Robot grinding integrated deformation prediction method based on stiffness model

Abstract

The application discloses a robot grinding comprehensive deformation prediction method based on a stiffness model, and comprises the following steps: acquiring six-dimensional deformation of a robot end after loading by means of an improved stiffness identification device; kinematically modeling the improved stiffness identification device; identifying joint stiffness of the robot based on a static stiffness model to obtain a robot joint stiffness matrix; analyzing a flexible deformation source in a grinding system to obtain robot grinding processing deformation parameters, and constructing a robot processing deformation prediction model which comprehensively considers self-weight and grinding force of the grinding system to reflect deformation in robot grinding processing. The stiffness identification system solves the problems of complicated robot joint stiffness identification steps and high cost, and comprehensively considers robot deformation caused by the weight of external load and cutting force, thereby improving the precision and accuracy of deformation prediction.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of robot machining precision optimization, and in particular to a robot grinding comprehensive deformation prediction method based on a stiffness model. BACKGROUND

[0002] Industrial robots have been widely used in various applications in many industries, and one of the main obstacles limiting the application of industrial robots in high-precision machining is the insufficient stiffness of the robot. The low stiffness characteristic can cause deformation of the robot end effector, thereby reducing the precision of the machining size, so considering the deformation caused by the cutting force and the deformation caused by the grinding system comprehensively can more accurately reflect the deformation in the robot grinding machining.

[0003] The traditional stiffness identification method has complicated steps, and when measuring the actual pose of the robot end effector with a laser tracker, the system needs to obtain the position through laser reflection, so it is necessary to ensure that there is no light interruption. In addition, the cost of the laser tracker device is extremely high, so the design of a stiffness identification device can solve the problems of complicated steps and high cost of robot joint stiffness identification. SUMMARY

[0004] This section aims to summarize some aspects of the embodiments of the present application and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section and the abstract and title of the specification to avoid obscuring the purpose of this section, abstract and title, and such simplifications or omissions cannot be used to limit the scope of the present application.

[0005] In view of the above existing problems, the present application is proposed.

[0006] To solve the above technical problems, the present application provides the following technical solutions: a six-dimensional deformation of a robot end effector after loading is obtained through an improved stiffness identification device;

[0007] Kinematic modeling is performed on the improved stiffness identification device;

[0008] Joint stiffness identification of the robot is performed based on a static stiffness model, and a joint stiffness matrix of the robot is obtained;

[0009] The source of flexible deformation in the grinding system is analyzed, the robot grinding machining deformation parameters are obtained, and a robot machining deformation prediction model that comprehensively considers the self-weight and grinding force of the grinding system is constructed to reflect the deformation in the robot grinding machining.

[0010] As a preferred scheme of the robot grinding comprehensive deformation prediction method based on the stiffness model, the improved stiffness identification device comprises a base, a moving platform and a driving unit, the base is an aluminum frame, the moving platform is a six-degree-of-freedom industrial robot end, and the driving unit is fixedly installed above the base.

[0011] The driving unit is composed of a motor, an absolute value encoder, a speed reducer, a reel and a transmission mechanism.

[0012] The ropes wound and unwound by the driving unit are connected in a body diagonal manner at each vertex of the robot end.

[0013] As a preferred scheme of the robot grinding comprehensive deformation prediction method based on the stiffness model, the six-dimensional deformation comprises linear deformation and rotational deformation.

[0014] As a preferred scheme of the robot grinding comprehensive deformation prediction method based on the stiffness model, the kinematic modeling comprises:

[0015] The connection points of the ropes on the base and the robot end are respectively denoted as A i and R i , and i represents the number of ropes.

[0016] A global coordinate system is established on the base, and a local coordinate system is established on the robot end, and the pose of the robot end in the global coordinate system is defined as

[0017] Wherein, r = [x y z] T represents a position vector, represents an attitude vector (represented by XYZ Euler angles), and α, β and γ respectively represent the angles of rotation around ox, oy and oz.

[0018] As a preferred scheme of the robot grinding comprehensive deformation prediction method based on the stiffness model, the robot is moved to a good dexterity area, an electric spindle is installed at the robot end, a six-dimensional force sensor is installed between the robot end and the spindle assembly, the forces in x, y and z directions of the robot end are measured by the six-dimensional force sensor, the deformation value of the robot end is measured by the improved stiffness identification device, the joint stiffness of the robot is identified based on the static stiffness model, and the obtained robot joint stiffness matrix is obtained.

[0019] As a preferred scheme of the robot grinding comprehensive deformation prediction method based on the stiffness model, the center of gravity of the grinding processing system is defined to be concentrated at the robot end, and the deformation caused thereby is calculated as follows:

[0020] ΔXspindle =C spindle G z

[0021] wherein, ΔX spindle represents the displacement caused by the grinding system, G z represents the gravity of the grinding system.

[0022] As a preferred scheme of the robot grinding comprehensive deformation prediction method based on the stiffness model, the force in the robot grinding process directly acts on the tool tip, and in order to calculate the deformation caused by the grinding force, the Cartesian stiffness matrix at the tool tip needs to be established, and the mathematical expression formula is as follows:

[0023]

[0024] wherein, J TCP is the Jacobian matrix at the tool tip of the robot.

[0025] As a preferred scheme of the robot grinding comprehensive deformation prediction method based on the stiffness model, the grinding force in the grinding process can be divided into the normal grinding force F n along the radial direction of the grinding wheel, the tangential grinding force F t along the tangential direction of the grinding wheel, and the axial grinding force F a along the rotation axis of the grinding wheel, which is expressed in the tool tip space coordinates after coordinate transformation, and the mathematical expression is as follows:

[0026]

[0027] The deformation calculation formula caused by the grinding force is as follows:

[0028] ΔX TCP =C TCP [F x F y F z ] T

[0029] The projection of the grinding force to the robot base coordinate system direction realizes the unification of the deformation caused by the grinding system and the deformation caused by the grinding force, and the comprehensive deformation in the robot grinding process is represented by the following mathematical formula:

[0030]

[0031] wherein, c x , c y , c y respectively represent the flexibility of the robot in the three main directions of the base coordinate system.

[0032] The beneficial effects of the present invention are as follows: The present invention solves the problems of cumbersome and costly steps in identifying robot joint stiffness through a stiffness identification system, and comprehensively considers the robot deformation caused by the weight of external loads and cutting forces, thereby improving the accuracy and precision of deformation prediction. Attached Figure Description

[0033] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0034] Figure 1 This is a flowchart illustrating the robot grinding comprehensive deformation prediction method based on a stiffness model as shown in this invention.

[0035] Figure 2 This is a schematic diagram of a stiffness identification system according to the present invention;

[0036] Figure 3 This is a schematic diagram of another stiffness identification system according to the present invention. Detailed Implementation

[0037] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0038] Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without inventive effort should fall within the scope of protection of this invention.

[0039] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0040] Example 1

[0041] The present invention aims to provide a comprehensive deformation prediction method for robot grinding based on a stiffness model, which considers both the deformation caused by cutting force and the deformation caused by the grinding system, so as to more accurately reflect the deformation in robot grinding.

[0042] According to an embodiment of the present invention, in combination Figure 1The flowchart shown illustrates a method for predicting comprehensive deformation in robot grinding based on a stiffness model, which specifically includes the following steps:

[0043] S1: Obtain the six-dimensional deformation of the robot's end effector after loading using an improved stiffness identification device. Note that the following points should be noted in this step:

[0044] The improved stiffness identification device includes a base, a moving platform, and a drive unit. The base is a rectangular aluminum frame, the moving platform is the end effector of a six-degree-of-freedom industrial robot, and the drive unit is fixedly installed above the base.

[0045] The drive unit consists of a motor, an absolute encoder, a reducer, a drum, and a transmission mechanism;

[0046] The ropes, which are released and retracted by the drive unit, are interlaced at the vertices of the robot's end effector in a body-diagonal manner.

[0047] As an example, six-dimensional deformation includes linear deformation and rotational deformation.

[0048] S2: Perform kinematic modeling on the improved stiffness identification device. It should also be noted that:

[0049] Reference Figure 2 Let A be the connection point of the rope at the base and the end of the robot. i and R i , where i represents the number of ropes;

[0050] Establish the global coordinate system on the base and the local coordinate system on the robot's end effector. Define the pose of the robot's end effector in the global coordinate system as follows:

[0051] Where r = [xyz] T Represents a position vector. The attitude vector is represented by XYZ Euler angles, where α, β, and γ represent the angles of rotation around ox, oy, and oz, respectively.

[0052] Furthermore, in this embodiment, the elasticity and mass of the rope are ignored, and the rope is defined as a massless rigid rope. Then, the following relationship exists between the rope length and the robot's end effector pose:

[0053] l i ·e i =M·c i +rd i

[0054] Among them, l i and e i Let c represent the length of rope i and the unit direction vector, respectively. i and d iPoint R i Position and point A in the local coordinate system i The coordinates in the global coordinate system, and matrix M is the rotation matrix from the local coordinate system to the global coordinate system;

[0055] Define the rope length vector as s, and differentiate the above equation to obtain the rope velocity vector:

[0056]

[0057] Where w is the angular velocity of the rope. It is a Jacobian matrix, and its specific form is:

[0058]

[0059] Where e1, e2, e3, and e4 represent the unit direction vectors of ropes 1, 2, 3, and 4, respectively, and vectors c1, c2, c3, and c4 represent the positions of points R1, R2, R3, and R4 in the local coordinate system, respectively.

[0060] Specifically, this embodiment takes into account the angular velocity ω and the Euler angle. There is a relationship between them:

[0061]

[0062] Here, cos(·) is denoted as c(·), and sin(·) is denoted as s(·);

[0063] From the above formula, we can see that:

[0064]

[0065] The rope velocity vector can be obtained. and robot end-effector velocity vector The relationship between them is as follows:

[0066]

[0067] S3: Based on the static stiffness model, perform joint stiffness identification on the robot to obtain the robot joint stiffness matrix. It is worth noting in this step that:

[0068] The robot is moved to a region with good dexterity, and an electric spindle is installed at the robot's end effector. A six-dimensional force sensor is installed between the robot's end effector and the spindle assembly. The force in the x, y, and z directions of the robot's end effector is measured using the six-dimensional force sensor. An improved stiffness identification device is used to measure the deformation value of the robot's end effector. Then, based on the static stiffness model, the joint stiffness of the robot is identified, and the resulting robot joint stiffness matrix k is obtained. θ .

[0069] Specifically, in this embodiment, the elastic joint of the industrial robot is approximated by the ratio of elastic torsion springs and reduction gears. Since the stiffness of the rod is much greater than that of the joint, it can be approximated as a rigid body.

[0070] Define k θi If we consider the joint stiffness of the i-th joint, we can obtain a diagonal matrix describing the spatial stiffness characteristics of the robot's joints:

[0071] k θ =diag(k) θ1 ,k θ2 ,k θ3 ,k θ4 ,k θ5 ,k θ6 )

[0072] The static stiffness matrix of the end effector of an industrial robot can be described as:

[0073] K = J -T (k θ -k c )J -1

[0074] Where k c The supplementary stiffness matrix is ​​calculated using the following formula:

[0075]

[0076] Where F represents the external six-dimensional force and torque, J represents the Jacobian matrix of the industrial robot, θ represents the joint angle, and the supplementary stiffness k c The effect on translational and rotational deformation within the joint space of an industrial robot is very small, especially when the robot's posture is far from singular positions. Therefore, the static stiffness matrix can be simplified as follows:

[0077] K = J - Tk θ J -1

[0078] Furthermore, the stiffness characteristics of industrial robots in Cartesian space are influenced by the joint stiffness matrix and the Jacobian matrix, resulting in a difference between the Jacobian matrix of the robot's end effector and that of the robot's cutting edge. Based on the assumption of flexible deformation, the deformation of the robot's end effector under the action of external forces can be expressed as:

[0079] ΔX=C(p)F

[0080] Where ΔX represents the six-dimensional deformation of the robot's end effector, including linear and rotational deformation, and C(p) represents the 6×6 compliance matrix, which can be divided into four 3×3 submatrices:

[0081]

[0082] Where, C(p) fx Let C(p) represent the force-linear displacement compliance submatrix. nx Let C(p) represent the torque-linear displacement compliance submatrix. fδ Let C(p) represent the force-angular displacement compliance matrix. nδ This represents the torque-angular displacement compliance matrix.

[0083] Combining ΔX=C(p)F, we have:

[0084]

[0085] Where f represents the end force vector, n represents the end torque vector, d represents the end displacement deformation, and δ represents the end rotation deformation.

[0086] The force-line displacement compliance submatrix describes the relationship between the end-effector force vector f and the end-effector deformation x:

[0087] x = C(p) fx f

[0088] Considering the unit line deformation ||x|| = 1, a force vector f needs to be applied at the end. Let:

[0089] ||x||=x T x = 1

[0090] Combining the two equations above, we can obtain the robot force-linear stiffness ellipsoid model:

[0091] f T C T (p) fd C(p) fx f = 1

[0092] Similarly, the corresponding force-angular stiffness ellipsoid model, moment-linear stiffness ellipsoid model, and moment-angular stiffness ellipsoid model can be obtained, which will not be described in detail in this embodiment.

[0093] Furthermore, embodiments of the present invention employ a static stiffness-based model to identify the joint stiffness of the robot:

[0094]

[0095] make We can obtain:

[0096]

[0097] Among them, J ij Let F represent the Jacobian matrix at row i and column j. iThe i-th row represents the force vector, where X represents the translational and torsional deformations in space under the action of F, and c i This represents the i-th element of the flexibility column vector.

[0098] S4: Analyze the sources of flexible deformation in the grinding system, obtain the deformation parameters of the robot grinding process, and construct a robot grinding deformation prediction model that comprehensively considers the self-weight of the grinding system and the grinding force to reflect the deformation situation in robot grinding. This step also requires detailed explanation of:

[0099] The center of gravity of the grinding system is defined as being concentrated at the end of the robot body, and the resulting deformation is calculated as follows:

[0100] ΔX spindle =C spindle G z

[0101] Where, ΔX spindle G represents the displacement caused by the grinding system. z Indicates the gravity of the grinding system;

[0102] In robotic grinding, the force acts directly on the tool tip. To calculate the deformation caused by the grinding force, it is necessary to establish the Cartesian stiffness matrix at the tool tip. The mathematical expression of this matrix is ​​as follows:

[0103]

[0104] Among them, J TCP Let be the Jacobian matrix at the tip of the robot's blade.

[0105] The grinding force during the grinding process can be divided into the normal grinding force F along the radial direction of the grinding wheel. n Tangential grinding force F along the tangential direction of the grinding wheel t and the axial grinding force F along the axis of rotation of the grinding wheel. a After coordinate transformation, its mathematical expression, which acts in the spatial coordinates of the blade tip, is as follows:

[0106]

[0107] The formula for calculating the deformation caused by grinding force is:

[0108] ΔX TCP =C TCP [F x F y F z ] T

[0109] By projecting the grinding force onto the robot's base coordinate system to unify it with the deformation caused by the grinding system and the deformation caused by the grinding force, the comprehensive deformation during the robot grinding process can be expressed by the following mathematical formula:

[0110]

[0111] Among them, c x c y c y These represent the robot's compliance in the three dominant directions of the base system.

[0112] Preferably, the prediction model provided in this embodiment comprehensively considers the deformation of the robot end effector caused by the self-weight of the grinding system and the grinding force, and achieves the unification of the deformation caused by the two, so as to more accurately reflect the deformation in robot grinding.

[0113] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for predicting comprehensive deformation in robot grinding based on a stiffness model, characterized in that, include: The six-dimensional deformation of the robot end effector after being loaded is obtained by using an improved stiffness identification device. The improved stiffness identification device includes a base, a moving platform, and a drive unit. The base is a rectangular aluminum frame, the moving platform is the end effector of a six-degree-of-freedom industrial robot, and the drive unit is fixedly installed above the base. The drive unit consists of a motor, an absolute encoder, a reducer, a drum, and a transmission mechanism; The ropes released and retracted by the drive unit are interlaced at the vertices of the robot's end effector in a body diagonal manner; Kinematic modeling is performed on the improved stiffness identification device; Based on the static stiffness model, the joint stiffness of the robot is identified, and the joint stiffness matrix of the robot is obtained. The sources of flexible deformation in the grinding system are analyzed to obtain the deformation parameters of the robot grinding process. A robot grinding deformation prediction model that comprehensively considers the self-weight of the grinding system and the grinding force is constructed to reflect the deformation situation in the robot grinding process. The center of gravity of the grinding system is defined as being concentrated at the end of the robot body, and the resulting deformation is calculated as follows: in, This indicates the displacement caused by the grinding system. Indicates the gravity of the grinding system; In robotic grinding, the force acts directly on the tool tip. To calculate the deformation caused by the grinding force, it is necessary to establish the Cartesian stiffness matrix at the tool tip. The mathematical expression of this matrix is ​​as follows: in, The Jacobian matrix at the tip of the robot's blade; The grinding force during the grinding process can be divided into the normal grinding force along the radial direction of the grinding wheel. Tangential grinding force along the tangential direction of the grinding wheel and the axial grinding force along the axis of rotation of the grinding wheel. After coordinate transformation, its mathematical expression, which acts in the spatial coordinates of the blade tip, is as follows: in, Represents the attitude vector; The formula for calculating the deformation caused by grinding force is: By projecting the grinding force onto the robot's base coordinate system to unify it with the deformation caused by the grinding system and the deformation caused by the grinding force, the comprehensive deformation during the robot grinding process can be expressed by the following mathematical formula: in, , , These represent the robot's compliance in the three dominant directions of the base system.

2. The method for predicting comprehensive deformation in robot grinding based on a stiffness model according to claim 1, characterized in that, The six-dimensional deformation includes linear deformation and rotational deformation.

3. The method for predicting comprehensive deformation in robot grinding based on a stiffness model according to claim 1, characterized in that, The kinematic modeling includes: The connection points of the rope at the base and the end of the robot are respectively denoted as... and , where i represents the number of ropes; Establish the global coordinate system on the base and the local coordinate system on the robot's end effector. Define the pose of the robot's end effector in the global coordinate system as X= ; in, = Represents a position vector. The attitude vector is represented by the XYZ Euler angles. These represent the angles of rotation around ox, oy, and oz, respectively.

4. The method for predicting comprehensive deformation in robot grinding based on a stiffness model according to claim 1, characterized in that, The robot is moved to a region with good dexterity, and an electric spindle is installed at the end of the robot. A six-dimensional force sensor is installed between the end of the robot and the spindle assembly. The force in the x, y, and z directions of the end of the robot is measured using the six-dimensional force sensor. The deformation value of the end of the robot is measured using the improved stiffness identification device. Then, the joint stiffness of the robot is identified based on the static stiffness model to obtain the robot joint stiffness matrix.

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