A spindle radial / angle static stiffness synchronous precise testing system and testing method

Abstract

This invention discloses a synchronous and accurate testing system and method for the radial and angular static stiffness of a spindle, belonging to the fields of precision manufacturing and ultra-precision measurement technology. The testing system includes: a loading module for applying a known magnitude and constant direction radial static load to the spindle rotor; a displacement measurement module for measuring the radial displacement of the outer surface of the spindle rotor at the loading point; and a tilt angle measurement module for measuring the minute tilt angle generated by the spindle rotor under the action of an offset force. This invention simultaneously measures the loading force, the displacement at the loading point, and the tilt angle of the gas static pressure spindle. Based on theoretical mechanics and geometry, it decouples the tilting motion caused by the offset loading force, thereby calculating the pure radial displacement of the theoretical center point of the gas static pressure spindle, ultimately obtaining an accurate and stable radial static stiffness value, and based on this, the angular stiffness value.

Description

Technical Field

[0001] This invention belongs to the field of precision manufacturing and ultra-precision measurement technology, specifically relating to a synchronous and accurate testing system and method for the radial / angular static stiffness of a spindle. Background Technology

[0002] In the fields of precision manufacturing and ultra-precision measurement, gas hydrostatic spindles, with their core advantages of high precision, low friction, and high stability, have become key components of high-end equipment. Their radial static stiffness, as a crucial performance indicator for evaluating the spindle's ability to resist deformation under external radial loads, directly affects machining accuracy, measurement accuracy, and the long-term reliability of the equipment. Therefore, developing a method to accurately and reliably test the radial static stiffness of gas hydrostatic spindles is of significant theoretical and practical importance for optimizing spindle design, ensuring process quality, and achieving precise performance evaluation.

[0003] Currently, commonly used radial static stiffness testing methods in the industry have the following limitations: The first method uses a cylinder or similar device to apply tension to the gas hydrostatic spindle in a single radial direction and measures its deformation using a displacement sensor, calculating the stiffness based on the force-to-displacement ratio. The main drawback of this method is that the applied load easily introduces additional torque, causing the gas hydrostatic spindle to tilt during the test. Since the radial displacement varies at different axial positions of the gas hydrostatic spindle under tilt, the measurement results heavily depend on the specific installation position of the displacement sensor, resulting in poor repeatability and high dispersion of the test data, making it impossible to accurately characterize the true radial static stiffness of the gas hydrostatic spindle. The second method, in order to overcome the tilting problem, attempts to simultaneously apply radial loads to the front and rear ends of the gas hydrostatic spindle, or fix the front and rear ends of the gas hydrostatic spindle and apply radial loads to the bearing housings, hoping to force the gas hydrostatic spindle to translate as a whole. However, this method faces significant difficulties in practical operation: a complete gas static pressure spindle system is usually connected to a drive motor at one end, making it structurally difficult to implement synchronous loading; if the motor is disassembled for testing, the test state is seriously inconsistent with the actual working state of the gas static pressure spindle, and the obtained stiffness data cannot effectively reflect its performance under real working conditions, thus losing the engineering application value of the test.

[0004] In summary, existing testing methods either suffer from inaccurate measurement results due to flaws in their underlying principles, or fail to reflect real-world working conditions due to implementation conditions that are detached from reality. The fundamental problem lies in the inability to effectively address coupling errors introduced during loading processes by factors such as force line offset and structural asymmetry, making it difficult to obtain stable, accurate, and engineering-representative radial static stiffness values. Therefore, there is an urgent need for a novel testing method that can eliminate coupling errors and closely approximate actual working conditions. Summary of the Invention

[0005] This invention provides a synchronous and accurate testing system and method for the radial and angular static stiffness of a spindle. The core of this invention lies in simultaneously measuring the applied force, the displacement of the loading point, and the spindle tilt angle. Based on theoretical mechanics and geometry, the tilting motion caused by the applied force bias is decoupled, thereby calculating the pure radial displacement of the theoretical center point of the spindle. This ultimately yields an accurate and stable radial static stiffness value, and based on this, the angular stiffness value of the gas static pressure spindle is obtained.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A synchronous and accurate testing system for the radial / angular static stiffness of a spindle includes: The loading module is used to apply a known, constant radial static load to the spindle rotor; The displacement measurement module is used to measure the radial displacement of the outer surface of the spindle rotor at the loading point; The tilt measurement module is used to measure the spindle rotor under bias force. The small tilt angle produced by the action .

[0007] A further improvement of the present invention is that the loading module includes a cylinder, a cylinder support, a cylinder tie rod, a tension sensor, and a sensor connecting rod; The cylinder is fixed to the test substrate by a cylinder support, and the output direction of its piston rod is adjusted to be parallel to the radial direction of the gas static pressure main shaft. One end of the cylinder connecting rod is connected to the piston rod of the cylinder, and the other end is connected to the sensor connecting rod through a force sensor. The force sensor is used to measure the force applied by the cylinder in real time. The end of the sensor connecting rod is connected to the outer cylindrical surface of the main shaft rotor via a flexible connector.

[0008] A further improvement of the present invention is that the displacement measurement module includes an inductance meter and its sensor mount; the sensor mount is securely mounted on the gas static pressure spindle, and the inductance meter is mounted on the sensor mount.

[0009] A further improvement of the present invention is that the position of the sensor seat enables the probe of the inductance meter to contact the outer surface of the main shaft rotor and to be precisely aligned with the loading point or to be in the same axial section as the loading point.

[0010] A further improvement of the present invention is that the tilt measurement module includes a photoelectric autocollimator, a mounting plate and a reflector; the photoelectric autocollimator is fixed on the test substrate by the mounting plate, and its optical axis is adjusted to be strictly parallel to the axis of the gas static pressure main shaft in the horizontal plane; the reflector is fixed to the end of the main shaft rotor by a stress-free installation method, and its reflecting surface is perpendicular to the axis of the gas static pressure main shaft.

[0011] A further improvement of this invention is that when the gas static pressure main shaft tilts, the reflector deflects accordingly, causing the parallel light emitted by the autocollimator to deflect after reflection. The photoelectric autocollimator can then accurately measure the tilt angle. .

[0012] A test method for a synchronous and accurate test system for the radial / angular static stiffness of a spindle includes the following steps: 1) System installation and parameter calibration Supply gas to the gas static pressure spindle and start it, waiting for it to reach a stable levitation state; install all measurement modules, and use precision instruments to measure and record the horizontal offset distance between the loading point and the theoretical center line of the spindle rotor. ; 2) Applying load and synchronous data acquisition The control cylinder actuates, applying a radial force to the spindle rotor via the tie rod system. The force value is read and recorded in real time by the tension sensor; under this steady-state load, three key data points are collected simultaneously: the force value from the tension sensor. Displacement at the loading point of the inductance meter ; Inclination angle of the gas static pressure principal shaft from the photoelectric autocollimator ; 3) Mechanical decomposition and geometric decoupling From the measured mixed displacement The displacement of the center point caused by the pure radial force is separated from the center point. 4) Calculate radial static stiffness Obtain the true displacement of the center point Then, based on the definition of static stiffness—the ratio of load to displacement in the direction of the load—the accurate radial static stiffness after eliminating tilt coupling errors can be calculated. ; 5) Calculate angular stiffness Obtain the tilt angle of the gas static pressure spindle and cylinder radial force Then, according to the definition of angular stiffness—the ratio of torque to the angle produced in the direction of the load—the angular stiffness can be calculated. .

[0013] A further improvement of this invention lies in the tilt angle of the gas static pressure spindle. It is on the order of arcseconds.

[0014] A further improvement of the present invention lies in that, from the measured mixed displacement The displacement of the center point caused by the pure radial force is separated from the following: 301) Establishment of the mechanical model: due to the applied force Acting on the offset distance At this point, according to theoretical mechanics, the force system can be equivalently decomposed into two parts: a pure radial force acting at the theoretical center point of the main shaft rotor. A couple acting on the rotor ; 302) Motion decomposition: The main shaft rotor under eccentric load The actual motion under action, i.e., from position arrive Consider it as a superposition of two ideal motions: Step a, translation: force at the center point Under the action of the rotor, the rotor moves from the initial position Generate pure radial displacement to position At this time, the displacement of the center point is Step b, rotation: in the couple Under the action of the rotor, the rotor moves from position Rotation angle To position ; 303) Geometric relationship solution: In the geometric model, the measured total displacement Corresponding line segments Due to the angle Minimal, approximately considered According to geometric relationships: line segment This represents the effect of rotation. The additional displacement produced by the angle at the loading point is of value line segment This refers to the actual radial displacement of the theoretical center point of the spindle rotor caused by the required pure radial force. ; Therefore: .

[0015] A further improvement of this invention lies in the accurate radial static stiffness. as follows:

[0016] Among them, stiffness value It characterizes the spindle rotor's ability to resist pure radial deformation, which is independent of the position of the measurement point; Based on accurate measurement of radial static stiffness, angular stiffness as follows: .

[0017] Compared with the prior art, the present invention has at least the following beneficial technical effects: The present invention provides a synchronous and accurate testing system and method for the radial / angular static stiffness of a spindle, which has the following significant advantages and positive effects: 1. Significant improvements in accuracy and reliability. This invention, by simultaneously measuring the tilt angle of a gas hydrostatic spindle under load, utilizes a mechanical model to precisely decouple the rotational component of the displacement, thereby directly obtaining the pure translational displacement of the theoretical center point. This fundamentally eliminates the tilt coupling error caused by the sensitivity of the measurement point position in traditional methods. It not only ensures the uniqueness and accuracy of stiffness measurement results but also makes the test data exhibit extremely high repeatability and stability under different times, different operators, and different orientations, establishing a reliable benchmark for product performance comparison, condition assessment, and quality control.

[0018] 2. Measurements are performed under full working conditions, ensuring accurate and reliable test results with high engineering guidance value. The method of this invention is tested directly on a complete assembly of a gas hydrostatic spindle with a motor and load. The loading system only needs to apply a single-point load at a radial position at one end of the gas hydrostatic spindle (usually the non-drive end). This completely avoids the predicament of the second method (dual-point synchronous loading), which cannot be implemented due to interference from the motor and other structures, or requires disassembly of components leading to distorted test conditions. Therefore, the radial static stiffness data obtained by this invention truly reflects the performance of the gas hydrostatic spindle under actual working configuration, and has direct and reliable guiding significance for evaluating its accuracy retention capability under real working conditions and predicting its machining or measurement performance.

[0019] 3. The system has a simple structure, a straightforward method, and is easy to implement. This invention adopts a single-point loading design. The system mainly consists of a standard pneumatic loading unit, a high-precision displacement sensor, and a photoelectric autocollimator. It eliminates the need for complex synchronization mechanisms, significantly reducing system complexity and making operation simple and efficient.

[0020] 4. Enables simultaneous testing of radial static stiffness and angular stiffness, improving testing efficiency. This invention, during a single loading and a set of synchronous data acquisition processes, not only obtains high-precision radial static stiffness through a decoupling algorithm, but also directly calculates angular stiffness using the same force value, offset distance, and tilt angle data, greatly improving testing efficiency. Attached Figure Description

[0021] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0022] Figure 1 This is a schematic diagram of the process for solving the radial static stiffness and angular stiffness of the hydrostatic spindle of the present invention.

[0023] Figure 2 This is a schematic diagram of the structure of the synchronous and accurate testing system for the radial / angular static stiffness of the main shaft of the present invention.

[0024] Figure 3 This is a schematic diagram of the structure of the synchronous and accurate testing system for the radial / angular static stiffness of the main shaft of the present invention.

[0025] Figure 4 This is a schematic diagram of the method for solving the radial static stiffness of the hydrostatic spindle according to the present invention.

[0026] Explanation of reference numerals in the attached figures: 1. Gas static pressure spindle; 2. Test base plate; 3. Cylinder support; 4. Cylinder; 5. Photoelectric autocollimator; 6. Mounting plate; 7. Sensor mount; 8. Cylinder connecting rod; 9. Reflector; 10. Inductance meter; 11. Sensor connecting rod; 12. Tension sensor. Detailed Implementation

[0027] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope of the invention. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0028] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0029] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0030] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection, an electrical connection, or a communication connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0031] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature being directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature being directly above or diagonally above the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.

[0032] It should be understood that, when used in this specification and the appended claims, the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0033] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0034] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0035] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0036] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0037] Example 1 This invention provides a synchronous and accurate testing system for the radial / angular static stiffness of a spindle, comprising: Reference Appendix Figure 2 and attached Figure 3 The testing system of this invention mainly includes a loading module, a displacement measurement module, an inclination measurement module, and an ultra-precision gas hydrostatic spindle as the test object. All modules are mounted on a test substrate 2 with high rigidity and high flatness to ensure the overall stability of the testing system.

[0038] 1. Test Object Ultra-precision gas hydrostatic spindle 1: As the test object, its rotor is in a free-floating state supported by a gas film. The spindle is rigidly fixed to the test substrate 2 by its housing. The test objective is to obtain the displacement response of the theoretical center point of the spindle rotor under radial force.

[0039] 2. Loading modules This loading module is used to apply a known, constant radial static load to the spindle rotor. It mainly consists of a cylinder 4, a cylinder support 3, a cylinder rod 8, a force sensor 12, and a sensor connecting rod 11. The cylinder 4 is fixed to the test base plate 2 via the cylinder support 3, and the output direction of its piston rod is precisely adjusted to be parallel to the radial direction of the gas static pressure spindle. One end of the cylinder rod 8 is connected to the piston rod of the cylinder 4, and the other end is connected to the sensor connecting rod 11 via the force sensor 12. The force sensor 12 is used to measure the force applied by the cylinder in real time and with high accuracy. The end of the sensor connecting rod 11 is connected to the outer cylindrical surface of the main shaft rotor via a flexible connector (such as a thin rope) with appropriate stiffness. Crucially, the connection point (i.e., the loading point) is not the center of the main shaft rotor, but rather has a fixed horizontal offset distance. This distance Precise measurements must be taken using precision measuring instruments (such as height gauges or laser rangefinders) before testing.

[0040] 3. Displacement Measurement Module This displacement measurement module is used to measure the radial displacement of the outer surface of the spindle rotor at the loading point. It typically includes a high-precision inductance meter 10 and its sensor mount 7. The sensor mount 7 is securely mounted on the hydrostatic spindle 1, positioned such that the probe of the inductance meter 10 contacts the outer surface of the spindle rotor and is precisely aligned near the loading point (or at the same axial section as the loading point). When the spindle rotor undergoes displacement, the inductance meter 10 measures the displacement at the loading point. .

[0041] 4. Inclination Measurement Module This tilt measurement module is used to measure the spindle rotor under bias force. The small tilt angle produced by the action This is a key parameter for decoupling calculations. The module mainly includes an opto-autocollimator 5, a mounting plate 6, and a reflector 9. The opto-autocollimator 5 is fixed to the test substrate 2 via the mounting plate 6, and its optical axis is adjusted to be strictly parallel to the main shaft axis in the horizontal plane. The reflector 9 is fixed to the end of the main shaft rotor using a stress-free mounting method, and its reflecting surface is perpendicular to the main shaft axis. When the gas static pressure main shaft tilts, the reflector 9 deflects accordingly, causing the parallel light emitted by the autocollimator to deflect after reflection. The opto-autocollimator 5 can then accurately measure the tilt angle. .

[0042] Example 2 This invention provides a test method for a synchronous and accurate test system for the radial / angular static stiffness of a spindle, comprising: Combination Figure 1 Flowcharts and Figure 4 The calculation principle diagram is shown below. The test method of this invention is carried out according to the following steps: 1) System installation and parameter calibration 1) Supply gas to the gas static pressure spindle and start it, waiting for it to reach a stable suspended state. Precisely install all measuring modules, and use precision instruments to measure and record the horizontal offset distance between the loading point and the theoretical center line of the spindle rotor. .

[0043] 2) Applying load and synchronous data acquisition The control cylinder 4) actuates, applying a radial force to the main shaft rotor via the tie rod system. The force value is read and recorded in real time by the tension sensor 12). Under this steady-state load, three key data points are collected simultaneously: the force value from the tension sensor 12). Displacement at the loading point from inductance meter 10) ; Main shaft tilt angle from photoelectric autocollimator 5) On the order of arcseconds.

[0044] 3) Mechanical decomposition and geometric decoupling The purpose of this step is to measure the mixed displacement. The displacement of the center point caused by the pure radial force is separated from the center point.

[0045] 301) Establishment of mechanical model: such as Figure 4 As shown, due to the loading force Acting on the offset distance According to theoretical mechanics, this force system can be equivalently decomposed into two parts: a pure radial force acting at the theoretical center point of the main shaft rotor. A couple acting on the rotor.

[0046] 302) Motion decomposition: The main shaft rotor under eccentric load Actual motion under action (from position) arrive This can be viewed as the superposition of two ideal motions: Step a (translation): at the center point force Under the action of the rotor, the rotor moves from the initial position Generate pure radial displacement to position At this time, the displacement of the center point is Step b (rotation): In the couple Under the action of the rotor, the rotor moves from position Rotation angle To position .

[0047] 303) Solving geometric relationships: In Figure 4 In the geometric model, the measured total displacement Corresponding line segments Due to the angle Extremely small, can be approximated as According to geometric relationships: line segment This represents the effect of rotation. The additional displacement produced by the angle at the loading point is of value line segment This refers to the actual radial displacement of the theoretical center point of the spindle rotor caused by the required pure radial force. .

[0048] Therefore:

[0049] 4) Accurately calculate radial static stiffness and angular stiffness Obtain the true displacement of the center point Then, based on the definition of static stiffness—the ratio of load to displacement in the direction of the load—the accurate radial static stiffness after eliminating tilt coupling errors can be calculated. :

[0050] This stiffness value It characterizes the spindle rotor's ability to resist pure radial deformation, independent of the measurement point's location, and exhibits high accuracy and repeatability.

[0051] Based on accurate measurement of radial static stiffness, angular stiffness as follows: .

[0052] Example 3 To verify the feasibility and superiority of the method described in this invention, a comparative test case for a certain model of ultra-precision air hydrostatic spindle is provided below.

[0053] 1. Test Subjects and Conditions ① Test object: A certain ultra-precision gas static electric spindle with a rotor diameter of 80mm and a design speed of 30,000 rpm.

[0054] ② Test environment: constant temperature (20±0.5℃) clean laboratory, gas static pressure spindle supply pressure is stable at 0.5MPa.

[0055] ③ Loading and measuring equipment: low-friction cylinder, tension sensor, inductance meter, photoelectric autocollimator, data acquisition system.

[0056] 2. Testing Process The test was conducted in the same radial direction (set as 0°) on the non-drive end of the gas static pressure spindle. The horizontal offset distance between the loading point and the spindle center was accurately measured. =100mm. Apply a radial static load F=100N.

[0057] (1) Testing using the method of the present invention Under steady-state load, the following data were collected synchronously: Displacement at loading point (measured by an inductance meter): =10.52

[0058] Spindle tilt angle (measured by autocollimator): =0.5 arcsecond (2) Calculations are performed using the decoupling model proposed according to the method of this invention. ① Calculate the additional displacement at the loading point caused by tilting: =0.242

[0059] ② Calculate the actual radial displacement of the spindle center: =10.278

[0060] ③ Calculate the precise radial stiffness: =9.73

[0061] ④ Calculate angular stiffness: =4.125 m / rad (3) Simulate the traditional single-point loading method To mitigate the shortcomings of traditional methods, under the same loading (F=100.0N), two additional displacement measurements were performed at different heights (5mm to the left and 5mm to the right of the loading point) on the same axial section of the spindle using an inductance meter. The stiffness was then directly calculated using force / displacement. Position 1 (Loading Point): Displacement 10.52 The calculated stiffness is 9.51. ; Position 2 (5mm above the loading point): Displacement 10.28 The calculated stiffness is 9.73. ; Position 3 (5mm below the loading point): Displacement 10.75 The calculated stiffness is 9.30.

[0062] (4) Results Comparison and Conclusion

[0063] The inventive points protected by this invention are as follows: 1. Core Method: Protect the overall process of "separating the rotational component from the total displacement at the loading point by synchronously measuring the tilt angle of the gas static pressure spindle, thereby solving for the pure radial displacement of the spindle center point and finally obtaining the accurate static stiffness".

[0064] 2. Decoupling Algorithm: Protecting the "Use of Formulas" The specific data processing model and decoupling algorithm for "calculating stiffness".

[0065] 3. System Structure: The protection system consists of a dedicated testing system architecture comprising a "single-point offset loading device, displacement sensor, and tilt measuring instrument (such as an opto-autocollimator)".

[0066] 4. Application scenario: Protect the practical test mode of "accurately testing radial static stiffness by implementing single-point loading under the complete working state including the drive motor".

[0067] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the scope of the invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0068] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can be appropriately combined to form other embodiments that can be understood by those skilled in the art. The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A testing method of a spindle radial and angular static stiffness synchronous precision testing system, characterized in that, The testing system upon which this testing method is based includes: The loading module is used to apply a known, constant radial static load to the spindle rotor; The displacement measurement module is used to measure the radial displacement of the outer surface of the spindle rotor at the loading point; An inclination measuring module for measuring a small angle of rotation of a main shaft rotor under a radial force action ; The tilt measurement module includes a photoelectric autocollimator, a mounting plate, and a reflector. The photoelectric autocollimator is fixed on the test substrate by the mounting plate, and its optical axis is adjusted to be strictly parallel to the axis of the gas static pressure main shaft in the horizontal plane. The reflector is fixed to the end of the main shaft rotor by a stress-free mounting method, and its reflecting surface is perpendicular to the axis of the gas static pressure main shaft. The testing method includes the following steps: 1) System installation and parameter calibration The aerostatic spindle is supplied with gas and started, and is kept in a stable suspension state; all measuring modules are installed, and the horizontal offset distance of the loading point from the theoretical center line of the spindle rotor is measured and recorded using precision instruments ; 2) Applying load and synchronous data acquisition The control cylinder actuates, applying a radial force to the spindle rotor via the tie rod system. This force value is read and recorded in real time by a tension sensor; under this steady-state load, three key data points are collected simultaneously: the radial force from the tension sensor. Displacement at the loading point of the inductance meter ; Rotation angle of the gas static pressure spindle from the photoelectric autocollimator ; 3) Mechanical decomposition and geometric decoupling Displacement from the measured loading point The displacement of the center point caused by the pure radial force is separated from the following: Mechanical model establishment: due to radial force Acting on the offset distance At this point, according to theoretical mechanics, the force system can be equivalently decomposed into two parts: a pure radial force acting at the theoretical center point of the main shaft rotor. A couple acting on the rotor ; Motion breakdown: Spindle rotor in radial force The actual motion under action, i.e., from position arrive Consider it as a superposition of two ideal motions: Step a, translation: under pure radial force Under the action of the rotor, the rotor moves from the initial position Generate pure radial displacement to position At this time, the radial displacement of the center point is Step b, rotation: in the couple Under the action of the rotor, the rotor moves from position Rotation angle To position ; Geometric relationship solution: In the geometric model, the displacement at the loading point is measured. Corresponding line segments Due to the rotation angle Minimal, approximately considered According to geometric relationships: line segment This represents the effect of rotation. The additional displacement generated at the loading point has a value of line segment This refers to the required radial displacement of the theoretical center point of the spindle rotor caused by pure radial force. ; Therefore: ; 4) Calculate radial static stiffness Obtain the radial displacement of the center point Then, based on the definition of static stiffness—the ratio of load to displacement in the direction of the load—the accurate radial static stiffness after eliminating tilt coupling errors can be calculated. ; 5) Calculate angular stiffness Obtain the rotation angle of the gas static pressure spindle and cylinder radial force Then, according to the definition of angular stiffness—the ratio of torque to the angle produced in the direction of the load—the angular stiffness can be calculated. .

2. The test method of the synchronous and accurate test system for the radial and angular static stiffness of a spindle according to claim 1, characterized in that, The loading module includes a cylinder, a cylinder support, a cylinder tie rod, a force sensor, and a sensor connecting rod; The cylinder is fixed to the test substrate by a cylinder support, and the output direction of its piston rod is adjusted to be parallel to the radial direction of the gas static pressure main shaft. One end of the cylinder tie rod is connected to the piston rod of the cylinder, and the other end is connected to the sensor connecting rod through a force sensor. The force sensor is used to measure the radial force applied by the cylinder in real time. The end of the sensor connecting rod is connected to the outer cylindrical surface of the main shaft rotor via a flexible connector.

3. The test method of the synchronous and accurate test system for the radial and angular static stiffness of a spindle according to claim 2, characterized in that, The displacement measurement module includes an inductance meter and its sensor mount; the sensor mount is securely mounted on the gas static pressure spindle, and the inductance meter is mounted on the sensor mount.

4. The test method of the synchronous and accurate test system for the radial and angular static stiffness of a spindle according to claim 3, characterized in that, The sensor mount is positioned such that the inductance meter probe contacts the outer surface of the spindle rotor and is precisely aligned with the loading point or is in the same axial section as the loading point.

5. The test method of the synchronous and accurate test system for the radial and angular static stiffness of a spindle according to claim 1, characterized in that, When the gas static pressure principal shaft tilts, the reflector deflects accordingly, causing the parallel light emitted by the autocollimator to deflect after reflection. The photoelectric autocollimator can then accurately measure the angle of rotation. .

6. The test method of the synchronous and accurate test system for the radial and angular static stiffness of a spindle according to claim 1, characterized in that, Gas static pressure spindle rotation angle It is on the order of arcseconds.

7. The test method of the synchronous and accurate test system for the radial and angular static stiffness of a spindle according to claim 1, characterized in that, Precise radial static stiffness as follows: Among them, stiffness value It characterizes the spindle rotor's ability to resist pure radial deformation, which is independent of the position of the measurement point; Based on accurate measurement of radial static stiffness, angular stiffness as follows: 。

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