Calibration method of five-axis 3D printing system, computer equipment and storage medium

Abstract

The invention discloses a calibration method of a five-axis 3D printing system, and provides a five-axis 3D printer motion axis calibration method realized by using a calibration object by providing the calibration object with a calibration ball. The method comprises the following steps: firstly, establishing a five-axis 3D printing equipment machine tool coordinate system and workpiece coordinate system transformation model, giving a to-be-calibrated quantity of each motion axis, and then providing a measurement method based on a four plus one measurement point scheme and a spherical surface least square fitting method to obtain a center coordinate of a calibration ball; and establishing an equation related to a linear axis to-be-calibrated quantity by using a transformation relation between a calibration object coordinate system and a machine tool coordinate system, calibrating the linear axis, and calibrating the rotating shaft based on plane normal vector solution and a least square fitting method of a circle.

Description

Technical Field

[0001] The present application relates to the technical field of three-dimensional printing, and particularly to a calibration method for a five-axis 3D printing system. Background Art

[0002] The motion control of a five-axis device is based on the commands of each axis in the machine tool coordinate system, while the tool path is completed in the workpiece coordinate system. The kinematic model of a five-axis device is to establish the mapping relationship between the two. Five-axis devices with different motion structures have different kinematic models, and the parameters in the model are mainly related to the actual directions of each motion axis, the actual positions of the rotating axes, and the tool dimensions, etc. Due to various inevitable errors in each axis, the actual tool size may also have a certain deviation from the designed size, and there is a deviation between the actual parameters and the ideal parameters in the kinematic model. In order to improve the printing accuracy, it is necessary to identify the actual parameters.

[0003] Currently, the research on the identification of kinematic parameters of five-axis machine tools is relatively mature, but the measurement methods of kinematic parameters of five-axis machine tools are mostly for small-error measurement occasions and equipment with a large space. However, the accuracy requirements of a five-axis 3D printing system are different, and the installation errors of components such as the nozzle are also large, making it difficult to measure with traditional measurement tools.

[0004] Therefore, a new technical solution needs to be proposed to solve the above technical problems. Summary of the Invention

[0005] Object of the Invention: Aiming at the above deficiencies of the prior art, the present invention provides a calibration method for a five-axis 3D printing system, which solves the technical problems of poor printing accuracy of the five-axis 3D printing system and unknown geometric parameters of each motion axis.

[0006] In order to achieve the above object, the technical solution that can be adopted by the calibration method for a five-axis 3D printing system provided by the present invention is as follows:

[0007] A calibration method for a five-axis 3D printing system, which is used for a five-axis linkage machining center including a linear axis x, a linear axis y, a linear axis z, a rotating axis a, and a rotating axis c, and includes the following steps:

[0008] (1) Establish a transformation model between the machine tool coordinate system and the workpiece coordinate system;

[0009] (2) Provide a calibration object, which includes a base and five calibration balls supported on the base. Use a edge finder to take points and measure on each spherical surface, that is, make the probe of the edge finder contact the side surface of a calibration ball to obtain the coordinates of a point on the spherical surface, take one point in the front, back, left, right, and top of a calibration ball respectively, and substitute the obtained measurement points into the objective function to obtain the center coordinates of the calibration ball;

[0010] (3) Calibrate the linear axes x, y, z and the rotary axes a, c using the center coordinates of the spheres obtained in step (2).

[0011] For the linear axes x, y, z: Arbitrarily select 3 calibration spheres on the calibration object. The coordinates of the centers of these 3 calibration spheres in the calibration object coordinate system are: d D 1 =( d x D1 , d y D1 , d z D1 ) T , d D 2 =( d x D2 , d y D2 , d z D2 ) T , d D 3 =( d x D3 , d y D3 , d z D3 ) T , and their corresponding coordinates in the machine tool coordinate system are: b B 1 =( b x B1 , b y B1 , b z B1 ) T , b B 2 =( b x B2 , b y B2 , b z B2 ) T , b B 3 =( b x B3 , b y B3 , b z B3 ) T , and the offset of the workpiece coordinate system relative to the machine tool coordinate system is w b =( b x 0 , b y 0 ,b z 0 ) T , the three direction vectors of the linear axes of the machine tool coordinate system are obtained by solving the transformation relationship from any point in the machine tool coordinate system to the calibration object coordinate system and the offset w of the calibration object coordinate system relative to the machine tool coordinate system b =( b x 0 , b y 0 , b z 0 ) T ;

[0012] For the rotary axis a and the rotary axis c: Suppose there is a point Q1 that rotates along a circle with q j as the center at a fixed angle along with the rotary axis, and points Q2, Q3,..., Qn on the circle are obtained. Arbitrarily select three consecutive points among them to determine two vectors e 1 , e 2 , and the normal vector ω j =e 1 ×e 2 is the direction vector of the rotary axis to be calibrated; Using the coordinates of Q1, Q2,..., Qn in the machine tool coordinate system b Q i =( b x Qi , b y Qi , b z Qi )(i = 1, 2... n) to fit out b q j =( b x qj , b y qj , b z qj ), and then according to the transformation relationship from the machine tool coordinate system to the calibration object coordinate system, the coordinates of this point in the calibration object coordinate system are obtained d q j =( d x qj , d y qj , d z qj ).

[0013] Furthermore, in step (1), the transformation model between the machine tool coordinate system and the workpiece coordinate system is as follows:

[0014] e represents the natural logarithm, ξ a , ξ c are the screw vectors of the rotary axis, ξx , ξ y , ξ z is a straight-axis twist, and θ x , θ y , θ z , θ a , θ c is the amount of movement of each motion axis g bw (0) represents the homogeneous transformation matrix of the workpiece coordinate system relative to the machine tool coordinate system under the initial state, T 1 represents the homogeneous transformation matrix of the nozzle coordinate system relative to the machine tool coordinate system, T 2 represents the homogeneous transformation matrix of the workpiece coordinate system relative to the machine tool coordinate system.

[0015] Furthermore, in step (2), the objective function is:

[0016]

[0017] ( b x Pj , b y Pj , b z Pj ), j = 1, 2, 3, 4, 5; represents the coordinates of the 5 calibration points P1, P2, P3, P4, P5 taken on the calibration sphere in the machine tool coordinate system, where R represents the radius of the calibration sphere;

[0018] ( b x Di , b y Di , b z Di ), i = 1, 2...5; represents the coordinates of the centers of the 5 calibration spheres in the machine tool coordinate system.

[0019] Furthermore, in step (3), the calibration of the straight axis specifically includes:

[0020] Suppose there is a unit vector in the machine tool coordinate system XYZ Its projection on the XOY plane is Suppose The angle with the Z-axis is β, The angle with the X-axis is γ, then this unit vector is expressed as:

[0021]

[0022] Similarly, the 3 direction vectors of the straight axis of the five-axis 3D printing system are expressed in the standard machine tool coordinate system as:

[0023]

[0024] where β n (n = x, y, z) are respectively the 3 direction vectors of the linear axes of the five-axis 3D printing system the angles with the Z-axis of the machine tool coordinate system, γ n (n = x, y, z) are respectively the angles between the projections on the XOY plane of the machine tool coordinate system and the X-axis;

[0025] The offset of the workpiece coordinate system relative to the machine tool coordinate system is w b = ( b x 0 , b y 0 , b z 0 ) T , since the calibration object coordinate system and the workpiece coordinate system coincide, then for any point b P = ( b x P , b y P , b z P ) the transformation relationship to the calibration object coordinate system is:

[0026]

[0027] Let then the above formula becomes:

[0028] d P = G · b P + w b

[0029] where d P = ( d x P , d y P , d z P ) is the point in the machine tool coordinate system b P = ( b x P , b y P , b z P ) is the coordinate in the calibration object coordinate system;

[0030] Arbitrarily select 3 calibration balls on the calibration object. The known coordinates of the centers of these 3 calibration balls in the calibration object coordinate system are: d D 1 = ( d x D1 , d yD1 , d z D1 ) T , d D 2 =( d x D2 , d y D2 , d z D2 ) T , d D 3 =( d x D3 , d y D3 , d z D3 ) T , the corresponding coordinates in the machine tool coordinate system are: b B 1 =( b x B1 , b y B1 , b z B1 ) T , b B 2 =( b x B2 , b y B2 , b z B2 ) T , b B 3 =( b x B3 , b y B3 , b z B3 ) T , then there is:

[0031]

[0032] Using the Newton iteration method to solve the above formula to obtain three direction vectors of the linear axes in the machine tool coordinate system and the offset w of the calibration object coordinate system relative to the machine tool coordinate system b =( b x 0 , b y 0 , b z 0 ) T .

[0033] Furthermore, in step (3), the solution process using the Newton iteration method specifically includes:

[0034] Expand the formula to obtain a system of non-linear equations. The iterative format of Newton's iteration method is as follows:

[0035] x (k+1) = x (k) - F′(x (k) ) -1 F(x (k) ), k = 0, 1,...

[0036] where x (k+1) is the value obtained after iteration, x (k) is the initial value of iteration,

[0037] According to F(x (k) ), obtain the corresponding Jacobian matrix F′(x (k) )

[0038] After obtaining F(x (k) ) and F′(x (k) ), use the iterative format of Newton's iteration method and set the initial values of the parameters to be calibrated for iterative solution to obtain the solutions of the parameters to be calibrated for the linear axis, that is, obtain the three direction vectors of the linear axis in the machine tool coordinate system and the offset w b = ([[]] b x 0 , b y 0 , b z 0 ) T .

[0039] Furthermore, in step (3), b Q i = ([[]] b x Qi , b y Qi , b z Qi )(i = 1, 2... n) to fit b q j = ([[]] b x qj , b y qj , b z qj ) The specific steps are as follows:

[0040] In the calibration object coordinate system d, the equation of the circle is:

[0041] ( d x Qi - d xqj ) 2 +( d y Qi - d y qj ) 2 =r 3 2

[0042] where d q j =( d x qj , d y qj ,0)(j = a, c) is the coordinate of the center q in the calibration object coordinate system d, and r 3 is the fitting circle radius. The center is fitted using the least squares method, and the objective function is:

[0043]

[0044] where From the above formula, we can get:

[0045]

[0046] Solving the equation shown above d x qj , d y qj , r 3 , we obtain the coordinate of the center in the machine tool coordinate system b q j =( b x qj , b y qj , b z qj ) is b q j =M· d q j ;

[0047] The center b q j =( b x qj , b y qj , b z qj ) in the calibration object coordinate system is :

[0048] d q j =G· b q j +w b

[0049] The transformation relationship from the machine tool coordinate system to the calibration object coordinate system d can be obtained:

[0050] d Q i = M -1 · b Q i

[0051] Among them, d Q i = ( d x Qi , d y Qi , d z Qi )(i = 1, 2... n) represents the coordinates of Q i in the calibration object coordinate system d, and M is the transformation matrix:

[0052]

[0053] From d Q i = M -1 · b Q i it is obtained that b Q 1 , b Q 2 ... b Q n the coordinates in the calibration object coordinate system d d Q 1 , d Q 2 ... d Q n .

[0054] Furthermore, in step (2), the five calibration balls include an intermediate calibration ball located in the middle position and four peripheral calibration balls evenly distributed on the same circumference around the intermediate calibration ball. The distance from the center of each peripheral calibration ball to the center of the intermediate calibration ball is equal.

[0055] Furthermore, the five calibration balls on the base have the same height, and each calibration ball is fixed on the base through a corresponding support rod.

[0056] Compared with the prior art, the beneficial effects of the present invention are as follows: The surface printed by the 3D printing system calibrated by the calibration method of the five-axis 3D printing system provided by the present invention can reduce the average deviation and standard deviation, the printing position accuracy is improved relatively high, the printing surface quality is also improved, and the point cloud data fits well with the ideal model, and the comprehensive printing accuracy is significantly improved.

[0057] The present invention also provides a computer device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the steps of the above method are implemented.

[0058] The present invention also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the above method are implemented. Description of the Drawings

[0059] Figure 1 It is a structural diagram of a calibration object. Detailed Embodiments

[0060] To make the above features and advantages of the present invention more obvious and understandable, the following will specifically describe embodiments in conjunction with the drawings.

[0061] A calibration method for a five-axis 3D printing system includes the following steps:

[0062] (1) Establish a transformation model between the machine tool coordinate system and the workpiece coordinate system. According to the tool motion chain and workpiece motion chain of the five-axis 3D printing system, the five-axis 3D printing system includes a linear axis x, a linear axis y, a linear axis z, a rotary axis a, and a rotary axis c.

[0063] The transformation model between the machine tool coordinate system and the workpiece coordinate system is as follows:

[0064]

[0065] e represents the natural logarithm, ξ a 、ξ c is the screw of the rotary axis, ξ x 、ξ y 、ξ z is the screw of the linear axis, θ x 、θ y 、θ z 、θ a 、θ c is the movement amount of each motion axis, g bw (0) represents the homogeneous transformation matrix of the workpiece coordinate system relative to the machine tool coordinate system under the initial state, T 1 represents the homogeneous transformation matrix of the nozzle coordinate system relative to the machine tool coordinate system, T 2 represents the homogeneous transformation matrix of the workpiece coordinate system relative to the machine tool coordinate system.

[0066] (2) Provide a calibration object, which includes a base and five calibration balls supported on the base. The five calibration balls include an intermediate calibration ball located at the middle position and four peripheral calibration balls evenly distributed on the same circumference around the intermediate calibration ball. Each calibration ball is fixed to the base through a corresponding support rod. In this embodiment, the base is cross-shaped, and the distance from the center of each peripheral calibration ball to the center of the intermediate calibration ball is equal. In this embodiment, the positioning accuracy between the fixed hole positions is ±0.05 mm, the diameter accuracy of the calibration balls reaches ±0.005 mm, the roundness accuracy is ±0.001 mm, the base plate material is SKD11 steel, and the calibration ball material is GCr15 steel.

[0067] Based on the "four plus one" measurement point scheme, use an edge finder to take measurement points on each spherical surface. That is, make the probe of the edge finder contact the side of a calibration ball to obtain the coordinates of a point on the spherical surface. Take one point in front, behind, left, right, and on the top of a calibration ball, and substitute the obtained measurement points into the objective function to obtain the center coordinates of the calibration ball; each calibration ball needs to execute this measurement point scheme once. It should be noted that in this embodiment, the selected edge finder is set to have the same length as the nozzle of the 3D printing system, so the center coordinates of the calibration ball can be directly obtained through the edge finder for measurement point operation. In different actual use environments, such as when the length of the edge finder is different from the length of the nozzle, the nozzle needs to be used to replace the edge finder to contact the calibration ball for measurement points, and the length compensation measurement commonly used in this technical field is carried out. For the calibration object used in this embodiment, the end of the nozzle can be used to touch point D0 to obtain the offset between the actual machine tool coordinate system and the workpiece coordinate system. This point D0 is an arbitrarily set point on the base of the calibration object. Since both the calibration object and the nozzle are metals, when they come into contact, they become a connected conductor. Therefore, a multimeter can be used to detect whether the end of the nozzle touches the point to be measured. Turn the multimeter to the ohm range, fix the black test lead on the calibration object with tape, hold the red test lead against the nozzle, and observe the position of the end of the nozzle when the nozzle and the calibration ball are used for measurement points, and try to make the center of the end contact the tip of D0 as much as possible. When the parameters of the multimeter jump or the buzzer alarms, record the current coordinate value, and this current coordinate value is the center coordinate of the calibration ball after compensation.

[0068] (3) Calibrate the linear axis x, linear axis y, linear axis z, rotary axis a, and rotary axis c using the center coordinates obtained in step (2).

[0069] Specifically, for the linear axis x, linear axis y, and linear axis z:

[0070] Use the least squares method to fit the coordinates of the center of the ball in the machine tool coordinate system. Substitute the measurement points obtained in step (1) into the objective function to obtain the center coordinates of the ball. The objective function is:

[0071]

[0072] ( b x Pj , b y Pj , b z Pj ), j = 1, 2, 3, 4, 5; representing the coordinates of five calibration points P1, P2, P3, P4, P5 taken on the calibration sphere in the machine tool coordinate system;

[0073] ( b x Di , b y Di , b z Di ), i = 1, 2...5; representing the coordinates of the centers of five calibration spheres in the machine tool coordinate system, and preparing for the calibration algorithm of linear axes and rotary axes based on the coordinates of the centers of the five obtained calibration spheres in the machine tool coordinate system.

[0074] Suppose there is a unit vector in the machine tool coordinate system XYZ Its projection on the XOY plane is Suppose The angle with the Z - axis is β, The angle with the X - axis is γ, then this unit vector Can be expressed as:

[0075]

[0076] Similarly, the three direction vectors Of the linear axes of the five - axis 3D printing system can be expressed in the standard machine tool coordinate system as:

[0077]

[0078] In the formula, β n (n = x, y, z) are respectively the three direction vectors Of the linear axes of the five - axis 3D printing system and the angle with the Z - axis of the machine tool coordinate system, γ n (n = x, y, z) are respectively The angle between the projection on the XOY plane of the machine tool coordinate system and the X - axis.

[0079] The offset of the workpiece coordinate system relative to the machine tool coordinate system is w b =( b x 0 , b y 0 , b z 0 ) T , since the calibration object coordinate system and the workpiece coordinate system coincide, then any point bP = ([ b x P , b y P , b z P ]) The transformation relationship transformed to the calibration object coordinate system is:

[0080]

[0081] Let Then the above formula becomes:

[0082] d P = G · b P + w b (6)

[0083] In the formula, d P = ([ d x P , d y P , d z P ]) is the point in the machine tool coordinate system b P = ([ b x P , b y P , b z P ]) is the coordinate of the point in the calibration object coordinate system.

[0084] To sum up, the transformation model between the machine tool coordinate system and the calibration object coordinate system contains a total of

[0085] {β x γ x β y γ y β z γ z b x 0 b 0 y b 0 z d} and other 9 unknowns to be solved. At least 3 different target points' coordinates in the calibration object coordinate system and the machine tool coordinate system are required to solve these 9 unknowns.

[0086] Arbitrarily select 3 calibration balls on the calibration object. The coordinates of the centers of these 3 calibration balls in the calibration object coordinate system are known as: d D 1 = ([ d x D1 , d y D1 , d z D1 ]) T ​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​, d D 2 =( d x D2 , d y D2 , d z D2 ) T , d D 3 =( d x D3 , d y D3 , d z D3 ) T , and the corresponding coordinates in the machine tool coordinate system are: b B 1 =( b x B1 , b y B1 , b z B1 ) T , b B 2 =( b x B2 , b y B2 , b z B2 ) T , b B 3 =( b x B3 , b y B3 , b z B3 ) T , then according to Equation (6), we have:

[0087]

[0088] The above equation can be solved by the Newton iteration method. Expanding Equation (7) gives:

[0089]

[0090] Let p - q = m (9)

[0091] This is a system of non-linear equations, and its Newton iteration format is:

[0092] x (k+1) = x (k) - F'(x (k) ) -1 F(x (k) ), k = 0, 1,... (10)

[0093] where x (k+1) is the value obtained after iteration, and x (k) is the initial value of iteration, and:

[0094] F(x (k) ) = m + q - p (11)

[0095] According to F(x (k) ), the corresponding Jacobian matrix F′(x (k) ) is obtained:

[0096]

[0097] F′(x (k) ) -1 is the inverse matrix of the Jacobi matrix. After obtaining F(x (k) ) and F′(x (k) ), using the iteration format of Equation (10) and setting the initial values of the parameters to be calibrated for iterative solution can obtain the solutions of the parameters to be calibrated for the linear axis, that is, the three direction vectors of the linear axis in the machine tool coordinate system and the offset w b = ([[]] b x 0 , b y 0 , b z 0 ) T .

[0098] For the rotary axis a and the rotary axis c: The calibration of the rotary axis requires calibrating the coordinates of a point b q j = ([[]] b x qj , b y qj , b z qj )(j = a, c) in the calibration object coordinate system d q j = ([[]] d x qj , d y qj , d z qj )(j = a, c) and the direction vector ω a , ω c . Suppose a point Q1 rotates along a circle centered at q j at a fixed angle with the rotary axis, and points Q2, Q3,..., Qn on the circle are obtained. Arbitrarily select three consecutive points among them to determine two vectors e 1 , e 2, the normal vector ω is obtained j = e 1 × e 2 That is the direction vector of the rotation axis to be calibrated; Using the coordinates of Q1, Q2, ..., Qn in the machine tool coordinate system b Q i = ([[]] b x Qi , b y Qi , b z Qi )(i = 1, 2... n) to fit b q j = ([[]] b x qj , b y qj , b z qj ), and then according to the transformation relationship from the machine tool coordinate system to the calibration object coordinate system, the coordinates of this point in the calibration object coordinate system are obtained d q j = ([[]] d x qj , d y qj , d z qj ).

[0099] In the calibration object coordinate system d, the equation of the circle is:

[0100] ([[]] d x Qi - d x qj ) 2 +([[]] d y Qi - d y qj ) 2 = r 3 2 (13)

[0101] Among them, d q j = ([[]] d x qj , d y qj , 0)(j = a, c) is the coordinate of the center q in the calibration object coordinate system d, and r 3 is the fitting circle radius. Using the least squares method to fit its center, the objective function is:

[0102]

[0103] Among them, From the above formula, it can be obtained that:

[0104]

[0105] Solving the equation shown above, we can get d x qj , d y qj 、r 3 .

[0106] The coordinates of the center of the circle in the machine tool coordinate system can be obtained b q j =( b x qj , b y qj , b z qj ):

[0107] b q j =M· d q j (16)

[0108] Center b q j =( b x qj , b y qj , b z qj ) in the coordinate system of the calibration object for:

[0109] d q j =G· b q j +w b (17)

[0110] The transformation relationship from the machine tool coordinate system to the calibration object coordinate system d can be obtained:

[0111] d Q i =M -1 · b Q i (18)

[0112] in, d Q i =( d x Qi , d y Qi , d z Qi )(i=1,2...n) represents Q i The coordinates in the calibration object coordinate system d, M is the transformation matrix:

[0113]

[0114] It can be obtained from Equation (18) that b Q 1 , b Q 2 ... b Q n coordinates in the calibration object coordinate system d d Q 1 , d Q 2 ... d Q n .

[0115] Based on the above calibration method, the method was verified in an experiment. In this verification experiment, the edge finder selected a mach3 3D probe, and the repeat positioning accuracy was 5μm. First, it was necessary to install the calibration object and the edge finder. The calibration object was fixed on the working table of the equipment by a threaded clamp to prevent relative displacement of the calibration object during the calibration process.

[0116] Then, measure the coordinates of the points required for linear axis calibration. Keep the calibration object stationary, and measure 5 points on the surfaces of calibration balls D1 - D5 according to the "four plus one" measuring point method described above, for a total of 25 points.

[0117] Furthermore, measure the coordinates of the points required for rotary axis calibration. First, measure the points required for calibrating the C axis. Select any calibration ball among the calibration balls with a height of 30mm in the Z direction in the calibration object coordinate system. Let the initial ball center position be Q1, and make the C axis rotate 60° each time to drive the ball to rotate 60° as well. Rotate 5 times, and measure 5 points on the spherical surface in sequence, for a total of 25 points. Second, measure the points required for calibrating the A axis. To prevent interference between the edge finder and the calibration object when calibrating the A axis, select the calibration ball with a height of 60mm in the Z direction in the calibration object coordinate system, whose initial ball center is D3, here set as Q3. Let the A axis rotate 15° each time to drive the ball to rotate 15° as well. Rotate 5 times, and measure 5 points on the spherical surface in sequence, for a total of 25 points.

[0118] Substitute the coordinates of all the measured points into the least squares algorithm of the ball center to obtain the coordinates of the centers of the 5 calibration balls required for linear axis calibration ( b x Di , b y Di , b z Di )(i = 1, 2... 5), and the results are shown in Table 1. Obtain the coordinates of the centers of the calibration balls required for calibrating the C axis ( b x Q1 , b y Q1 , b z Q1), and the results are shown in Table 2 to obtain the coordinates of the calibration ball center (x Q3 , y Q3 , z Q3 ) for calibrating the A-axis, and the results are shown in Table 3.

[0119] Table 1: Coordinates of the calibration ball center

[0120]

[0121] Table 2: Coordinates of the calibration ball center required for calibrating the rotary axis C

[0122]

[0123] Table 3: Coordinates of the calibration ball center required for calibrating the rotary axis A

[0124]

[0125] Substitute the coordinates of the calibration ball center in Table 1 into the linear axis calibration algorithm described in Step 3 to solve for the direction vectors ω x , ω y , ω z and w b . Substitute the coordinates of the calibration ball center in Tables 2 and 3 into the rotary axis calibration algorithm described in Step 4 to solve for the direction vectors ω a , ω c and a point q a , q c on the rotary axis. The calibration results are shown in Table 4.

[0126] Table 4: Calibration results

[0127]

[0128]

[0129] For the surface printed by the printing system calibrated through this verification case, the average deviation is 0.002, the standard deviation is 0.089, and the point cloud data fits well with the ideal model. Compared with the prior art, after calibration through the above verification case, the average deviation of the printed surface is reduced by 91.3% compared with the calibration method using a square calibration object, the printing position accuracy is improved significantly, the standard deviation is reduced by 35.97%, the printing surface quality is also improved, and the comprehensive printing accuracy is significantly improved. The above verification results show that the calibration method proposed by the present invention can effectively improve the accuracy of the 3D printing system.

Claims

1. A calibration method for a five-axis 3D printing system, for a five-axis linkage machining center including a linear axis x, a linear axis y, a linear axis z, a rotation axis a, and a rotation axis c, characterized in that: The following steps are included: (1) Establish the transformation model between the machine tool coordinate system and the workpiece coordinate system; (2) providing a calibration object, which includes a base and five calibration balls supported on the base, and using an edge finder to measure points on each spherical surface, that is, making the edge finder probe contact the side of a calibration ball to obtain the coordinates of a point on the spherical surface, and taking a point on the front, back, left, right, and top of a calibration ball, and substituting the obtained measured points into the objective function to obtain the coordinates of the center of the calibration ball; (3) using the spherical center coordinates obtained in step (2) to calibrate the linear axis x, the linear axis y, the linear axis z, the rotation axis a, and the rotation axis c; For the linear axis x, linear axis y, and linear axis z: randomly select three calibration balls on the calibration object. The coordinates of the centers of the three calibration balls in the calibration object coordinate system are known to be: d D1=( d x D1 , d y D1 , d z D1 ) T , d D2=( d x D2 , d y D2 , d z D2 ) T , d D3=( d x D3 , d y D3 , d z D3 ) T , the corresponding coordinates in the machine tool coordinate system are: b B1=( b x B1 , b y B1 , b z B1 ) T , b B2=( b x B2 , b y B2 , b z B2 ) T , b B3=( b x B3 , b y B3 , b z B3 ) T , the offset of the workpiece coordinate system relative to the machine tool coordinate system is w b =( b x0, b y0, b z0) T , the three direction vectors of the linear axis of the machine tool coordinate system are obtained by transforming any point of the machine tool coordinate system to the calibration object coordinate system And the offset w of the calibration object coordinate system relative to the machine tool coordinate system b =( b x0, b y0, b z0) T ; For the rotation axis a and the rotation axis c: Suppose a point Q1 is along the axis q at a fixed angle j The circle with the center as the axis of rotation rotates, and we get points Q2, Q3, ..., Qn on the circle. We can select any three consecutive points to determine two vectors e1 and e2, and get the normal vector ω. j =e1×e2 is the direction vector of the rotation axis to be calibrated; using the coordinates of Q1, Q2, ..., Qn in the machine tool coordinate system b Q i =( b x Qi , b y Qi , b z Qi )(i=1,2...n) fits b q j =( b x qj , b y qj , b z qj ), and then the coordinates of the point in the calibration object coordinate system are obtained according to the transformation relationship from the machine tool coordinate system to the calibration object coordinate system d q j =( d x qj , d y qj , d z qj ).

2. The calibration method of the five-axis 3D printing system according to claim 1, characterized in that: In step (1), the transformation model of the machine tool coordinate system and the workpiece coordinate system is as follows: e represents the natural logarithm, ξ a , c is the rotation axis spin, ξ x , y , z is the linear axis rotation, θ x ,θ y ,θ z ,θ a ,θ c is the amount of motion of each axis g bw (0) represents the homogeneous transformation matrix of the workpiece coordinate system relative to the machine tool coordinate system in the initial state, T1 represents the homogeneous transformation matrix of the nozzle coordinate system relative to the machine tool coordinate system, and T2 represents the homogeneous transformation matrix of the workpiece coordinate system relative to the machine tool coordinate system.

3. The calibration method of the five-axis 3D printing system according to claim 1, characterized in that: In step (2), the objective function is: ( b x Pj , b y Pj , b z Pj ), j = 1, 2, 3, 4, 5; represents the coordinates of the five calibration points P1, P2, P3, P4, P5 taken on the calibration sphere in the machine tool coordinate system, where R represents the radius of the calibration sphere; ( b x Di , b y Di , b z Di ), i = 1, 2...5; represents the coordinates of the centers of the five calibration balls in the machine tool coordinate system.

4. The calibration method of the five-axis 3D printing system according to claim 1, characterized in that: In step (3), calibrating the linear axis specifically includes: Assume that there is a unit vector in the machine tool coordinate system XYZ Its projection on the XOY plane is set up The angle with the Z axis is β, The angle between the vector and the X-axis is γ, then the unit vector It is expressed as: Similarly, the three direction vectors of the linear axis of the five-axis 3D printing system In the standard machine tool coordinate system, it is expressed as: In the formula, β n (n=x,y,z) are the three direction vectors of the linear axis of the five-axis 3D printing system The angle with the Z axis of the machine tool coordinate system, γ n (n=x,y,z) are The angle between the projection on the XOY plane of the machine tool coordinate system and the X axis; The offset of the workpiece coordinate system relative to the machine tool coordinate system is w b =( b x0, b y0, b z0) T Since the calibration object coordinate system and the workpiece coordinate system coincide, any point in the machine tool coordinate system b P=( b x P , b y P , b z P ) to the calibration object coordinate system is: make Then the above formula becomes: d P=G· b P+w b In the formula, d P=( d x P , d y P , d z P ) is a point in the machine tool coordinate system b P=( b x P , b y P , b z P ) in the coordinate system of the calibration object; Take any three calibration balls on the calibration object, and the coordinates of the centers of the three calibration balls in the calibration object coordinate system are known to be: d D1=( d x D1 , d y D1 , d z D1 ) T , d D2=( d x D2 , d y D2 , d z D2 ) T , d D3=( d x D3 , d y D3 , d z D3 ) T , the corresponding coordinates in the machine tool coordinate system are: b B1=( b x B1 , b y B1 , b z B1 ) T , b B2=( b x B2 , b y B2 , b z B2 ) T , b B3=( b x B3 , b y B3 , b z B3 ) T , then: Use Newton's iteration method to solve the above equation to get the three direction vectors of the linear axis of the machine tool coordinate system And the offset w of the calibration object coordinate system relative to the machine tool coordinate system b =( b x0, b y0, b z0) T .

5. The calibration method of the five-axis 3D printing system according to claim 4, characterized in that: In step (3), the solution process using the Newton iteration method specifically includes: General The expansion results in a nonlinear system of equations, whose Newton iteration method iteration format is: x (k+1) =x (k) -F′(x (k) ) -1 F(x (k) ),k=0,1,... where x (k+1) is the value obtained after iteration, x (k) is the initial value of the iteration, According to F(x (k) ) to obtain the corresponding Jacobian matrix F′(x (k) ) We get F(x (k) ) and F′(x (k) ), the Newton iteration method is used to iterate the parameters, and the initial values ​​of the parameters to be calibrated are set to iterate and solve the problem. The solution of the linear axis parameters to be calibrated can be obtained, that is, the three direction vectors of the linear axis of the machine tool coordinate system can be obtained. And the offset w of the calibration object coordinate system relative to the machine tool coordinate system b =( b x0, b y0, b z0) T .

6. The calibration method of the five-axis 3D printing system according to claim 1, characterized in that: In step (3), b Q i =( b x Qi , b y Qi , b z Qi )(i=1,2...n) fits b q j =( b x qj , b y qj , b z qj ) are as follows: In the calibration object coordinate system d, the equation of the circle is: in, d q j =( d x qj , d y qj ,0)(j=a,c) is the coordinate of the center q in the calibration object coordinate system d, r 3 In order to fit the circle radius, the least squares method is used to fit its center, and the objective function is: in, From the above formula, we can get: Solving the above equation yields d x qj , d y qj , r3, get the coordinates of the center of the circle in the machine tool coordinate system b q j =( b x qj , b y q j, b z qj )for b q j =M· d q j ; Center b q j =( b x qj , b y qj , b z qj ) in the coordinate system of the calibration object for: d q j =G· b q j +w b The transformation relationship from the machine tool coordinate system to the calibration object coordinate system d can be obtained: d Q i =M -1 · b Q i in, d Q i =( d x Qi , d y Qi , d z Qi )(i=1,2...n) represents Q i The coordinates in the calibration object coordinate system d, M is the transformation matrix: Depend on d Q i =M -1 · b Q i have to b Q1. b Q2... b Q n Coordinates in the calibration object coordinate system d d Q1. d Q2... d Q n .

7. The calibration method of the five-axis 3D printing system according to claim 1, characterized in that: In step (2), the five calibration balls include a middle calibration ball located in the middle position and four peripheral calibration balls evenly distributed on the same circumference around the middle calibration ball, and the distance from the center of each peripheral calibration ball to the center of the middle calibration ball is equal.

8. The calibration method of the five-axis 3D printing system according to claim 1 or 7, characterized in that: The five calibration balls on the base have equal heights, and each calibration ball is fixed to the base via a corresponding support rod.

9. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 6 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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