阅读说明：本技术 基于R-test测量仪的五轴数控机床全工作空间热误差测量方法 (Full-working-space thermal error measuring method of five-axis numerical control machine tool based on R-test measuring instrument ) 是由 苗恩铭 张仁杰 杨勇 江涛 谭人铭 于 2021-07-22 设计创作，主要内容包括：本发明涉及五轴数控机床热误差测量领域,公开了一种基于R-test测量仪的五轴数控机床全工作空间热误差测量方法,将R-test测量仪配置到五轴数控机床的刀库中,在机床工作台上布置标准球并对标准球进行编号；控制机床主轴带动-test测量仪依次测量每个标准球的球心坐标,获得第一批次球心坐标数据,作为参考球心坐标数据；重复以下步骤,直到获取到的数据量满足需求：通过换刀系统切换R-test测量仪与刀具,当切换为刀具时运行五轴机床至发热；当切换为R-test测量仪,依次测量每个标准球的球心坐标,获得球心坐标数据；根据获取到的球心坐标数据计算热误差。本发明突破了R-test测量仪只能适用于局部工作空间的热误差测量的局限,拓展了R-test测量仪在五轴数控机床全工作空间热误差测量中的应用。(The invention relates to the field of thermal error measurement of five-axis numerical control machines, and discloses a method for measuring the thermal error of a whole working space of a five-axis numerical control machine based on an R-test measuring instrument, wherein the R-test measuring instrument is configured in a tool magazine of the five-axis numerical control machine, and a standard ball is arranged on a worktable of the machine and is numbered; controlling a machine tool spindle to drive a test measuring instrument to sequentially measure the spherical center coordinates of each standard ball to obtain first batch of spherical center coordinate data serving as reference spherical center coordinate data; repeating the following steps until the obtained data volume meets the requirement: switching the R-test measuring instrument and the cutter through a cutter changing system, and operating the five-axis machine tool to generate heat when the cutter is switched; when the standard ball is switched to the R-test measuring instrument, the sphere center coordinates of each standard ball are measured in sequence to obtain sphere center coordinate data; and calculating the thermal error according to the acquired sphere center coordinate data. The invention breaks through the limitation that the R-test measuring instrument can only be suitable for measuring the thermal error of the local working space, and expands the application of the R-test measuring instrument in the measurement of the thermal error of the full working space of the five-axis numerical control machine tool.)

1. A five-axis numerical control machine tool full-working-space thermal error measuring method based on an R-test measuring instrument is characterized by comprising the following steps:

the R-test measuring instrument is configured in a tool magazine of a five-axis numerical control machine tool, so that the R-test measuring instrument and a tool can be switched through a tool changing system; and mounting the R-test measuring instrument on a main shaft of the machine tool in a mode of mounting a cutter;

arranging standard balls on a machine tool workbench and numbering the standard balls: a central support is arranged in the center of a machine tool workbench, and a plurality of edge supports are uniformly distributed around the central support; the central support is provided with standard balls through connecting rods parallel to the table top of the machine tool workbench, a plurality of layers of central standard balls are arranged on the central support from top to bottom, and the connecting rods of the upper and lower adjacent central standard balls are parallel to each other; the central standard balls of each layer are distributed annularly, and the annular distribution range of the central standard balls is gradually enlarged from top to bottom; the edge supports are provided with standard balls through connecting rods parallel to the working table of the machine tool, a plurality of layers of edge standard balls are arranged on each edge support from top to bottom, and the connecting rods of the adjacent edge standard balls are parallel to each other; the edge standard balls of the upper equal-height layers of each edge support are distributed in a ring shape around the central support;

controlling a machine tool spindle to drive the R-test measuring instrument to sequentially measure the sphere center coordinate of each standard sphere to obtain first batch of sphere center coordinate data serving as reference sphere center coordinate data;

repeating the following steps until the obtained data volume meets the requirement: switching the R-test measuring instrument and the cutter through a cutter changing system, and operating the five-axis machine tool to generate heat when the cutter is switched; when the standard ball is switched to the R-test measuring instrument, the sphere center coordinates of each standard ball are measured in sequence to obtain sphere center coordinate data;

and calculating the thermal error according to the acquired sphere center coordinate data.

2. The R-test measuring instrument-based thermal error measurement method for the full-working space of the five-axis numerical control machine tool is characterized in that the central support comprises a base and a rectangular upright post arranged on the base, the base is fixed on a machine tool workbench through a pressing device, the cross section of the rectangular upright post is square, each layer of central standard balls comprises 4 standard balls, and the central standard balls are connected to 4 side faces of the rectangular upright post through connecting rods respectively.

3. The method for measuring the thermal error of the full working space of the five-axis numerical control machine tool based on the R-test measuring instrument as claimed in claim 2, wherein edge supports are correspondingly arranged on 4 extension lines of a diagonal line of the rectangular upright column to form an annular distribution; the connecting rods of each layer of edge standard balls on each edge bracket are arranged on corresponding extension lines of diagonals of the rectangular upright posts.

4. The method for measuring the thermal error of the full working space of the five-axis numerical control machine tool based on the R-test measuring instrument as claimed in claim 1, wherein the edge support is a stepped support with a hollow interior, each layer of edge standard balls is respectively installed on the vertical surface of each step of the stepped support, and the stepped support is fixed on a machine tool workbench through a pressing device inserted into the stepped support.

5. The method for measuring the thermal error of the full working space of the five-axis numerical control machine tool based on the R-test measuring instrument as claimed in claim 1, wherein the Z-axis axial thermal error is as follows:wherein, Δ Z_iThe thermal error of the I-th standard ball along the Z-axis direction on the position of the working space is represented;the Z-axis reference coordinate of the ith standard ball is represented, namely the Z-axis coordinate of the first batch of the ith standard ball;the Z-axis coordinate of the nth lot of the ith standard sphere is shown.

6. Five-axis R-test-based measuring instrument according to claim 5The method for measuring the thermal error of the full working space of the numerical control machine is characterized in that the X-axis axial thermal error is as follows:wherein, AX_iRepresenting the thermal error along the X-axis direction on the position of the working space where the I-th standard ball is located;the X-axis reference coordinate of the ith standard ball is represented, namely the X-axis coordinate of the first batch of the ith standard ball;the n-th lot X-axis coordinates of the i-th standard sphere are shown.

7. The method for measuring the thermal error of the full working space of the five-axis numerical control machine tool based on the R-test measuring instrument as claimed in claim 5, wherein the Y-axis axial thermal error is as follows: delta Y_i＝Y_i ⁿ-Y_i ¹Wherein, Δ Y_iRepresenting the thermal error along the Y-axis direction on the working space position where the ith standard ball is located; y is_i ¹The Y-axis reference coordinate of the ith standard ball is represented, namely the Y-axis coordinate of the first batch of the ith standard ball;the n-th lot of Y-axis coordinates of the I-th calibration sphere are shown.

8. The method for measuring the thermal error of the full working space of the five-axis numerical control machine tool based on the R-test measuring instrument as claimed in claim 6, wherein the thermal error of the angle generated by the rotation around the Y axis is as follows:

wherein, Delta alpha Y_iIndicating the work in the ith standard ballAngular thermal error, Δ X, produced by rotation in spatial position about the Y axis_iRepresenting the thermal error along the X-axis direction on the position of the working space where the I-th standard ball is located; Δ X_jAnd the thermal error along the X-axis direction at the position of the working space where the jth standard ball is located is shown, and the connecting rod of the jth standard ball is parallel to the connecting rod of the ith standard ball.

9. The method for measuring the thermal error of the full working space of the five-axis numerical control machine tool based on the R-test measuring instrument as claimed in claim 7, wherein the thermal error of the angle generated by the rotation around the X axis is as follows:

wherein, Delta alpha X_iRepresenting the angular thermal error, Δ X, produced by rotation about the Y-axis at the position of the workspace in which the I-th calibration sphere is located_iRepresenting the thermal error along the Y-axis direction on the working space position where the ith standard ball is located; Δ X_jAnd the thermal error along the Y-axis direction at the position of the working space where the jth standard ball is located is shown, and the connecting rod of the jth standard ball is parallel to the connecting rod of the ith standard ball.

10. The method for measuring the thermal error of the full working space of the five-axis numerical control machine tool based on the R-test measuring instrument as claimed in claim 1, wherein a straight line where the connecting rod of any edge standard ball is located and a straight line where the connecting rod of any edge standard ball is located are coplanar straight lines; the measurements were performed on the standard spheres of each layer in one of the following sampling paths: sampling path a): from outside to inside and from bottom to top, sampling is spirally raised; sampling path b): from inside to outside, and from top to top, the samples were taken spirally down.

Technical Field

The invention relates to the field of thermal error measurement of five-axis numerical control machines.

Background

The development quality of the numerically controlled machine tool is an important index for measuring the level of equipment manufacturing in China, which is called an industrial master machine of the equipment manufacturing industry. The thermal error caused by the temperature accounts for 40-70% of the total errors of the machine tool machining, and the evaluation of the thermal error performance of the numerical control machine tool is one of the indispensable core technologies of high-end numerical control equipment.

The thermal characteristic measurement technology is very important in the field of machine tool research, and currently, the thermal error measurement of the machine tool adopts the international standard part 3 of the machine tool inspection general rule: determination of thermal effects (ISO 230-3: 2001 IDT) "five-point method". However, the method mainly carries out single-point measurement on the working space of the three-axis numerical control machining center, the thermal error change condition on the working space of the whole machine tool cannot be reflected, and the five-axis machine tool has two more rotating shafts compared with the three-axis machine tool, and the rotating and swinging motion of the workbench or the main shaft interferes with the measurement of a five-point method, so that the method is not suitable for the thermal error measurement of the whole working space of the five-axis numerical control machine tool.

The R-test measuring instrument is a sphere center measuring device and comprises a measuring base and three displacement sensors, wherein a certain arrangement mode is arranged among the three displacement sensors, and the three displacement sensors are used for sensing the sphere center position coordinates of a standard sphere.

At present, an R-test measuring instrument is generally arranged on a working table of a five-axis machine tool, a standard ball is arranged on a main shaft to measure the thermal error of the five-axis machine tool, and the single R-test measuring instrument can only be suitable for measuring the thermal error of the local working space of the five-axis machine tool due to the limited measuring range of the R-test measuring instrument. If a plurality of R-test measuring instruments are installed, the cost is high, and the R-test measuring instruments are large in size and are in wired connection, so that the R-test measuring instruments are difficult to arrange on a workbench of a five-axis machine tool.

Disclosure of Invention

Aiming at the defects of the prior art, the invention provides a method for measuring the thermal error of the whole working space of a five-axis numerical control machine tool based on an R-test measuring instrument, and solves the technical problem of how to realize the measurement of the thermal error of the whole working space of the five-axis numerical control machine tool by using the R-test measuring instrument.

In order to solve the technical problems, the invention adopts the following technical scheme: a five-axis numerical control machine tool full-working-space thermal error measuring method based on an R-test measuring instrument comprises the following steps:

the R-test measuring instrument is configured in a tool magazine of a five-axis numerical control machine tool, so that the R-test measuring instrument and a tool can be switched through a tool changing system; and mounting the R-test measuring instrument on a main shaft of the machine tool in a mode of mounting a cutter;

arranging standard balls on a machine tool workbench and numbering the standard balls: a central support is arranged in the center of a machine tool workbench, and a plurality of edge supports are uniformly distributed around the central support; the central support is provided with standard balls through connecting rods parallel to the table top of the machine tool workbench, a plurality of layers of central standard balls are arranged on the central support from top to bottom, and the connecting rods of the upper and lower adjacent central standard balls are parallel to each other; the central standard balls of each layer are distributed annularly, and the annular distribution range of the central standard balls is gradually enlarged from top to bottom; the edge supports are provided with standard balls through connecting rods parallel to the working table of the machine tool, a plurality of layers of edge standard balls are arranged on each edge support from top to bottom, and the connecting rods of the adjacent edge standard balls are parallel to each other; the edge standard balls of the upper equal-height layers of each edge support are distributed in a ring shape around the central support; the standard balls at the edge of any layer are not equal to the standard balls at the center of any layer in height;

controlling a machine tool spindle to drive the R-test measuring instrument to sequentially measure the sphere center coordinate of each standard sphere to obtain first batch of sphere center coordinate data serving as reference sphere center coordinate data;

repeating the following steps until the obtained data volume meets the requirement: switching the R-test measuring instrument and the cutter through a cutter changing system, and operating the five-axis machine tool to generate heat when the cutter is switched; when the standard ball is switched to the R-test measuring instrument, the sphere center coordinates of each standard ball are measured in sequence to obtain sphere center coordinate data;

and calculating the thermal error according to the acquired sphere center coordinate data.

Further, the Z-axis axial thermal error is:wherein, Δ Z_iThe thermal error of the ith standard ball along the Z-axis direction at the position of the working space of the ith standard ball is represented;the Z-axis reference coordinate of the ith standard ball is represented, namely the Z-axis coordinate of the first batch of the ith standard ball;the Z-axis coordinate of the nth lot of the ith standard sphere is shown.

Further, the X-axis axial thermal error is:wherein, Δ X_iRepresenting the thermal error along the X-axis direction on the position of the working space where the ith standard ball is located;the X-axis reference coordinate of the ith standard ball is represented, namely the X-axis coordinate of the first batch of the ith standard ball;the n-th lot X-axis coordinates of the i-th standard sphere are shown.

Further, the Y-axis axial thermal error is:wherein, Delta Y_iRepresenting the thermal error along the Y-axis direction on the working space position where the ith standard ball is located;the Y-axis reference coordinate of the ith standard ball is represented, namely the Y-axis coordinate of the first batch of the ith standard ball;the n-th lot Y-axis coordinates of the i-th standard ball are shown.

Further, the thermal error of the angle generated by the rotation around the Y axis is:

wherein the content of the first and second substances,representing the angular thermal error, Δ X, produced by rotation about the Y axis at the location of the workspace in which the ith calibration sphere is located_iRepresenting the thermal error along the X-axis direction on the position of the working space where the ith standard ball is located; Δ X_jAnd the thermal error along the X-axis direction at the position of the working space where the jth standard ball is located is shown, and the connecting rod of the jth standard ball is parallel to the connecting rod of the ith standard ball.

Further, the angular thermal error generated by rotation about the X-axis is:

wherein, Δ aX_iRepresenting the angular thermal error, Δ X, produced by rotation about the Y axis at the location of the workspace in which the ith calibration sphere is located_iRepresenting the thermal error along the Y-axis direction on the working space position where the ith standard ball is located; Δ X_jAnd the thermal error along the Y-axis direction at the position of the working space where the jth standard ball is located is shown, and the connecting rod of the jth standard ball is parallel to the connecting rod of the ith standard ball.

Further, the central support comprises a base and a rectangular stand column arranged on the base, the base is fixed on a machine tool workbench through a pressing device, the cross section of the rectangular stand column is square, each layer of central standard balls comprises 4 standard balls, and the central standard balls are connected to 4 side faces of the rectangular stand column through connecting rods respectively.

Further, edge brackets are correspondingly arranged on 4 extension lines of the diagonal line of the rectangular upright column to form annular distribution; the connecting rods of each layer of edge standard balls on each edge bracket are arranged on corresponding extension lines of diagonals of the rectangular upright posts.

Furthermore, the edge support is a step-shaped support with a hollow interior, the edge standard balls of each layer are respectively installed on the vertical face of each step of the step-shaped support, and the step-shaped support is fixed on a machine tool workbench through a pressing device inserted into the step-shaped support.

Furthermore, the straight line where the connecting rod of any edge standard ball is located and the straight line where the connecting rod of any edge standard ball is located are non-coplanar straight lines; the measurements were performed on the standard spheres of each layer in one of the following sampling paths: sampling path a): from outside to inside and from bottom to top, sampling is spirally raised; sampling path b): from inside to outside, and from top to top, the samples were taken spirally down.

Compared with the prior art, the invention has the following beneficial effects:

1. the invention breaks through the limitation that the R-test measuring instrument in the prior art can only be applied to the thermal error measurement of the local working space of the five-axis machine tool, and expands the application of the R-test measuring instrument in the thermal error measurement of the whole working space, thereby fully exerting the advantage that the R-test measuring instrument can directly detect the coordinates of the sphere center, improving the sampling efficiency and improving the thermal error measurement efficiency.

2. The invention realizes the sampling of the thermal error of the five-axis numerical control machine tool in the whole working space by exchanging the mounting position between the R-test measuring instrument and the standard ball and simultaneously carrying out innovative design on the layout of the standard ball, thereby improving the data base for the thermal error calculation.

3. According to the invention, the standard balls are distributed in an XY plane to form concentric circles covering the plane of the workbench of the machine tool, and the multilayer standard balls cover different height ranges in the Z-axis direction, so that the whole working space of the machine tool is covered.

4. The calculation of the angle thermal error takes the parallel position relation between an upper standard ball and a lower standard ball on the same bracket as a geometric basis, and meanwhile, the calculation result of the axial thermal error is utilized, so that the data acquisition quantity is simplified.

5. The straight line of the connecting rod of any edge standard ball and the straight line of the connecting rod of any edge standard ball are non-coplanar straight lines, so that the standard balls cover different directions of a working space of a machine tool as much as possible under the condition of sparse distribution, and meanwhile, the R-test measuring instrument can be well prevented from interfering in the movement process due to sparse distribution.

6. The invention has continuous sampling path, can improve the sampling efficiency and shorten the sampling time.

7. The central support adopts a rectangular upright post, has smaller volume, and reserves more space for a central standard ball so as to be beneficial to more comprehensively covering the central area of the working space of the machine tool; the edge support adopts a stepped support, and the space hierarchy is rich, so that the edge standard ball can more comprehensively cover the edge area of the working space of the machine tool.

Drawings

FIG. 1 is a schematic view of the overall mounting structure in this embodiment;

FIG. 2 is an enlarged view of a portion of FIG. 1;

fig. 3 is a schematic diagram of a sampling path in this embodiment.

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings and preferred embodiments.

One), installation instructions

The R-test measuring instrument is configured in a tool magazine of a five-axis numerical control machine tool, so that the R-test measuring instrument and a tool can be switched through a tool changing system; and the R-test measuring instrument is installed on the main shaft of the machine tool in a mode of installing the tool. The positioning of the R-test meter 10 is achieved by controlling the movement of the machine tool spindle.

The standard balls are arranged on the machine table 8 and the standard balls 2 are numbered (refer to 2-1 to 2-24 in fig. 3): a central support is arranged in the center of a machine tool workbench, and a plurality of edge supports are uniformly distributed around the central support; the central support is provided with standard balls through connecting rods parallel to the table top of the machine tool workbench, a plurality of layers of central standard balls are arranged on the central support from top to bottom, and the connecting rods of the upper and lower adjacent central standard balls are parallel to each other; the central standard balls of each layer are distributed annularly, and the annular distribution range of the central standard balls is gradually enlarged from top to bottom; the edge supports are provided with standard balls through connecting rods parallel to the working table of the machine tool, a plurality of layers of edge standard balls are arranged on each edge support from top to bottom, and the connecting rods of the adjacent edge standard balls are parallel to each other; the edge standard balls of the higher level on each edge support form a ring distribution around the central support.

In this embodiment, the straight line where the connecting rod of any edge standard ball is located and the straight line where the connecting rod of any edge standard ball is located are coplanar straight lines. The straight line of the connecting rod of any edge standard ball and the straight line of the connecting rod of any edge standard ball are non-coplanar straight lines, so that the standard balls cover different directions of a working space of a machine tool as much as possible under the condition of sparse distribution, and meanwhile, the R-test measuring instrument can be well prevented from interfering in the movement process due to sparse distribution.

In this specific embodiment, the central support 9 includes a base and a rectangular column disposed on the base, the base is fixed on the machine tool workbench through a pressing device, the cross section of the rectangular column is square, each layer of central standard balls includes 4 standard balls, and the central standard balls are connected to 4 sides of the rectangular column through connecting rods respectively.

In the specific embodiment, the edge brackets are correspondingly arranged on 4 extension lines of the diagonal line of the rectangular upright column to form annular distribution; the connecting rods of each layer of edge standard balls on each edge bracket are arranged on corresponding extension lines of diagonals of the rectangular upright posts.

In this embodiment, the edge support 3 is a stepped support with a hollow interior, the edge standard balls of each layer are respectively installed on the vertical surfaces of the steps of the stepped support, and the stepped support is fixed on the machine tool workbench through a pressing device inserted into the stepped support.

The central support can be cylindrical or prismatic, even the combination of stepped supports, and the edge supports can also be cylindrical or prismatic. Threaded holes are formed in the central support and the edge support, the connecting rod is a threaded rod, and the connecting rod is in threaded connection with the central support and the edge support. However, the central support adopts a rectangular upright post, has smaller volume, and leaves more space for the central standard ball, so as to be beneficial to more comprehensively covering the central area of the working space of the machine tool; the edge support adopts a stepped support, and the space hierarchy is rich, so that the edge standard ball can more comprehensively cover the edge area of the working space of the machine tool.

The pressing device comprises a T-shaped bolt 4, a nut 5, a pressing plate 6 and a triangular toothed pressing plate positioning clamp 7, and the pressing device can be realized by adopting the prior art, and the details are not needed to be repeated.

Two), acquiring sampling data

The center coordinates of each standard ball are measured by operating the R-test measuring instrument 10 according to the sampling path to obtain the center coordinates of the standard ballsRecording and storing are performed, in the embodiment, i is 1, 2, 3 … 24, and represents 24 standard balls, wherein n is 1, 2, 3 … m, and represents a batch of measurement data; for exampleThe first lot of center coordinate data expressed as the first standard ball is used as the reference center coordinate data.

Referring to fig. 3, measurements were taken on the respective layers of standard spheres in one of the following sampling paths: sampling path a): from outside to inside and from bottom to top, sampling is spirally raised; sampling path b): from inside to outside, and from top to top, the samples were taken spirally down.

After the first batch of data is processed, the sphere center measuring device 10 is replaced into a tool magazine of the machine tool, a tool is taken out, and then the five-axis machine tool is operated according to a preset program to heat the five-axis machine tool;

repeating the following steps until the obtained data volume meets the requirement: switching the R-test measuring instrument and the cutter through a cutter changing system, and operating the five-axis machine tool to generate heat when the cutter is switched; and when the standard ball is switched to the R-test measuring instrument, sequentially measuring the sphere center coordinates of each standard ball to obtain the sphere center coordinate data.

Three), data processing

Thermal error measurement is realized in principle by relative measurement methods, so that thermal error displacements along X, Y and Z and angular deviations around X and Y directions of each measurement point can be obtained.

The Z-axis axial thermal error is as follows:wherein, Δ Z_iThe thermal error of the ith standard ball along the Z-axis direction at the position of the working space of the ith standard ball is represented;the Z-axis reference coordinate of the ith standard ball is represented, namely the Z-axis coordinate of the first batch of the ith standard ball;the Z-axis coordinate of the nth lot of the ith standard sphere is shown.

The X-axis axial thermal error is:wherein, Δ X_iRepresenting the thermal error along the X-axis direction on the position of the working space where the ith standard ball is located;the X-axis reference coordinate of the ith standard ball is represented, namely the X-axis coordinate of the first batch of the ith standard ball;the n-th lot X-axis coordinates of the i-th standard sphere are shown.

The Y-axis axial thermal error is:wherein, Delta Y_iRepresenting the thermal error along the Y-axis direction on the working space position where the ith standard ball is located;the Y-axis reference coordinate of the ith standard ball is represented, namely the Y-axis coordinate of the first batch of the ith standard ball;the n-th lot Y-axis coordinates of the i-th standard ball are shown.

The angular thermal error generated by rotation about the Y-axis is:

wherein, Delta alpha Y_iRepresenting the angular thermal error, Δ X, produced by rotation about the Y axis at the location of the workspace in which the ith calibration sphere is located_iRepresenting the thermal error along the X-axis direction on the position of the working space where the ith standard ball is located; Δ X_jAnd the thermal error along the X-axis direction at the position of the working space where the jth standard ball is located is shown, and the connecting rod of the jth standard ball is parallel to the connecting rod of the ith standard ball.

The angular thermal error produced by rotation about the X-axis is:

wherein, Delta alpha X_iRepresenting the angular thermal error, Δ X, produced by rotation about the Y axis at the location of the workspace in which the ith calibration sphere is located_iRepresenting the thermal error along the Y-axis direction on the working space position where the ith standard ball is located; Δ X_jAnd the thermal error along the Y-axis direction at the position of the working space where the jth standard ball is located is shown, and the connecting rod of the jth standard ball is parallel to the connecting rod of the ith standard ball.

The invention breaks through the limitation that the R-test measuring instrument in the prior art can only be applied to the thermal error measurement of the local working space of the five-axis machine tool, and expands the application of the R-test measuring instrument in the thermal error measurement of the whole working space, thereby fully exerting the advantage that the R-test measuring instrument can directly detect the coordinates of the sphere center, improving the sampling efficiency and improving the thermal error measurement efficiency.