selected within the motion range of each joint, and the end braking coefficient under any combination is calculated. In order to ignore the influence of cutting parameters, it is assumed that the cutting force in each direction is 100 N, and 46656 groups of data are calculated. Parallel coordinates are used to visualize high-dimensional data and analyze the influence of the change of each joint angle on the vibration suppression effect. The parallel coordinates of the braking coefficients in the X, Y and Z directions which have greater influence on machining stability are shown in Figures Figure 6 , Figure 7 and Figure 8 .

[0100] Table 1, ABB IRB6660 robot joint operating angle range

[0101] Joint Range of motion angle 1 +180° to -180° 2 +85° to -42° 3 +120° to 20° 4 +300° to -300° 5 +120° to -120° 6 +300° to -300°

[0102] Figure 6 Figure 4 is a parallel coordinate diagram of the mapping relationship between each joint angle and the end braking coefficient in the X direction. From Figure 6 ​It can be seen that the end brake coefficient (X direction) is small near 180, 36, -180 degrees of joint 1, -40, 36, 60 degrees of joint 2, -50, -120 degrees of joint 3, -210, -90 degrees of joint 6, and the vibration suppression effect is good. The parallel coordinate diagram of the mapping relationship between the joint angle and the brake coefficient in the Y and Z directions is shown in FIGS. Figure 7 and Figure 8 Through analysis, the angle range of each joint with good vibration suppression effect is obtained, as shown in Table 2:

[0103] Table 2: Joint angle optimization range

[0104]

[0105] The posture with good suppression effect (posture 1) and the posture with poor suppression effect (posture 2) are selected for example application to verify the effectiveness of joint damper vibration suppression and the effectiveness of the vibration suppression posture optimization method. The robot joint configuration corresponding to the two postures is shown in Table 3, and the experimental cutting tool is a ring-shaped cutter, and the cutting parameters are shown in Table 4:

[0106] Table 3: Joint angle range

[0107]

[0108] Table 4: Simulation and experimental cutting parameter table

[0109]

[0110] The application setting of the embodiment is shown in Figure 9 When the joint damper is energized, it shows a certain vibration suppression effect, as shown in FIG. 10. The vibration suppression effects of groups A-F are 59.74%, 60.77%, 33.87%, 52.76%, 31.15%, and 34.54%, respectively. The vibration suppression effect under stable conditions is about 38.08%, and the vibration suppression effect under low-frequency chatter conditions is about 60.26%. In addition, under the same cutting conditions, the vibration suppression effects of posture 1 and posture 2 are about 43.32% and 32.85%, respectively. The vibration suppression effect of posture 1 selected after optimizing the joint angle based on the end brake coefficient is about 10.47% higher than that of posture 2. It is proved that optimizing the joint angle can improve the vibration suppression effect. The example application results show that under different machining conditions, the joint damper shows a certain vibration suppression effect, and it is proved that the proposed joint angle optimization strategy effectively enhances the vibration suppression effect of the joint damper.

[0111] The application further provides a robot milling low-frequency chatter suppression system based on joint damper, which comprises a memory and a processor, the memory stores a computer program, and the processor executes the computer program to execute the robot milling low-frequency chatter suppression method based on joint damper.

[0112] The application further provides a computer readable storage medium, which stores machine executable instructions, and the machine executable instructions, when called and executed by a processor, make the processor realize the robot milling low-frequency chatter suppression method based on joint damper.

[0113] Those skilled in the art can easily understand that the above description is only the preferred embodiment of the application, and is not used to limit the application, and any modification, equivalent replacement and improvement made within the spirit and principle of the application should be included in the protection scope of the application.

Claims

1. A joint damper based robot milling low frequency chatter suppression method, characterized by, The method comprises the following steps: (1) performing magnetic circuit analysis based on an equivalent magnetic circuit model of the joint damper to obtain the inner diameter and the outer diameter of the magneto-rheological fluid layer; the joint damper is arranged at a joint of the robot; (2) deriving the relationship between the braking torque of the joint damper and the force acting on the joint of the robot in the joint space based on the characteristics of Bingham fluid, and then analyzing to obtain a relationship diagram between the joint angles of the robot and the vibration suppression effect, and determining the optimal joint angles of each joint based on the relationship diagram, so that the robot works at the optimal joint angles to suppress the milling low-frequency chatter; Based on the characteristics of Bingham fluid, the relationship between the braking torque of the joint damper and the forces on the robot joints in the joint space is derived. The attenuation rate of the joint forces is defined as the joint braking coefficient. Based on the joint braking coefficient and robot static analysis, the end-effector braking coefficient is determined, and then the relationship between each joint angle and the end-effector braking coefficient is obtained. Based on the relationship diagram, the optimal joint angle for each joint is determined, so that the robot operates at the optimal joint angle to suppress low-frequency chatter during milling. The joint braking coefficient is mapped to the end-effector Cartesian space to derive the end-effector braking coefficient A. e = [ α e,x , α e,y , α e,z , α e,ωx , α e,ωy , α e, ωz ],in, α e,x , α e,y , α e,z These are the braking coefficients in the X, Y, and Z directions of the robot's end effector, respectively. α e,ωx , α e,ωy , α e, ωz These are the braking coefficients for the robot's end effector in the X, Y, and Z rotation directions, respectively; the end effector braking coefficient represents the vibration damping effect.

2. The joint damper based robotic milling low frequency chatter suppression method of claim 1, wherein: The equivalent magnetic circuit model of the joint damper is used to perform magnetic circuit analysis to obtain the number of turns of the coil and the rated current value of the joint damper, and then the mapping relationship between the braking torque of the joint damper and the inner diameter and the outer diameter of the magneto-rheological fluid layer is derived, so as to determine the inner diameter and the outer diameter of the magneto-rheological fluid layer.

3. The joint damper based robotic milling low frequency chatter suppression method of claim 1, wherein: The equivalent magnetic circuit model of the joint damper and the thickness of the joint damper are used to analyze the total magnetic motive force of the exciting coil, and then the number of turns of the coil and the rated current value of the joint damper are determined.

4. The joint damper based robotic milling low frequency chatter suppression method of claim 1, wherein: Based on the number of turns of the coil and the rated current value of the joint damper, the calculation formula of the braking torque and the calculation formula of the magnetic flux density, the mapping relationship between the braking torque and the outer diameter and the inner diameter of the magneto-rheological fluid layer is derived, and then the outer diameter and the inner diameter of the magneto-rheological fluid layer are determined.

5. The joint damper based robotic milling low frequency chatter suppression method of claim 1, wherein: Joint braking coefficient α q,i The expression for the joint braking coefficient is wherein T is the braking torque; M i ( t ) is the torque acting on the joint.

6. The joint damper based robotic milling low frequency chatter suppression method of claim 5, wherein: The end vibration speed and the cutting force in the milling process of the robot are mapped into the joint space through the Jacobian matrix, and the corresponding formula is: where J F ( q ) = J T ( q ) is the force Jacobian matrix, q v = [ q v,1 , q v,2 , q v,3 , q v,4 , q v,5 , q v,6 ] T denotes the vibration velocity of each joint, v e = [ v e,x , v e,y , v e,z , v e,ωx , v e,ωy , v e,ωz ] T denotes the vibration velocity of the robot end X, Y and Z direction and rotation direction, M( t ) = [ M 1( t ), M 2( t ), M 3( t ), M 4( t ), M 5( t ), M 6( t )] T denotes the torque on each joint, F( t ) = [ F x ( t ), F y ( t ), F z ( t ), M x ( t ), M y ( t ), M z ( t T represents the cutting force and moment in three directions of the robot end.​ 7. A joint damper based robot milling low frequency chatter suppression system, characterized by: The system comprises a memory and a processor, the memory stores a computer program, and the processor executes the computer program to execute the joint damper-based robot milling low-frequency chatter suppression method of any one of claims 1-6.

8. A computer-readable storage medium, characterized in that: The computer readable storage medium stores machine executable instructions, and when the machine executable instructions are called and executed by the processor, the machine executable instructions cause the processor to implement the joint damper-based robot milling low-frequency chatter suppression method of any one of claims 1-6.

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