CN113478272B - Full-working-space thermal error measuring method of five-axis numerical control machine tool based on R-test measuring instrument - Google Patents

Abstract

The invention relates to the field of thermal error measurement of five-axis CNC machine tools, and discloses a method for measuring thermal errors in the entire working space of a five-axis CNC machine tool based on an R-test measuring instrument. The R-test measuring instrument is configured in a tool magazine of a five-axis CNC machine tool , arrange the standard balls on the machine tool table and number the standard balls; control the spindle of the machine tool to drive the ‑test measuring instrument to measure the center coordinates of each standard ball in turn, and obtain the first batch of center coordinate data as the reference center Coordinate data; repeat the following steps until the amount of data obtained meets the requirements: switch the R-test measuring instrument and the tool through the tool change system, and run the five-axis machine tool to heat when switching to the tool; when switching to the R-test measuring instrument, The center coordinates of each standard sphere are measured in turn to obtain the center coordinate data; the thermal error is calculated according to the obtained center coordinate data. The invention breaks through the limitation that the R-test measuring instrument can only be applied to the thermal error measurement of the local working space, and expands the application of the R-test measuring instrument in the thermal error measurement of the full working space of the five-axis numerical control machine tool.

Description

Thermal Error Measurement of Full Working Space of Five-axis CNC Machine Tool Based on R-test Measuring Instrument method

technical field

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

Background technique

CNC machine tools are known as the "industrial mother machine" of the equipment manufacturing industry, and their development quality is an important indicator to measure the level of a country's equipment manufacturing industry. The thermal error caused by temperature accounts for 40-70% of the total error of machine tool processing. The evaluation of the thermal error performance of CNC machine tools is one of the indispensable core technologies of high-end CNC equipment.

Thermal characteristic measurement technology is very important in the field of machine tool research. At present, the "five-point method" proposed by the international standard "General Rules for Machine Tool Inspection Part 3: Determination of Thermal Effects" (ISO 230-3:2001 IDT) is used to measure the thermal error of machine tools . However, this method is mainly for single-point measurement of the working space of the three-axis CNC machining center, which cannot reflect the variation of thermal errors in the entire machine tool working space, and the five-axis machine tool has two more rotation axes than the three-axis machine tool. The rotation and swing motion of the table or spindle will interfere with the "five-point method" measurement, so it is not suitable for the thermal error measurement of the entire working space of the five-axis CNC machine tool.

The R-test measuring instrument is a ball center measuring device, including a measuring base and three displacement sensors. There is a certain arrangement between the three displacement sensors, and the three displacement sensors are used to sense the coordinates of the center of the standard ball.

At present, the R-test measuring instrument is generally installed on the workbench of the five-axis machine tool, and the standard ball is installed on the spindle to measure the thermal error of the five-axis machine tool. Due to the limited measurement range of the R-test measuring instrument, a single R-test The measuring instrument can only be applied to the thermal error measurement of the local working space of the five-axis machine tool. It is not only costly to install multiple R-test measuring instruments, but also it is difficult to arrange multiple R-test measuring instruments on the table of a five-axis machine tool due to their large size and wired connections.

Contents of the invention

In view of the deficiencies in the prior art above, the present invention provides a method for measuring the thermal error of the full working space of a five-axis CNC machine tool based on an R-test measuring instrument, and solves how to use the R-test measuring instrument to realize the thermal error of the full working space of a five-axis CNC machine tool Measurement technical issues.

In order to solve the above technical problems, the present invention adopts the following technical scheme: a method for measuring thermal error in the full working space of a five-axis CNC machine tool based on an R-test measuring instrument, comprising the following steps:

Configure the R-test measuring instrument in the tool magazine of the five-axis CNC machine tool, so that the R-test measuring instrument and the tool can be switched through the tool change system; and install the R-test measuring instrument on the machine tool spindle in the way of installing the tool superior;

Arrange standard balls on the machine tool table and number the standard balls: install a central support in the center of the machine tool work table, and evenly distribute several edge supports around the central support; the central support is installed through connecting rods parallel to the machine tool table surface Standard spheres, install multi-layer central standard spheres from top to bottom on the central bracket, and the connecting rods of the upper and lower adjacent central standard spheres are parallel to each other; each layer of central standard spheres is distributed in a ring, and the ring distribution range of the central standard spheres is from gradually increases from top to bottom; the edge bracket is installed with standard balls through connecting rods parallel to the machine table, and multi-layer edge standard balls are installed from top to bottom on each edge bracket, and the upper and lower adjacent edge standard balls The connecting rods are parallel to each other; the edge standard balls of the same height on each edge support form a ring distribution around the central support; the edge standard balls of any layer are not of the same height as the central standard balls of any layer;

Control the spindle of the machine tool to drive the R-test measuring instrument to measure the center coordinates of each standard ball in turn, and obtain the first batch of center coordinate data as the reference center coordinate data;

Repeat the following steps until the amount of data obtained meets the requirements: switch the R-test measuring instrument and the tool through the tool change system, and run the five-axis machine tool to heat when switching to the tool; when switching to the R-test measuring instrument, measure each The coordinates of the center of a standard sphere are obtained to obtain the coordinate data of the center of the sphere;

Calculate the thermal error based on the acquired coordinate data of the center of the sphere.

其中，ΔZ_i表示第i个标准球在其所在工作空间位置上沿Z轴方向的热误差；/>

表示第i标准球的Z轴参考坐标，即第i标准球的第一批次Z轴坐标；/>

表示第i个标准球的第n批次Z轴坐标。Further, the axial thermal error of the Z axis is:

Among them, ΔZ _i represents the thermal error along the Z-axis direction of the i-th standard sphere at its position in the workspace;/>

Indicates the Z-axis reference coordinates of the i-th standard sphere, that is, the first batch of Z-axis coordinates of the i-th standard sphere;/>

Indicates the Z-axis coordinates of the nth batch of the i-th standard sphere.

其中，ΔX_i表示在第i个标准球所在的工作空间位置上沿X轴方向的热误差；/>

表示第i标准球的X轴参考坐标，即第i标准球的第一批次X轴坐标；/>

表示第i个标准球的第n批次X轴坐标。Further, the axial thermal error of the X-axis is:

Among them, ΔX _i represents the thermal error along the X-axis direction at the position of the working space where the i-th standard sphere is located; />

Indicates the X-axis reference coordinates of the i-th standard sphere, that is, the first batch of X-axis coordinates of the i-th standard sphere;/>

Indicates the X-axis coordinates of the nth batch of the i-th standard sphere.

其中，ΔY_i表示在第i个标准球所在的工作空间位置上沿Y轴方向的热误差；/>

表示第i标准球的Y轴参考坐标，即第i标准球的第一批次Y轴坐标；/>

表示第i个标准球的第n批次Y轴坐标。Further, the axial thermal error of the Y axis is:

Among them, ΔY _i represents the thermal error along the Y-axis direction at the position of the working space where the i-th standard sphere is located; />

Indicates the Y-axis reference coordinate of the i-th standard sphere, that is, the first batch of Y-axis coordinates of the i-th standard sphere;/>

Indicates the Y-axis coordinates of the nth batch of the i-th standard sphere.

Further, the angular thermal error generated by rotating around the Y axis is:

表示在第i个标准球所在的工作空间位置上的绕Y轴旋转产生的角度热误差，ΔX_i表示在第i个标准球所在的工作空间位置上沿X轴方向的热误差；ΔX_j表示在第j个标准球所在的工作空间位置上沿X轴方向的热误差，且第j个标准球的连杆平行于第i个标准球的连杆。in,

Indicates the angular thermal error generated by the rotation around the Y-axis at the position of the i-th standard sphere in the work space, ΔX _i represents the thermal error along the X-axis direction at the position of the i-th standard sphere in the work space; ΔX _j represents The thermal error along the X-axis direction at the position of the working space where the j-th standard sphere is located, and the connecting rod of the j-th standard sphere is parallel to the connecting rod of the i-th standard sphere.

Further, the angular thermal error generated by rotating around the X axis is:

Among them, ΔaX _i represents the angular thermal error generated by the rotation around the Y-axis at the position of the work space where the i-th standard sphere is located, and ΔX _i represents the thermal error along the Y-axis direction at the position of the work space where the i-th standard sphere is located ; ΔX _j represents the thermal error along the Y-axis direction at the position of the working space where the j-th standard sphere is located, and the connecting rod of the j-th standard sphere is parallel to the connecting rod of the i-th standard sphere.

Further, the central support includes a base and a rectangular column arranged on the base, the base is fixed on the machine tool table through a pressing device, the cross section of the rectangular column is square, and each layer of central standard balls includes 4 standard The ball is connected to the 4 sides of the rectangular column through connecting rods respectively.

Further, edge brackets are correspondingly arranged on the four extension lines of the diagonals of the rectangular columns to form a circular distribution; the connecting rods of each layer of edge standard balls on each edge bracket are at the diagonals of the rectangular columns. Corresponding extension of the line.

Further, the edge bracket is a stepped bracket that is hollowed out inside, and the edge standard balls of each layer are respectively installed on the facades of the steps of the stepped bracket, and the stepped bracket is fixed on the machine tool by inserting a pressing device inside it. on stage.

Further, the straight line where the connecting rod of any edge standard ball is located and the straight line where the connecting rod of any standard ball is located are straight lines of different planes; each layer of standard balls is measured according to one of the following sampling paths: sampling path a): from outside to inside, And from bottom to top, spiral upward sampling; sampling path b): from inside to outside, and from top to bottom upward, spiral downward sampling.

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

1. The present 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 , so as to give full play to the advantages that the R-test measuring instrument can directly detect the coordinates of the center of the sphere, improve the sampling efficiency, and improve the efficiency of thermal error measurement.

2. The present invention realizes the thermal error sampling of the entire working space of the five-axis CNC machine tool by exchanging the installation position between the R-test measuring instrument and the standard sphere, and at the same time innovatively designs the layout of the standard sphere, which improves the thermal error calculation. data base.

3. The layout of the standard balls in the present invention forms concentric circles covering the plane of the machine tool table in the XY plane, and covers different height ranges in the Z-axis direction through the multi-layer standard balls, thereby covering the entire working space of the machine tool.

4. The calculation of angular thermal error is based on the parallel positional relationship between the upper and lower standard spheres on the same support as the geometric basis. At the same time, the calculation result of axial thermal error is used to simplify the amount of data collection.

5. The straight line where the connecting rod of any edge standard ball is located and the straight line where any standard ball is located are straight lines of different planes, so that when the distribution of standard balls is relatively sparse, it can cover as many different orientations of the machine tool work space as possible. It is relatively sparse, which can well avoid the interference of the R-test measuring instrument during the movement.

6. The sampling path of the present invention is continuous, which can improve sampling efficiency and shorten sampling time.

7. The central support adopts a rectangular column, which is small in size, leaving more space for the central standard ball, so as to facilitate a more comprehensive coverage of the central area of the machine tool workspace; the edge support adopts a ladder-shaped support, with rich spatial levels, making the edge standard The ball can more comprehensively cover the edge area of the machine working space.

Description of drawings

Fig. 1 is a schematic diagram of the overall installation structure in this specific embodiment;

Figure 2 is a partially enlarged view of Figure 1;

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

Detailed ways

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

1) Installation instructions

Configure the R-test measuring instrument in the tool magazine of the five-axis CNC machine tool, so that the R-test measuring instrument and the tool can be switched through the tool change system; and install the R-test measuring instrument on the machine tool spindle in the way of installing the tool superior. The position of the R-test measuring instrument 10 is realized by controlling the movement of the spindle of the machine tool.

Arrange the standard balls on the machine tool workbench 8 and number the standard balls 2 (refer to Figure 3, 2-1 to 2-24): install a central support in the center of the machine tool workbench, and evenly distribute several edge supports around the central support ; Described central support installs the standard ball by the connecting rod parallel to the machine tool table top, installs multi-layer central standard ball from top to bottom on the central support, and the connecting rods of the adjacent central standard balls up and down are parallel to each other; The central standard balls are distributed in a ring shape, and the ring-shaped distribution range of the central standard balls gradually increases from top to bottom; the edge brackets are equipped with standard balls through connecting rods parallel to the worktable of the machine tool, and are mounted on each edge bracket from top to bottom. Multi-layer edge standard balls are installed, and the connecting rods of the upper and lower adjacent edge standard balls are parallel to each other; the edge standard balls of the upper layers on each edge support form a ring distribution around the central support.

In this specific 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 standard ball is located are straight lines of different planes. The straight line where the connecting rod of any edge standard sphere is located and the straight line where the connecting rod of any standard sphere is a straight line of different planes, so that when the distribution of standard spheres is relatively sparse, it can cover as many different orientations of the machine tool workspace as possible, and because the distribution is relatively sparse , which can well avoid the interference of the R-test measuring instrument during the movement.

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

In this specific embodiment, edge brackets are correspondingly arranged on four extension lines of the diagonals of the rectangular columns to form a circular distribution; On the corresponding extension of the diagonal of .

In this specific embodiment, the edge bracket 3 is a stepped bracket hollowed out inside, and the edge standard balls of each layer are respectively installed on the facades of the steps of each step of the stepped bracket, and the stepped bracket is passed through the pressing device inserted into it. Fixed on the machine table.

The central bracket can be cylindrical, prismatic, or even a combination of stepped brackets, and the edge brackets can also be cylindrical and prismatic. The central support and the edge support are provided with threaded holes, the connecting rod is a threaded rod, and the connecting rod is threadedly connected to the central support and the edge support. However, the central bracket adopts a rectangular column, which is smaller in size, leaving more space for the central standard ball to cover the central area of the machine tool work space more comprehensively; the edge bracket adopts a stepped bracket with rich spatial levels, making the edge standard The ball can more comprehensively cover the edge area of the machine working space.

The pressing device comprises a T-shaped bolt 4, a nut 5, a pressing plate 6, and a triangular-toothed pressing plate positioning clip 7, and the pressing device can adopt the prior art, so it is not necessary to repeat them here.

2) Obtain sampling data

并进行记录保存，本具体实施方式中，i＝1，2，3…24，表示24个标准球，其中n＝1，2，3…m，表示测量数据的批次；例如/>

表示为第一个标准球的第一批次球心坐标数据，作为参考球心坐标数据。Measure the center coordinates of each standard sphere according to the sampling path by operating the R-test measuring instrument 10 to obtain the center coordinates of the standard sphere

And carry out record preservation, in this specific embodiment, i=1, 2, 3...24, represent 24 standard spheres, wherein n=1, 2, 3...m, represent the batch of measurement data; For example />

Expressed as the first batch of center coordinate data of the first standard sphere, it is used as the reference center coordinate data.

As shown in Fig. 3, each layer of standard sphere is measured according to one of the following sampling paths: sampling path a): from outside to inside, and from bottom to top, spiral upward sampling; sampling path b): from inside to outside, and Spiral downsampling from top to bottom.

After the first batch of data processing is completed, the spherical center measuring device 10 is replaced in the tool magazine of the machine tool and a tool is taken out, and then the five-axis machine tool is operated according to a predetermined program to make the five-axis machine tool generate heat;

Repeat the following steps until the amount of data obtained meets the requirements: switch the R-test measuring instrument and the tool through the tool change system, and run the five-axis machine tool to heat when switching to the tool; when switching to the R-test measuring instrument, measure each The coordinates of the center of a standard sphere are obtained to obtain the coordinate data of the center of the sphere.

3), data processing

In principle, the thermal error measurement is realized by the relative measurement method, so the thermal error displacement of each measurement point along X, Y, and Z, as well as the angular deviation around X and Y directions can be obtained.

其中，ΔZ_i表示第i个标准球在其所在工作空间位置上沿Z轴方向的热误差；/>

表示第i标准球的Z轴参考坐标，即第i标准球的第一批次Z轴坐标；/>

表示第i个标准球的第n批次Z轴坐标。The axial thermal error of the Z axis is:

Among them, ΔZ _i represents the thermal error along the Z-axis direction of the i-th standard sphere at its position in the workspace;/>

Indicates the Z-axis reference coordinates of the i-th standard sphere, that is, the first batch of Z-axis coordinates of the i-th standard sphere;/>

Indicates the Z-axis coordinates of the nth batch of the i-th standard sphere.

其中，ΔX_i表示在第i个标准球所在的工作空间位置上沿X轴方向的热误差；/>

表示第i标准球的X轴参考坐标，即第i标准球的第一批次X轴坐标；/>

表示第i个标准球的第n批次X轴坐标。The axial thermal error of the X axis is:

Among them, ΔX _i represents the thermal error along the X-axis direction at the position of the working space where the i-th standard sphere is located; />

Indicates the X-axis reference coordinates of the i-th standard sphere, that is, the first batch of X-axis coordinates of the i-th standard sphere;/>

Indicates the X-axis coordinates of the nth batch of the i-th standard sphere.

其中，ΔY_i表示在第i个标准球所在的工作空间位置上沿Y轴方向的热误差；/>

表示第i标准球的Y轴参考坐标，即第i标准球的第一批次Y轴坐标；/>

表示第i个标准球的第n批次Y轴坐标。The axial thermal error of the Y axis is:

Among them, ΔY _i represents the thermal error along the Y-axis direction at the position of the working space where the i-th standard sphere is located; />

Indicates the Y-axis reference coordinate of the i-th standard sphere, that is, the first batch of Y-axis coordinates of the i-th standard sphere;/>

Indicates the Y-axis coordinates of the nth batch of the i-th standard sphere.

The angular thermal error generated by rotating around the Y axis is:

Among them, ΔαY _i represents the angular thermal error caused by the rotation around the Y axis at the position of the i-th standard sphere in the work space, and ΔX _i represents the thermal error along the X-axis direction at the position of the i-th standard sphere in the work space ; ΔX _j represents the thermal error along the X-axis direction at the position of the working space where the j-th standard sphere is located, and the connecting rod of the j-th standard sphere is parallel to the connecting rod of the i-th standard sphere.

The angular thermal error generated by rotating around the X axis is:

Among them, ΔαX _i represents the angular thermal error generated by the rotation around the Y-axis at the position of the work space where the i-th standard sphere is located, and ΔX _i represents the thermal error along the Y-axis direction at the position of the work space where the i-th standard sphere is located ; ΔX _j represents the thermal error along the Y-axis direction at the position of the working space where the j-th standard sphere is located, and the connecting rod of the j-th standard sphere is parallel to the connecting rod of the i-th standard sphere.

The present 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 Give full play to the advantage that the R-test measuring instrument can directly detect the coordinates of the center of the sphere, improve the sampling efficiency, and improve the efficiency of thermal error measurement.

Claims (8)

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 and numbering standard balls on a machine tool workbench: 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 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 respectively connected to 4 side faces of the rectangular upright post through connecting rods; correspondingly arranging edge brackets 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;

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 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.

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 is characterized by comprising the following steps of,the Z-axis axial thermal error is as follows:

wherein, Δ Z _i The 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.

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 3, wherein the X-axis axial thermal error is as follows:

wherein, Δ X _i Representing 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 nth lot X-axis coordinate of the ith standard sphere is represented.

5. 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 Y-axis axial thermal error is as follows: delta Y _i ＝Y _i ⁿ -Y _i ¹ Wherein, Δ Y _i Representing the thermal error along the Y-axis direction on the working space position where the ith standard ball is located; y is _i ¹ 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; y is _i ⁿ The n-th lot Y-axis coordinates of the i-th standard ball are shown.

6. 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 4, wherein the thermal error of the angle generated by the rotation around the Y axis is as follows:

wherein, delta alpha Y _i 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 _i Representing the thermal error along the X-axis direction on the position of the working space where the ith standard ball is located; Δ X _j The thermal error along the X-axis direction at the working space position of the jth standard ball is shown, and the connecting rod of the jth standard ball is parallel to the connecting rod of the ith standard ball.

7. The method for measuring the thermal error of the five-axis numerical control machine tool based on the R-test measuring instrument in the whole working space is characterized in that the thermal error of the angle generated by the rotation around the X axis is as follows:

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

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 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.

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