Design method of orifice throttling aerostatic bearing throttler considering displacement impedance performance

Abstract

The invention discloses a method for designing a throttling device of a small-hole throttling air static pressure bearing by considering displacement impedance performance, which comprises the following steps of: solving flow field pressure distribution according to a given design parameter value; according to the balance relation between the bearing capacity of the bearing and the load, the gas film thickness of the bearing in operation is calculated based on the fluid-solid coupling principle; inputting sine displacement excitation by utilizing a dynamic grid method, recording an output dynamic load, and calculating rigidity and damping values of an air film of the aerostatic bearing according to a relation between the input sine displacement excitation and the output dynamic load; normalizing the displacement impedance value of each frequency characteristic point by taking a maximum value which can be reached in a design variable range as a standard, and carrying out weighted summation by using a preset weight to obtain a design target value; and according to an optimization design algorithm, iteratively calculating a design parameter value until optimization iteration converges. On the basis of the fluid-solid coupling principle and in combination with the numerical simulation technology, the flow controller parameters enabling the displacement impedance performance of the small-hole throttling air static pressure bearing to be optimal can be effectively obtained in an optimal design mode.

Description

Technical Field

[0001] The invention relates to a design method for a small hole throttling air static pressure bearing throttle considering displacement impedance performance, and belongs to the field of ultra-precision machining and measurement. Background Art

[0002] Aerostatic bearings are widely used in ultra-precision machining and measurement as important functional components. This type of bearing mainly uses external air source for pressure supply, and has the advantages of near zero friction, low heat generation, and good vibration isolation performance during operation. Among the various throttles that can be used for aerostatic bearings, small hole throttles have the characteristics of simple manufacturing and low maintenance cost, and have the widest application.

[0003] The mechanical properties of air static pressure bearings have a direct impact on the performance of various types of equipment using such bearings. The mechanical properties of bearings mainly include static properties and dynamic properties. Static properties mainly refer to static load-bearing capacity and static stiffness, etc., which mainly reflect the resistance of the bearing air film to external static loads; dynamic properties mainly refer to dynamic stiffness and damping related to the excitation frequency, as well as the self-excited vibration performance of the bearing, which mainly reflects the resistance of the bearing to external dynamic loads. The research on static properties is relatively in-depth, and the research results are widely used in bearing design. However, due to the difficulty in mechanism analysis and calculation solution, dynamic performance has not been effectively considered in bearing design. However, if the influence of dynamic performance is considered in bearing design and the dynamic performance of the bearing is optimized, the bearing's resistance to external dynamic loads can be effectively improved, thereby improving the bearing's operating stability.

[0004] The displacement impedance performance of the supported part-air film system of the air hydrostatic bearing is defined as the complex ratio of the external dynamic load to the displacement. Its amplitude directly reflects the resistance of the bearing dynamic system to the external dynamic load. When the displacement impedance is larger, the system has a stronger resistance to the external dynamic load. Therefore, in the design of the air hydrostatic bearing, if the optimization and improvement of the displacement impedance performance is considered and the optimal throttling parameters are obtained, the bearing can obtain the best ability to resist external dynamic loads, and the bearing has a better ability to maintain stable operation under external disturbances. Summary of the invention

[0005] The invention provides a design method of a small hole throttling air static pressure bearing throttle considering displacement impedance performance, so as to realize the optimization design of parameters of the small hole throttling air static pressure bearing throttle.

[0006] The technical solution of the present invention is:

[0007] According to a first aspect of the present invention, a method for designing a throttle of a small-hole throttling air static pressure bearing considering displacement impedance performance is provided, comprising the following steps:

[0008] S1. Given the bearing load, air supply pressure, bearing diameter, and the design parameter values ​​of the small-hole throttling air static pressure bearing throttle;

[0009] S2. According to the design parameter values ​​in S1, the flow field analysis numerical simulation software is used to solve the flow field pressure distribution by using the finite volume method; since the resultant force of the bearing clearance pressure on the bearing surface is the bearing capacity, the thickness of the bearing air film in operation can be obtained by calculating based on the balance relationship between the bearing capacity and the load and the fluid-solid coupling principle;

[0010] S3, according to the air film thickness obtained in step S2, using the finite volume method and the dynamic grid method, inputting the sinusoidal displacement excitation, recording the output dynamic load, and calculating the stiffness and damping values ​​of the air film of the air static pressure bearing according to the relationship between the input sinusoidal displacement excitation and the output dynamic load;

[0011] S4. According to the stiffness and damping values ​​of the bearing air film obtained in S3, the displacement impedance value of the bearing supported component-air film system is calculated at the corresponding multiple frequency characteristic points within the external load frequency range, the displacement impedance value of each frequency characteristic point is normalized based on the maximum value that can be achieved within the design variable range, and the design target value is obtained by weighted summing with a preset weight;

[0012] S5, iteratively calculating the design parameter values ​​according to the design target value obtained in step S4 and the optimization design algorithm;

[0013] S6. Determine whether the design target value obtained according to step S4 meets the convergence standard, that is, the difference between the two convergence targets is less than the convergence accuracy. If so, the iteration ends and the obtained design parameters are the optimal design parameters. If not, the design parameter values ​​obtained in step S5 are assigned to the corresponding parameters in step S1, and steps S1 to S6 are continued to be iterated until the optimization iteration converges.

[0014] Furthermore, the small-hole throttling air static pressure bearing adopts a cylindrical cavity small-hole throttle, and the throttle design parameter values ​​include the air cavity depth, air cavity diameter, and throttling small hole diameter of the cylindrical cavity small-hole throttle.

[0015] Furthermore, the objective function used to calculate the design target value in S4 is:

[0016]

[0017] Among them, k i is the i-th preset weight, W i is the displacement impedance value of the i-th frequency characteristic point, W imax The maximum value of the displacement impedance corresponding to the i-th frequency characteristic point in the design domain; I is the number of selected frequency characteristic points.

[0018] Furthermore, the optimization design algorithm is an optimization design algorithm based on sequential quadratic programming.

[0019] According to a second aspect of the present invention, a processor is provided, the processor being used to execute operations, the operations comprising executing any one of the above-mentioned methods for designing a small-hole throttling air static pressure bearing throttle taking into account displacement impedance performance.

[0020] The beneficial effects of the present invention are as follows: based on the fluid-solid coupling principle and combined with numerical simulation technology, the present invention obtains throttle parameters that optimize the displacement impedance performance of the small-hole throttling air hydrostatic bearing through an optimized design method, thereby effectively improving the ability of the air hydrostatic support bearing to resist dynamic loads. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 It is a schematic diagram of the design process of the present invention;

[0022] Figure 2 It is a schematic diagram of the objective function iteration process given according to Example 2 of the present invention. DETAILED DESCRIPTION

[0023] In order to make the purpose, technical scheme and advantages of the embodiments of the present invention clearer, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. It should be noted that the embodiments in this application and the features in the embodiments can be combined with each other arbitrarily without conflict.

[0024] Example 1: Figure 1 As shown, according to a first aspect of an embodiment of the present invention, a method for designing a throttle of a small-hole throttling air static pressure bearing considering displacement impedance performance is provided, comprising the following steps:

[0025] S1. Given the bearing load, air supply pressure, and bearing diameter, the design parameter values ​​of the small-hole throttling air static pressure bearing throttle are given, that is, the size of the small-hole throttling air static pressure bearing throttle, such as the cylindrical cavity small-hole throttle, which is the air cavity depth, air cavity diameter, and throttling small hole diameter. The initial design parameter values ​​need to be given in the first iteration; the small-hole throttling air static pressure bearing throttle can be used in the small-hole throttling air static pressure bearing, and the small-hole throttling air static pressure bearing throttle includes a small hole and an air cavity;

[0026] S2. According to the design parameter values ​​in S1, the flow field analysis numerical simulation software is used to solve the flow field pressure distribution by using the finite volume method; since the resultant force of the bearing clearance pressure on the bearing surface is the bearing capacity, the thickness of the bearing air film in operation can be obtained by calculating based on the balance relationship between the bearing capacity and the load and the fluid-solid coupling principle;

[0027] S3, according to the air film thickness obtained in step S2, using the finite volume method and the dynamic grid method, inputting the sinusoidal displacement excitation, recording the output dynamic load, and calculating the stiffness and damping values ​​of the air film of the air static pressure bearing according to the relationship between the input sinusoidal displacement excitation and the output dynamic load;

[0028] S4. According to the stiffness and damping values ​​of the bearing air film obtained in S3, the displacement impedance value of the bearing supported component-air film system is calculated at the corresponding multiple frequency characteristic points within the external load frequency range, the displacement impedance value of each frequency point is normalized based on the maximum value that can be achieved within the design variable range, and the design target value is obtained by weighted summing with a weight of 1;

[0029] S5. According to the design target value obtained in step S4, the design parameter value is iteratively calculated based on the sequential quadratic programming (SQP) optimization design algorithm;

[0030] S6. Based on the convergence accuracy set by the SQP optimization algorithm, determine whether the design target value obtained according to step S4 meets the convergence standard, that is, the difference between the two convergence targets is less than the convergence accuracy ε. If so, the iteration ends and the obtained design parameters are the optimal design parameters. If not, the design parameter values ​​obtained in step S5 are assigned to the corresponding parameters in step S1, and steps S1 to S6 are iterated until the optimization iteration converges.

[0031] Furthermore, the objective function used to calculate the design target value in S4 is:

[0032]

[0033] Among them, k i is the i-th preset weight, W i is the displacement impedance value of the i-th frequency characteristic point, W imax The maximum value of the displacement impedance corresponding to the i-th frequency characteristic point in the design domain; I is the number of selected frequency characteristic points.

[0034] According to the second aspect of the embodiment of the present invention, a small hole throttling air static pressure bearing throttle design system considering displacement impedance performance is provided, including a module of the small hole throttling air static pressure bearing throttle design method considering displacement impedance performance as described in any of the above items. Specifically including: a first module, used to execute S1: given small hole throttling air static pressure bearing throttle design parameter values; a second module, used to execute S2: according to the design parameter values ​​in S1, using flow field analysis numerical simulation software, using finite volume method to solve the flow field pressure distribution; since the resultant force of the bearing clearance pressure on the bearing surface is the bearing capacity, the thickness of the bearing air film in operation can be calculated based on the balance relationship between the bearing capacity and the load and the fluid-solid coupling principle; a third module, used to execute S3: according to the air film thickness obtained in step S2, according to the finite volume method, using the dynamic grid method, input sinusoidal displacement excitation, record the output dynamic load, and calculate the stiffness and damping values ​​of the air static pressure bearing air film according to the relationship between the input sinusoidal displacement excitation and the output dynamic load; a fourth module, used to execute S4: according to the stiffness and damping of the bearing air film obtained in S3 numerical value, calculate the displacement impedance value of the bearing supported part-air film system at the corresponding multiple frequency characteristic points within the external load frequency range, normalize the displacement impedance value of each frequency characteristic point with the maximum value that can be achieved within the design variable range as the standard, and obtain the design target value by weighted summation with preset weights; the fifth module is used to execute S5: according to the design target value obtained in step S4, iteratively calculate the design parameter value according to the optimization design algorithm; the sixth module is used to execute S6: determine whether the design target value obtained according to step S4 meets the convergence standard, that is, the difference between the two convergence targets is less than the convergence accuracy ε, if it is achieved, the iteration ends, and the obtained design parameters are the optimal design parameters; if it is not achieved, the design parameter value obtained in step S5 is assigned to the corresponding parameter in step S1, and steps S1 to S6 are continued to be iteratively executed until the optimization iteration converges. As used above, the term "module" can be a combination of software and / or hardware that implements a predetermined function. Although the system described in the above embodiment is preferably implemented in software, it is also possible and conceivable to implement it in hardware, or a combination of software and hardware. For the parts that are not described in detail in each module, please refer to the relevant description of this embodiment.

[0035] According to a third aspect of an embodiment of the present invention, a processor is provided, wherein the processor is used to execute operations, wherein the operations include executing any one of the above-mentioned methods for designing a small-hole throttling air static pressure bearing throttle taking into account displacement impedance performance.

[0036] Embodiment 2: The present invention is further described below in combination with simulation data:

[0037] A design method for a small-hole throttling air static pressure bearing throttle considering displacement impedance performance comprises the following steps:

[0038] S1. A cylindrical cavity small hole throttle is used in a small hole throttling air static pressure bearing. The cylindrical cavity small hole throttle includes a small hole and an air cavity. The bearing load is 120N, the air supply pressure is 0.45MPa, and the bearing diameter is 20mm. The initial design parameter values ​​of the cylindrical cavity small hole throttle are given as follows: the air cavity depth is 0.1mm, the air cavity diameter is 6mm, and the throttling small hole diameter is 0.15mm.

[0039] S2. According to the design parameter values ​​in S1, the flow field analysis numerical simulation software is used to solve the flow field pressure distribution using the finite volume method. Since the resultant force of the bearing clearance pressure on the bearing surface is the bearing capacity, the thickness of the bearing air film during operation can be obtained by calculating the balance between the bearing capacity and the load based on the fluid-solid coupling principle. The thickness of the air film is 12 μm.

[0040] S3. According to the air film thickness obtained in step S2, the finite volume method is used to utilize the dynamic grid method to input sinusoidal displacement excitation, record the output dynamic load, and calculate the stiffness and damping values ​​of the air film of the air static pressure bearing according to the relationship between the input sinusoidal displacement excitation and the output dynamic load; for example, within the common excitation frequency range of 0-1000Hz, considering the excitation frequency points of 10Hz, 100Hz, 200Hz, 500Hz, and 1000Hz, the stiffness corresponding to these five frequency points are 16.45N / μm, 16.49N / μm, 17.88N / μm, 18.03N / μm, and 18.31N / μm, respectively; the damping are 0.199N·s / μm, 0.198N·s / μm, 0.185N·s / μm, 0.183N·s / μm, and 0.182N·s / μm, respectively.

[0041] S4. According to the stiffness and damping values ​​of the bearing air film obtained in S3, the displacement impedance value of the bearing supported component-air film system is calculated at the corresponding multiple frequency characteristic points within the external load frequency range, and the maximum value that can be achieved within the design variable range is used as the standard for normalization. The displacement impedance value of each frequency point is weighted and summed with a weight of 1 to obtain the design target value; if the excitation frequency points are 10Hz, 100Hz, 200Hz, 500Hz, and 1000Hz, the displacement impedances corresponding to these frequency points in this iteration step are: W 10 =105.93N / μm, W 100 =1196.74N / μm, W 200 =2453.35N / μm, W 500 =6301.44N / μm, W 1000 =12751.17N / μm, and the corresponding maximum displacement impedance in the design domain is W 10max =354.89N / μm, W 100max =3609.11N / μm, W 200max=7216.06N / μm, W 500max =18121.74N / μm, W 1000max =36199.29N / μm, then the objective function value OBJ is composed of: OBJ = k1*W 10 / W 10max +k2*W 100 / W 100max +k3*W 200 / W 200max +k4*W 500 / W 500max +k5*W 1000 / W 1000max =1.67, where k1=k2=k3=k4=k5=1 is the weight.

[0042] S5. According to the design target value obtained in step S4, the design parameter value is iteratively calculated based on the sequential quadratic programming (SQP) optimization design algorithm; the objective function iteration process is as follows: Figure 2 shown.

[0043] S6, set the convergence accuracy ε to 0.000001, based on the convergence accuracy ε set by the SQP optimization algorithm, determine whether the design parameters obtained according to step S4 meet the convergence criteria. If so, the iteration ends, and the obtained design parameters are the optimal design parameters; if not, assign the design parameter values ​​obtained in step S5 to the corresponding parameters in step S1, and continue to iterate steps S1 to S6 until the optimization iteration converges. The final parameters are: air supply pressure 0.33MPa, air cavity depth 0.05mm, air cavity diameter 5.009mm, throttling orifice diameter 0.12mm, and the corresponding air film thickness is 7.6μm.

[0044] Based on the method of the present invention, the bearing's ability to resist external dynamic loads is effectively improved by improving the bearing displacement impedance. Taking the micro-vibration caused by external excitation of vortex flow in the bearing air film flow field as an example, when the initial values ​​of the bearing design parameters are taken as: small hole diameter d = 0.15 mm, air cavity diameter U = 6 mm, air cavity depth V = 0.1 mm, and air supply pressure P s =0.45MP, and when the bearing load is 120N, after optimized design, the variance of the micro-vibration acceleration amplitude is reduced to 0.62 times of the initial value, which effectively weakens the influence of external excitation.

[0045] The specific implementation modes of the present invention are described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above implementation modes, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

Claims

1. A design method for a small-hole throttling air static pressure bearing throttle considering displacement impedance performance, characterized in that: The following steps are involved: S1. Given the bearing load, air supply pressure, bearing diameter, and the design parameter values ​​of the small-hole throttling air static pressure bearing throttle; S2. According to the design parameter values ​​in S1, the flow field analysis numerical simulation software is used to solve the flow field pressure distribution by using the finite volume method; since the resultant force of the bearing clearance pressure on the bearing surface is the bearing capacity, the thickness of the bearing air film in operation can be obtained by calculating based on the balance relationship between the bearing capacity and the load and the fluid-solid coupling principle; S3, according to the air film thickness obtained in step S2, using the finite volume method and the dynamic grid method, inputting the sinusoidal displacement excitation, recording the output dynamic load, and calculating the stiffness and damping values ​​of the air film of the air static pressure bearing according to the relationship between the input sinusoidal displacement excitation and the output dynamic load; S4. According to the stiffness and damping values ​​of the bearing air film obtained in S3, the displacement impedance value of the bearing supported component-air film system is calculated at the corresponding multiple frequency characteristic points within the external load frequency range, the displacement impedance value of each frequency characteristic point is normalized based on the maximum value that can be achieved within the design variable range, and the design target value is obtained by weighted summing with a preset weight; S5, iteratively calculating the design parameter values ​​according to the design target value obtained in step S4 and the optimization design algorithm; S6. Determine whether the design target value obtained according to step S4 meets the convergence standard, that is, the difference between the two convergence targets is less than the convergence accuracy. If so, the iteration ends and the obtained design parameters are the optimal design parameters. If not, the design parameter values ​​obtained in step S5 are assigned to the corresponding parameters in step S1, and steps S1 to S6 are continued to be iterated until the optimization iteration converges.

2. The design method of a small hole throttling air static pressure bearing throttle considering displacement impedance performance according to claim 1 is characterized in that: The small hole throttling air static pressure bearing adopts a cylindrical cavity small hole throttle, and the throttle design parameter values ​​include the air cavity depth, air cavity diameter, and throttling small hole diameter of the cylindrical cavity small hole throttle.

3. The design method of a small hole throttling air static pressure bearing throttle considering displacement impedance performance according to claim 1, characterized in that: The objective function used to calculate the design target value in S4 is: Among them, k i is the i-th preset weight, W i is the displacement impedance value of the i-th frequency characteristic point, W imax The maximum value of the displacement impedance corresponding to the i-th frequency characteristic point in the design domain; I is the number of selected frequency characteristic points.

4. The design method of a small hole throttling air static pressure bearing throttle considering displacement impedance performance according to claim 1, characterized in that: The optimization design algorithm is an optimization design algorithm based on sequential quadratic programming.

5. A processor, the processor being used to perform an operation, characterized in that: The operation includes executing the small hole throttling air static pressure bearing throttle design method considering displacement impedance performance as described in any one of claims 1-4.

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