Five-axis machine tool rotating shaft error measurement method based on ball bar

Abstract

The invention discloses a five-axis machine tool rotating shaft error measuring method based on a ball bar. The method comprises the following specific steps that a coordinate system is established for a five-axis machine tool; some preparatory work needs to be carried out before measurement; eight PIGEs of the A axis and the C axis of the five-axis machine tool are identified; s4, a ball rod instrument is installed; measuring the error process of the rotating shaft by using a ball rod; and eight PIGEs of the A axis and the C axis of the five-axis machine tool are calculated. According to the method, the installation method of the ball bar is improved, the precision deviation of the micrometer and the position error generated when the tool nose is in contact with the gauge block are eliminated, the error caused when the ball bar is installed can be reduced to a great extent, and the measured PIGEs result of the rotating shaft is more accurate; in addition, it is not required that personnel operating the machine tool have high professional ability, only the NC codes need to be called out of the code library, the version control system can be used for tracking and managing the modification history of the NC codes, and operation is very convenient.

Description

Technical Field

[0001] The present invention relates to the technical field of five-axis machine tools, and in particular to a method for measuring the rotation axis error of a five-axis machine tool based on a ballbar. Background Art

[0002] The five-axis machine tool achieves the flexibility of arbitrary tool and workpiece posture in space through the rotating axis, which makes it have higher production efficiency, stronger flexibility, and less workpiece clamping time compared to the three-axis machine tool. However, with the introduction of two rotating axes, additional geometric errors are also caused, such as the parallelism error between the rotating axis and the translation axis. These errors are directly related to the machining accuracy of the five-axis machine tool, so it is very important to accurately identify these errors.

[0003] The errors of rotary axes can be divided into two categories: position-dependent geometric errors (PDGEs) and position-independent geometric errors (PIGEs). PDGEs are mainly caused by manufacturing defects of the rotary axis itself, while PIGEs are mainly caused by the assembly of the rotary axis by the machine tool manufacturer.

[0004] In recent years, scholars have used various experimental equipment to measure the error of rotating axes. Common equipment include R-test, probe and ballbar. Ballbar is a mature measurement tool that can quickly and effectively measure the change of machine tools relative to the reference length during motion through simple circular trajectory tests. Compared with measurement tools such as R-test and probe, ballbar is relatively cheap and easy to purchase. For this reason, many scholars have studied the identification of PIGEs errors of rotating axes through different ballbar measurement modes. Figure 1 As shown in the figure, the main components of the ballbar are two high-precision mounting balls and a high-precision linear displacement sensor installed inside the telescopic rod, which can accurately measure the relative displacement between the two measuring balls.

[0005] After the ballbar is installed, the CNC machine tool issues a circular trajectory command, using the ballbar on the worktable side as the center of the circular interpolation motion, so that the center of the ball on the spindle side performs circular interpolation motion. In the machine tool coordinate system, the worktable side ball P 0 The coordinates of the center of the sphere are (X 0 ,Y 0 ,Z 0 ), the center coordinate of the sphere P1 on the main axis side is marked as (X 1 ,Y 1 ,Z 1 ).

[0006] The distance between the two sphere centers is the total length of the ballbar and can be expressed as:

[0007]

[0008] Due to the existence of geometric errors, the actual positions of the two balls on the machine tool are P′ 0 (X′ 0 , Y′ 0 ,Z′ 0 ) and P′ 1 (X′ 1 ,Y′ 1 ,Z′ 1 ), so the actual axial expansion and contraction of the ballbar can be expressed as:

[0009]

[0010] After simplification, the basic measurement principle of the ballbar can be obtained:

[0011]

[0012] Among them, C x ,C y and C z are the components of the rod length change in the X, Y and Z directions respectively.

[0013] In the ballbar-based measurement methods proposed by many scholars, the translation axis and the rotation axis are usually moved together to achieve circular trajectory motion. However, since the translation axis error cannot be accurately compensated, this will undoubtedly introduce the translation axis error into the final error data.

[0014] Therefore, some scholars have proposed a more accurate measurement method: keep the translation axis stationary and only rotate the rotation axis, thereby avoiding the error introduced by the movement of the translation axis. Figure 2 As shown, the new method mainly uses a gauge block and a micrometer to determine the axis position of the rotating axis C axis. The following is a brief description of the method:

[0015] Step 1: Place a gauge block on the C-axis rotary table and use a micrometer to measure it to make it exactly parallel to the X-axis.

[0016] Step 2: First move the tool tip to the approximate position of the C-axis axis and set it as the zero point; then move the tool tip to point P1 (in contact with the gauge block) and record the current Y coordinate value as R1.

[0017] Step 3: Rotate the C axis 180° and move the Y axis in the opposite direction to move the tool tip to P2 (contacting the gauge block), and record the current Y coordinate value as R2. In general, since the starting point of the tool tip is not on the axis, R1 and R2 are not equal, and ΔR is recorded as the difference between R1 and R2. Half of the difference ΔR / 2 is the distance between the starting point of the tool tip and the true axis. Move the Y axis a distance of ΔR / 2 to move the tool tip from point C1 to point C2. Repeat the above steps in different X coordinate systems to reduce the positioning error. Finally, determine the Y coordinate of the C axis axis.

[0018] Similarly, the X coordinate of the C-axis axis can be determined. With the X and Y coordinates, the position of the C-axis axis in the XY plane is determined.

[0019] Finally, repeat the above steps at different Z coordinates to completely determine the position of the C-axis axis in the entire space.

[0020] However, the accuracy of determining the C-axis axis depends on the accuracy of the micrometer, the proficiency of human operation and the results of multiple measurements. Since the highest accuracy of the micrometer is 1μm, even after repeated measurements, the determination error of the C-axis axis is about 2μm, which will have a great impact on the correctness of the final error identification result; and this method requires technicians to have good machine tool operation ability and strong professionalism. Summary of the invention

[0021] The purpose of the present invention is to solve the shortcomings of the prior art and to propose a method for measuring the rotation axis error of a five-axis machine tool based on a ballbar.

[0022] In order to achieve the above object, the present invention adopts the following technical solutions:

[0023] A method for measuring the rotation axis error of a five-axis machine tool based on a ballbar comprises the following specific steps:

[0024] S1: Establish the following coordinate systems for the five-axis machine tool: establish the C-axis coordinate system (CCS) at the center of the rotary table; establish the A-axis coordinate system (ACS) at the intersection of the A-axis and C-axis axes; establish the Z-axis coordinate system (ZCS) at the spindle head and directly above the CCS; establish the Y-axis coordinate system (YCS) on the Y axis and directly below the CCS; in addition, for the convenience of CNC programming, make the workpiece coordinate system (WCS) coincide with the CCS, and make the machine coordinate system (MCS) coincide with the YCS; all of the above coordinate systems are located on the same axis;

[0025] S2: Some preparation work needs to be done before measurement: the ambient temperature is controlled at about 20℃, and since the ballbar test does not require the machine tool to move violently, the influence of thermal error can be ignored;

[0026] S3: Identify the eight PIGEs of the A-axis and C-axis of the five-axis machine tool. The eight PIGEs include α AY , β AY , γ AY , β CA , δ xAY , δ yAY , δ zAY and δ yCA ,The measurement process is divided into two modes. In mode 1, only the C axis rotates during the measurement process, and in mode 2, only the A axis rotates;

[0027] S4: Install the ballbar: The high-precision mounting ball needs to be accurately placed on the axis of the A-axis and C-axis to minimize the installation error of the ballbar.

[0028] S41: In mode 1, first enter the NC code to move each translation axis and rotation axis to the initial position on the established coordinate system. It should be noted that the Z axis is the main axis of the machine tool at this time; then position the main axis to the position that is colinear with the C axis, and move the ball O 1 Precisely place the ball on the spindle and 2 Place it on the rotating table; 1 Move to the position (0,0,640) in the machine tool coordinate system, and then move the ball O on the worktable side 2 Installed at (150,0,60) of the workpiece coordinate system, the height of the ballbar cup is 60 mm;

[0029] S42: In mode 2, input the NC code similar to mode 1 to 1 Place it precisely on the axis of the A-axis, then install the fixture on the C-axis rotary table and 2 Place the ball O on the spindle side on the fixture. 1 Move to the position (180,0,500) in the machine tool coordinate system, and then move the ball O on the worktable side 2 Installed to the workpiece coordinate system (60,0,30), which is on the axis of the A axis;

[0030] S5: Procedure for measuring rotation axis errors using a ballbar:

[0031] S51: In mode 1, the A-axis and other translational axes remain stationary, the C-axis is rotated from 0° to 360°, and ballbar data is collected simultaneously;

[0032] S52: In mode 2, keep the C-axis and the translation axis stationary, rotate the A-axis from -45° to +45°, and collect ballbar data at the same time;

[0033] S6: Calculate the eight PIGEs of the A and C axes of the five-axis machine tool: Mode 1 is that the C axis rotates one circle from 0° to 360°. When θ=π / 2, π, 3π / 2 and 2π, record the ballbar readings respectively, which are recorded as L 1 , L 2 , L 3 and L 4 ; Mode 2 is when the A axis rotates from -45° to +45°. When θ=0, π / 4, and -π / 4, the ballbar readings are recorded respectively and recorded as L 5 , L 6 and L 7 ; The 8-term PIGE can be obtained by solving the system of equations:

[0034] S61: As shown in the following formula, from L 1 , L 2 , L 3 and L 4 Solve the equation for δ zAY :

[0035]

[0036] S62: As shown in the following formula, β AY From L 5 , L 6 and L 7 From the equation we get:

[0037] L 6 2 -L7 2 =62400sin(γ AY )·sin45°+360δ yAY ·sin45° (2)

[0038]

[0039] S63: The δ obtained in S61 and S62 is zAY and β AY Substitute into L 4 and L 5 , we can solve for β CA and δ xAY :

[0040]

[0041] S64: As shown in the following formula, from L 1 and L 3 We can get α AY , δ yCA and δ yAY The mathematical relationship between:

[0042]

[0043] S65: α AY , δ xAY , β AY , δ zAY and β CA Solving δ by the least squares method yCA and δ yAY , then solve α from equation (6) AY ;

[0044] S66: δ yAY Substituting into equation (2), we can solve for γ AY :

[0045]

[0046] As a further technical solution of the present invention, in S3, α AY β is the angular error of the A-axis relative to the Y-axis of the machine tool about the X-axis; AY and γ AY are the angular errors of the A-axis relative to the Y-axis of the machine tool about the Y-axis and the Z-axis; β CA is the angular error of the C axis relative to the A axis about the Y axis; δ xAY , δ yAY and δ zAY are the position errors of the A-axis relative to the Y-axis of the machine tool in the X, Y, and Z directions respectively; δ yCAis the position error of the C-axis relative to the A-axis in the Y direction. For a five-axis machine tool, the Y-axis coordinate system coincides with the machine tool coordinate system. Therefore, the subscript "AY" of the above error actually represents the A-axis relative to the machine tool coordinate system, that is, the above "relative to the machine tool Y-axis" can be understood as "relative to the machine tool".

[0047] As a further technical solution of the present invention, in said S42, the operation process of the mode 2 at the beginning is similar to that of the mode 1, except that after the spindle is positioned on the axis of the A-axis, the ballbar cannot be installed immediately, but the spindle must be translated upward for a distance, which is the distance of the ballbar. 1 The radius of the ball and the length of the ball cup are the sum of the radius of the ball and the length of the ball cup, so as to ensure that the ball O 1 The center of the sphere is located on the axis of the A axis.

[0048] The beneficial effects of the present invention are as follows: the ballbar installation method is improved. In order to eliminate the inherent precision deviation of the micrometer and the position error caused by the contact between the tool tip and the gauge block, a reasonable machine tool coordinate system is first established. Then, on this basis, the spindle is positioned on the axis of the C-axis and the A-axis respectively by inputting the NC code. Finally, the ballbar is accurately installed, which can greatly reduce the error caused by the installation of the ballbar and make the measured rotation axis PIGEs result more accurate. Moreover, it does not require the personnel operating the machine tool to have strong professional ability. It only needs to call out the NC code from the code library, and the version control system (such as Git) can be used to track and manage the modification history of the NC code, which is very convenient to operate. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 This is the measurement principle diagram of the ballbar;

[0050] Figure 2 This is a diagram of the method for determining the C-axis axis;

[0051] Figure 3 Create a schematic diagram for the coordinate system of a five-axis machine tool;

[0052] Figure 4 8-term PIGE schematic diagram of the rotation axis in relative representation;

[0053] Figure 5 This is a simple example NC code schematic;

[0054] Figure 6 This is a schematic diagram of measurement mode 1 where only the C-axis rotates;

[0055] Figure 7 This is a schematic diagram of measurement mode 2 where only the A axis rotates;

[0056] Figure 8 This is a schematic diagram of the Quaser UX600 five-axis machine tool;

[0057] Fig. 9 It is the technical roadmap of the present invention;

[0058] Fig.10 This is a schematic diagram of the measurement process of mode 1 where only the C-axis rotates;

[0059] Fig.11 This is a schematic diagram of the measurement process of mode 2 where only the A-axis rotates. DETAILED DESCRIPTION

[0060] In order to make the technical means, creative features, objectives and effects achieved by the present invention easy to understand, the present invention is further explained below in conjunction with specific implementation methods.

[0061] A method for measuring the rotation axis error of a five-axis machine tool based on a ballbar comprises the following specific steps:

[0062] S1: Establish the following coordinate system for the five-axis machine tool, such as Figure 3 As shown in the figure: the C-axis Coordinate System (CCS) is established at the center of the rotary table; the A-axis Coordinate System (ACS) is established at the intersection of the A-axis and C-axis axes; the Z-axis Coordinate System (ZCS) is established on the spindle head and is located directly above the CCS; the Y-axis Coordinate System (YCS) is established on the Y axis and is located directly below the CCS; in addition, for the convenience of CNC programming, the workpiece coordinate system (WCS) is made to coincide with the CCS, and the machine coordinate system (MCS) is made to coincide with the YCS; all of the above coordinate systems are located on the same axis;

[0063] S2: Some preparation work needs to be done before measurement: the ambient temperature is controlled at about 20℃, and since the ballbar test does not require the machine tool to move violently, the influence of thermal error can be ignored;

[0064] S3: Identify the eight PIGEs of the A-axis and C-axis of the five-axis machine tool. The eight PIGEs include α AY , β AY , γ AY , β CA , δ xAY , δ yAY , δ zAY and δ yCA These errors are Figure 4As shown, the measurement process is divided into two modes. In the measurement process of mode 1, only the C-axis rotates, and in the measurement process of mode 2, only the A-axis rotates;

[0065] The key to using the ballbar to measure the rotation axis error is to place a high-precision ball on the axis of the A-axis or C-axis. In order to eliminate the installation error caused by the installation of the ballbar in the existing measurement mode, the present invention establishes a Figure 3 Based on the machine coordinate system shown, the spindle, A-axis or C-axis is moved to the target position by entering specific NC codes.

[0066] S4: Install the ballbar: The high-precision mounting ball needs to be accurately placed on the axis of the A-axis and C-axis to minimize the installation error of the ballbar.

[0067] S41: In mode 1, first enter the NC code to move each translation axis and rotation axis to the initial position on the established coordinate system. It should be noted that the Z axis is the main axis of the machine tool at this time; then position the main axis to the position that is colinear with the C axis, and move the ball O 1 Precisely place the ball on the spindle and 2 Place it on the rotating table; 1 Move to the position (0,0,640) in the machine tool coordinate system, and then move the ball O on the worktable side 2 Installed at (150,0,60) of the workpiece coordinate system, the height of the ballbar cup is 60 mm;

[0068] S42: In mode 2, input the NC code similar to mode 1 to 1 Place it precisely on the axis of the A-axis, then install the fixture on the C-axis rotary table and 2 Place the ball O on the spindle side on the fixture. 1 Move to the position (180,0,500) in the machine tool coordinate system, and then move the ball O on the worktable side 2 Installed to the workpiece coordinate system (60,0,30), which is on the axis of the A axis;

[0069] Figure 5 Shown is a simple example NC code that can be used to position the spindle in line with the C-axis axis.

[0070] S5: Procedure for measuring rotation axis errors using a ballbar:

[0071] S51: Figure 6The figure shows mode 1. In mode 1, the A-axis and other translation axes remain stationary, and the C-axis is rotated from 0° to 360° while the ballbar data is collected. Since the ball O1 is on the rotation axis of the C-axis, the ball O1 remains stationary during the entire measurement process, while the ball O2 rotates around the axis.

[0072] S52: Figure 7 The figure shows mode 2. In mode 2, the C-axis and the translation axis are kept stationary, and the A-axis is rotated from -45° to +45°, while the ballbar data is collected. 1 On the axis of A, so when A rotates, the ball remains stationary, while ball O 2 The movement trajectory of Figure 7 As shown by the dotted line in;

[0073] S6: Calculate the eight PIGEs of the A and C axes of the five-axis machine tool: Mode 1 is that the C axis rotates one circle from 0° to 360°. When θ=π / 2, π, 3π / 2 and 2π, record the ballbar readings respectively, which are recorded as L 1 , L 2 , L 3 and L 4 ; Mode 2 is when the A axis rotates from -45° to +45°. When θ=0, π / 4, and -π / 4, the ballbar readings are recorded respectively and recorded as L 5 , L 6 and L 7 ; The 8-term PIGE can be obtained by solving the system of equations:

[0074] S61: As shown in the following formula, from L 1 , L 2 , L 3 and L 4 Solve the equation for δ zAY :

[0075]

[0076] S62: As shown in the following formula, β AY From L 5 , L 6 and L 7 From the equation we get:

[0077] L 6 2 -L 7 2 =62400sin(γ AY )·sin45°+360δ yAY ·sin45° (2)

[0078]

[0079] S63: The δ obtained in S61 and S62 is zAY and β AY Substitute into L 4 and L 5 , we can solve for β CA and δ xAY :

[0080]

[0081] S64: As shown in the following formula, from L 1 and L 3 We can get α AY , δ yCA and δ yAY The mathematical relationship between:

[0082]

[0083] S65: α AY , δ xAY , β AY , δ zAY and β CA Solving δ by the least squares method yCA and δ yAY , then solve α from equation (6) AY ;

[0084] S66: δ yAY Substituting into equation (2), we can solve for γ AY :

[0085]

[0086] In a preferred embodiment, because the PDGEs and PIGEs of the rotating axis can be measured by a ballbar, the present invention mainly describes the measurement method of the PIGEs of the rotating axis. Currently in the international academic and industrial circles, there are two definition methods for the PIGEs error of the rotating axis, namely "absolute expression" and "relative expression". The present invention adopts the definition method of "relative expression".

[0087] In S3, α AY β is the angular error of the A-axis relative to the Y-axis of the machine tool about the X-axis; AY and γ AY are the angular errors of the A-axis relative to the Y-axis of the machine tool about the Y-axis and the Z-axis respectively; β CA is the angular error of the C axis relative to the A axis about the Y axis; δ xAY , δ yAY and δ zAY are the position errors of the A-axis relative to the Y-axis of the machine tool in the X, Y, and Z directions respectively; δ yCAis the position error of the C axis relative to the A axis in the Y direction; Figure 3 For the five-axis machine tool shown, the Y-axis coordinate system coincides with the machine tool coordinate system, so the subscript "AY" of the above error actually represents the A-axis relative to the machine tool coordinate system, that is, the above "relative to the machine tool Y-axis" can be understood as "relative to the machine tool."

[0088] In a preferred embodiment, in S42, the operation process of the first mode 2 is similar to that of the first mode, except that after the spindle is positioned on the axis of the A-axis, the ballbar cannot be installed immediately, but the spindle must be translated upward for a distance, which is the distance of the ballbar. 1 The radius of the ball and the length of the ball cup are the sum of the radius of the ball and the length of the ball cup, so as to ensure that the ball O 1 The center of the sphere is located on the axis of the A axis.

[0089] Example

[0090] This implementation case is Figure 8 The machine is operated on a Quaser five-axis machine tool shown in the figure. The maximum spindle speed is 24000r / min and the CNC controller is Heidenhain530. Fig. 9 The technical route shown is used to identify the 8 PIGEs of its rotating axis.

[0091] The two measurement modes of the measurement method of the present invention are repeated to measure and record data, and the average value is taken after processing multiple sets of data sets. Finally, α is obtained. AY , β AY , γ AY , β CA , δ xAY , δ yAY , δ zAY and δ yCA The deviation values ​​are -6.3", -6.6", -18.1", 11.9", -15μm, -7μm, 12.5μm and 5.5μm respectively. The α measured by the rotation axis error measurement method using the gauge block and micrometer is AY , β AY , γ AY , β CA , δ xAY , δ yAY , δ zAY and δ yCA The deviation values ​​are -8.6″, -7.9″, -24.1″, 15.6″, -20μm, -9μm, 17μm and 7μm respectively. By comparison, it can be found that the measured deviation values ​​are significantly reduced, so it can be proved that this method can greatly reduce the installation error of the ballbar.

[0092] From the above description, it can be seen that the above embodiments of the present invention achieve the following technical effects: the ballbar installation method is improved. In order to eliminate the precision deviation of the micrometer and the position error caused by the contact between the tool tip and the gauge block, a reasonable machine tool coordinate system is first established. Then, on this basis, the spindle is positioned on the axis of the C-axis and the A-axis respectively by inputting the NC code. Finally, the ballbar is accurately installed, which can greatly reduce the error caused by the installation of the ballbar and make the measured rotation axis PIGEs result more accurate. Moreover, it does not require the personnel operating the machine tool to have strong professional ability. It only needs to call out the NC code from the code library. The version control system (such as Git) can also be used to track and manage the modification history of the NC code, which is very convenient to operate.

[0093] Those skilled in the art should understand that the discussion of any of the above embodiments is merely illustrative and is not intended to imply that the scope of the present invention (including the claims) is limited to these examples. Under the concept of the present invention, the technical features in the above embodiments or different embodiments may be combined, the steps may be implemented in any order, and there are many other variations of the different aspects of the present invention as described above, which are not provided in detail for the sake of simplicity.

[0094] The present invention is intended to cover all such substitutions, modifications and variations that fall within the broad scope of the claims. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for measuring the rotation axis error of a five-axis machine tool based on a ballbar, characterized in that: The specific steps include: S1: Establish the following coordinate systems for the five-axis machine tool: establish the C-axis coordinate system (CCS) at the center of the rotary table; establish the A-axis coordinate system (ACS) at the intersection of the A-axis and C-axis axes; establish the Z-axis coordinate system (ZCS) at the spindle head and directly above the CCS; The Y-axis Coordinate System (YCS) is established on the Y axis and is located directly below the CCS. In addition, to facilitate CNC programming, the workpiece coordinate system (WCS) is made to coincide with the CCS, and the machine coordinate system (MCS) is made to coincide with the YCS. All of the above coordinate systems are located on the same axis. S2: Some preparation work needs to be done before measurement: the ambient temperature is controlled at about 20℃, and since the ballbar test does not require the machine tool to move violently, the influence of thermal error can be ignored; S3: Identify the eight PIGEs of the A-axis and C-axis of the five-axis machine tool. The eight PIGEs include α AY , β AY , γ AY , β CA , δ xAY , δ yAY , δ zAY and δ yCA ,The measurement process is divided into two modes. In mode 1, only the C axis rotates during the measurement process, and in mode 2, only the A axis rotates; S4: Install the ballbar: The high-precision mounting ball needs to be accurately placed on the axis of the A-axis and C-axis to minimize the installation error of the ballbar. S41: In mode 1, firstly, each translation axis and rotation axis is moved to the initial position in the established coordinate system by inputting NC code. It should be noted that the Z axis is the spindle of the machine tool at this time; then the spindle is positioned to a position colinear with the C axis, ball O1 is accurately placed on the spindle and ball O2 is placed on the rotary table; ball O1 on the spindle side is moved to the position (0,0,640) in the machine tool coordinate system, and ball O2 on the table side is installed to (150,0,60) in the workpiece coordinate system. The height of the ballbar cup is 60 mm; S42: In mode 2, input the NC code similar to mode 1, place ball O1 precisely on the axis of A-axis, then install the fixture on the C-axis rotary table, and place ball O2 on the fixture, move ball O1 on the spindle side to the position (180,0,500) in the machine tool coordinate system, and then install ball O2 on the table side to (60,0,30) in the workpiece coordinate system, which is on the axis of A-axis; S5: Procedure for measuring rotation axis errors using a ballbar: S51: In mode 1, the A-axis and other translational axes remain stationary, the C-axis is rotated from 0° to 360°, and ballbar data is collected simultaneously; S52: In mode 2, keep the C-axis and the translation axis stationary, rotate the A-axis from -45° to +45°, and collect ballbar data at the same time; S6: Calculate the eight PIGEs of the A-axis and C-axis of the five-axis machine tool: Mode 1 is that the C-axis rotates one circle from 0° to 360°, and when θ=π / 2, π, 3π / 2 and 2π, the ballbar readings are recorded respectively, which are recorded as L1, L2, L3 and L4; Mode 2 is that the A-axis rotates from -45° to +45°, and when θ=0, π / 4, -π / 4, the ballbar readings are recorded respectively, which are recorded as L5, L6 and L7. The eight PIGEs can be obtained by solving the equation group: S61: As shown below, find δ from the equations for L1, L2, L3 and L4 zAY : S62: As shown in the following formula, β AY It can be obtained from the L5, L6 and L7 equations: <h2 style=";text-align:left;direction:ltr">L6<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> -L7<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> =62400sin(γ<h2 style=";text-align:left;direction:ltr"> AY <h2 style=";text-align:left;direction:ltr"> )·sin45°+360δ<h2 style=";text-align:left;direction:ltr"> yAY <h2 style=";text-align:left;direction:ltr"> sin45° (2) S63: The δ obtained in S61 and S62 is zAY and β AY Substituting into L4 and L5, we can solve for β CA and δ xAY : S64: As shown in the following formula, α can be obtained from L1 and L3 AY , δ yCA and δ yAY The mathematical relationship between: S65: α AY , δ xAY , β AY , δ zAY and β CA Solving δ by the least squares method yCA and δ yAY , then solve α from equation (6) AY ; S66: δ yAY Substituting into equation (2), we can solve for γ AY :

2. The method for measuring the rotation axis error of a five-axis machine tool based on a ballbar according to claim 1, characterized in that: In S3, α AY β is the angular error of the A-axis relative to the Y-axis of the machine tool about the X-axis; AY and γ AY are the angular errors of the A-axis relative to the Y-axis of the machine tool about the Y-axis and the Z-axis respectively; β CA is the angular error of the C axis relative to the A axis about the Y axis; δ xAY , δ yAY and δ zAY are the position errors of the A-axis relative to the Y-axis of the machine tool in the X, Y, and Z directions respectively; δ yCA is the position error of the C-axis relative to the A-axis in the Y direction.

3. The method for measuring the rotation axis error of a five-axis machine tool based on a ballbar according to claim 2, characterized in that: For five-axis machine tools, the Y-axis coordinate system coincides with the machine tool coordinate system, so the subscript "AY" in the above error actually indicates that the A-axis is relative to the machine tool coordinate system, that is, the above "relative to the machine tool Y-axis" can be understood as "relative to the machine tool".

4. The method for measuring the rotation axis error of a five-axis machine tool based on a ballbar according to claim 1, characterized in that: In S42, the operation process at the beginning of Mode 2 is similar to that of Mode 1, except that the ballbar cannot be installed immediately after the spindle is positioned on the axis of the A-axis. Instead, the spindle must be translated upward for a distance that is the sum of the radius of the ball O1 and the length of the ball cup, so as to ensure that the center of the ball O1 is located on the axis of the A-axis.

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