Hybrid detection and adaptive control method for magnetic suspension axial bearing of air compressor

By using a hybrid detection method that combines real-time and theoretical data to adjust the rotor shaft position of the magnetic levitation air compressor, the problem of inaccurate displacement data detection in the magnetic levitation air compressor is solved, achieving higher precision bearing control and a reduced failure rate.

CN121184387BActive Publication Date: 2026-04-07SHANGHAI SCREW COMPRESSOR CO LTD
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-11-25
Publication Date
2026-04-07

AI Technical Summary

Technical Problem

The existing bearing displacement control method for magnetic levitation air compressors has the problem of inaccurate displacement data detection, which affects the stable operation of the equipment.

Method used

A hybrid detection method is adopted to collect the axial displacement and temperature values ​​of the magnetic levitation air compressor in real time. The theoretical displacement value is generated by expansion calculation and trend function fitting. The axial position of the rotor shaft is adjusted to maintain a suitable clearance by combining real-time and theoretical data for weighted calculation.

Benefits of technology

This improves the displacement detection accuracy of magnetic levitation bearings, reduces the failure rate, and ensures that the equipment can still operate safely when the displacement sensor fails.

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Abstract

The application discloses a kind of hybrid detection and adaptive control method of air compressor magnetic suspension axial bearing, comprising: the axial displacement value of the detection ring of air compressor is collected in real time, intake temperature value and exhaust temperature value;Collect the temperature value of each component of air compressor;Calculate the real-time expansion value of each component;The real-time expansion value of each component is constructed first matrix;According to the expansion trend function of each component that is generated by fitting first matrix;With real-time exhaust temperature value is assigned to expansion trend function to calculate and obtain the theoretical displacement value of each component;The theoretical real-time displacement value of rotor shaft is obtained by weighted calculation of the theoretical displacement value of each component;Bearing controller controls magnetic suspension axial bearing to adjust the axial position of rotor shaft.The application solves the problem of inaccurate displacement data detection in the bearing displacement control method of magnetic suspension air compressor.
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Description

Technical Field

[0001] This invention relates to the field of magnetic levitation air compressor technology, specifically to a hybrid detection and adaptive control method for a magnetic levitation axial bearing of an air compressor. Background Technology

[0002] In recent years, with the rapid development of magnetic levitation technology, its products have become increasingly popular and are found in various industries. Among these, the most critical technologies—bearing control and displacement control of magnetic levitation air compressors—have encountered considerable challenges in application, especially displacement control, which is crucial to the stable operation of the equipment. Current displacement detection technologies typically use sensors, including eddy current sensors and inductive sensors. Both types of sensors carry inherent risks; mechanical or physical malfunctions can affect sensor accuracy, leading to inaccurate displacement data, which in turn affects the bearing controller's judgment and renders the equipment unusable. Summary of the Invention

[0003] To overcome the shortcomings of existing technologies, a hybrid detection and adaptive control method for magnetic levitation axial bearings of air compressors is provided to solve the problem of inaccurate displacement data detection in the bearing displacement control method of magnetic levitation air compressors.

[0004] To achieve the above objectives, a hybrid detection and adaptive control method for a magnetic levitation axial bearing of an air compressor is provided, comprising the following steps:

[0005] The axial displacement value of the detection ring of the magnetic levitation air compressor and the intake and exhaust temperatures of the magnetic levitation air compressor are collected in real time.

[0006] The temperature values ​​of each component of the magnetic levitation air compressor were collected;

[0007] Calculate the real-time expansion value of each component based on its temperature value;

[0008] Construct a first matrix by combining the real-time expansion values ​​of each component with the intake air temperature, bearing temperature, temperature difference, expansion coefficient, and initial length of each component.

[0009] The expansion trend function of each component is generated by fitting the first matrix.

[0010] The real-time exhaust temperature value is used as the bearing temperature value and assigned to the expansion trend function to calculate the theoretical displacement value of each component.

[0011] The real-time axial displacement value of the detection ring is compared with the theoretical displacement value to determine the displacement value weight of each component.

[0012] Based on the theoretical displacement values ​​and weights of each component, the theoretical real-time displacement value of the rotor shaft of the magnetic levitation air compressor is obtained by weighted calculation of the theoretical displacement values ​​of each component.

[0013] Based on the theoretical real-time displacement value, the bearing controller controls the magnetic levitation axial bearing to adjust the axial position of the rotor shaft, so that the gap between the magnetic levitation axial bearing and the rotor shaft is maintained at the same gap level.

[0014] Furthermore, the components include a centrifugal impeller, a magnetic levitation axial bearing, an axial displacement sensor assembly, a bearing housing, a rotor, a magnet, and a housing.

[0015] Furthermore, based on the temperature values ​​of each component, the real-time expansion value of each component is calculated using the expansion calculation formula, which is:

[0016] ,

[0017] in, This represents the real-time expansion value of each component;

[0018] This represents the initial length of each component;

[0019] The coefficient of thermal expansion of each component;

[0020] This refers to the temperature changes of each component.

[0021] Furthermore, the axial displacement sensor assembly includes two displacement sensors for real-time acquisition of the displacement value of the detection ring. The step of determining the displacement value weight of each component when comparing the real-time axial displacement value of the detection ring with the theoretical displacement value includes:

[0022] A second matrix is ​​constructed by combining the displacement values ​​of the two displacement sensors with the intake air temperature value, the bearing temperature value, and the temperature difference.

[0023] The trend function of the detected values ​​of the displacement sensor is generated by fitting the second matrix;

[0024] The weight is calculated by calling the detection value trend function value.

[0025] Furthermore, the step of calling the detection value trend function value to calculate the weight includes calculating the difference between the gap value between the displacement sensor and the detection ring and the detection value trend function value of the two displacement sensors respectively, and calling the detection value trend function value of the displacement sensor with the smaller difference to calculate the weight.

[0026] Furthermore, when implementing the step of the bearing controller controlling the magnetic levitation axial bearing to adjust the axial position of the rotor shaft, when the displacement sensor is operating normally, the bearing controller calls the detection value trend function value to control the magnetic levitation axial bearing to adjust the axial position of the rotor shaft; when the displacement sensor malfunctions, the bearing controller calls the theoretical real-time displacement value to control the magnetic levitation axial bearing to adjust the axial position of the rotor shaft.

[0027] Furthermore, the expansion trend function is:

[0028] A=a n ×10 -19 X 6 -b n ×10 -17 X 5 +c n ×10 -16 X 4 -d n ×10 -15 X 3 +e n ×10 -15 X 2 +f n ×X+f n ,

[0029] Where A is the expansion value of the component;

[0030] X represents the temperature difference;

[0031] a n b n c n d n e n f n It is a constant in a polynomial function.

[0032] The beneficial effect of the present invention is that the hybrid detection and adaptive control method of the air compressor magnetic levitation axial bearing of the present invention detects the axial displacement data of the detection ring according to the axial displacement sensor assembly and feeds it back to the bearing controller. The bearing controller adjusts the real-time position of the axial clearance of the rotor shaft according to the axial displacement data, so that the axial displacement of the rotor shaft is kept within a small fluctuation range, thereby avoiding axial friction and failure of the rotor shaft.

[0033] The hybrid detection and adaptive control method for the magnetic levitation axial bearing of an air compressor of this invention collects multiple displacement data, either theoretical or real-time. Based on the operating conditions, it calls upon the appropriate control mode and feeds it back to the bearing controller. The bearing controller analyzes and calculates the most suitable displacement data and adjusts the axial position of the shaft through the axial bearing, thereby ensuring that the rotor shaft always operates safely within a suitable displacement range. This hybrid detection and adaptive control method for the magnetic levitation axial bearing of the air compressor of this invention, through a combination of theoretical and real-time detection, makes the axial displacement adjustment of the magnetic levitation axial bearing more precise and reduces the failure rate.

[0034] The present invention proposes a hybrid detection and adaptive control method for the magnetic levitation axial bearing of an air compressor. This method generates an empirical calculation method based on real-time detection data and the physical characteristics of each component, and cross-checks it with the real-time detection data. This solves the problem that the magnetic levitation air compressor can still operate based on empirical data when the displacement sensor fails during operation. Attached Figure Description

[0035] Other features, objects, and advantages of this application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0036] Figure 1 This is a schematic diagram of the structure of a magnetic levitation air compressor according to an embodiment of the present invention.

[0037] Figure 2 This is a partially enlarged schematic diagram of the magnetic levitation air compressor according to an embodiment of the present invention.

[0038] Figure label:

[0039] 1. Housing; 2. Centrifugal impeller; 3. Magnetic levitation axial bearing; 4. Axial displacement sensor assembly; 5. Displacement sensor 1; 6. Displacement sensor 2; 7. Primary bearing housing; 8. Secondary bearing housing; 9. Rotor; 10. Rotor shaft; 11. Magnet; 12. Detection ring; 13. Temperature sensor. Detailed Implementation

[0040] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0041] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0042] Reference Figure 1 and Figure 2The diagram shows the structure of a magnetic levitation air compressor. Specifically, the components of the magnetic levitation air compressor (model SH200 Scorero air compressor) include a centrifugal impeller 2, a magnetic levitation axial bearing 3, an axial displacement sensor assembly 4, bearing housings (primary bearing housing 5 and secondary bearing housing 51), a rotor 6, a magnet 7, a housing 1, and a detection ring 8. Magnetic levitation air compressors are existing technology, and their specific structure will not be described in detail here.

[0043] This invention provides a hybrid detection and adaptive control method for a magnetic levitation axial bearing of an air compressor, comprising the following steps:

[0044] S1. Real-time acquisition of the axial displacement value of the detection ring 8 of the magnetic levitation air compressor and the intake and exhaust temperature values ​​of the magnetic levitation air compressor.

[0045] In this embodiment, the axial displacement value of the detection ring 8 of the magnetic levitation air compressor is collected in real time by the axial displacement sensor assembly.

[0046] The intake and exhaust temperatures of the magnetic levitation air compressor are collected using temperature sensors.

[0047] S2. Collect the temperature values ​​of each component of the magnetic levitation air compressor.

[0048] In this embodiment, temperature values ​​of various components of the magnetic levitation air compressor are collected using temperature sensors.

[0049] S3. Calculate the real-time expansion value of each component based on the temperature value of each component.

[0050] In this embodiment, the real-time expansion value of each component is calculated based on its temperature value using the expansion calculation formula. The expansion calculation formula is as follows:

[0051] ,

[0052] in, This represents the real-time expansion value of each component;

[0053] This represents the initial length of each component;

[0054] The coefficient of thermal expansion of each component;

[0055] This refers to the temperature changes of each component.

[0056] S4. Construct the first matrix by combining the real-time expansion values ​​of each component with the intake air temperature, bearing temperature, temperature difference, expansion coefficient, and initial length of each component.

[0057] Specifically, a matrix is ​​constructed based on the calculated expansion values, as shown in Table 1 below:

[0058] Table 1. First Matrix Table for Constructing Expansion Values

[0059]

[0060] S5. Generate the expansion trend function of each component based on the first matrix fitting.

[0061] The expansion trend function is:

[0062] A=a n ×10 -19 X 6 -b n ×10 -17 X 5 +c n ×10 -16 X 4 -d n ×10 -15 X 3 +e n ×10 -15 X 2 +f n ×X+f n ,

[0063] Where A is the expansion value of the component;

[0064] X represents the temperature difference;

[0065] a n b n c n d n e n f n It is a constant in a polynomial function.

[0066] Specifically, based on the first matrix and the fitted expansion trend function based on the physical properties of each component affected by temperature (20~120℃):

[0067] Trend function of centrifugal impeller expansion value A:

[0068] A = a1 × 10 -19 X 6 -b1×10 -17 X 5 +c1×10 -16 X 4 -d1×10 -15 X 3 +e1×10 -15 X 2 +f1×X+f1.

[0069] Trend function of expansion value B of magnetic levitation axial bearing:

[0070] B = a² × 10 -19 X 6 -b2×10 -17 X 5 +c2×10 -16 X 4 -d2×10 -15 X 3 +e2×10 -15 X 2 +f2×X+f2.

[0071] Trend function of expansion value C of axial displacement sensor assembly:

[0072] C = a³ × 10 -19 X 6 -b3×10 -17 X 5 +c3×10 -16 X 4 -d3×10 -15 X 3 +e3×10 -15 X 2 +f3×X+f3.

[0073] Trend function of expansion value D of primary bearing housing:

[0074] D = a⁴ × 10 -19 X 6 -b4×10 -17 X 5 +c4×10 -16 X 4 -d4×10 -15 X 3 +e4×10 -15 X 2 +f4×X+f4.

[0075] Trend function of the expansion value E of the detection ring:

[0076] E=a5×10 -19 X 6 -b5×10 -17 X 5 +c5×10 -16 X 4 -d5×10 -15 X 3 +e5×10 -15 X 2 +f5×X+f5.

[0077] Rotor expansion value F trend function:

[0078] F = a6 × 10 -19 X 6 -b6×10 -17 X 5 +c6×10 -16 X 4 -d6×10 -15 X 3 +e6×10 -15 X 2 +f6×X+f6.

[0079] Trend function of magnet expansion value G:

[0080] G = a7 × 10 -19 X 6 -b7×10 -17 X 5 +c7×10 -16 X 4 -d7×10 -15 X 3 +e7×10 -15 X 2 +f7×X+f7.

[0081] Trend function of casing expansion value H:

[0082] H = a8 × 10 -19 X 6 -b8×10 -17 X 5 +c8×10 -16 X 4 -d8×10 -15 X 3 +e8×10 -15 X 2 +f8×X+f8.

[0083] Trend function of secondary bearing housing expansion value I:

[0084] I=a9×10 -19 X 6 -b9×10 -17 X 5 +c9×10 -16 X 4 -d9×10 -15 X 3 +e9×10 -15 X 2 +f9×X+f9.

[0085] The components of a magnetic levitation air compressor include, but are not limited to, the components mentioned above, depending on the design.

[0086] X = △T, and the remaining variables are generated by a trend function.

[0087] When selecting materials for each component, the following condition must be met: D+H+I>A+B+C+E+F+G. Therefore, the following calculation formula must be satisfied:

[0088] α1=β1-A×n1-B×n2-C×n3-E×n5-F×n6-G×n7-H×n8-I×n9;

[0089] n1+n2+n3+n4+n5+n6+n7+n8+n9=100%;

[0090] Where α1 is the theoretical real-time displacement value.

[0091] β1 is the gap between the displacement sensor and the detection ring;

[0092] n1……n9 represent the proportion of each component's influence on the displacement change, i.e., the weights.

[0093] S6. The real-time exhaust temperature value is used as the bearing temperature value and assigned to the expansion trend function to calculate the theoretical displacement value of each component.

[0094] S7. Compare the real-time axial displacement value of the detection ring 8 with the theoretical displacement value to determine the displacement weight of each component.

[0095] In this embodiment, the axial displacement sensor assembly 4 includes two displacement sensors for real-time acquisition of the displacement value of the detection ring 8. The step of determining the displacement value weight of each component when comparing the real-time axial displacement value of the detection ring 8 with the theoretical displacement value includes:

[0096] S71. Construct a second matrix by combining the displacement values ​​of the two displacement sensors with the intake air temperature value, bearing temperature value, and temperature difference.

[0097] Specifically, the second matrix is ​​shown in Table 2 below:

[0098] Table 2. Second Matrix Table for Constructing Displacement Values

[0099]

[0100] S72. Generate a trend function of the detection value of the displacement sensor by fitting the second matrix.

[0101] In this embodiment, the trend function of the detected value of displacement sensor 41 is as follows:

[0102] J=a 10 ×10 -19 X 6 -b 10 ×10 -17 X5 +c 10 ×10 -16 X 4 -d 10 ×10 -15 X 3 +e 10 ×10 -15 X 2 +f 10 ×X+f 10 .

[0103] Trend function of the detected value of displacement sensor 42:

[0104] K=a 11 ×10 -19 X 6 -b 11 ×10 -17 X 5 +c 11 ×10 -16 X 4 -d 11 ×10 -15 X 3 +e 11 ×10 -15 X 2 +f 11 ×X+f 11 .

[0105] S73. Call the detection value trend function value to calculate the weight.

[0106] Specifically, the step of calling the detection value trend function value to calculate the weight includes calculating the difference between the gap value between the displacement sensor and the detection ring 8 and the detection value trend function value of the two displacement sensors respectively, and calling the detection value trend function value of the displacement sensor with the smaller difference to calculate the weight.

[0107] In this embodiment, the method for calling the trend function value of the detection values ​​of the two displacement sensors is as follows:

[0108] Function call method 1: If |β1-J| < |β1-K|, then the J trend function is selected;

[0109] Function call method 2: |β1-J| =|β1-K|, then both J and K trend functions can be selected;

[0110] Function call method 3: If |β1-J| > |β1-K|, then the K-trend function is selected.

[0111] The J or K function value is compared with the α1 function value to ensure that the α1 value is equal to or infinitely close to the J or K function value under the same conditions. Based on this value, multiple measured values ​​of β1 are detected within the corresponding temperature difference range (20-120℃). These measured values ​​are then compared with multiple values ​​calculated by the A...I function generated under this temperature difference. Simultaneously, it is verified whether D+H+I>A+B+C+E+F+G satisfies the requirement. If this equation is satisfied, the α1 value is made equal to... The β1 values ​​are equal, thus determining the weight allocation ratio (n1...n9). In general, the theoretical value is calculated based on the measured value, and the control is ultimately supported by both the theoretical and measured values. In the event of a displacement sensor failure, the theoretical value can be used for control, allowing the equipment to continue operating. The proportional allocation value of n1...n9 in α1 = β1 - A×n1 - B×n2 - C×n3 - E×n5 - F×n6 - G×n7 - H×n8 - I×n9 is written into the bearing controller for later use.

[0112] S8. Based on the theoretical displacement values ​​and weights of each component, the theoretical displacement values ​​of each component are weighted and calculated to obtain the theoretical real-time displacement value of the rotor shaft 61 of the magnetic levitation air compressor.

[0113] S9. Based on the theoretical real-time displacement value, the bearing controller controls the magnetic levitation axial bearing 3 to adjust the axial position of the rotor shaft 61 so that the gap between the magnetic levitation axial bearing 3 and the rotor shaft 61 is maintained at the same gap level.

[0114] In this embodiment, when implementing the step of the bearing controller controlling the magnetic levitation axial bearing 3 to adjust the axial position of the rotor shaft 61, when the displacement sensor is operating normally, the bearing controller calls the detection value trend function value to control the magnetic levitation axial bearing 3 to adjust the axial position of the rotor shaft 61; when the displacement sensor malfunctions, the bearing controller calls the theoretical real-time displacement value to control the magnetic levitation axial bearing 3 to adjust the axial position of the rotor shaft 61.

[0115] The hybrid detection and adaptive control method for the magnetic levitation axial bearing of the air compressor of the present invention detects the axial displacement data of the detection ring by the axial displacement sensor assembly and feeds it back to the bearing controller. The bearing controller adjusts the real-time position of the axial clearance of the rotor shaft according to the axial displacement data, so that the axial displacement of the rotor shaft is kept within a small fluctuation range, thereby avoiding axial friction and failure of the rotor shaft.

[0116] The hybrid detection and adaptive control method for the magnetic levitation axial bearing of an air compressor of this invention collects multiple displacement data, either theoretical or real-time. Based on the operating conditions, it calls upon the appropriate control mode and feeds it back to the bearing controller. The bearing controller analyzes and calculates the most suitable displacement data and adjusts the axial position of the shaft through the axial bearing, thereby ensuring that the rotor shaft always operates safely within a suitable displacement range. This hybrid detection and adaptive control method for the magnetic levitation axial bearing of the air compressor of this invention, through a combination of theoretical and real-time detection, makes the axial displacement adjustment of the magnetic levitation axial bearing more precise and reduces the failure rate.

[0117] The adjustment route of the hybrid detection and adaptive control method for the magnetic levitation axial bearing of the air compressor of the present invention is as follows: temperature acquisition → expansion calculation → data fusion (sensor measured value vs. theoretical value) → PID control → current output → displacement adjustment.

[0118] The present invention proposes a hybrid detection and adaptive control method for the magnetic levitation axial bearing of an air compressor. This method generates an empirical calculation method based on real-time detection data and the physical characteristics of each component, and cross-checks it with the real-time detection data. This solves the problem that the magnetic levitation air compressor can still operate based on empirical data when the displacement sensor fails during operation.

[0119] The above description is merely a preferred embodiment of this application and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in this application is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features with similar functions disclosed in this application.

Claims

1. A hybrid detection and adaptive control method for a magnetic levitation axial bearing of an air compressor, characterized in that, Includes the following steps: The axial displacement value of the detection ring of the magnetic levitation air compressor and the intake and exhaust temperatures of the magnetic levitation air compressor are collected in real time. The temperature values ​​of each component of the magnetic levitation air compressor were collected; Calculate the real-time expansion value of each component based on its temperature value; Construct a first matrix by combining the real-time expansion values ​​of each component with the intake air temperature, bearing temperature, temperature difference, expansion coefficient, and initial length of each component. The expansion trend function of each component is generated by fitting the first matrix. The real-time exhaust temperature value is used as the bearing temperature value and assigned to the expansion trend function to calculate the theoretical displacement value of each component. The real-time axial displacement value of the detection ring is compared with the theoretical displacement value to determine the displacement value weight of each component. Based on the theoretical displacement values ​​and weights of each component, the theoretical real-time displacement value of the rotor shaft of the magnetic levitation air compressor is obtained by weighted calculation of the theoretical displacement values ​​of each component. Based on the theoretical real-time displacement value, the bearing controller controls the magnetic levitation axial bearing to adjust the axial position of the rotor shaft, so that the gap between the magnetic levitation axial bearing and the rotor shaft is maintained at the same gap level; The components include a centrifugal impeller, a magnetic levitation axial bearing, an axial displacement sensor assembly, a bearing housing, a rotor, a magnet, a housing, and a detection ring. Based on the temperature values ​​of each component, the real-time expansion value of each component is calculated using the expansion calculation formula, which is: , in, This represents the real-time expansion value of each component; This represents the initial length of each component; The coefficient of thermal expansion of each component; For the temperature changes of each component; The axial displacement sensor assembly includes two displacement sensors for real-time acquisition of the displacement value of the detection ring. The step of determining the displacement value weight of each component when comparing the real-time axial displacement value of the detection ring with the theoretical displacement value includes: A second matrix is ​​constructed by combining the displacement values ​​of the two displacement sensors with the intake air temperature value, the bearing temperature value, and the temperature difference. The trend function of the detected values ​​of the displacement sensor is generated by fitting the second matrix; The weight is calculated by calling the detection value trend function value.

2. The hybrid detection and adaptive control method for the magnetic levitation axial bearing of an air compressor according to claim 1, characterized in that, The step of calling the detection value trend function value to calculate the weight includes calculating the difference between the gap value between the displacement sensor and the detection ring and the detection value trend function value of the two displacement sensors respectively, and calling the detection value trend function value of the displacement sensor with the smaller difference to calculate the weight.

3. The hybrid detection and adaptive control method for the magnetic levitation axial bearing of an air compressor according to claim 2, characterized in that, When implementing the step of the bearing controller controlling the magnetic levitation axial bearing to adjust the axial position of the rotor shaft, when the displacement sensor is operating normally, the bearing controller calls the detection value trend function value to control the magnetic levitation axial bearing to adjust the axial position of the rotor shaft; when the displacement sensor malfunctions, the bearing controller calls the theoretical real-time displacement value to control the magnetic levitation axial bearing to adjust the axial position of the rotor shaft.

4. The hybrid detection and adaptive control method for the magnetic levitation axial bearing of an air compressor according to claim 2, characterized in that, The expansion trend function is: A=a n ×10 -19 X 6 -b n ×10 -17 X 5 +c n ×10 -16 X 4 -d n ×10 -15 X 3 +e n ×10 -15 X 2 +f n ×X+f n , Where A is the expansion value of the component; X represents the temperature difference; a n b n c n d n e n f n It is a constant in a polynomial function.

Citation Information

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