CN116484755A - Inner curve hydraulic motor roller optimal design method based on elastic flow lubrication - Google Patents
Inner curve hydraulic motor roller optimal design method based on elastic flow lubrication Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 16
- 238000005461 lubrication Methods 0.000 title claims abstract description 14
- 230000004048 modification Effects 0.000 claims abstract description 35
- 238000012986 modification Methods 0.000 claims abstract description 35
- 238000009826 distribution Methods 0.000 claims abstract description 18
- 238000004364 calculation method Methods 0.000 claims description 16
- 238000005457 optimization Methods 0.000 claims description 13
- 238000002939 conjugate gradient method Methods 0.000 claims description 4
- 239000012530 fluid Substances 0.000 claims description 4
- 239000000463 material Substances 0.000 claims description 4
- 238000007493 shaping process Methods 0.000 claims description 3
- 239000003921 oil Substances 0.000 description 35
- 230000000694 effects Effects 0.000 description 3
- 238000004458 analytical method Methods 0.000 description 2
- 230000005540 biological transmission Effects 0.000 description 2
- 239000010687 lubricating oil Substances 0.000 description 2
- 238000002715 modification method Methods 0.000 description 2
- 238000005299 abrasion Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000006073 displacement reaction Methods 0.000 description 1
- 230000002068 genetic effect Effects 0.000 description 1
- 239000000314 lubricant Substances 0.000 description 1
- 238000005096 rolling process Methods 0.000 description 1
- 238000010998 test method Methods 0.000 description 1
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- G06F30/28—Design optimisation, verification or simulation using fluid dynamics, e.g. using Navier-Stokes equations or computational fluid dynamics [CFD]
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- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
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Abstract
The invention discloses an inner curve hydraulic motor roller optimal design method based on elastic flow lubrication. An improved roller busbar logarithmic modification equation is introduced first, the singularity of the traditional equation at the roller end is eliminated, and then two variables are introduced into the modification equation as optimal design parameters. And calculating the contact pressure distribution between the roller and the guide rail according to the elastic mechanics theory, then dispersing the roller into a plurality of slices along the axial direction, and calculating the thickness of an oil film between each slice and the guide rail based on the elastic flow lubrication theory. And finally, optimizing the logarithmic contour of the roller with the aim of reducing the contact pressure, increasing the oil film thickness, improving the contact pressure and the oil film thickness distribution uniformity and improving the bearing capacity, and finally obtaining the optimal logarithmic repair type roller design parameters.
Description
Technical Field
The invention belongs to the technical fields of tribology and fluid transmission, and particularly relates to an inner curve hydraulic motor roller optimization design method based on elastohydrodynamic lubrication.
Background
The roller in the inner curve hydraulic motor is one of the most important transmission parts of the motor, is in a line contact state with the inner curve guide rail, and converts hydraulic pressure into mechanical torque for pushing the motor to rotate through rolling. However, the straight busbar roller is easy to generate stress concentration at two ends of the roller under heavy load, and the fatigue life of the roller is affected. Lundberg proposed a roller profile logarithmic modification method, which has been considered as one of the most optimal roller modification methods in the dry friction state. However, in practical application, the roller and the guide rail thereof are often in a spring-flow lubrication state, and the edge effect at two ends of the roller cannot be reduced to the greatest extent by the conventional modification mode. In addition, the edge stress cannot be completely eliminated due to the fact that the roller is too small in modification amount, and the contact stress at the center of a roller bus is increased due to the fact that the roller is too large in modification amount. Therefore, there is a problem of optimizing design in the modification amount design.
The calculation of the film thickness of the elastic lubricating oil of the roller and the guide rail thereof usually adopts an analytical empirical formula or a two-dimensional Reynolds equation numerical method. However, the analysis of the empirical formula treats the roller as a wireless length, the axial oil film thickness is constant, and the axial oil film distribution under the influence of stress concentration cannot be described. The numerical solution of the two-dimensional Reynolds equation is too complex, a great deal of time is consumed in the optimization process, and the optimization calculation efficiency is low.
In summary, a simple and effective method is provided to calculate the thickness of the lubricant film between the roller and the guide rail, and to optimally design the bus profile.
Disclosure of Invention
The invention aims to provide a simple and effective method for calculating the thickness of the lubricating oil film between a roller and a guide rail, optimally designing the contour of a bus, improving the bearing capacity and the fatigue life of the roller, and reducing friction and abrasion. Has the advantages of high efficiency, low cost, strong practicability and the like. Can be combined with a test method to guide the test, and save the test cost.
The invention is realized by the following technical scheme: the method is used for optimizing the design of the contour of the bus of the limited long-line contact friction pair of the inner curve hydraulic motor, and specifically comprises the following steps:
(1) According to the logarithmic modification equation, two variables are introduced into the coefficient and logarithmic term of the logarithmic modification equation, so that the singularity of the roller end is eliminated;
(2) According to the elastic mechanics theory, a conjugate gradient method is adopted to calculate the contact pressure distribution between the roller and the guide rail thereof, the bus profile after the modification of the modified roller pair modification equation in the step (1) is considered during calculation, and the working condition of the roller is considered;
(3) Dispersing the roller into a plurality of slices along the axial direction, and calculating the contact pressure between each slice and the guide rail through the step (2); according to the elastic fluid dynamic pressure lubrication theory, the load parameter in the oil film thickness calculation formula is calculated through the contact pressure of each slice, and then the oil film thickness of each slice in contact with the guide rail is calculated;
(4) Taking two variables introduced in the improved logarithmic modification equation in the step (1) as optimization design parameters of the inner curve hydraulic motor roller, so as to reduce contact pressure, increase oil film thickness, improve uniformity of contact pressure and oil film thickness distribution and improve bearing capacity as targets, optimizing the logarithmic profile of the roller, wherein the contact pressure and the oil film thickness distribution are respectively obtained through calculation in the step (2) and the step (3); and finally obtaining the optimal logarithmic repair type roller design parameters.
Further, according to the logarithmic modification proposed by Lundberg, the modified logarithmic modification equation is:
wherein C is k (y) is the amount of modification of the roller in the axial direction, y is the roller axisThe axial coordinates are directed, and the origin of the coordinates is the axial center of the roller; p is p H The Hertz contact pressure between the roller and the guide rail under the current working condition is represented by E, the equivalent elastic modulus is represented by Σρ, the sum of contact curvatures of the roller and the guide rail is represented by l, the length of the roller is represented by k 1 And k 2 The initial values of the optimal design variables of the roller shaping profile are all set to be 1.
Further, the minimum oil film thickness calculation formula is:
wherein H is m Is a dimensionless film thickness parameter, h m For actual oil film thickness, R x Is equivalent radius of curvature; g * 、U * The non-dimensional material parameters and the non-dimensional speed parameters are respectively.
Further, in the step (4), the logarithmic contour optimization objective function of the roller is:
wherein p is max And p c Maximum contact pressure and center pressure, h, respectively, of the axial contact length of the roller min And h c The minimum oil film thickness and the center oil film thickness of the axial contact length of the roller are respectively.
The invention has the beneficial effects that:
according to the non-Hertz contact stress distribution between the roller and the guide rail, an oil film thickness calculation formula between the roller and the guide rail is deduced, so that a complex numerical iteration process of an oil film thickness numerical calculation method is avoided, and the defect that the axial oil film distribution cannot be described by a traditional analysis method is overcome. The optimal logarithmic repair type roller design parameters are obtained by optimizing the logarithmic contour of the roller, so that the effects of reducing contact pressure, increasing oil film thickness, improving the uniformity of contact pressure and oil film thickness distribution and improving bearing capacity are achieved.
Drawings
FIG. 1 is a flow chart of an inner curve motor roller optimization design.
Fig. 2 is a partial schematic view of a roller-rail in an inner curve hydraulic motor.
FIG. 3 is a graph comparing contact pressure between the optimized front and rear roller tracks.
FIG. 4 is a graph of oil film thickness comparisons between the optimized front and rear roller tracks.
Detailed Description
The invention will be described in detail with reference to the accompanying drawings and specific examples, as shown in fig. 1 and 2, comprising the following steps:
(1) The roller end singularity is eliminated by improving the logarithmic modification equation according to Lundberg. Two variables were introduced into the modified logarithmic modification equation, with the initial value set to 1.
(2) According to the elastic mechanics theory, a conjugate gradient method is adopted to calculate the contact pressure distribution between the roller and the guide rail thereof, and the roller modification equation established in the step (1) is considered during calculation, and meanwhile, the working condition of the roller is considered.
(3) The roller is axially discretized into a plurality of slices, and the contact pressure between each slice and the guide rail is calculated in the step (2). According to the elastic fluid dynamic pressure lubrication theory, the load parameter in the oil film thickness calculation formula is calculated through the contact stress of each slice, and then the oil film thickness of each slice in contact with the guide rail is calculated.
(4) And (3) optimizing the logarithmic contour of the roller with the two variables determined in the step (1) as optimization design parameters and aiming at reducing the contact pressure, increasing the oil film thickness, improving the uniformity of the contact pressure and the oil film thickness distribution and improving the bearing capacity, wherein the contact pressure and the oil film thickness distribution are calculated by the step (2) and the step (3), respectively. And finally obtaining the optimal logarithmic repair type roller design parameters.
To eliminate the singularities at both ends of the logarithmic repair roller, the improved logarithmic repair equation is:
wherein C is k And (y) is the axial modification quantity of the roller, y is the axial coordinate of the roller, and the origin of the coordinate is the axial center of the roller. P is p H The Hertz contact pressure between the roller and the guide rail under the current working condition is represented by E, the equivalent elastic modulus is represented by Σρ, the sum of contact curvatures of the roller and the guide rail is represented by l, the length of the roller is represented by k 1 And k 2 The design variable is optimized for the roller shaping profile.
To calculate the contact pressure between the roller and the rail, the Boussineq equation describing the relationship between contact stress and contact deformation in infinite half space needs to be solved, namely:
where w (x, y) is the contact deformation at the coordinates (x, y), p (ζ, η) is the contact pressure at the coordinates (ζ, η), v is the poisson's ratio of the material, and E is the elastic modulus. Furthermore, the gap h (x, y) between the roller and the rail can be described as:
h(x,y)＝B(x,y)+w(x,y)-δ
where δ is the relative displacement of the roller and rail under external load and B (x, y) is the initial gap between the roller and rail:
wherein R is 1 And R is 2 The radii of the rollers and the guide rail are respectively, and beta is the relative deflection angle between the rollers and the guide rail. In order to balance with the external load W, the contact pressure between the roller and the rail needs to satisfy the balance equation:
wherein A is c Is the actual contact area of the roller and the rail. There are two additional conditions:
when h (x, y) is greater than 0, the rollers are not in contact with the guide rail, and the contact pressure is 0; when h (x, y) is less than 0, the rollers and the guide rail are in contact, and the contact pressure is greater than 0. According to the equation, the contact pressure is calculated iteratively by adopting a conjugate gradient method, and the contact deformation calculation in iteration adopts a discrete convolution-fast Fourier transform (DC-FFT) method.
The minimum oil film thickness calculation formula is:
H m ＝h m /R x ＝2.65G *0.54 U *0.7 W *(-0.13)
wherein H is m Is a dimensionless film thickness parameter, h m For actual oil film thickness, R x Is the equivalent radius of curvature. G * 、U * 、W * The non-dimensional material parameter, the non-dimensional speed parameter and the non-dimensional load parameter are respectively. Non-dimensional oil film thickness parameter W * The method comprises the following steps: w (W) * ＝W/ER x l. According to the Hertz contact theory, the relationship between the external load and the maximum contact stress of the roller is as follows:
substituting to calculate dimensionless oil film thickness parameter W * . Substituting the contact pressure of each slice of the roller axial direction and the guide rail into p H The minimum oil film thickness of the slice and the guide rail can be calculated.
The roller modification parameter optimization aims at reducing contact pressure, increasing oil film thickness, improving contact pressure and oil film thickness distribution uniformity and improving bearing capacity, and the objective function is as follows:
wherein p is max And p c Maximum contact pressure and center pressure, h, respectively, of the axial contact length of the roller min And h c The minimum oil film thickness and the center oil film thickness of the axial contact length of the roller are respectively.
Finally with f (k) 1 ,k 2 ) Minimum value for objective function, k 1 ，k 2 And for designing variables, adopting a genetic algorithm to solve the optimal logarithmic modification parameters, and improving the bearing capacity and the lubrication state of the roller.
Further described in one embodiment, the roller radius R 1 7mm, a roller length l of 26mm, a rail diameter R 2 45mm, the external load of the roller is 10kN, the relative deflection angle between the roller and the guide rail is 0.1 DEG, a logarithmic modification mode is adopted, and the initial modification parameter k is the initial modification parameter 1 ，k 2 All set to 0. Optimized modification parameter k 1 ，k 2 1.38 and 0.84, respectively. The initial parameters gave an objective function result of 0.0628 and the optimized parameters gave an objective function result of 0.0254. The contact pressure and the oil film thickness of the two groups of parameters are respectively shown in fig. 3 and 4, and compared with an unmodified roller, the initial modification parameters can effectively reduce the contact pressure concentration caused by the edge effect and improve the oil film thickness of the edge of the roller, but the contact pressure and the oil film thickness are uneven. The optimized modification parameters not only reduce the edge contact pressure, but also make the pressure distribution and oil film thickness distribution of the whole contact length more uniform, and improve the bearing capacity of the roller.
The above-described embodiments are intended to illustrate the present invention, not to limit it, and any modifications and variations made thereto are within the spirit of the invention and the scope of the appended claims.
Claims (4)
1. The optimization design method for the inner curve hydraulic motor roller based on the elastic flow lubrication is characterized by being used for optimizing the contour of the limited long line contact friction pair bus of the inner curve hydraulic motor, and specifically comprising the following steps:
(1) According to the logarithmic modification equation, two variables are introduced into the coefficient and logarithmic term of the logarithmic modification equation, so that the singularity of the roller end is eliminated;
(2) According to the elastic mechanics theory, a conjugate gradient method is adopted to calculate the contact pressure distribution between the roller and the guide rail thereof, the bus profile after the modification of the modified roller pair modification equation in the step (1) is considered during calculation, and the working condition of the roller is considered;
(3) Dispersing the roller into a plurality of slices along the axial direction, and calculating the contact pressure between each slice and the guide rail through the step (2); according to the elastic fluid dynamic pressure lubrication theory, the load parameter in the oil film thickness calculation formula is calculated through the contact pressure of each slice, and then the oil film thickness of each slice in contact with the guide rail is calculated;
(4) Taking two variables introduced in the improved logarithmic modification equation in the step (1) as optimization design parameters of the inner curve hydraulic motor roller, so as to reduce contact pressure, increase oil film thickness, improve uniformity of contact pressure and oil film thickness distribution and improve bearing capacity as targets, optimizing the logarithmic profile of the roller, wherein the contact pressure and the oil film thickness distribution are respectively obtained through calculation in the step (2) and the step (3); and finally obtaining the optimal logarithmic repair type roller design parameters.
2. The optimization design method for the inner curve hydraulic motor roller based on the elastic flow lubrication according to claim 1 is characterized in that according to the logarithmic modification proposed by Lundberg, the improved logarithmic modification equation is as follows:
wherein C is k (y) is the amount of modification of the roller in the axial direction, y is the roller axisThe axial coordinates are directed, and the origin of the coordinates is the axial center of the roller; p is p H The Hertz contact pressure between the roller and the guide rail under the current working condition is represented by E, the equivalent elastic modulus is represented by Σρ, the sum of contact curvatures of the roller and the guide rail is represented by l, the length of the roller is represented by k 1 And k 2 The initial values of the optimal design variables of the roller shaping profile are all set to be 1.
3. The optimal design method for the inner curve hydraulic motor roller based on the elastic flow lubrication according to claim 2 is characterized in that a minimum oil film thickness calculation formula is as follows:
wherein H is m Is a dimensionless film thickness parameter, h m For actual oil film thickness, R x Is equivalent radius of curvature; g * 、U * The non-dimensional material parameters and the non-dimensional speed parameters are respectively.
4. The optimization design method for the inner curve hydraulic motor roller based on the elastic flow lubrication according to claim 2, wherein in the step (4), the logarithmic contour optimization objective function of the roller is as follows:
wherein p is max And p c Maximum contact pressure and center pressure, h, respectively, of the axial contact length of the roller min And h c The minimum oil film thickness and the center oil film thickness of the axial contact length of the roller are respectively.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102644663A (en) * | 2012-04-26 | 2012-08-22 | 北京石油化工学院 | Cylindrical roller multi-circular-arc variable curvature profile engineering simulation method |
| CN110765617A (en) * | 2019-10-25 | 2020-02-07 | 常州市乾憬轴承科技有限公司 | Lubrication theory-based cylindrical roller bearing roller logarithmic modification design method |
| CN111919040A (en) * | 2018-03-28 | 2020-11-10 | Ntn株式会社 | Tapered roller bearing |
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- 2023-01-18 CN CN202310057286.6A patent/CN116484755B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102644663A (en) * | 2012-04-26 | 2012-08-22 | 北京石油化工学院 | Cylindrical roller multi-circular-arc variable curvature profile engineering simulation method |
| CN111919040A (en) * | 2018-03-28 | 2020-11-10 | Ntn株式会社 | Tapered roller bearing |
| CN110765617A (en) * | 2019-10-25 | 2020-02-07 | 常州市乾憬轴承科技有限公司 | Lubrication theory-based cylindrical roller bearing roller logarithmic modification design method |
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