A method for detecting the diameter of an inner support rod of a hemispherical resonator

Abstract

The application provides a kind of hemispherical resonator inner support rod diameter in situ detection method, it is related to ultra-precision grinding technical field, to solve the existing in situ detection method the problem that the mathematical model is too cumbersome to establish, the solution process is complex and the measurement accuracy is limited. Including the following steps: S1, establish the geometric relationship model of the relative distance between the radial of hemispherical resonator support rod and laser displacement sensor and the inner support rod diameter in the static state;S2, construct the profile change rule model of hemispherical resonator inner support rod in the rotating state, solve the radial runout of hemispherical resonator inner support rod by using the special point substitution method;S3, based on the obtained radial runout, construct the relationship model of the relative distance between the radial of support rod and laser displacement sensor and the inner support rod diameter of hemispherical resonator in the rotating state, solve the inner support rod diameter of hemispherical resonator. The present application greatly simplifies the complexity of the existing modeling and solving method, and can realize higher measurement accuracy.

Description

Technical Field

[0001] This invention relates to the field of ultra-precision grinding technology, and more specifically, to a method for detecting the diameter of the inner support rod of a hemispherical resonator in situ. Background Technology

[0002] Complex thin-walled components, due to their superior properties, are widely used in defense, medical, and aerospace fields. However, complex thin-walled components such as hemispherical resonators are made of hard and brittle materials and have complex shapes, making it difficult to guarantee the final machining accuracy to meet application requirements using conventional machining methods. Ultra-precision grinding, with its unique advantages, has gradually become one of the most effective methods for machining such structural components. Typically, hemispherical resonators are fixed to the base by an internal support rod, which imposes strict requirements on its dimensions. During ultra-precision grinding of hemispherical resonators, issues such as wear of the ball end grinding wheel and the weak stiffness of the workpiece and grinding wheel lead to a difference between the actual cutting depth and the theoretical result, making it impossible to guarantee the diameter of the internal support rod of the resonator. Therefore, how to ensure the dimensions of the hemispherical resonator support rod during machining is an urgent problem to be solved.

[0003] Offline inspection, in-situ contact inspection, and in-situ non-contact inspection are the most common methods for measuring object dimensions. Offline inspection technology can accurately measure the dimensions of the object being measured, but secondary clamping errors introduced during assembly and disassembly will affect processing efficiency and quality. In-situ contact inspection quickly obtains the dimensions of the internal support rod of a hemispherical resonator under specific working conditions, but contact may scratch the already machined surface, degrading the surface and subsurface quality of the workpiece and ultimately failing to meet final processing requirements. Non-contact in-situ inspection technology can flexibly measure the dimensions of parts of different types and structures, but it often suffers from overly cumbersome mathematical modeling, complex solution processes, and limited measurement accuracy. Summary of the Invention

[0004] The technical problem to be solved by this invention is:

[0005] Existing in-situ detection methods suffer from problems such as overly cumbersome mathematical modeling, complex solution processes, and limited measurement accuracy.

[0006] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0007] This invention provides a method for detecting the in-situ diameter of the internal support rod of a hemispherical resonator, comprising the following steps:

[0008] S1. Build a laser displacement sensor data sampling system, determine the acquisition position, and collect the relative distance data between the radial direction of the inner support rod of the hemispherical harmonic oscillator and the laser displacement sensor in a static state. Establish a geometric relationship model between the relative distance between the radial direction of the support rod and the laser displacement sensor and the diameter of the inner support rod in a static state.

[0009] S2. While the hemispherical harmonic oscillator is rotating at a constant speed, the relative distance data between the radial direction of the inner support rod of the hemispherical harmonic oscillator and the laser displacement sensor is collected while keeping the position of the laser displacement sensor unchanged. Based on the difference in the relative distance between the ball end grinding wheel and the laser displacement sensor under different registration angles, a model of the profile change law of the inner support rod of the hemispherical harmonic oscillator is constructed. The radial runout of the inner support rod of the hemispherical harmonic oscillator is solved by substituting special points.

[0010] S3. Based on the obtained radial runout of the inner support rod of the hemispherical harmonic oscillator, construct a model relating the relative distance between the radial direction of the support rod and the laser displacement sensor in the rotating state to the diameter of the inner support rod of the hemispherical harmonic oscillator. Combine this with the geometric relationship model in S1 relating the relative distance between the radial direction of the support rod and the laser displacement sensor in the stationary state to the diameter of the inner support rod, and solve for the diameter of the inner support rod of the hemispherical harmonic oscillator.

[0011] Furthermore, the laser displacement sensor data sampling system described in S1 consists of a laser displacement sensor, a data acquisition card, and a computer connected in series. By adjusting the relative position of the laser displacement sensor and the ball-head grinding wheel, the laser beam emitted by the laser displacement sensor can be received by the sensor again after being reflected by the surface contour of the grinding wheel.

[0012] Furthermore, as described in S1, the relative distance data between the radial direction of the inner support rod of the hemispherical harmonic oscillator and the laser displacement sensor is collected in a static state. The sampling frequency f is 5KHz, and the filtering method adopts low-pass filtering with a cutoff frequency of 0.1Hz.

[0013] Furthermore, S1 also includes preprocessing of the collected data, specifically using Hilbert-Huang transform to reduce noise in the data.

[0014] Furthermore, the preprocessing of the collected data described in S1 also includes multiple samplings and averaging to eliminate sampling errors of the laser displacement sensor.

[0015] Furthermore, the geometric relationship model between the radial distance of the support rod and the laser displacement sensor in the static state, as described in S1, and the diameter of the inner support rod is as follows:

[0016]

[0017] In the formula, Dis is the relative distance between the radial direction of the inner support rod and the laser displacement sensor, L is the actual distance between the laser displacement sensor and the axis of the inner support rod of the hemispherical resonator, D is the diameter of the inner support rod of the hemispherical resonator, and Rz is the value of the protrusion or pit caused by grinding, that is, the surface roughness value of the inner support rod.

[0018] Furthermore, in S2, the relative distance data between the radial direction of the inner support rod of the hemispherical harmonic oscillator and the laser displacement sensor is collected while the hemispherical harmonic oscillator is rotating at a constant speed. The sampling frequency f is 5KHz, the filtering method is low-pass filtering, and the cutoff frequency is 1Hz.

[0019] Furthermore, the model for the variation law of the inner support rod profile of the hemispherical harmonic oscillator described in S2 is as follows:

[0020]

[0021] In the formula, Dis ε With Dis ξ R represents the relative distance between the ball-end grinding wheel and the laser displacement sensor when the registration angles θ = ε and θ = ξ, respectively. out Let R be the radial runout of the inner support rod, and R be the radius of the inner support rod's circumference. For ease of writing, let R be... Recorded as

[0022] Furthermore, the radial runout of the inner support rod of the hemispherical harmonic oscillator is solved by substituting special points as described in S2, including the following process:

[0023] By substituting special points, let θ 11 =δ, θ 12 =δ+β and θ 13 =δ-β, where β is the angular increment of the registration angle δ. According to (2), we can obtain:

[0024]

[0025]

[0026] By combining equations (3) and (4), we can obtain:

[0027]

[0028] Will Let it be X1, then:

[0029]

[0030] Since there is an error between the sampled data and the true value of the laser displacement sensor, then:

[0031]

[0032] Based on the repeatability accuracy value of the laser displacement sensor, the sampling error err is eliminated by calculating the average value of the data.

[0033]

[0034] Equation (8) is fitted with a cosine function, and the amplitude of the fitting result is divided by -4·sin(β / 2). 2 This is the radial runout R of the inner support rod. out .

[0035] Furthermore, the relationship model between the radial distance of the support rod and the laser displacement sensor in the rotating state, as described in S3, and the diameter of the support rod inside the hemispherical harmonic oscillator is as follows:

[0036]

[0037] Compared with the prior art, the beneficial effects of the present invention are:

[0038] a) This invention, based on a laser displacement sensor, constructs a model of the profile variation of the inner support rod of a hemispherical resonator based on the difference in relative distance between the ball-end grinding wheel and the laser displacement sensor under different registration angles. It then uses a special point substitution method to solve for the radial runout of the inner support rod, achieving in-situ detection of the diameter of the inner support rod. This significantly simplifies the complexity of existing modeling and solution methods and achieves high measurement accuracy, laying the foundation for efficient and high-quality ultra-precision grinding.

[0039] b) By detecting the diameter of the internal support rod of the hemispherical resonator in situ, it is possible to determine in a timely and accurate manner whether the dimensional accuracy meets the processing requirements during the grinding process. This provides technical guidance for the formulation of subsequent grinding processes (especially single cutting depth) and lays the foundation for achieving efficient and high-precision ultra-precision grinding.

[0040] c) This method has a certain degree of universality and can be extended to non-contact in-situ detection of cylindrical rod diameter during all ultra-precision grinding processes. Attached Figure Description

[0041] Figure 1 This is a flowchart of the in-situ detection method for the diameter of the internal support rod of the hemispherical harmonic oscillator in an embodiment of the present invention;

[0042] Figure 2 This is a schematic diagram of the in-situ detection of the diameter of the internal support rod of the hemispherical harmonic oscillator in an embodiment of the present invention;

[0043] Figure 3 This is a comparison diagram of the time-domain signals before and after the Hilbert-Huang transform in an embodiment of the present invention;

[0044] Figure 4 This is a comparison diagram of the time-domain waveforms of the sampling signal before and after preprocessing in an embodiment of the present invention;

[0045] Figure 5 This is a schematic diagram of the runout of the internal support rod of the hemispherical harmonic oscillator in an embodiment of the present invention;

[0046] Figure 6 The image shows the time-domain signal and fitting result after removing the sampling error err in this embodiment of the invention.

[0047] Figure 7 The image shows the time-domain signal and fitting result after removing the sampling error err in this embodiment of the invention.

[0048] Figure 8 The figures show the measurement results and error rate curves of different methods in the embodiments of the present invention. Detailed Implementation

[0049] In the description of this invention, it should be noted that the terms "first," "second," and "third" mentioned in the embodiments of this invention are for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined with "first," "second," and "third" may explicitly or implicitly include one or more of that feature.

[0050] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0051] Specific Implementation Plan 1: (e.g.) Figure 1 As shown, the present invention provides a method for in-situ detection of the diameter of the internal support rod of a hemispherical resonator, comprising the following steps:

[0052] S1. Build a laser displacement sensor data sampling system, determine the acquisition position, and collect the relative distance data between the radial direction of the inner support rod of the hemispherical harmonic oscillator and the laser displacement sensor in a static state. Establish a geometric relationship model between the relative distance between the radial direction of the support rod and the laser displacement sensor and the diameter of the inner support rod in a static state.

[0053] S2. While the hemispherical harmonic oscillator is rotating at a constant speed, the relative distance data between the radial direction of the inner support rod of the hemispherical harmonic oscillator and the laser displacement sensor is collected while keeping the position of the laser displacement sensor unchanged. Based on the difference in the relative distance between the ball end grinding wheel and the laser displacement sensor under different registration angles, a model of the profile change law of the inner support rod of the hemispherical harmonic oscillator is constructed. The radial runout of the inner support rod of the hemispherical harmonic oscillator is solved by substituting special points.

[0054] S3. Based on the obtained radial runout of the inner support rod of the hemispherical harmonic oscillator, construct a model relating the relative distance between the radial direction of the support rod and the laser displacement sensor in the rotating state to the diameter of the inner support rod of the hemispherical harmonic oscillator. Combine this with the geometric relationship model in S1 relating the relative distance between the radial direction of the support rod and the laser displacement sensor in the stationary state to the diameter of the inner support rod, and solve for the diameter of the inner support rod of the hemispherical harmonic oscillator.

[0055] Before data acquisition, the surface of the inner support rod needs to be wiped clean. Since the grinding fluid used in ultra-precision machining is a water-oil mixture, any residual grinding fluid on the inner support rod can affect the reflection process of the laser beam, thus impacting the analysis results. Therefore, the surface of the inner support rod must be thoroughly wiped with alcohol before each measurement.

[0056] This invention not only significantly simplifies the cumbersome nature of existing non-contact in-situ measurement modeling and analysis, but also avoids damage to the surface quality of the workpiece and the introduction of secondary errors. It enables real-time and accurate measurement of the diameter of the inner support rod of the hemispherical harmonic oscillator, providing technical guidance for setting ultra-precision machining process parameters.

[0057] Specific Implementation Scheme Two: The laser displacement sensor data sampling system described in S1 consists of a laser displacement sensor, a data acquisition card, and a computer connected in series. The relative position of the laser displacement sensor and the ball-end grinding wheel is adjusted so that the laser beam emitted by the sensor can be received again by the sensor after being reflected by the surface contour of the grinding wheel. All other aspects of this implementation scheme are the same as in Specific Implementation Scheme One.

[0058] like Figure 2 As shown, in this embodiment, a laser displacement sensor is used to detect the diameter of the inner support rod of the hemispherical resonator in situ. The distance between the inner support rod of the hemispherical resonator and the laser displacement sensor is adjusted. By adjusting the X, Y and Z axes of the machine tool, the laser displacement sensor and the inner support rod of the hemispherical resonator are placed in the optimal position to ensure that the emitted beam can be received by the sensor a second time. The entire assembly is fixed in the XY plane of the machine tool using screws.

[0059] Specific Implementation Scheme 3: As described in S1, the relative distance data between the radial direction of the inner support rod of the hemispherical resonator and the laser displacement sensor is collected in a static state. The sampling frequency f is 5KHz, and the filtering method is low-pass filtering with a cutoff frequency of 0.1Hz. All other aspects of this implementation scheme are the same as in Specific Implementation Scheme 1.

[0060] Specific Implementation Plan Four: (e.g.) Figure 3 As shown, S1 also includes preprocessing the collected data, specifically using Hilbert-Huang transform to reduce noise. The rest of this implementation scheme is the same as that of specific implementation scheme three.

[0061] Since the lowest cutoff frequency of the laser displacement sensor is 0.1Hz, noise reduction filtering is required to obtain the data at the desired frequency (0Hz). The Hilbert-Huang transform not only preserves the data characteristics to the greatest extent but also has a good noise reduction effect.

[0062] Specific Implementation Scheme 5: The preprocessing of the collected data described in S1 also includes multiple samplings and averaging to eliminate sampling errors from the laser displacement sensor. The rest of this implementation scheme is the same as Specific Implementation Scheme 4.

[0063] Specific Implementation Plan Six: (e.g.) Figure 5 As shown in (a), the geometric relationship model between the radial distance of the support rod and the laser displacement sensor in the static state described in S1 and the diameter of the inner support rod is as follows:

[0064]

[0065] In the formula, Dis is the relative distance between the radial direction of the inner support rod and the laser displacement sensor, L is the actual distance between the laser displacement sensor and the axis of the inner support rod of the hemispherical resonator, D is the diameter of the inner support rod of the hemispherical resonator, and Rz is the value of the protrusions or pits caused by grinding, i.e., the surface roughness value of the inner support rod. Other aspects of this implementation scheme are the same as in specific implementation scheme one.

[0066] Specific Implementation Scheme Seven: In S2, while the hemispherical resonator is rotating at a constant speed, the relative distance data between the radial direction of the inner support rod of the hemispherical resonator and the laser displacement sensor is collected. The sampling frequency f is 5KHz, and the filtering method is low-pass filtering with a cutoff frequency of 1Hz. All other aspects of this implementation scheme are the same as in Specific Implementation Scheme One.

[0067] In this embodiment, the rotational speed of the hemispherical harmonic oscillator is set to 30 r / min, which is equivalent to a frequency of 0.5 Hz. Therefore, the cutoff frequency is changed from 0.1 Hz in the static state to 1 Hz.

[0068] After a period of precision grinding, the internal support rod of the hemispherical resonator may have low surface roughness in some areas, resulting in weak laser beam reflection and outliers in the sampling data. Therefore, it is necessary to remove these outliers before analyzing the sampling data, such as... Figure 4 As shown in the figure. Then, the laser displacement sensor sampling data is filtered and denoised, and the Hilbert-Huang transform is also used to denoise the data.

[0069] Specific Implementation Plan Eight: Since the collected data is the relative distance between the laser displacement sensor and the surface of the inner support rod, the data difference reflects the true variation law of the circumferential contour of the inner support rod of the resonator. Specifically, the contour variation law model of the hemispherical resonator inner support rod described in S2 is as follows:

[0070]

[0071] In the formula, Dis ε With Dis ξ R represents the relative distance between the ball-end grinding wheel and the laser displacement sensor when the registration angles θ = ε and θ = ξ, respectively. out Let R be the radial runout of the inner support rod, and R be the radius of the inner support rod's circumference. For ease of writing, let R be... Recorded as This implementation plan is otherwise the same as Specific Implementation Plan 1.

[0072] Specific implementation plan nine: The radial runout of the inner support rod of the hemispherical harmonic oscillator is solved by substituting special points as described in S2, including the following process:

[0073] By substituting special points, let θ 11 =δ, θ 12 =δ+β and θ 13 =δ-β, where β is the angular increment of the registration angle δ, which can be taken as 0.1°. According to (2), we can obtain:

[0074]

[0075]

[0076] By combining equations (3) and (4), we can obtain:

[0077]

[0078] Will Let it be X1, then:

[0079]

[0080] Because there is an error between the sampled data and the true value of the laser displacement sensor, the single sampling accuracy of the LK-H020 laser displacement sensor is ±1.2μm. Therefore:

[0081]

[0082] Based on the repeatability accuracy of the laser displacement sensor, the LK-H020 model laser displacement sensor has a repeatability accuracy of ±0.01μm, eliminating sampling error err through data averaging. Figure 7 As shown in (a):

[0083]

[0084] According to the form of equation (8), It is derived from the cosine trigonometric function -4·R out ·cosδ·sin(β / 2) 2 Based on the residual value X1, the cosine function of formula (9) is fitted using the cftool toolbox in MATLAB, and the fitting result is divided by -4·sin(β / 2). 2 This is the radial runout R of the inner support rod. out ,like Figure 7 As shown in (b). Simultaneously, the angle δ corresponding to the minimum value is 0°. This implementation scheme is otherwise the same as specific implementation scheme eight.

[0085] Specific Implementation Scheme Ten: The characteristic of this scheme is that the relationship model between the radial distance of the support rod and the laser displacement sensor in the rotational state described in S3 and the diameter of the support rod inside the hemispherical harmonic oscillator is as follows:

[0086]

[0087] This implementation plan is otherwise the same as Specific Implementation Plan 1.

[0088] Due to factors such as ball-end grinding wheel wear and radial runout, as well as the weak stiffness of the workpiece and grinding wheel, the roundness of the inner support rod after grinding has an error of 1-2 μm. To ensure the reliability of the measurement results, the diameter of the inner support rod of the resonator corresponding to the three registration angles was calculated, and the average value was taken as the true value of the diameter of the inner support rod of the hemispherical resonator.

[0089] Example 1

[0090] To verify the accuracy of the method proposed in this invention, the diameter of the inner support rod of the hemispherical resonator at different grinding depths was measured and compared using both the method of this invention and existing contact-based in-situ measurement methods. Specific results are shown in Table 1 and... Figure 8 As shown.

[0091] Table 1.

[0092]

[0093] Through Table 1 and Figure 8 The comparison results show that the error rate of the method of this invention and the contact-based in-situ measurement of the inner support rod diameter is within 0.5%, with a maximum error of 21 micrometers. The causes of these errors include: differences in the roundness of the support rod at different locations, uneven grinding, inconsistencies in the detection positions of the two methods causing some deviation, measurement errors from the laser displacement sensor, and measurement errors from the contact-based in-situ measurement micrometer. However, overall, the accuracy of the in-situ detection method for the inner support rod diameter of the hemispherical resonator provided by this invention fully meets the processing requirements.

[0094] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A method for detecting the in-situ diameter of the internal support rod of a hemispherical resonator, characterized in that, Includes the following steps: S1. Build a laser displacement sensor data sampling system, determine the acquisition position, and collect the relative distance data between the radial direction of the inner support rod of the hemispherical harmonic oscillator and the laser displacement sensor in a static state. Establish a geometric relationship model between the relative distance between the radial direction of the support rod and the laser displacement sensor and the diameter of the inner support rod in a static state. S2. While the hemispherical harmonic oscillator is rotating at a constant speed, the position of the laser displacement sensor remains unchanged. The relative distance data between the radial direction of the inner support rod of the hemispherical harmonic oscillator and the laser displacement sensor is collected. Based on the difference in the relative distance between the ball-end grinding wheel and the laser displacement sensor under different registration angles, a model of the profile change law of the inner support rod of the hemispherical harmonic oscillator is constructed. The radial runout of the inner support rod of the hemispherical harmonic oscillator is solved by substituting special points. S3. Based on the obtained radial runout of the inner support rod of the hemispherical harmonic oscillator, construct a model relating the relative distance between the radial direction of the support rod and the laser displacement sensor in the rotating state to the diameter of the inner support rod of the hemispherical harmonic oscillator. Combine this with the geometric relationship model in S1 relating the relative distance between the radial direction of the support rod and the laser displacement sensor in the stationary state to the diameter of the inner support rod, and solve for the diameter of the inner support rod of the hemispherical harmonic oscillator.

2. The method for detecting the diameter of the internal support rod of a hemispherical harmonic oscillator in situ according to claim 1, characterized in that, The laser displacement sensor data sampling system described in S1 consists of a laser displacement sensor, a data acquisition card, and a computer connected in series. By adjusting the relative position of the laser displacement sensor and the ball head grinding wheel, the laser beam emitted by the laser displacement sensor can be received by the sensor again after being reflected by the surface contour of the grinding wheel.

3. The method for detecting the diameter of the internal support rod of a hemispherical harmonic oscillator in situ according to claim 1, characterized in that, As described in S1, the relative distance data between the radial direction of the inner support rod of the hemispherical harmonic oscillator and the laser displacement sensor is collected in a static state. The sampling frequency f is 5KHz, the filtering method is low-pass filtering, and the cutoff frequency is 0.1Hz.

4. The method for detecting the diameter of the internal support rod of a hemispherical harmonic oscillator in situ according to claim 3, characterized in that, S1 also includes preprocessing of the collected data, specifically using Hilbert-Huang transform to reduce noise in the data.

5. The method for detecting the diameter of the internal support rod of a hemispherical harmonic oscillator in situ according to claim 4, characterized in that, The preprocessing of the collected data described in S1 also includes multiple samplings and averaging to eliminate sampling errors of the laser displacement sensor.

6. The method for detecting the diameter of the internal support rod of a hemispherical harmonic oscillator in situ according to claim 1, characterized in that, The geometric relationship model between the radial distance of the support rod and the laser displacement sensor in the static state, as described in S1, and the diameter of the inner support rod is as follows: In the formula, Dis is the relative distance between the radial direction of the inner support rod and the laser displacement sensor, L is the actual distance between the laser displacement sensor and the axis of the inner support rod of the hemispherical resonator, D is the diameter of the inner support rod of the hemispherical resonator, and Rz is the value of the protrusion or pit caused by grinding, that is, the surface roughness value of the inner support rod.

7. The method for detecting the diameter of the internal support rod of a hemispherical harmonic oscillator in situ according to claim 1, characterized in that, In S2, the relative distance data between the radial direction of the inner support rod of the hemispherical harmonic oscillator and the laser displacement sensor is collected while the hemispherical harmonic oscillator is rotating at a constant speed. The sampling frequency f is 5KHz, the filtering method is low-pass filtering, and the cutoff frequency is 1Hz.

8. The method for detecting the diameter of the internal support rod of a hemispherical harmonic oscillator in situ according to claim 1, characterized in that, The model for the change in the profile of the internal support rod of the hemispherical harmonic oscillator described in S2 is as follows: In the formula, Dis ε With Dis ξ R represents the relative distance between the ball-end grinding wheel and the laser displacement sensor when the registration angles θ = ε and θ = ξ, respectively. out Let R be the radial runout of the inner support rod, and R be the radius of the inner support rod's circumference. For ease of writing, let R be... Recorded as 9. The method for detecting the diameter of the inner support rod of a hemispherical harmonic oscillator in situ according to claim 8, characterized in that, The radial runout of the inner support rod of the hemispherical harmonic oscillator, as described in S2, is solved by substituting special points, and includes the following process: By substituting special points, let θ 11 =δ, θ 12 =δ+β and θ 13 =δ-β, where β is the angular increment of the registration angle δ. According to (2), we can obtain: By combining equations (3) and (4), we can obtain: Will Let it be X1, then: Since there is an error between the sampled data and the true value of the laser displacement sensor, then: Based on the repeatability accuracy value of the laser displacement sensor, the sampling error err is eliminated by calculating the average value of the data. Equation (8) is fitted with a cosine function, and the amplitude of the fitting result is divided by -4·sin(β / 2). 2 This is the radial runout R of the inner support rod. out .

10. The method for detecting the diameter of the inner support rod of a hemispherical harmonic oscillator in situ according to claim 9, characterized in that, The relationship model between the radial distance of the support rod and the laser displacement sensor in the rotating state, as described in S3, and the diameter of the support rod inside the hemispherical harmonic oscillator is as follows:

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