CN111950206B - Design method of parabolic groove on surface of miniature dynamic pressure gas thrust bearing - Google Patents
Design method of parabolic groove on surface of miniature dynamic pressure gas thrust bearing Download PDFInfo
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Abstract
The invention provides a design method of a parabolic groove on the surface of a miniature dynamic pressure gas thrust bearing, aiming at the texture shape of the parabolic groove on the surface, different convergence ratios, relative groove depths and outlet non-texture ratios of the texture of the parabolic groove are set as particles with different positions and speeds in a population, the particles are initialized, and the population is randomly initialized; establishing a three-dimensional model of a calculation domain, carrying out grid division on the three-dimensional model to generate a grid file, and carrying out bearing capacity calculation of bearings with different convergence ratios by using a CFD (computational fluid dynamics) technology; and then Pareto dominant sorting is carried out to obtain individual optimal particles, population optimal particles and Pareto solution sets, and then surface parabolic grooves are designed. The invention provides a design method capable of rapidly and efficiently obtaining globally optimal texture parameters and distribution forms.
Description
Technical Field
The invention belongs to the technical field of gas bearings, and particularly relates to a design method of a parabolic groove on the surface of a miniature dynamic pressure gas thrust bearing.
Background
The energy problem is more and more prominent in the modern society, and the surface texture has the characteristics of good lubrication improvement, surface texture hydrophobicity, resistance reduction, noise reduction, turbulence resistance reduction, deicing and the like, so that the method is applied, and the method becomes an effective way for energy conservation and consumption reduction in the industry with high traditional energy consumption. The reasonable surface texture shape can effectively improve and enhance the tribological and other mechanical properties of the surface of the part. Surface texturing is widely used in mechanical seals, diesel cylinder liners, cylinder surface lubrication, aerodynamic lubrication of magnetic hard disks, and roll surface forming tools during sheet stamping due to excellent tribological properties.
The conventional surface engineering technology mainly utilizes surface finishing technologies such as polishing, grinding and the like to reduce the roughness of the friction surface, so that the surface is as smooth as possible. However, surface roughness is always limited due to the effects of material properties and machining accuracy. The surface texture technology can change the geometric shape of the surface, achieve the aim of improving the contact mode and the lubrication state of the surface, further improve the friction and wear performance of the surface of the friction pair, and have important significance for improving the energy utilization rate, prolonging the service life of the machine, protecting the environment and the like.
In previous studies, the optimal texture size, shape, distribution form, etc. were obtained by a trial-and-error method, which, although finding relatively good parameter values in a local range, is not time-consuming, nor accurate.
It is noted that this section is intended to provide a background or context for the embodiments of the invention that are recited in the claims. The description herein is not admitted to be prior art by inclusion in this section.
Disclosure of Invention
The invention aims to provide a design method of a parabolic groove on the surface of a miniature dynamic pressure gas thrust bearing, which solves the problem of poor hydrodynamic pressure effect in the prior art, and realizes rapid and efficient acquisition of globally optimal texture parameters and distribution forms.
The invention adopts the following technical scheme to realize the purposes:
the design method of the parabolic groove on the surface of the miniature dynamic pressure gas thrust bearing comprises the following steps:
s1: aiming at the shape of the parabolic groove texture on the surface, different convergence ratios, relative groove depths and outlet non-texture ratios of the parabolic groove texture are set as particles with different positions and speeds in the population, the particles are initialized, and the population is randomly initialized;
s2: establishing a three-dimensional model of a calculation domain, carrying out grid division on the three-dimensional model to generate a grid file, and carrying out bearing capacity calculation of bearings with different convergence ratios by using a CFD (computational fluid dynamics) technology;
S3: and (3) performing Pareto dominant sorting according to the bearing capacity calculation result of the particles obtained in the step (S2) to obtain individual optimal particles, population optimal particles and Pareto solution sets, and then designing a surface parabolic groove.
Further, the principle of updating the position and velocity of the particles in step S1 is as follows:
Wherein v id is the optimal speed of the global particles; x id is the optimal position of the global particle; i is the particle number; d is the moment; w is inertial weight; c 1、c2 is a learning factor; p id is the optimal position of the particle; r 1、r2 is a random value between 0 and 1.
Further, the step S2 specifically includes the following steps:
S201, calculating a calculation domain convergence ratio of the parabolic groove texture;
Wherein, κ is the convergence ratio of the calculated domain, h i is the film thickness at the inlet of the calculated domain, and h o is the film thickness at the outlet of the calculated domain;
S202, calculating dimensionless bearing capacity of the miniature dynamic pressure gas thrust bearing with parabolic groove textures:
Wherein W o is the dimensional bearing capacity of the bearing, U is the calculated domain gas movement speed, mu is the dynamic viscosity of the gas, b is the calculated domain width, and l is the calculated domain length.
Further, the step S3 specifically includes the following steps:
S301: sorting based on Pareto dominant relations according to fitness, comparing the current individual position with the individual history optimal position, and selecting individual optimal particles, population optimal particles and Pareto solution sets;
S302: updating the Pareto solution set according to the dominant relationship among the populations, wherein the positions and the speeds of the individual optimal particles and the population optimal particles are used as the basis for updating the positions and the speeds of the next generation particles;
S303: judging whether the genetic algebra is an integer multiple of 10, if so, designing by using a steepest descent method, and executing the step S2;
S304: if the step S303 is not satisfied, it is determined whether the convergence criterion is satisfied, if yes, a Pareto solution set is output, otherwise, the position and the speed of the particles are updated, and step S2 is executed.
Further, the optimal descent method in the step S303 is specifically as follows:
S30301: setting an initial weight vector w (0), and then generating a series of weight vectors, so that the cost function J (w) is reduced at each iteration of the algorithm, and the following formula is satisfied:
J(w(n+1))＜J(w(n)) (4)
s30302: the weight vector w is continuously adjusted along the steepest descent direction, i.e. along the negative gradient direction, the gradient vector is expressed as follows:
the steepest descent algorithm may be performed by:
wherein: n represents the iteration number and μ is the step size;
in the iterative process, the adjustment quantity of the weight vector is as follows:
Until the control error epsilon > 0, step 2 is further performed.
The invention has the beneficial effects that:
the parabolic groove textures of the invention improve the dimensionless bearing capacity of the bearing, and especially the dimensionless bearing capacity is improved more obviously when the convergence ratio is smaller; with the increase of the wide-neck ratio, the parabolic groove textures show greater potential in improving the dimensionless bearing capacity of the bearing; the friction surface is locally textured in the inlet area, so that the rigidity and stability of a lubricating oil film are improved, abrasion and friction force can be reduced, and an ideal effect can be obtained by designing geometric parameters and depth of textures under different working conditions. And provides a design method capable of quickly and efficiently obtaining globally optimal texture parameters and distribution forms.
Drawings
FIG. 1 is a schematic diagram of a miniature dynamic pressure gas thrust bearing model of the present invention;
FIG. 2 is a cross-sectional view of a miniature dynamic pressure gas thrust bearing of the present invention;
FIG. 3 is a front view of the texture of the thrust disc groove of the present invention;
FIG. 4 is a top view of the groove texture of the present invention;
FIG. 5 is an end view of the groove texture of the present invention;
FIG. 6 is a schematic representation of the lubrication calculation fields between a segment and a rotor of the present invention;
FIG. 7 is a flow chart of the parabolic trough texture parameter design of the present invention.
In the figure, 1-axis, 2-rotor turntable, 3-thrust disk, 4-parabolic groove texture.
Detailed Description
Example embodiments will now be described more fully with reference to the accompanying drawings. However, the exemplary embodiments may be embodied in many forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of the example embodiments to those skilled in the art. The described features or characteristics may be combined in any suitable manner in one or more embodiments.
As shown in fig. 1, the model schematic diagram of the present invention is: the rotor turntable 2 is directly connected with the shaft 1, so that a larger rotor rotating speed can be achieved, the thrust disks 3 are arranged on two sides of the rotor turntable, and parabolic groove textures 4 are uniformly distributed on the thrust disks 2.
As shown in fig. 5, l d is the width of the parabolic groove texture 4, h d is the maximum depth, and the parabolic groove texture 4 can be considered to be located in a rectangular unit.
When the gas flows at high speed, the gas film gap is a wedge gap (left high and right low) as shown in fig. 6, dynamic pressure is formed due to the wedge effect of the trapezoid calculation domain and the local dynamic pressure effect of the parabolic groove, a dynamic pressure gas film is formed in the wedge gap, and the higher the speed of the device is, the larger the dynamic pressure is.
The precise carving technology is adopted when the parabolic groove on the bearing surface is processed, and the precise carving technology comprises a system carving CAM technology, a high-speed milling technology, a computer numerical control technology and the like. During machining, the engraving and milling machine clamps the fine cutter of the non-standard part and is machined by a numerical control milling machine of a high-power and high-speed spindle motor. The precise engraving machine commonly uses small and medium cutters to process various complex curved surfaces, has high processing precision of detail parts and low surface roughness, and can meet the processing requirement of bearing friction pair surface micro-modeling.
The invention performs grid division on the calculation domain of the miniature dynamic pressure gas thrust bearing with the parabolic groove texture, performs grid encryption treatment on the near wall surface of the parabolic groove texture, performs 6 layers of grid encryption on the y direction of the parabolic groove texture, and the distance between adjacent grid nodes in the x direction is less than or equal to 0.05 times of the width of the groove texture.
The invention carries out simulation calculation on the calculation domain based on the CFD technology, adopts the SIMPLE method and the second-order windward format to carry out dispersion and solution on the control equation, and further can obtain the distribution pressure and the bearing capacity of the gas in the calculation domain. The parabolic groove texture of the miniature dynamic pressure gas thrust bearing is designed by adopting a multi-target particle swarm algorithm based on the Pareto idea and combining a steepest descent method, a design flow chart is shown in fig. 7, and the method is implemented specifically according to the following steps:
Step 1: aiming at the shape of the surface parabolic groove texture, different convergence ratios, relative groove depths and outlet non-texture rates of the parabolic groove texture are set as particles with different positions and speeds in the population, the particles are initialized, the population is randomly initialized, an inertia weight is set, an evolutionary algebra is set as 0, and the speed position updating principle is as follows:
wherein: i represents a particle number; d represents the time; w is an inertial weight, typically set at 0.4; c 1、c2 is a learning factor, generally taking 2; p id denotes the optimal position of particle i; x id represents the optimal position of the global particle; r 1、r1 takes a random value between 0 and 1;
step 2: establishing a three-dimensional model of the calculation domain shown in fig. 5, carrying out grid division on the three-dimensional model to generate a grid file, and carrying out bearing capacity calculation of bearings with different convergence ratios by using a CFD (computational fluid dynamics) technology;
the step 2 is specifically implemented according to the following steps:
step 2.1: calculating the calculated domain convergence ratio of the parabolic groove texture:
Wherein, κ is the convergence ratio of the calculated domain, h i is the film thickness at the inlet of the calculated domain, and h o is the film thickness at the outlet of the calculated domain;
step 2.2: calculating dimensionless bearing capacity of the miniature dynamic pressure gas thrust bearing with parabolic groove textures:
Wherein: w o is the dimensional bearing capacity of the bearing, U is the calculated domain gas movement speed, mu is the dynamic viscosity of the gas, b is the calculated domain width, and l is the calculated domain length;
Step 3: performing Pareto dominant sorting according to the dimensionless bearing capacity W and the convergence ratio kappa of the particles obtained in the step 2, so as to obtain individual optimal particles, population optimal particles and Pareto solution sets;
the step 3 is specifically implemented according to the following steps:
Step 3.1: solving each objective function value, sorting based on Pareto dominant relation according to the fitness, comparing the current individual position with the individual history optimal position, and selecting individual optimal particles, population optimal particles and Pareto solution sets;
Step 3.2: updating the Pareto solution set according to the dominant relationship among the populations, wherein the positions and the speeds of the individual optimal particles and the population optimal particles are used as the basis for updating the positions and the speeds of the next generation particles;
step 3.4: judging whether the genetic algebra is an integer multiple of 10, if so, designing by using a steepest descent method, and executing the step 2;
The steepest descent method is specifically carried out according to the following steps:
Step 3.4.1: setting an initial weight vector w (0), and then generating a series of weight vectors, so that the cost function J (w) is reduced at each iteration of the algorithm, and the following formula is satisfied:
J(w(n+1))＜J(w(n)) (4)
Step 3.4.2: the weight vector w is continuously adjusted along the steepest descent direction, i.e. along the negative gradient direction, the gradient vector is expressed as follows:
the steepest descent algorithm may be performed by:
wherein: n represents the iteration number and μ is the step size;
in the iterative process, the adjustment quantity of the weight vector is as follows:
Until the control error epsilon > 0, step 2 is further performed.
Step 3.5: if the step 3.4 is not satisfied, judging whether the convergence criterion is met, if yes, outputting a Pareto solution set, otherwise, updating the position and the speed of the particles, and executing the step 2;
The invention relates to a design of a parabolic groove on the surface of a miniature dynamic pressure gas thrust bearing, which has the advantages that: compared with a bearing without parabolic groove textures, the bearing has the advantages that the dimensionless bearing capacity of the bearing is improved by the parabolic groove textures, and particularly, the dimensionless bearing capacity is improved more remarkably under the condition of smaller convergence ratio; with the increase of the wide-neck ratio, the parabolic groove textures show greater potential in improving the dimensionless bearing capacity of the bearing; the friction surface is locally textured in the inlet area, so that the rigidity and stability of a lubricating oil film are improved, abrasion and friction force can be reduced, and an ideal effect can be obtained by designing geometric parameters and depth of textures under different working conditions. And provides a design method capable of quickly and efficiently obtaining globally optimal texture parameters and distribution forms.
Other embodiments of the application will be apparent to those skilled in the art from consideration of the specification and practice of the application disclosed herein. This application is intended to cover any variations, uses, or adaptations of the application following, in general, the principles of the application and including such departures from the present disclosure as come within known or customary practice within the art to which the application pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the application being indicated by the following claims.
Claims (2)
1. The design method of the parabolic groove on the surface of the miniature dynamic pressure gas thrust bearing is characterized by comprising the following steps of:
s1: aiming at the shape of the parabolic groove texture on the surface, different convergence ratios, relative groove depths and outlet non-texture ratios of the parabolic groove texture are set as particles with different positions and speeds in the population, the particles are initialized, and the population is randomly initialized;
The principle of updating the position and velocity of the particles in step S1 is as follows:
Wherein v id is the optimal speed of the global particles; x id is the optimal position of the global particle; i is the particle number; d is the moment; w is inertial weight; c 1、c2 is a learning factor; p id is the optimal position of the particle; r 1、r2 is a random value between 0 and 1; p gd is the best position of the global particle;
s2: establishing a three-dimensional model of a calculation domain, carrying out grid division on the three-dimensional model to generate a grid file, and carrying out bearing capacity calculation of bearings with different convergence ratios by using a CFD (computational fluid dynamics) technology;
s3: performing Pareto dominant sorting according to the bearing capacity calculation result of the particles obtained in the step S2 to obtain individual optimal particles, population optimal particles and Pareto solution sets, and then designing a surface parabolic groove;
The step S3 specifically comprises the following steps:
S301: sorting based on Pareto dominant relations according to fitness, comparing the current individual position with the individual history optimal position, and selecting individual optimal particles, population optimal particles and Pareto solution sets;
S302: updating the Pareto solution set according to the dominant relationship among the populations, wherein the positions and the speeds of the individual optimal particles and the population optimal particles are used as the basis for updating the positions and the speeds of the next generation particles;
S303: judging whether the genetic algebra is an integer multiple of 10, if so, designing by using a steepest descent method, and executing the step S2;
The optimal descent method in step S303 is specifically as follows:
S30301: setting an initial weight vector w (0), and then generating a series of weight vectors, so that the cost function J (w) is reduced at each iteration of the algorithm, and the following formula is satisfied:
J(w(n+1))＜J(w(n)) (4)
s30302: the weight vector w is continuously adjusted along the steepest descent direction, i.e. along the negative gradient direction, the gradient vector is expressed as follows:
the steepest descent algorithm may be performed by:
wherein: n represents the iteration number and μ is the step size;
in the iterative process, the adjustment quantity of the weight vector is as follows:
Until the control error epsilon is more than 0, executing the step 2;
S304: if the step S303 is not satisfied, it is determined whether the convergence criterion is satisfied, if yes, a Pareto solution set is output, otherwise, the position and the speed of the particles are updated, and step S2 is executed.
2. The method for designing parabolic grooves on a miniature dynamic pressure gas thrust bearing surface according to claim 1, wherein said step S2 comprises the steps of:
S201, calculating a calculation domain convergence ratio of the parabolic groove texture;
Wherein, κ is the convergence ratio of the calculated domain, h i is the film thickness at the inlet of the calculated domain, and h o is the film thickness at the outlet of the calculated domain;
S202, calculating dimensionless bearing capacity of the miniature dynamic pressure gas thrust bearing with parabolic groove textures:
Wherein W o is the dimensional bearing capacity of the bearing, U is the calculated domain gas movement speed, mu is the dynamic viscosity of the gas, b is the calculated domain width, and l is the calculated domain length.
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