Self-adaptive modification method of cylindrical roller bearing for multi-wire cutting machine

Abstract

The invention discloses a self-adaptive modification method of a cylindrical roller bearing for a multi-wire cutting machine, which comprises the following steps of: selecting four modification parameters in a four-parameter modification model as design variables of an optimization model, and giving constraint conditions; and selecting a comprehensive performance evaluation index of roller bus oil film pressure distribution as an optimization target, and solving the target function under each group of design variables through the developed elastohydrodynamic lubrication model. And obtaining an optimal solution of the target function through an optimization algorithm. The corresponding modified contour is the modified contour of the cylindrical roller bearing for the multi-wire cutting machine with the optimal target. According to the method, the modification amount and the modification curvature can be sensitively adjusted through the improved logarithm modification function and the arc modification function, the lubricating performance of the cylindrical roller bearing for the multi-wire cutting machine can be accurately calculated through the developed elastohydrodynamic lubrication model, and the optimal modification contour can be efficiently obtained through the optimization algorithm; the method has the advantages of complete consideration factors, good calculation precision, high calculation efficiency and the like.

Description

Technical Field

[0001] This invention relates to the field of bearing design and modification technology, specifically to an adaptive modification method for cylindrical roller bearings used in multi-wire cutting machines. Background Technology

[0002] Multi-wire cutting machines are key equipment in the processing of hard and brittle materials such as semiconductors, photovoltaics, and sapphire. Their spindle systems generally use cylindrical roller bearings to meet the requirements of high speed and high precision.

[0003] Cylindrical roller bearings feature a line contact between the rollers and raceways, offering high load-carrying capacity but also making them prone to pressure concentration at the edges. Studies have shown that the oil film pressure distribution in cylindrical roller bearings significantly impacts bearing life. Under high-speed, heavy-load operating conditions, traditional cylindrical roller bearings are susceptible to edge effects and oil film rupture, severely affecting their service life.

[0004] To improve pressure distribution and eliminate edge effects, roller profiles are typically modified and optimized. Common modification methods include partial circular arc modification, full convex circular arc modification, and logarithmic modification. However, these modification methods may still result in localized oil film pressure peaks at the intersection of the arc and the straight line, or in the middle of the roller, leading to premature bearing failure. Furthermore, existing modification methods often employ fixed, single modification curves, lacking adaptability to actual operating conditions and bearing structural parameters. This makes it difficult to achieve optimal matching between the modified profile and specific application scenarios, thus limiting further improvements in bearing performance. Summary of the Invention

[0005] The purpose of this section is to outline some aspects of the embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0006] Therefore, the object of the present invention is to provide an adaptive shaping method for cylindrical roller bearings used in multi-wire cutting machines, so as to solve the problems mentioned in the background art.

[0007] To address the aforementioned technical problems, according to one aspect of the present invention, the present invention provides the following technical solution:

[0008] An adaptive profile modification method for cylindrical roller bearings used in multi-wire EDM machines, comprising the following steps:

[0009] S1. Improve the logarithmic shaping curve and circular arc shaping curve of the roller, introduce four shaping parameters to coordinately control the shaping amount and shaping curvature, and construct a four-parameter shaping model.

[0010] S2. Construct an elastohydrodynamic lubrication model suitable for cylindrical roller bearings used in multi-wire cutting machines. The elastohydrodynamic lubrication model is used to simulate the oil film pressure distribution and oil film thickness between the roller and the raceway.

[0011] S3. Select four shaping parameters as design variables for the optimization model and set constraints for each design variable. Use the comprehensive performance evaluation index of the oil film pressure distribution of the roller busbar as the optimization objective function. Calculate the optimization objective function value corresponding to each set of design variables through the elastohydrodynamic lubrication model.

[0012] S4. The design variables are iteratively optimized using an optimization algorithm until the convergence condition is met, and the optimal solution of the optimization objective function is obtained. The modified profile corresponding to the optimal solution is the optimal modified profile of the cylindrical roller bearing for the multi-wire cutting machine.

[0013] As a preferred embodiment of the adaptive shaping method for cylindrical roller bearings used in multi-wire cutting machines described in this invention, in step S1, the four shaping parameters are the load coefficient K1, the logarithmic crown length coefficient K2, the crown reduction of logarithmic shaping K3, and the end arc radius R. y Where K1 controls the overall shaping amount, K2 controls the length of the shaping area, K3 controls the descent rate of the shaping curve, and R... y Used to control the shape of the roller ends and the smoothness of the transition.

[0014] In a preferred embodiment of the adaptive shaping method for cylindrical roller bearings used in multi-wire cutting machines described in this invention, in step S1, the shaping function expression of the four-parameter shaping model is:

[0015]

[0016] In the formula: A=0.001K1; L1=(1-K2)L; L2=0.9L, and y is the direction coordinate of the roller generatrix.

[0017] As a preferred embodiment of the adaptive shaping method for cylindrical roller bearings used in multi-wire cutting machines according to the present invention, before step S1, a parameter acquisition step is included: acquiring the basic parameters and operating parameters of the cylindrical roller bearing used in multi-wire cutting machines. The basic parameters include roller length, roller diameter, bearing pitch circle diameter, and number of rollers. The operating parameters include bearing working load, rotational speed, and lubricating oil viscosity.

[0018] As a preferred embodiment of the adaptive modification method for cylindrical roller bearings used in multi-wire cutting machines according to the present invention, the construction process of the elastohydrodynamic lubrication model in step S2 includes: first establishing the contact pair film thickness equation for simultaneous modification of roller-raceway, and then coupling the Reynolds equation, the Roelands viscous compression equation, the Dowson-Higginson compaction equation and the roller load balance equation to form an elastohydrodynamic lubrication model suitable for high-speed heavy-load conditions of multi-wire cutting machines.

[0019] In a preferred embodiment of the adaptive shaping method for cylindrical roller bearings used in multi-wire cutting machines described in this invention, in step S3, the objective function expression of the comprehensive performance evaluation index is: F = α×(P max / N max ) + β×(P var / N var );

[0020] Where F is the comprehensive performance evaluation value; P max P represents the maximum oil film pressure in the direction of the busbar after the reshaping process. var The variance of oil film pressure in the direction of the busbar after shaping; N max This represents the maximum oil film pressure in the direction of the unmodified busbar; N var The variance of oil film pressure in the direction of the unmodified generatrix; α and β are weighting coefficients, and satisfy α + β = 1, α > 0, β > 0.

[0021] In a preferred embodiment of the adaptive shaping method for cylindrical roller bearings used in multi-wire cutting machines described in this invention, the weighting coefficient α ranges from 0.6 to 0.8, and the weighting coefficient β ranges from 0.2 to 0.4.

[0022] As a preferred embodiment of the adaptive shaping method for cylindrical roller bearings used in multi-wire cutting machines described in this invention, in step S3, the constraints of each design variable are: K1∈(0,5], K2∈(0,1], K3∈[1,10], R y ∈[5,50]; where K1, K2, and K3 are dimensionless parameters.

[0023] As a preferred embodiment of the adaptive shaping method for cylindrical roller bearings used in multi-wire cutting machines according to the present invention, in step S4, the optimization algorithm is a genetic algorithm or a particle swarm optimization algorithm; the convergence condition is that the change in the objective function value between two adjacent generations during the iteration process is less than a set threshold, or the number of iterations reaches the preset maximum number of genetic generations.

[0024] As a preferred embodiment of the adaptive profile modification method for cylindrical roller bearings used in multi-wire cutting machines according to the present invention, after step S4, the method further includes the following steps: importing the parameter data of the optimal profile modification into a grinding equipment for roller grinding of the cylindrical roller bearings used in multi-wire cutting machines to manufacture adaptive profile modification cylindrical roller bearings.

[0025] Compared with the prior art, the beneficial effects of the present invention are:

[0026] 1. By flexibly combining the four shaping parameters, a wide variety of shaping curves can be generated, which can better adapt to different bearing structural parameters and actual working conditions, and achieve personalized optimal design.

[0027] 2. Based on the theory of elastohydrodynamic lubrication and with comprehensive performance evaluation indicators as the optimization target, the obtained optimal profile can simultaneously reduce the maximum oil film pressure and improve the uniformity of pressure distribution, effectively eliminating edge pressure concentration, thereby significantly improving the bearing's load-bearing capacity and fatigue life.

[0028] 3. Balancing efficiency and accuracy: By coupling advanced optimization algorithms with professional performance calculation models, the optimization process is automated while ensuring the accuracy of calculation results, greatly improving design efficiency and overcoming the limitations of traditional trial-and-error methods or single curve methods. Attached Figure Description

[0029] To more clearly illustrate the technical solutions of the embodiments of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and detailed embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0030] Figure 1 This is a flowchart of an adaptive shaping method for cylindrical roller bearings used in multi-wire cutting machines according to the present invention;

[0031] Figure 2 A schematic diagram of the outline of the four-parameter shaping model provided by the present invention;

[0032] Figure 3 A comparative schematic diagram of oil film pressure distribution under four loading conditions for unmodified rollers provided by the present invention.

[0033] Figure 4 This is a comparative schematic diagram of oil film pressure distribution under the optimal roller-raceway allocation provided by the present invention. Detailed Implementation

[0034] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0035] like Figure 1 As shown, the present invention discloses an adaptive shaping method for cylindrical roller bearings used in multi-wire EDM machines, the specific steps of which are as follows:

[0036] S1. Improve the logarithmic and circular arc shaping curves of the rollers by introducing four shaping parameters to coordinately control the shaping amount and curvature, and construct a four-parameter shaping model. The four shaping parameters are the load coefficient K1, the logarithmic convexity length coefficient K2, the convexity reduction of the logarithmic shaping K3, and the end arc radius R. y Where K1 controls the overall shaping amount, K2 controls the length of the shaping area, K3 controls the descent rate of the shaping curve, and R... y The shaping function expression of the four-parameter shaping model, used to control the shape and smoothness of the roller end, is as follows:

[0037]

[0038] In the formula: A = 0.001K1; L1 = (1-K2)L; L2 = 0.9L, y is the coordinate of the roller generatrix direction. As an optimal choice, the constraints of each design variable are: K1∈(0,5], K2∈(0,1], K3∈[1,10], R y ∈[5,50]; where K1, K2, and K3 are dimensionless parameters.

[0039] S2. Construct an elastohydrodynamic lubrication model suitable for cylindrical roller bearings used in multi-wire cutting machines. The elastohydrodynamic lubrication model is used to simulate the oil film pressure distribution and oil film thickness between the roller and the raceway. The construction process of the elastohydrodynamic lubrication model includes: first establishing the contact pair film thickness equation with simultaneous roller-raceway modification, and then coupling the Reynolds equation, the Roelands viscous pressure equation, the Dowson-Higginson pressure equation and the roller load balance equation to form an elastohydrodynamic lubrication model suitable for high-speed and heavy-load conditions of multi-wire cutting machines.

[0040] S3. Select four shaping parameters as design variables for the optimization model, and set constraints for each design variable. Use the comprehensive performance evaluation index of the roller generatrix oil film pressure distribution as the optimization objective function. Calculate the optimization objective function value corresponding to each set of design variables using the elastohydrodynamic lubrication model. The objective function expression for the comprehensive performance evaluation index is: F = α × (P max / N max ) + β×(P var / N var ); where F is the comprehensive performance evaluation value; P maxP represents the maximum oil film pressure in the direction of the busbar after the reshaping process. var The variance of oil film pressure in the direction of the busbar after shaping; N max This represents the maximum oil film pressure in the direction of the unmodified busbar; N var The variance of oil film pressure in the direction of the unmodified busbar is denoted as α; α and β are weighting coefficients, and satisfy α + β = 1, α > 0, β > 0. As a preferred choice, the value range of the weighting coefficient α is 0.6-0.8, and the value range of the weighting coefficient β is 0.2-0.4.

[0041] S4. The design variables are iteratively optimized using an optimization algorithm until the convergence condition is met, and the optimal solution of the optimization objective function is obtained. The modified profile corresponding to the optimal solution is the optimal modified profile of the cylindrical roller bearing for the multi-wire cutting machine. Preferably, the optimization algorithm is a genetic algorithm or a particle swarm optimization algorithm. The convergence condition is that the change in the objective function value between two adjacent generations is less than a set threshold, or the number of iterations reaches the preset maximum number of genetic generations.

[0042] Preferably, before step S1, a parameter acquisition step is included: acquiring the basic parameters and operating parameters of the cylindrical roller bearing for the multi-wire cutting machine. The basic parameters include roller length, roller diameter, bearing pitch circle diameter, and number of rollers. The operating parameters include bearing working load, speed, and lubricating oil viscosity. After step S4, the following step is included: importing the parameter data of the optimal profile into a grinding machine for roller grinding of the cylindrical roller bearing for the multi-wire cutting machine to manufacture an adaptive profile cylindrical roller bearing.

[0043] To illustrate the technical effect of the adaptive shaping method for cylindrical roller bearings used in multi-wire cutting machines according to the present invention, the following description uses the NU2218E cylindrical roller bearing as an example, mainly including the following steps:

[0044] First, based on the actual working requirements of the multi-wire cutting machine and the bearing structure, the basic parameters of the cylindrical roller bearing are determined, including roller length L, roller diameter, bearing pitch circle diameter, number of rollers, etc., and its working load, speed, lubricating oil viscosity and other working condition parameters are clarified to provide input conditions for subsequent shape modification design and analysis.

[0045] Secondly, a brief explanation of the mathematical expression for traditional reshaping methods will be provided to facilitate comparison and understanding:

[0046] The contour function for full-circle arc shaping is usually expressed as:

[0047]

[0048] In the formula, R is the radius of the full circular arc.

[0049] The empirical formulas given by Palmgren are commonly used in the calculation of cylindrical roller bearings:

[0050]

[0051] In the formula: E1 and E2 are the elastic moduli of the rolling element and raceway materials, and v1 and v2 are the Poisson's ratios of the materials.

[0052] The contour function of logarithmic shaping is usually expressed as:

[0053]

[0054] Although the aforementioned traditional shaping methods are widely used, they still suffer from problems such as uneven pressure distribution and significant edge effects.

[0055] Therefore, the four-parameter shaping function proposed in this invention is used to mathematically characterize the roller profile. This shaping function is an improvement on the traditional logarithmic curve and circular arc curve, and its expression is:

[0056]

[0057] In the formula: A = 0.001K1; L1 = (1-K2)L; L2 = 0.9L; K1 is the load coefficient, used to control the overall shaping amount; K2 is the logarithmic convexity length coefficient, used to control the length of the shaping area; K3 is the convexity decrease of the logarithmic shaping, used to control the curve descent rate; R y y is the end radius, used to control the end shape and smooth transition; y is the roller generatrix direction coordinate. By adjusting these four parameters, a shape like... can be generated. Figure 2 The various profiles shown enable flexible and precise control over the roller convexity.

[0058] Then, based on the roller's shape modification method, the equation for the contact pair film thickness is determined as follows:

[0059]

[0060] Where E' is the equivalent elastic modulus, 2 / E'=(1-v1) 2 ) / E1+(1- v2 2 ) / E2,h o Let E′ be the rigid body center-to-center distance at the center of the contact area, E′ be the equivalent elastic modulus, Ω be the entire computational domain, and R be the rigid body center-to-center distance. x Let z(y) be the equivalent curvature radius of the cylindrical roller after the raceway is equivalent to that of the raceway, and z(y) be the shape modification equation.

[0061] Then, an elastohydrodynamic (EHL) analysis model suitable for high-speed, heavy-load operation of multi-wire EDM machines was constructed. This model couples the Reynolds equation, the Roelands viscous-compression equation, the Dowson-Higginson compressive equation, and the roller load balance equation. It can accurately simulate key performance indicators such as oil film thickness distribution, oil film pressure distribution, and elastic deformation in the roller-raceway region, providing an accurate and reliable calculation tool for bearing performance evaluation under each set of modified parameters. The model's output will be used to obtain the maximum oil film pressure (P) in the generatrix direction after modification. max ) and pressure variance (P var ).

[0062] The Reynolds equations for isothermal finite-length line contact elastohydrodynamics are as follows:

[0063]

[0064] The Roelands viscous-compression equation is shown below:

[0065]

[0066] The Dowson-Higginson pressure equations are shown below:

[0067]

[0068] The load balance equations are as follows:

[0069]

[0070] Where: p is the pressure; h is the film thickness; u is the entrainment speed between the rolling element and the raceway, u=πn / 120D pw (1-γ 2 ); n is the rotational speed (r / min) of the inner or outer ring; γ=D w / D pw η and ρ are the viscosity and density of the lubricant, respectively; α0 is the pressure-viscosity coefficient; η0 is the viscosity at atmospheric temperature; Q is the load on the roller.

[0071] Next, an optimization design model is established. The objective function is the comprehensive performance evaluation index F, which reflects the magnitude and uniformity of oil film pressure distribution. Four shaping parameters K1, K2, K3, and R are used as the model parameters. y These are design variables, and their constraint ranges are set based on engineering experience and bearing design requirements. For example: K1∈(0,5], K2∈(0,1], K3∈[1,10], R y ∈[5,50]. The expression for the objective function F is: F = α×(P max / N max ) + β×(Pvar / N var ), where N max and N var These represent the maximum value and variance baseline value of the oil film pressure in the direction of the unmodified busbar, respectively, with α and β being weighting coefficients (preferably α=0.7, β=0.3 in this embodiment).

[0072] Finally, intelligent optimization algorithms such as Genetic Algorithm (GA) are used to automatically iterate and optimize the above model. The optimization process includes: initializing the population and randomly generating multiple sets of shaping parameters; calculating the oil film pressure distribution corresponding to each set of parameters using the EHL model; calculating the objective function F value accordingly; performing selection, crossover, and mutation operations based on the objective function value (the smaller the F value, the better the performance) to generate a new generation of population; iterating cyclically until the convergence condition is met (such as the change in the objective function being less than a set threshold or reaching the maximum number of iterations), and finally outputting the optimal shaping parameter combination that minimizes the objective function F value. The shaping profile determined by this optimal parameter combination is the adaptive optimal convexity profile sought in this invention.

[0073] like Figure 3 As shown in the figure, the edge pressure concentration between the unmodified roller and the raceway calculated in this embodiment is more pronounced under heavy load conditions, so the roller needs to be modified.

[0074] The optimized shaping parameters are substituted into the shaping function to generate the final shaped profile, and its performance is verified using an elastohydrodynamic (EHL) model. Figure 4 As shown, under four loads of 1000N, 4000N, 7000N, and 10000N (corresponding to sub-figures a, b, c, and d respectively), the method of this invention was applied to obtain a set of shaping parameters through iterative optimization. The four-parameter shaping profile proposed in this invention exhibits oil film pressure distribution characteristics superior to traditional full-circle shaping and logarithmic shaping. This shaping method effectively suppresses edge pressure concentration at the roller end, making the overall pressure distribution smoother, significantly reducing the maximum oil film pressure value, and demonstrating good load adaptability and stability. After verification that it meets the design requirements, the shaping profile data can be directly used for bearing grinding to manufacture high-performance adaptive shaping cylindrical roller bearings. This result proves that the optimized shaping profile can significantly improve the bearing capacity and service life under high-speed and heavy-load conditions.

[0075] Although the present invention has been described above with reference to embodiments, various modifications can be made and components can be replaced with equivalents without departing from the scope of the invention. In particular, as long as there is no structural conflict, the features in the disclosed embodiments can be combined with each other in any manner. The lack of an exhaustive description of these combinations in this specification is merely for the sake of brevity and resource conservation. Therefore, the present invention is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. An adaptive profile modification method for cylindrical roller bearings used in multi-wire cutting machines, characterized in that, The steps are as follows: S1. Improve the logarithmic shaping curve and circular arc shaping curve of the roller, introduce four shaping parameters to coordinately control the shaping amount and shaping curvature, and construct a four-parameter shaping model. S2. Construct an elastohydrodynamic lubrication model suitable for cylindrical roller bearings used in multi-wire cutting machines. The elastohydrodynamic lubrication model is used to simulate the oil film pressure distribution and oil film thickness between the roller and the raceway. S3. Select four shaping parameters as design variables for the optimization model and set constraints for each design variable. Use the comprehensive performance evaluation index of the oil film pressure distribution of the roller busbar as the optimization objective function. Calculate the optimization objective function value corresponding to each set of design variables through the elastohydrodynamic lubrication model. S4. The design variables are iteratively optimized using an optimization algorithm until the convergence condition is met, and the optimal solution of the optimization objective function is obtained. The modified profile corresponding to the optimal solution is the optimal modified profile of the cylindrical roller bearing for the multi-wire cutting machine.

2. The adaptive profile modification method for cylindrical roller bearings used in multi-wire cutting machines according to claim 1, characterized in that, In step S1, the four shaping parameters are the load factor K1, the logarithmic convexity length factor K2, the convexity reduction of the logarithmic shaping K3, and the end arc radius R. y Where K1 controls the overall shaping amount, K2 controls the length of the shaping area, K3 controls the descent rate of the shaping curve, and R... y Used to control the shape of the roller ends and the smoothness of the transition.

3. The adaptive profile modification method for cylindrical roller bearings used in multi-wire cutting machines according to claim 2, characterized in that, In step S1, the shape-modification function expression for the four-parameter shape-modification model is: ； In the formula: A=0.001K1; L1=(1-K2)L; L2=0.9L, and y is the direction coordinate of the roller generatrix.

4. The adaptive profile modification method for cylindrical roller bearings used in multi-wire cutting machines according to claim 1, characterized in that, Before step S1, a parameter acquisition step is also included: acquiring the basic parameters and operating parameters of the cylindrical roller bearing for the multi-wire cutting machine. The basic parameters include roller length, roller diameter, bearing pitch circle diameter and number of rollers. The operating parameters include bearing working load, speed and lubricating oil viscosity.

5. The adaptive profile modification method for cylindrical roller bearings used in multi-wire cutting machines according to claim 1, characterized in that, In step S2, the construction process of the elastohydrodynamic lubrication model includes: first establishing the contact pair film thickness equation with simultaneous roller-raceway shaping, and then coupling the Reynolds equation, Roelands viscous pressure equation, Dowson-Higginson pressure equation and roller load balance equation to form an elastohydrodynamic lubrication model suitable for high-speed heavy-duty conditions of multi-wire cutting machines.

6. The adaptive profile modification method for cylindrical roller bearings used in multi-wire cutting machines according to claim 1, characterized in that, In step S3, the objective function expression of the comprehensive performance evaluation index is: F = α×(P) max / N max ) + β×(P var / N var ); Where F is the comprehensive performance evaluation value; P max P represents the maximum oil film pressure in the direction of the busbar after the reshaping process. var The variance of oil film pressure in the direction of the busbar after shaping; N max This represents the maximum oil film pressure in the direction of the unmodified busbar; N var The variance of oil film pressure in the direction of the unmodified generatrix; α and β are weighting coefficients, and satisfy α + β = 1, α > 0, β > 0.

7. The adaptive profile modification method for cylindrical roller bearings used in multi-wire cutting machines according to claim 6, characterized in that, The weighting coefficient α ranges from 0.6 to 0.8, and the weighting coefficient β ranges from 0.2 to 0.

4.

8. The adaptive profile modification method for cylindrical roller bearings used in multi-wire cutting machines according to claim 2, characterized in that, In step S1, the constraints for each design variable are: K1∈(0,5], K2∈(0,1], K3∈[1,10], R y ∈[5,50]; where K1, K2, and K3 are dimensionless parameters.

9. The adaptive profile modification method for cylindrical roller bearings used in multi-wire cutting machines according to claim 1, characterized in that, In step S4, the optimization algorithm is a genetic algorithm or a particle swarm optimization algorithm; the convergence condition is that the change in the objective function value between two adjacent generations during the iteration process is less than a set threshold, or the number of iterations reaches the preset maximum number of genetic generations.

10. The adaptive profile modification method for cylindrical roller bearings used in multi-wire cutting machines according to claim 1, characterized in that, After step S4, the following steps are also included: importing the parameter data of the optimal profile into a grinding machine for roller grinding of cylindrical roller bearings for multi-wire cutting machine, and manufacturing adaptive profile cylindrical roller bearings.

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