A five-axis equipment geometric error calibration method and equipment based on line laser scanner

Abstract

The present invention belongs to the technical field related to the calibration of processing equipment, and discloses a method and equipment for calibrating the geometric errors of a five-axis device based on a line laser scanner. The method includes the following steps: Step 1, using a line laser scanner installed at the tool end of the five-axis device to scan a standard calibration sphere to obtain the actual position of the center of the calibration sphere in space, and subtracting the obtained actual position from the ideal position to obtain the spatial position deviation; Step 2, calculating various geometric error terms based on the obtained spatial position deviation and the deviation influence formula caused by different error terms relative to various directions in three-dimensional space; wherein, the deviation influence formula is derived based on a kinematic model considering errors, and the kinematic model considering errors is constructed under the condition of considering the position-related geometric errors and position-independent geometric errors of the rotating axis of the five-axis device. The present invention solves the problems of high cost and cumbersome operation in calibrating the geometric errors of the rotating axis.

Description

Technical Field

[0001] The present invention belongs to the technical field related to calibration of processing equipment, and more specifically, relates to a method and equipment for calibrating the geometric errors of a five-axis device based on a line laser scanner. Background Art

[0002] With the continuous development of the manufacturing industry, five-axis equipment has begun to be put into use more and more. In addition to traditional subtractive manufacturing, many lightweight and customized manufacturing applications have also begun to incorporate five-axis equipment. Currently, due to the high precision and flexibility of five-axis equipment within its workspace, it has been applied to the dispensing of small and detailed workpieces such as integrated circuits, precision parts, and glass.

[0003] Five-axis equipment typically consists of a rotary and a translational axis. The most common configuration is a dual-turret structure consisting of an XYZ translational axis and a UW rotational axis. The accuracy of the rotary axis is crucial to the performance of the five-axis equipment. However, due to the inevitable errors that occur during component manufacturing and installation, these errors can affect operational accuracy. Therefore, calibrating and compensating for the geometric errors of the rotary axis is crucial for ensuring the accuracy of five-axis dispensing equipment. A mathematical kinematic model must be established based on the structure of the five-axis equipment, and error modeling must be performed accordingly. Based on actual motion data, these errors are calculated and compensated to achieve high-precision motion.

[0004] Currently, the calibration of geometric errors in rotating axes typically uses instruments such as ballbars and laser interferometers. These devices are often expensive, increasing calibration costs. Furthermore, their operation requires a certain level of operator expertise. Furthermore, these instruments typically only measure motion deviations in a single spatial direction, requiring multiple measurements during the calibration process, making the process tedious and complex. In summary, these commonly used methods suffer from issues such as high instrument costs, complex execution processes, cumbersome operations, and high operator requirements. Summary of the Invention

[0005] In response to the above defects or improvement needs of the prior art, the present invention provides a five-axis device geometric error calibration method and equipment based on a line laser scanner, which aims to solve the problems of high cost and cumbersome operation of calibrating the geometric error of the rotating axis.

[0006] To achieve the above object, according to one aspect of the present invention, a method for calibrating the geometric error of a five-axis device based on a line laser scanner is provided, the method comprising the following steps:

[0007] Step 1: Use a line laser scanner installed on the tool end of the five-axis equipment to scan the standard calibration sphere to obtain the actual position of the calibration sphere center in space, and subtract the actual position from the ideal position to obtain the spatial position deviation;

[0008] Step 2: Calculate various geometric error terms based on the obtained spatial position deviation and the deviation influence formula caused by different error terms relative to each direction in three-dimensional space; wherein, the deviation influence formula is derived based on the kinematic model considering errors. The kinematic model considering errors is constructed under the condition of considering the position-dependent geometric error and position-independent geometric error of the rotation axis of the five-axis device, and its expression is:

[0009]

[0010] Where, T eU 、T eW are the error matrices of the rotation axes U and W respectively; Represents the homogeneous transformation matrix of coordinate system {Y} relative to coordinate system {B}; Represents the homogeneous transformation matrix of coordinate system {U} relative to coordinate system {Y}; Represents the homogeneous transformation matrix of coordinate system {W} relative to coordinate system {U}; Represents the homogeneous transformation matrix of coordinate system {G} relative to coordinate system {W}; Represents the homogeneous transformation matrix of the coordinate system {X} in the base coordinate system {B}, which also includes the rotation matrix and position vector Represents the homogeneous transformation matrix of coordinate system {Z} relative to coordinate system {X}; It represents the homogeneous transformation matrix of coordinate system {t} relative to coordinate system {Z}; coordinate system {B} is the base coordinate system; coordinate system {Z} is the coordinate system of translation axis Z; coordinate system {t} is the coordinate system of dispensing tool; coordinate system {S} is the coordinate system of line laser scanner; coordinate system {Y} is the coordinate system of translation axis Y; coordinate system {U} is the coordinate system of rotation axis U; coordinate system {W} is the coordinate system of rotation axis W; coordinate system {G} is the workpiece coordinate system.

[0011] Furthermore, according to the mechanical structure of the five-axis device, a kinematic model is constructed using the homogeneous transformation matrix; then, under the condition of considering the position-independent error and position-dependent error of the rotation axis of the five-axis device, errors are introduced into the kinematic model to obtain a kinematic model considering errors.

[0012] Furthermore, in the workpiece coordinate system {G}, the expression of the tool coordinate system {t} is:

[0013]

[0014] Where, Represents the rotation matrix of coordinate system {Y} relative to coordinate system {B}; Represents the position vector of coordinate system {Y} relative to coordinate system {B}; Represents the rotation matrix of coordinate system {U} relative to coordinate system {Y}; Represents the position vector of coordinate system {U} relative to coordinate system {Y}; Represents the rotation matrix of coordinate system {W} relative to coordinate system {U}; Represents the position vector of coordinate system {W} relative to coordinate system {U}; Represents the rotation matrix of coordinate system {G} relative to coordinate system {W}; Represents the position vector of coordinate system {G} relative to coordinate system {W}; Represents the rotation matrix of coordinate system {Z} relative to coordinate system {X}; Represents the position vector of coordinate system {Z} relative to coordinate system {X}; represents the rotation matrix of coordinate system {t} relative to coordinate system {Z}; Represents the position vector of coordinate system {t} relative to coordinate system {Z}.

[0015] Furthermore, the position coordinates of the center of the calibration ball in the coordinate system {S} are:

[0016]

[0017] The subscript 0 indicates an ideal state without error. Formula (2) can express the kinematic transformation relationship of the five-axis device and can be calculated after each joint of the five-axis device reaches a different position.

[0018] Furthermore, the effect of geometric errors on the motion of rotating axis components can also be expressed using a homogeneous transformation matrix:

[0019]

[0020]

[0021] Where T eU 、T eW are the error matrices of the rotation axes U and W respectively.

[0022] Furthermore, the sphere center coordinate expression obtained by the linear laser scanner is:

[0023]

[0024] In the base coordinate system, the position change relationship of the calibration sphere is:

[0025]

[0026] in Indicates the ideal position where the calibration ball should be located without error. The position of the calibration ball under the influence of the error, the position of the ball center obtained by the joint position and the scan Calculated; Therefore, the expression of the calibration sphere space deviation caused by geometric error is obtained through formulas (7) and (8):

[0027]

[0028] Furthermore, the line laser scanner measured a series of Combining the joint positions under these scanning states, the whole measurement process can be calculated by formula (8): That is, the actual position of the calibration ball in the base coordinate system; at the same time, according to the given motion command, the expected position of the calibration ball in the base coordinate system is calculated Thus calculated

[0029] Further, according to The error is solved based on the relationship between the φ and geometric error terms. The steps are as follows: first solve the 8 PIGE terms, then solve the PDGE in the order of U axis first and then W axis, and finally solve the error iteratively.

[0030] The present invention also provides a five-axis device geometric error calibration system based on a line laser scanner, the system includes a memory and a processor, the memory stores a computer program, and the processor executes the above-mentioned five-axis device geometric error calibration method based on a line laser scanner when executing the computer program.

[0031] The present invention also provides a computer-readable storage medium, which stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement the above-mentioned five-axis device geometric error calibration method based on a line laser scanner.

[0032] In general, compared with the prior art, the above technical solutions conceived by the present invention provide a method and device for calibrating the geometric errors of a five-axis device based on a line laser scanner, which has the following beneficial effects:

[0033] 1. The applied measurement tool only requires a line laser scanner and a calibration sphere, which greatly reduces calibration costs. In addition, the line laser scanner itself is simple to use, requiring the operator to only specify the movement position and then perform point cloud acquisition. Combined with the corresponding kinematic model, it saves calibration costs, simplifies the operation process, and improves accuracy.

[0034] 2. The line laser scanner used can directly obtain the three-dimensional point cloud of the calibration sphere, and fit the point cloud of the spherical surface to obtain the position of the sphere center. The position of the calibration sphere in the base coordinate system can be expressed through the transformation between the coordinate systems. The coordinate values ​​in the three directions obtained directly bring great convenience to the calibration calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is a flow chart of a geometric error calibration method for a five-axis device based on a line laser scanner provided by the present invention;

[0036] Figure 2 yes Figure 1 Schematic diagram of the coordinate system between the main parts of the equipment involved in the geometric error calibration method of the five-axis equipment based on the line laser scanner;

[0037] Figure 3(a) is Figure 1 Schematic diagram of modeling of the position-independent geometric error of the rotation axis involved in the geometric error calibration method of the five-axis equipment based on the line laser scanner;

[0038] Figure 3(b) is Figure 1 Schematic diagram of modeling of the geometric error related to the rotation axis position involved in the geometric error calibration method of the five-axis equipment based on the line laser scanner;

[0039] Figure 4 yes Figure 1 Schematic diagram of the specific process of real-time calibration and calculation operations involved in the geometric error calibration method of five-axis equipment based on line laser scanner. DETAILED DESCRIPTION

[0040] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is 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 for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0041] The present invention provides a five-axis device geometric error calibration method based on a line laser scanner. The calibration method uses a line laser scanner, which is cheaper than the equipment used for calibration in the existing technology. The scanned three-dimensional point cloud can be obtained after one scan, and continuous measurement can be performed after installation is completed. The operation is simple, saving calibration costs while also simplifying the operation process.

[0042] See also Figure 1 and Figure 4 , the calibration method mainly includes the following steps:

[0043] Step 1: Use a line laser scanner installed on the tool end of the five-axis equipment to scan the standard calibration sphere to obtain the actual position of the center of the calibration sphere in space, and subtract the actual position from the ideal position to obtain the spatial position deviation.

[0044] Step 2: Calculate various geometric error terms based on the obtained spatial position deviation and the deviation influence formula caused by different error terms relative to each direction in three-dimensional space; wherein, the deviation influence formula is derived based on the kinematic model considering errors. The kinematic model considering errors is constructed under the condition of considering the position-dependent geometric error and position-independent geometric error of the rotation axis of the five-axis device, and its expression is:

[0045]

[0046] Where, T eU 、T eW are the error matrices of the rotation axes U and W respectively; Represents the homogeneous transformation matrix of coordinate system {Y} relative to coordinate system {B}; Represents the homogeneous transformation matrix of coordinate system {U} relative to coordinate system {Y}; Represents the homogeneous transformation matrix of coordinate system {W} relative to coordinate system {U}; Represents the homogeneous transformation matrix of coordinate system {G} relative to coordinate system {W}; Represents the homogeneous transformation matrix of the coordinate system {X} in the base coordinate system {B}, which also includes the rotation matrix and position vector Represents the homogeneous transformation matrix of coordinate system {Z} relative to coordinate system {X}; It represents the homogeneous transformation matrix of coordinate system {t} relative to coordinate system {Z}; coordinate system {B} is the base coordinate system; coordinate system {Z} is the coordinate system of translation axis Z; coordinate system {t} is the coordinate system of dispensing tool; coordinate system {S} is the coordinate system of line laser scanner; coordinate system {Y} is the coordinate system of translation axis Y; coordinate system {U} is the coordinate system of rotation axis U; coordinate system {W} is the coordinate system of rotation axis W; coordinate system {G} is the workpiece coordinate system.

[0047] The acquisition of the deviation impact formula includes the following steps:

[0048] S1, based on the mechanical structure of the five-axis device, a kinematic model is constructed using the homogeneous transformation matrix.

[0049] To address the challenges of expensive equipment, complex execution processes, and cumbersome operations, this implementation utilizes a line laser scanner and a standard calibration sphere to calibrate the geometric errors of rotating axes, significantly reducing calibration costs. The calibration process requires only the operator to pre-set the acquisition path, move the five-axis machine, and scan the calibration sphere with the line laser scanner to collect data, greatly simplifying the calibration process.

[0050] The line laser scanner needs to be installed on the tool end of the five-axis dispensing equipment to join the equipment motion chain. The homogeneous coordinate transformation method is used to establish a kinematic model that includes the scanner coordinate system, Z-axis coordinate system, X-axis coordinate system, Y-axis coordinate system, U-axis coordinate system, W-axis coordinate system, base coordinate system and workpiece coordinate system. This kinematic model is used to express the transformation relationship between the workpiece space point in the scanner coordinate system and the world coordinate system. After introducing the position-independent geometric error (PIGE) and position-dependent geometric error (PDGE) caused by the manufacturing and installation of rotating axis components, the actual kinematic model considering errors can be obtained through this kinematic model. By comparing the position of the scanned calibration sphere with the ideal position, the PIGE and PDGE of each item can be decoupled by the spatial deviation of the calibration sphere.

[0051] The kinematic model in step S1 includes two kinematic chains: one kinematic chain includes the translation axis X, the translation axis Z, the dispensing tool, and the line laser scanner; the other kinematic chain includes the translation axis Z, the rotation axis U (rotating around the X direction), the rotation axis W (rotating around the Z direction), and the workpiece.

[0052] Establish a base coordinate system {B}, which is established at a position with a certain amount of translation away from the mechanical origin of the machine tool. As a fixed coordinate system, it is the reference coordinate system for expressing the spatial posture of each part;

[0053] Establish a coordinate system {X} of the translation axis X, whose X direction is the same as the movement direction of the translation axis X, and is fixed to the motion module of the translation axis X, and moves with the movement of the X axis;

[0054] Establish a coordinate system {Z} of the translation axis Z, whose Z direction is the same as the movement direction of the translation axis Z, and is fixed to the motion module of the translation axis Z, and moves with the movement of the Z axis;

[0055] Establish the dispensing tool coordinate system {t}, the direction of each axis of the coordinate system {t} is the same as {Z};

[0056] Establish the coordinate system {S} of the line laser scanner, whose origin is at the imaging position of the line laser scanner, has the direction specified by the device itself, and has a fixed transformation relationship with the tool coordinate system {t};

[0057] Establish the coordinate system {Y} of the translation axis Y, whose Y direction is the same as the movement direction of the translation axis Y, and is fixed to the motion module of the translation axis Y, and moves with the movement of the Y axis;

[0058] Establish a coordinate system {U} of the rotation axis U, whose X-axis direction is the same as the movement direction of the translation axis X, and the rotation axis U rotates around its own X-axis during the rotation process;

[0059] Establish the coordinate system {W} of the rotation axis W. In the initial position (neither the U nor the W axis has any rotation angle), the directions of the axes of {W} are the same as {U}, and it rotates around its own Z axis during the rotation of the rotation axis W.

[0060] Establish a workpiece coordinate system {G}, whose axis directions are the same as {W}, and there is only one offset in the Z direction from {W}. After the calibration sphere is installed, there is no relative position change between the calibration sphere and the worktable, and the calibration sphere's own coordinate system {b} can be directly expressed under {G}.

[0061] The motion of a rigid body in space is described by the rotation matrix R and the position vector p in the rigid body motion transformation theory, and the two are used to form a homogeneous transformation matrix T to describe the transformation between the above coordinate systems.

[0062] definition Represents the homogeneous transformation matrix of the coordinate system {X} in the base coordinate system {B}, which also includes the rotation matrix and position vector Similarly, we can define homogeneous transformation matrices between other coordinate systems, as well as rotation matrices and position vectors therein.

[0063] in: Respectively represent the homogeneous transformation matrix, rotation matrix and position vector of coordinate system {Z} relative to coordinate system {X};

[0064] They represent the homogeneous transformation matrix, rotation matrix and position vector of coordinate system {t} relative to coordinate system {Z} respectively;

[0065] They represent the homogeneous transformation matrix, rotation matrix and position vector of the coordinate system {S} relative to the coordinate system {t} respectively;

[0066] Respectively represent the homogeneous transformation matrix, rotation matrix and position vector of coordinate system {Y} relative to coordinate system {B};

[0067] Respectively represent the homogeneous transformation matrix, rotation matrix and position vector of coordinate system {U} relative to coordinate system {Y};

[0068] Respectively represent the homogeneous transformation matrix, rotation matrix and position vector of coordinate system {W} relative to coordinate system {U};

[0069] Respectively represent the homogeneous transformation matrix, rotation matrix and position vector of coordinate system {G} relative to coordinate system {W};

[0070] Represents the position vector of the calibration ball center {b} in the coordinate system {G};

[0071] In the above series of relationships, It is related to the current motion position of each motion axis of the five-axis device and forms a functional relationship with the joints of each motion axis; It is related to the definition of the mechanical structure and is a fixed value.

[0072] According to the above relationship, it can be expressed that in the workpiece coordinate system {G}, the expression of the tool coordinate system {t} is:

[0073]

[0074] This expression is used to express the transformation relationship of the Cartesian coordinate system when planning the workpiece processing path.

[0075] When the line laser scanner scans the calibration sphere, the position coordinates of the center of the calibration sphere in the coordinate system {S} can be fitted as follows:

[0076]

[0077] The subscript 0 indicates an ideal state with no error. This formula can express the kinematic transformation relationship of the five-axis device and can be calculated after each joint of the five-axis device reaches different positions.

[0078] In one embodiment, the purpose is to calibrate the geometric errors of the rotation axis of the five-axis dispensing device to compensate for higher accuracy. Figure 2 As shown, the five-axis device contains two kinematic chains, one along the base, X-axis, Z-axis, dispensing tool, and line laser scanner; the other along the base, Y-axis, U-axis, W-axis, workpiece mounting plate, and calibration ball. Figure 2 In the coordinate system shown, when all the moving joints are initially at position 0, the coordinate axes of all parts of the coordinate system are oriented in the same direction.

[0079] S2, under the condition of considering the position-independent error and position-dependent error of the rotation axis of the V-axis device, a kinematic model considering the error is constructed.

[0080] Analyze the impact of the geometric errors of the rotary axis on the above kinematic model: In ISO 230-7, the geometric errors of the rotary axis are divided into 12 position-dependent geometric errors (PDGE, also known as error elements) and 8 position-independent geometric errors (PIGE). These errors are expressed as follows:

[0081] δ x (U), δy(U), δ z (U) represents the position error of the coordinate system {U} in the X, Y, and Z directions during the rotation of the U axis;

[0082] ε x (U), ε y (U), ε z (U) represents the angular errors caused by the rotation of the coordinate system {U} around the X, Y, and Z directions respectively when the U axis is rotating;

[0083] δ x (W), δ y (W), δ z (W) represents the position error of the coordinate system {W} in the X, Y, and Z directions respectively when the W axis rotates;

[0084] ε x (W), ε y (W), ε z (W) represents the attitude errors caused by the rotation of the coordinate system {W} around the X, Y, and Z directions respectively when the W axis is rotating;

[0085] δ xAY , δ yAY , δ zAY They represent the fixed position errors of the coordinate system {U} in the X, Y, and Z directions respectively due to the installation of the U axis;

[0086] α AY , β AY , γ AYThey represent the fixed attitude errors caused by the rotation of the coordinate system {U} around the X, Y, and Z directions due to the installation of the U axis;

[0087] δ yCA Indicates the fixed position error of the coordinate system {W} relative to the coordinate system {U} in the Y direction caused by the installation of the W axis;

[0088] β CA Indicates the fixed attitude error caused by the rotation of the coordinate system {W} relative to the coordinate system {U} in the Y direction due to the installation of the W axis;

[0089] According to the theory of rigid body motion, the influence of the above geometric errors on the motion of the rotating shaft components can also be expressed by the homogeneous transformation matrix:

[0090]

[0091] Where T eU 、T eW are the error matrices of the rotation axes U and W respectively.

[0092] The kinematic model affected by the error will change to:

[0093]

[0094] After the geometric error of the rotating axis is introduced, a deviation will occur between the actual motion coordinates and the expected motion coordinates, which will cause the tool to fail to reach the specified position. Therefore, it is necessary to calibrate the various geometric errors in the above formula and correct the kinematic model to achieve error compensation and improve equipment accuracy.

[0095] In one embodiment, a kinematic model that takes errors into account is established based on the error model: Based on Tsutsumi's description in Identification and compensation of systematic deviations particular to 5-axis machining centers, the geometric description of the eight PIGEs is shown in Figure 3(b); and according to rigid body kinematics theory, each rotational axis will produce six directions of motion in space during motion, as shown in Figure 3(a). Based on the influence of these 20 geometric errors, error matrices such as Formulas (3) and (4) can be listed to represent the influence of the 20 geometric errors on motion, ultimately resulting in a kinematic model with errors as shown in Formula (5).

[0096] S3, based on the kinematic model considering errors, the formula for the deviation influence caused by different error terms relative to each direction in three-dimensional space is derived.

[0097] Analyze the impact of various geometric errors of the rotating axis on the workpiece end of the equipment in three-dimensional space: Since the rotating axis is located at one end of the workpiece motion chain, after the motion instructions of the X, Y, Z, U, and W joint axes are given, motion errors will be generated in the workpiece motion chain, causing the workpiece coordinate system to deviate from the desired position. Since the calibration ball is installed on the workpiece mounting plate, it will directly lead to deviations in the calibration ball position. According to formulas (2) and (5), it can be concluded that when affected by the error, the expression of the spherical center coordinates obtained by the linear laser scanner is:

[0098]

[0099] The above formula expresses the relationship between the actual measurement data of the scanner and the geometric error. Therefore, it can be concluded that the position change relationship of the calibration sphere in the base coordinate system is:

[0100]

[0101] in The position where the calibration ball should reach under ideal conditions without errors can be calculated from known quantities; The position of the calibration ball under the influence of the error can be obtained by the joint position and the center position of the ball obtained by scanning Calculation results show that: Therefore, the expression of the calibration sphere spatial deviation caused by geometric error can be obtained through equations (7) and (8):

[0102]

[0103] The specific step of obtaining the spatial position deviation corresponds to S4, and specifically includes the following steps:

[0104] Step S4.1: Mount the calibration sphere at a fixed position on the workpiece mounting plate, and mount the line laser scanner at the end of the Z axis, making sure that the line laser scanner and the coordinate axis of the base coordinate system are parallel as much as possible.

[0105] Step S4.2: perform hand-eye calibration on the line laser scanner to obtain the relationship between the line laser scanner and the tool.

[0106] Step S4.3: When both the U axis and the W axis are at 0, that is, when the workpiece mounting plate is kept horizontal, scan the calibration ball and calculate the installation position of the calibration ball based on the hand-eye calibration results.

[0107] Step S4.4: Design a series of spatial poses as motion trajectories in space, make the line laser scanner maintain this motion, shoot the calibration sphere at different poses, and finally obtain a series of joint axis motion positions and corresponding sphere center positions;

[0108] Step S4.5: Repeat the above steps for a total of three sets of data acquisition operations. According to formula (7) and formula (8), the expected center position of the sphere and the actual center position of the sphere are calculated, and the difference between the two is calculated using formula (9) for subsequent calculations.

[0109] Step S4.4 includes:

[0110] Step S4.4.1: Since the W axis is at the next level after the U axis in the kinematic chain at one end of the workpiece, in order to reduce the influence of the W axis when solving the U axis error, the first set of kinematic positions is designed so that W is always 0 and the U axis rotates at equal intervals within a certain range from negative to positive. Based on this, the scanning trajectory at each position is designed to obtain the Cartesian coordinates of the U axis rotation, and the calibration sphere is scanned at each position.

[0111] Step S4.4.2: Similar to the U-axis, the W-axis also requires the U-axis to remain unchanged during rotation. However, when the U-axis is 0 degrees, the Cartesian coordinate system will have countless sets of solutions in the inverse solution. Therefore, the U-axis needs to be set to a non-zero angle. On this basis, the W-axis is set to rotate one circle, and the calibration sphere is scanned at each position. The step of using the deviation influence formula to solve the various geometric errors corresponds to S5 and includes the following sub-steps:

[0112] Step S5.1: The line laser scanner measures a series of Combining the joint positions under these scanning states, the whole measurement process can be calculated by formula (8): That is, the actual position of the calibration ball in the base coordinate system; at the same time, according to the given motion command, the expected position of the calibration ball in the base coordinate system can be calculated Thus calculated

[0113] Step S5.2, according to The error is solved based on the relationship between the error terms and the geometric error terms. However, it is noted that the deviation in one direction in space is affected by multiple different errors. Moreover, since PIGE and PDGE exist at the same time, it is impossible to directly solve the two types of errors. Therefore, it is necessary to perform an iterative operation: first solve the 8 PIGE terms, then solve the PDGE in the order of U axis first and then W axis, and finally iterate to obtain a more accurate value.

[0114] In step S5.3, 20 geometric errors of the rotating axis are obtained through step-by-step and iterative solution. Among them, PIGE is a fixed value, and PDGE is a function related to the motion position of the rotating axis. By fitting PDGE with Fourier series, a function that can calculate the error at any position is obtained. Based on this, a kinematic model with errors can be established.

[0115] Step S5.2 includes the following sub-steps:

[0116] In step S5.2.1, the collected data includes the parts of the U-axis rotation and the W-axis rotation. First, solve the PIGE. Since some positions will not change during the rotation, the mapping matrix will be rank-deficient. Therefore, it is necessary to use the U and W data to solve the PIGE.

[0117] In step S5.2.2, PIGE and PDGE actually exist simultaneously and work together, so it is necessary to first assume that only PIGE exists. After calculating PIGE, the effect of PIGE is subtracted from the original data, and the remaining value is used to calculate PDGE. Since the W-axis is installed at the lower end of the U-axis, it is necessary to first calculate using the U-axis scan data to subtract the W-axis effect. Then, the W-axis data is subtracted from the effects of PIGE and the U-axis PDGE to calculate the W-axis PDGE.

[0118] Step S5.2.3: Through S5.2.2, the PDGE and PIGE of the U-axis and W-axis can be preliminarily obtained. To make this result more accurate, an iterative operation is required, that is, the influence of the calculated PDGE is subtracted from the original data, and step S5.2.2 is repeated. After a certain number of iterations, a more accurate conclusion can be obtained.

[0119] In one embodiment, the installation position of the calibration ball on the workpiece mounting plate is set Where x0, y0, z0 are the coordinates of the calibration ball center in the workpiece coordinate system. Combining formulas (7), (8), and (9), the position deviation of the calibration ball in space can be specifically expressed as and the geometric error, where Δx, Δy, and Δz are the positional deviations of the calibration sphere in the base coordinate system. Since the final result represents the coupling between the various geometric errors, a direct solution is not possible, so a linear approximation is required. Based on the theory of higher-order infinitesimals, the higher-order error terms in the deviation expression are removed to obtain the final result.

[0120]

[0121] Where Δx PIGE , Δy PIGE , Δz PIGE Respectively represent the position deviation caused by position-independent error in the X, Y, and Z directions of space, Δx PDGE , Δy PDGE , Δz PDGE They represent the position deviation caused by position-related errors in the X, Y, and Z directions of space. The definitions of these two parts are as follows:

[0122]

[0123] Where h is the distance between the origin of the workpiece coordinate system {G} and the axis of the U axis.

[0124] Under the above expression, various geometric errors are decoupled, and by collecting data under different motion states, the calculation of various errors can be realized.

[0125] In the process of designing the motion trajectory, since the errors of the rotation axes U and W will affect each other, it is set that when one rotation axis rotates, the other rotation axis remains unchanged to ensure that formula (10) can remove the influence of a certain part and thus achieve the solution.

[0126] The process of tracking scanning is as follows: In order to ensure that the scanner always scans the calibration ball, the Cartesian coordinate system motion planning is completed according to the scanner coordinate system {S} relative to the workpiece coordinate system {G}. It is a fixed value, so when the rotation axis rotates, a series of Cartesian coordinates of the scanner in the workpiece coordinate system {G} can be obtained. Through the inverse solution, the scanner can reach the specified position, and the X-axis moves another scanning distance to obtain the point cloud data of the calibration sphere surface.

[0127] Scanning is performed in two modes. One is that the W axis is kept at 0 degrees, and the U axis starts from a negative angle and rotates to a positive angle at a fixed interval angle to ensure that the rotation area includes the commonly used motion range; the other is that the U axis is kept at a certain angle and the W axis rotates one circle (because there is no unique solution for the inverse solution of the vertical state of the U axis being 0, the U axis needs to be kept at a certain angle); and the calibration sphere needs to be installed in three different positions for separate motion. After designing the motion position according to the above rules, a series of point cloud data on the surface of the calibration sphere can be collected, and the spherical point cloud can be fitted to obtain the coordinates of the sphere center. According to formula (8), the positions of the sphere center in the base coordinate system are calculated as follows:

[0128] When planning the motion trajectory, a series of By subtracting the two corresponding positions, we can get the spatial motion deviation caused by geometric error.

[0129] The U-axis rotation and the W-axis rotation will calculate the spatial position deviation in two cases. First, solve PIGE. Assuming that the U-axis and the W-axis are only affected by PIGE, PDGE in formula (10) can be regarded as 0, that is, directly use Δx, Δy, and Δz and substitute them into formula (11) for calculation. When calculating specifically, the following equation needs to be constructed:

[0130] Am=n (13)

[0131] Where A is the mapping matrix from each PIGE to the spatial error, that is, the coefficient of each PIGE in formula (11), m is the column vector composed of 8 PIGEs, and n is the three-dimensional sphere center deviation data calculated when the U axis and W axis move. In order to solve equation (13), the least squares method is used to find m:

[0132] m=(A T A) -1 A T n (14)

[0133] After obtaining PIGE, it can be substituted back into formula (11) to calculate the effect of this PIGE, and use formula (10) to calculate the effect of PDGE, and then use formula (12) to solve PDGE. Since the PDGE obtained is a series of discrete points, corresponding to the error generated by the rotation axis at the current position when scanning the calibration sphere, in order to achieve compensation effects at more positions, it is necessary to establish a functional relationship between PDGE and the position of the rotation axis. Due to the characteristics of the rotation axis, a periodic function such as the Fourier series is used to fit the PDGE of each rotation axis; then solving PDGE is converted into solving the coefficients of the Fourier series that can fit PDGE. In the fitting, the p-order Fourier series is set (usually 3 to 5 orders), and the coefficient calculation method is:

[0134] E=(B T B) -1 B T n ′

[0135] Where E is the discrete value of PDGE in six directions of space, B is the mapping matrix from each PDGE to spatial error obtained in formula (12), n ′ is the spatial deviation data after removing PIGE. Then solve the coefficients of the Fourier series:

[0136] C=E(D T D) -1 D T

[0137] Where D is the basis of the Fourier series at each scanning position, and C is the coefficient vector of the Fourier series. The PDGE at any position can be calculated by combining the coefficients into a Fourier series expansion form.

[0138] After calculating PIGE and PDGE, iteration is required to ensure accuracy. That is, the calculated PDGE is substituted into formula (10), and then PIGE is solved using formula (11). The above steps are repeated until the value of the geometric error tends to be stable. The accurate geometric error of the rotating axis can be obtained, so as to subsequently improve the motion accuracy.

[0139] The present invention also provides a five-axis device geometric error calibration system based on a line laser scanner, the system includes a memory and a processor, the memory stores a computer program, and the processor executes the above-mentioned five-axis device geometric error calibration method based on a line laser scanner when executing the computer program.

[0140] The present invention also provides a computer-readable storage medium, which stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement the above-mentioned five-axis device geometric error calibration method based on a line laser scanner.

[0141] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A five-axis device geometric error calibration method based on a line laser scanner, characterized in that: The method comprises the following steps: Step 1: Use a line laser scanner installed on the tool end of the five-axis equipment to scan the standard calibration sphere to obtain the actual position of the calibration sphere center in space, and subtract the actual position from the ideal position to obtain the spatial position deviation; Step 2: Calculate various geometric error terms based on the obtained spatial position deviation and the deviation influence formula caused by different error terms relative to each direction in three-dimensional space; wherein, the deviation influence formula is derived based on the kinematic model considering errors. The kinematic model considering errors is constructed under the condition of considering the position-dependent geometric error and position-independent geometric error of the rotation axis of the five-axis device, and its expression is: Where, T eU 、T eW are the error matrices of the rotation axes U and W respectively; Represents the homogeneous transformation matrix of coordinate system {Y} relative to coordinate system {B}; Represents the homogeneous transformation matrix of coordinate system {U} relative to coordinate system {Y}; Represents the homogeneous transformation matrix of coordinate system {W} relative to coordinate system {U}; Represents the homogeneous transformation matrix of coordinate system {G} relative to coordinate system {W}; Represents the homogeneous transformation matrix of the coordinate system {X} in the base coordinate system {B}, which also includes the rotation matrix and position vector Represents the homogeneous transformation matrix of coordinate system {Z} relative to coordinate system {X}; It represents the homogeneous transformation matrix of coordinate system {t} relative to coordinate system {Z}; coordinate system {B} is the base coordinate system; coordinate system {Z} is the coordinate system of translation axis Z; coordinate system {t} is the coordinate system of dispensing tool; coordinate system {S} is the coordinate system of line laser scanner; coordinate system {Y} is the coordinate system of translation axis Y; coordinate system {U} is the coordinate system of rotation axis U; coordinate system {W} is the coordinate system of rotation axis W; coordinate system {G} is the workpiece coordinate system.

2. The geometric error calibration method for a five-axis device based on a line laser scanner according to claim 1, wherein: According to the mechanical structure of the five-axis device, a kinematic model is constructed using the homogeneous transformation matrix. Then, errors are introduced into the kinematic model to obtain an error-considered kinematic model, taking into account the position-independent error and position-dependent error of the rotation axis of the five-axis device.

3. The geometric error calibration method of a five-axis device based on a line laser scanner according to claim 2, characterized in that: In the workpiece coordinate system {G}, the expression of the tool coordinate system {t} is: Where, Represents the rotation matrix of coordinate system {Y} relative to coordinate system {B}; Represents the position vector of coordinate system {Y} relative to coordinate system {B}; Represents the rotation matrix of coordinate system {U} relative to coordinate system {Y}; Represents the position vector of coordinate system {U} relative to coordinate system {Y}; Represents the rotation matrix of coordinate system {W} relative to coordinate system {U}; Represents the position vector of coordinate system {W} relative to coordinate system {U}; Represents the rotation matrix of coordinate system {G} relative to coordinate system {W}; Represents the position vector of coordinate system {G} relative to coordinate system {W}; Represents the rotation matrix of coordinate system {Z} relative to coordinate system {X}; Represents the position vector of coordinate system {Z} relative to coordinate system {X}; represents the rotation matrix of coordinate system {t} relative to coordinate system {Z}; Represents the position vector of coordinate system {t} relative to coordinate system {Z}.

4. The method for calibrating geometric errors of a five-axis device based on a line laser scanner according to claim 3, wherein: The position coordinates of the center of the calibration ball in the coordinate system {S} are: The subscript 0 indicates an ideal state without error. Formula (2) can express the kinematic transformation relationship of the five-axis device and can be calculated after each joint of the five-axis device reaches a different position.

5. The geometric error calibration method of a five-axis device based on a line laser scanner according to claim 3, characterized in that: The effect of geometric errors on the motion of rotating axis components can also be expressed using a homogeneous transformation matrix: Where T eU 、T eW are the error matrices of the rotation axes U and W respectively.

6. The geometric error calibration method of a five-axis device based on a line laser scanner according to claim 5, characterized in that: The coordinate expression of the sphere center obtained by the linear laser scanner is: In the base coordinate system, the position change relationship of the calibration sphere is: in Indicates the ideal position where the calibration ball should be located without error. The position of the calibration ball under the influence of the error, the position of the ball center obtained by the joint position and the scan Calculated; Therefore, the expression of the calibration sphere space deviation caused by geometric error is obtained through formulas (7) and (8):

7. The method for calibrating geometric errors of a five-axis device based on a line laser scanner according to claim 6, wherein: The line laser scanner measured a series of Combining the joint positions under these scanning states, the whole measurement process can be calculated by formula (8): That is, the actual position of the calibration ball in the base coordinate system; at the same time, according to the given motion command, the expected position of the calibration ball in the base coordinate system is calculated Thus calculated 8. The geometric error calibration method of a five-axis device based on a line laser scanner according to claim 7, characterized in that: according to The error is solved by the relationship between the error term and the geometric error term; The steps are as follows: first solve the 8 PIGEs, then solve the PDGEs in the order of U axis first and then W axis, and finally solve the errors iteratively.

9. A five-axis equipment geometric error calibration system based on a line laser scanner, characterized by: The system includes a memory and a processor, the memory stores a computer program, and the processor executes the geometric error calibration method of a five-axis device based on a line laser scanner as described in any one of claims 1 to 8 when executing the computer program.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by the processor, the machine-executable instructions prompt the processor to implement the five-axis device geometric error calibration method based on the line laser scanner according to any one of claims 1 to 8.

Images