Five-degree-of-freedom geometric error automatic measuring device and method for machine tool turntable

Abstract

The invention discloses a five-degree-of-freedom geometric error automatic measuring device for a machine tool turntable. The five-degree-of-freedom geometric error automatic measuring device comprises an upper computer, a bracket, a measuring core rod, a cutter handle, a standard ball and five displacement sensors, the standard ball is fixed at the upper end of the testing core rod, the measuring core rod is selectively mounted at the central axis of a machine tool turntable, the cutter handle is mounted at the mounting position of a spindle cutter handle of a machine tool, the bracket is fixed outside the cutter handle, one displacement sensor is vertically arranged, the measuring end of the displacement sensor is in contact with the standard ball, and the other four displacement sensors are divided into two pairs which are arranged up and down; the measuring ends of one pair are in contact with the measuring core rod in the X direction, and the measuring ends of the other pair are in contact with the testing core rod in the Z direction; and the five displacement sensors are linked to an upper computer through a sensor amplifier and a communication unit. The problems that errors of the machine tool rotary table cannot be rapidly measured and a numerical control machine tool needs to be manually operated many times in the measurement process in the prior art are solved.

Description

Technical Field

[0001] This invention belongs to the field of CNC machine tool equipment technology, specifically relating to an automatic measurement device for five-degree-of-freedom geometric errors of machine tool rotary tables, and also to an automatic measurement method for five-degree-of-freedom geometric errors of machine tool rotary tables. Background Technology

[0002] For machine tools, spatial geometric errors are the result of the combined effects of six geometric errors each for linear and rotary axes, perpendicularity error between linear axes, and parallelism error between the worktable and its T-slot and the linear axes. Improving the machining accuracy of machine tools requires precise compensation for these spatial geometric errors. For the six geometric errors of linear axes, perpendicularity error, and parallelism error, there are already relatively mature measurement solutions and engineering products. For the six geometric errors of rotary axes (such as...) Figure 5 As shown in the diagram, the angular positioning error can be measured using mature measurement solutions and commercially available tools such as circular grating encoders and laser interferometers. However, while other geometric errors can be measured using instruments such as laser interferometers, eddy current sensors, and dial indicators (for translational errors, including two radial runouts and one axial runout), these individual sensors can only measure a single error and cannot evaluate multiple errors in a single measurement. Furthermore, the errors measured by the above methods are position-dependent and do not accurately reflect the actual error of the rotating shaft.

[0003] In addition, there are devices that use high-precision capacitive displacement sensors for non-contact measurement of rotary axis errors (such as those from Lion). However, this measurement solution is mainly designed for high-speed, high-precision spindles and is relatively expensive. For low-speed, medium-precision applications on horizontal five-axis machine tool rotary tables, low-cost contact displacement sensors are more suitable.

[0004] Furthermore, the aforementioned spindle error measurement device is mainly used for measuring and evaluating the accuracy error of the spindle, but it does not communicate with the CNC system, and its measurement process requires manual control of the spindle movement. This technology, through the design of a reliable measuring device and a corresponding automatic measurement program, not only achieves communication with the CNC system, thus enabling control of the turntable rotation to complete turntable error measurement without excessive manual operation, but also achieves the separation of the five geometric errors of the turntable. Summary of the Invention

[0005] The first objective of this invention is to provide an automatic measurement device for five-degree-of-freedom geometric errors of machine tool rotary tables, which solves the problem that existing technologies cannot quickly measure the errors of machine tool rotary tables and that the measurement process requires multiple manual operations of the CNC machine tool.

[0006] To achieve the above objectives, the technical solution adopted in this invention is: a five-degree-of-freedom geometric error automatic measurement device for a machine tool rotary table, comprising a host computer, a support, a measuring mandrel, a tool holder, a standard ball, and five displacement sensors; the standard ball is fixed to the upper end of the measuring mandrel, the measuring mandrel is optionally mounted at the central axis of the machine tool rotary table, the tool holder is installed at the spindle tool holder mounting position of the machine tool, the support is fixed outside the tool holder, one displacement sensor is arranged vertically with its measuring end in contact with the standard ball, and the other four displacement sensors are divided into two pairs, each pair arranged vertically, one pair with its measuring end in contact with the measuring mandrel in the X direction, and the other pair with its measuring end in contact with the measuring mandrel in the Z direction; the five displacement sensors are connected to the host computer through a sensor amplifier and a communication unit.

[0007] As a preferred embodiment of the present invention, a pressure plate is provided at the lower end of the measuring mandrel, and the pressure plate is fixedly connected to the turntable of the machine tool.

[0008] As a preferred embodiment of the present invention, the pressure plate is fixedly connected to the T-slot in the turntable by a T-nut.

[0009] As a preferred embodiment of the present invention, the bracket includes a spindle end connector and a sensor mounting fixture; the spindle end connector is fixedly connected to the tool holder, the sensor mounting fixture is fixed below the spindle end connector, and five displacement sensors are mounted on the sensor mounting fixture.

[0010] As a preferred embodiment of the present invention, the bracket further includes reinforcing ribs, which are fixed between the spindle end connector and the sensor mounting fixture.

[0011] As a preferred embodiment of the present invention, the displacement sensor is fixed to the sensor mounting fixture by a clip.

[0012] As a preferred technical solution of the present invention, it also includes a numerical control system, which is connected to the machine tool and the host computer.

[0013] The second objective of this invention is to provide an automatic measurement method for five-degree-of-freedom geometric errors of machine tool rotary tables, which solves the problem that existing technologies cannot quickly measure the errors of machine tool rotary tables and that the measurement process requires multiple manual operations of the CNC machine tool.

[0014] To achieve the above objectives, the technical solution adopted by the present invention is: an automatic measurement method for five-degree-of-freedom geometric errors of a machine tool rotary table, comprising: installing a measuring mandrel in contact with the center hole of the rotary table through end face contact, ensuring that the rotation axis of the mandrel is coaxial with the rotation axis of the rotary table; using five sensors to measure the runout values ​​of five points on the mandrel, and then analyzing the five-degree-of-freedom errors of the rotary table other than the rotation positioning error based on the measurement data.

[0015] As a preferred technical solution of the present invention, the method for automatic measurement of five-degree-of-freedom geometric errors of a machine tool rotary table specifically comprises: Based on real-time data from five displacement sensors, the following five degrees of freedom geometric errors of the B-axis turntable were analyzed: radial runout EXB in the X direction, radial runout EZB in the Z direction, axial runout EYB in the Y direction, tilt error ECB around the Z-axis, and tilt error EAB around the X-axis. The calculation method is as follows: The five displacement sensors are designated as x4 displacement sensor, x5 displacement sensor, y8 displacement sensor, z... 10 Displacement sensor and z 11 The displacement sensor acquires data as follows: x4(θ), x5(θ), y8(θ), z 10 (θ), z 11 (θ), where x4 displacement sensor, x5 displacement sensor, and z are on the measuring mandrel. 10 Displacement sensor and z 11 The runout value of the displacement sensor includes the eccentric installation error e(θ) between the measuring mandrel and the center hole of the turntable, the radial runout error, the roundness error R of the mandrel, and the runout error caused by the tilting error of the mandrel; the runout value of the turntable mandrel is measured by the y8 displacement sensor, and the displayed value is the axial runout error; Since the displacement sensor readings include the five geometric errors of the rotation axis, namely EXB, EYB, EYZ, EAB and ECB, as well as the installation position errors of the mandrel XOB and ZOB; When EBB is zero and the mandrel rotation axis is coaxial with the turntable rotation axis, the calculation formula for the above sensor data is as follows:

[0016] in, Let X and Z be the eccentric installation errors, respectively, and e be the magnitude of the installation error vector. The initial angle for installation error. The rotation angle of the B-axis turntable is shown below. The measuring mandrel and the center hole of the turntable are fitted together by the end face to ensure that the axis of the mandrel is perpendicular to the plane of the turntable, that is, to ensure that the axis of the measuring mandrel is parallel to the axis of the turntable. The formula above derives the five-degree-of-freedom geometric error of the B-axis rotary table, as shown in the following formula:

[0017] In the above formula, the eccentric installation error e(θ) can be calculated by Fourier analysis or the least squares fitting method. The core measuring rod is a high-precision customized specimen, and its roundness error is negligible relative to the rotation error R of the spindle.

[0018] The beneficial effects of this invention are: (1) The present invention has a reasonable structural design. It can measure five errors of the rotary shaft in one installation and measurement. It adopts a contact displacement sensor method, which is suitable for measuring the geometric error of the turntable with low speed and medium precision, and is low cost.

[0019] (2) This invention enables an automatic error measurement process. During testing, multiple measurements are required under different rotational speeds and directions. The user sets the required rotation angle, rotational speed, and rotational direction in the host computer's turntable measurement software, and the host computer generates turntable rotation G-code 1 according to the user's needs. Furthermore, since a contact sensor is used, to reduce wear on the sensor's side, the sensor needs to be moved away from the measuring mandrel when not in use. To achieve this, the host computer generates linear axis movement G-code 2. Linear axis movement G-code 2 enables: when measurement is required, the linear axis is moved to a designated position 1, causing the sensor to contact the mandrel for measurement. The linear axis movement G-code 3 can achieve the following: when not measuring, move the linear axis to a designated position 2 outside the mandrel, causing the sensor to detach from the measuring mandrel; the above two types of G-codes (G-codes that cause the turntable to rotate and G-codes that move the linear axis to a designated position) can communicate with the CNC system through the host computer to transmit the G-codes to the CNC system. In this way, the measurement user only needs to press the program start button after the G-code is transmitted to the CNC system, without the need to manually compile G-codes or operate the CNC machine tool handwheel to control the movement of the machine tool linear axis or turntable, realizing automatic measurement, simplifying the measurement process, and improving measurement efficiency.

[0020] (3) The present invention can communicate with the CNC system and transmit the G code required for automatic measurement from the host computer to the CNC system. It does not require manual compilation of G code or shaking of the CNC machine tool handwheel to move the linear axis or rotary table of the machine tool, and has great potential for widespread use. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the structure of an automatic measurement device for five degrees of freedom geometric errors for a machine tool rotary table according to the present invention; Figure 2 This is a front view of an automatic five-degree-of-freedom geometric error measuring device for a machine tool rotary table according to the present invention; Figure 3 This is a side view of an automatic measurement device for five degrees of freedom geometric errors for a machine tool rotary table according to the present invention.

[0022] Figure 4 This is a schematic diagram of an automatic measurement method for five-degree-of-freedom geometric errors of a machine tool rotary table according to the present invention. Figure 5This is a schematic diagram of the six-degree-of-freedom error of the B-axis rotary table.

[0023] In the diagram: 1. Host computer; 2. Bracket; 201. Spindle end connector; 202. Reinforcing rib; 203. Sensor mounting fixture; 3. Measuring mandrel; 4. x4 displacement sensor (upper X-axis radial runout measurement displacement sensor); 5. x5 displacement sensor (lower X-axis radial runout measurement displacement sensor); 6. Pressure plate; 7. Tool holder (non-flat tail Morse taper bore tool holder); 8. y8 displacement sensor (Y-axis axial runout measurement displacement sensor); 9. Standard ball; 10. z 10 Displacement sensor (contact displacement sensor for measuring radial runout of the Z-axis); 11. z 11 12. Rotary table (rotary worktable of a horizontal five-axis machine tool with a fork swing). Detailed Implementation

[0024] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0025] Example 1 like Figures 1 to 3 As shown, the present invention discloses an automatic measurement device for five-degree-of-freedom geometric errors of a machine tool rotary table, comprising a host computer 1, a support 2, a measuring mandrel 3, a tool holder 7, a standard ball 9, and five displacement sensors. The standard ball 9 is fixed to the upper end of the test mandrel 3, the measuring mandrel 3 is optionally mounted at the central axis of the machine tool rotary table, the tool holder 7 is installed at the spindle tool holder mounting position of the machine tool, the support 2 is fixed outside the tool holder 7, one displacement sensor is arranged vertically with its measuring end in contact with the standard ball 9, and the other four displacement sensors are divided into two pairs, each pair arranged vertically. The measuring end of one pair is in contact with the measuring mandrel 3 in the X direction, and the measuring end of the other pair is in contact with the test mandrel 3 in the Z direction. The five contact-type displacement sensors are electrically connected to the host computer 1 through a sensor amplifier and a communication unit.

[0026] This invention relates to an automatic measurement device for five-degree-of-freedom geometric errors of a machine tool rotary table, comprising a host computer 1, a bracket 2 for mounting contact displacement sensors, a measuring mandrel 3, a pressure plate 6, a Morse taper tool holder without a flat tail 7, a high-precision standard ball 9 located in the center hole on the upper side of the measuring mandrel 3, and x4 displacement sensors 4, x5 displacement sensors 5, y8 displacement sensors 8, and z displacement sensors 9 fixed on the bracket 2. 10 Displacement sensor 10 and z 11 Displacement sensor 11.

[0027] See Figure 1The host computer 1 is connected to the communication module of the five displacement sensor acquisition modules via a network cable. It is used for data acquisition and analysis, automatically calculates the five degrees of freedom geometric error value of the turntable, and can generate G-codes for driving linear and rotary axes required in automatic measurement. It can also transmit the G-codes required in automatic measurement from the host computer to the CNC system.

[0028] Reference Figure 2 The bracket 2 is fixed to the Morse taper tool holder 7 without a flat tail by clamping. Two x4 displacement sensors 4 and x5 displacement sensors 5 are fixed to the right side of the measuring mandrel. They are fixed to the bracket 2 by the sensor's own clip and arranged vertically at a spacing L (the spacing L can be adjusted in stages by the reserved mounting holes). They are used to measure the radial runout of the mandrel generatrix in the X direction. At the same time, the difference between the two position error values ​​is divided by the spacing L of the displacement sensors. The quotient is the tilt geometric error of the B-axis turntable axis around the Z-axis.

[0029] See Figure 3 The Morse taper tool holder 7 without a flat tail is fixed in the taper hole by the machine tool's own tool holder pull-out mechanism, while the spindle's orientation function ensures that the tool holder 7 does not rotate. The y8 displacement sensor 8, fixed to the upper side of the measuring mandrel, cannot directly contact the end of the spindle mandrel due to the presence of the center hole at the end of the measuring mandrel; it needs to contact a high-precision standard ball 9 glued to the center hole of the mandrel for measuring axial runout in the Y direction. The z... 10 Displacement sensor 10 and z 11 The displacement sensor 11 is fixed to the bracket 2 by the sensor's own clip and arranged vertically at a spacing L (the spacing L can be adjusted in stages through the reserved mounting holes). It is used to measure the radial runout of the mandrel generatrix in the Z direction. At the same time, the difference between the two position error values ​​is divided by the spacing L of the displacement sensor, and the quotient is the tilt geometric error of the B-axis turntable axis around the X-axis.

[0030] When in use, the measuring mandrel 3 rotates together with the turntable 12. Through the automatic operation program, the measuring device drives the contact displacement sensor to automatically approach and fully contact the generatrix and upper end face of the measuring mandrel, obtain the sensor runout value at the corresponding position, and complete the calculation of the five-degree-of-freedom geometric error on the host computer 1 according to the corresponding data processing algorithm.

[0031] Example 2 like Figure 1 As shown, unlike Embodiment 1, in Embodiment 2, in an automatic measurement device for five-degree-of-freedom geometric errors of a machine tool turntable according to the present invention, a pressure plate 6 is provided at the lower end of the measuring mandrel 3. The pressure plate 6 is fixedly connected to the turntable of the machine tool, and the pressure plate 6 is fixedly connected to the T-slot in the turntable by a T-nut.

[0032] See Figure 2 The measuring mandrel 3 and the positioning hole on the turntable 12 are fitted with a small clearance, and the end face flange is used for positioning. Finally, it is fixed on the worktable by the pressure plate 6 and the T-nut in the T-slot, which makes the installation relatively convenient.

[0033] Example 3 like Figure 2 As shown, unlike Embodiment 2, in Embodiment 3, the bracket 2 of the present invention, which is a five-degree-of-freedom geometric error automatic measuring device for a machine tool rotary table, includes a spindle end connector 201 and a sensor mounting fixture 203; the spindle end connector 201 is fixedly connected to the tool holder 7; the sensor mounting fixture 203 is fixed below the spindle end connector 201, and five displacement sensors are mounted on the sensor mounting fixture 203.

[0034] The bracket 2 consists of three parts: a spindle end connector 201, a sensor mounting fixture 203, and a reinforcing rib 202. The spindle end connector 201 is used to connect to the Morse taper tool holder 7 without a flat tail, and the sensor mounting fixture 203 is used to fix five displacement sensors.

[0035] Example 4 Unlike Embodiment 3, in Embodiment 4, the bracket 2 of the present invention, which is an automatic measurement device for five degrees of freedom geometric error of a machine tool rotary table, further includes a reinforcing rib 202. The reinforcing rib 202 is fixed between the spindle end connector 201 and the sensor mounting fixture 203. The connection reinforcement between the spindle end connector 201 and the sensor mounting fixture 203 can ensure the stability of the connection.

[0036] Example 5 Unlike Embodiment 4, in Embodiment 5, a five-degree-of-freedom geometric error automatic measuring device for a machine tool rotary table according to the present invention, the displacement sensor is fixed on the sensor mounting fixture 203 by a clip, which makes disassembly and assembly more convenient.

[0037] Example 6 Combination Figure 4 The present invention provides an automatic measurement method for five-degree-of-freedom geometric errors of a machine tool rotary table, comprising: mounting a measuring mandrel in contact with the center hole of the rotary table via an end face, ensuring that the rotation axis of the mandrel is coaxial with the rotation axis of the rotary table; measuring the runout values ​​at five points on the mandrel using five sensors; and then analyzing the five-degree-of-freedom errors of the rotary table, excluding rotational positioning errors, based on the measurement data. Specifically: Based on the real-time data from five displacement sensors, the five-degree-of-freedom geometric error of the B-axis rotary table was analyzed (e.g., Figure 5As shown, the five errors (excluding the rotational positioning error EBB) include the radial runout EXB of the B-axis turntable in the X direction, the radial runout EZB of the B-axis turntable in the Z direction, the axial runout EYB of the B-axis turntable in the Y direction, the tilt error ECB of the B-axis turntable around the Z-axis, and the tilt error EAB of the B-axis turntable around the X-axis. The calculation method is as follows: The five displacement sensors are designated as x4 displacement sensor, x5 displacement sensor, y8 displacement sensor, z... 10 Displacement sensor and z 11 The displacement sensor acquires data as follows: x4(θ), x5(θ), y8(θ), z 10 (θ), z 11 (θ), where x4 displacement sensor, x5 displacement sensor, and z are on the measuring mandrel. 10 Displacement sensor and z 11 The runout value of the displacement sensor includes the eccentric installation error e(θ) between the measuring mandrel and the center hole of the turntable, the radial runout error, the roundness error R of the mandrel, and the runout error caused by the tilting error of the mandrel; the runout value of the turntable mandrel is measured by the y8 displacement sensor, and the displayed value is the axial runout error; Since the displacement sensor readings include the five geometric errors of the rotation axis, namely EXB, EYB, EYZ, EAB and ECB, as well as the installation position errors of the mandrel XOB and ZOB; When EBB is zero and the mandrel rotation axis is coaxial with the turntable rotation axis, the calculation formula for the above sensor data is as follows:

[0038] in, Let X and Z be the eccentric installation errors, respectively, and e be the magnitude of the installation error vector. The initial angle for installation error. The rotation angle of the B-axis turntable is shown below. The measuring mandrel and the center hole of the turntable are fitted together by the end face to ensure that the axis of the mandrel is perpendicular to the plane of the turntable, that is, to ensure that the axis of the measuring mandrel is parallel to the axis of the turntable. The formula above derives the five-degree-of-freedom geometric error of the B-axis rotary table, as shown in the following formula:

[0039] In the above formula, the eccentric installation error e(θ) can be calculated by Fourier analysis or the least squares fitting method. The core measuring rod is a high-precision customized specimen, and its roundness error is negligible relative to the rotation error R of the spindle.

Claims

1. An automatic measurement device for five-degree-of-freedom geometric errors of a machine tool rotary table, characterized in that, The system includes a host computer, a support, a measuring mandrel, a tool holder, a standard ball, and five displacement sensors. The standard ball is fixed to the upper end of the test mandrel. The measuring mandrel is optionally mounted on the central axis of the machine tool turntable. The tool holder is installed at the spindle tool holder mounting position of the machine tool. The support is fixed to the outside of the tool holder. One displacement sensor is arranged vertically with its measuring end in contact with the standard ball. The other four displacement sensors are divided into two pairs, each pair arranged vertically. One pair's measuring end contacts the measuring mandrel in the X direction, and the other pair's measuring end contacts the test mandrel in the Z direction. The five displacement sensors are electrically connected to the host computer through a sensor amplifier and a communication unit.

2. The five-degree-of-freedom geometric error automatic measuring device for a machine tool rotary table according to claim 1, characterized in that, The lower end of the measuring mandrel (3) is provided with a pressure plate (6), which is fixedly connected to the turntable of the machine tool.

3. The five-degree-of-freedom geometric error automatic measuring device for a machine tool rotary table according to claim 2, characterized in that, The pressure plate (6) is fixedly connected to the T-slot in the turntable by a T-nut.

4. The five-degree-of-freedom automatic geometric error measuring device for a machine tool rotary table according to claim 3, characterized in that, The bracket (2) includes a spindle end connector (201) and a sensor mounting fixture (203); the spindle end connector (201) is fixedly connected to the tool holder (7), the sensor mounting fixture (203) is fixed below the spindle end connector (201), and five displacement sensors are mounted on the sensor mounting fixture (203).

5. The five-degree-of-freedom automatic geometric error measuring device for a machine tool rotary table according to claim 4, characterized in that, The bracket (2) also includes a reinforcing rib (202) which is fixed between the spindle end connector (201) and the sensor mounting fixture (203).

6. The five-degree-of-freedom automatic geometric error measuring device for a machine tool rotary table according to claim 5, characterized in that, The displacement sensor is fixed to the sensor mounting fixture (203) by a clip.

7. The five-degree-of-freedom geometric error automatic measuring device for a machine tool rotary table according to claim 6, characterized in that, It also includes a numerical control system (7), which is connected to the machine tool and the host computer (1).

8. An automatic measurement method for five-degree-of-freedom geometric errors of a machine tool rotary table, implemented based on the automatic measurement device for five-degree-of-freedom geometric errors of a machine tool rotary table as described in any one of claims 1-7, characterized in that, include: The measuring mandrel is installed in the center hole of the turntable through end face contact, ensuring that the rotation axis of the mandrel is coaxial with the rotation axis of the turntable. Five sensors were used to measure the runout values ​​at five points on the mandrel, and then the error of the turntable in five degrees of freedom, excluding the rotational positioning error, was analyzed based on the measurement data.

9. The automatic measurement method for five-degree-of-freedom geometric errors of a machine tool rotary table according to claim 8, characterized in that, Specifically: Based on real-time data from five displacement sensors, the following five degrees of freedom geometric errors of the B-axis turntable were analyzed: radial runout EXB in the X direction, radial runout EZB in the Z direction, axial runout EYB in the Y direction, tilt error ECB around the Z-axis, and tilt error EAB around the X-axis. The calculation method is as follows: The five displacement sensors are designated as x4 displacement sensor, x5 displacement sensor, y8 displacement sensor, z... 10 Displacement sensor and z 11 The displacement sensor acquires data as follows: x4(θ), x5(θ), y8(θ), z 10 (θ), z 11 (θ), where x4 displacement sensor, x5 displacement sensor, and z are on the measuring mandrel. 10 Displacement sensor and z 11 The runout value of the displacement sensor includes the eccentric installation error e(θ) between the measuring mandrel and the center hole of the turntable, the radial runout error, the roundness error R of the mandrel, and the runout error caused by the tilting error of the mandrel; the runout value of the turntable mandrel is measured by the y8 displacement sensor, and the displayed value is the axial runout error; Since the displacement sensor readings include the five geometric errors of the rotation axis, namely EXB, EYB, EYZ, EAB and ECB, as well as the installation position errors of the mandrel XOB and ZOB; When EBB is zero and the mandrel rotation axis is coaxial with the turntable rotation axis, the calculation formula for the above sensor data is as follows: in, Let X and Z be the eccentric installation errors, respectively, and e be the magnitude of the installation error vector. The initial angle for installation error. The rotation angle of the B-axis turntable is shown below. The measuring mandrel and the center hole of the turntable are fitted together with the end face to ensure that the axis of the mandrel is perpendicular to the plane of the turntable, that is, to ensure that the axis of the measuring mandrel is parallel to the axis of the turntable. The formula above derives the five-degree-of-freedom geometric error of the B-axis rotary table, as shown in the following formula: In the above formula, the eccentric installation error e(θ) can be calculated by Fourier analysis or the least squares fitting method. The core measuring rod is a high-precision customized specimen, and its roundness error is negligible relative to the rotation error R of the spindle.

Images