CN113468695B - Convexity optimization design method for roller - Google Patents
Convexity optimization design method for roller Download PDFInfo
- Publication number
- CN113468695B CN113468695B CN202110834115.0A CN202110834115A CN113468695B CN 113468695 B CN113468695 B CN 113468695B CN 202110834115 A CN202110834115 A CN 202110834115A CN 113468695 B CN113468695 B CN 113468695B
- Authority
- CN
- China
- Prior art keywords
- roller
- convexity
- formula
- profile
- design
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T11/00—2D [Two Dimensional] image generation
- G06T11/20—Drawing from basic elements, e.g. lines or circles
- G06T11/203—Drawing of straight lines or curves
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/60—Analysis of geometric attributes
- G06T7/62—Analysis of geometric attributes of area, perimeter, diameter or volume
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/60—Analysis of geometric attributes
- G06T7/64—Analysis of geometric attributes of convexity or concavity
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/30—Subject of image; Context of image processing
- G06T2207/30108—Industrial image inspection
- G06T2207/30164—Workpiece; Machine component
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Landscapes
- Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- Geometry (AREA)
- General Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Vision & Pattern Recognition (AREA)
- Computational Mathematics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- General Engineering & Computer Science (AREA)
- Rolling Contact Bearings (AREA)
Abstract
The invention provides a convexity optimization design method of a roller, which is based on a traditional formula to establish a roller convexity design formula as follows: hc (y) =zm×f (x). In the above formula, zm is the convexity value of the edge of the roller profile, and f (x) is the non-dimensionalized convexity profile. The invention only needs to know a certain rated dynamic load ratio d, the roller diameter Dwe and the roller length Lwe, thereby avoiding a large number of complicated calculations, reducing the calculation difficulty, and being capable of being designed without professional designers.
Description
Technical Field
The invention relates to the technical field of bearing machining, in particular to an optimal design method for roller convexity.
Background
The boundary stress concentration of the two ends of the rolling bodies of the straight busbar roller bearing is unavoidable after the bearing is loaded, and the so-called edge effect is generated, so that the fatigue life of the bearing is greatly reduced. The roller surface is designed to be convex in the subsequent design to overcome.
The traditional basic method for designing the logarithmic convexity of the roller bearing comprises the processes of rolling body maximum load calculation, contact stress calculation, logarithmic convexity design calculation and the like. The maximum load calculation mode needs to calculate radial load and joint load by looking up a table respectively; the contact stress is calculated according to the Hertz contact theory, and the calculation modes of the roller, the cylindrical roller and the tapered roller bearing are different, and the correction factors such as materials are also involved; and finally, calculating by adopting a convexity two-calculation formula shown in fig. 1. Therefore, the design method has the advantages of multiple parameters and complex calculation process.
Based on this, the present application is presented.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a convexity optimization design method of a roller, solves the problems of complex convexity quantity design process and large calculation amount of the roller in the prior art, simplifies the convexity design process of the roller, and is suitable for practical use.
In order to achieve the above purpose, the convexity optimization design method of the roller of the invention comprises the following steps:
firstly, setting different loads according to a standard curve to design a contour curve, then adopting curve fitting to obtain convexity values of the contour edge of the roller related to the diameter and the length of the roller, and finally establishing a roller convexity design formula as follows: hc (y) =zm×f (x), where Zm is the convexity value of the roller profile edge and f (x) is the dimensionless convexity profile;
wherein Zm is calculated to obtain the convexity value of the edge of the roller profile according to the formula zm=a (Dwe + Lwe) +b, wherein: a=0.3055×3.0175 d ，b=(2.3303*d) 0.2346/d The method comprises the steps of carrying out a first treatment on the surface of the Where d is the rated dynamic load (Cr) of the bearing with a certain ratio, dwe is the roller diameter and Lwe is the roller length;
wherein f (x) is according to formula f (x) =3.577×10 -3 *exp([ln(2x)+1.529] 2 0.414) calculating to obtain a convexity profile curve, wherein: where x is the ratio of the distance from a point on the roller profile to the midpoint of the roller to the effective length of the roller.
In the present invention, the effective length of the roller means the length of the roller which, in use, makes contact with the raceway and is loaded, except for the chamfer.
The invention is further provided as follows: and d is the ratio of the design load to the rated dynamic load.
The invention is further provided as follows: and d is 0.2 Cr-0.5 Cr. In this range, the optimization design method provided by the invention has a better effect of smoothing stress at the edge.
The invention is further provided as follows: the x is required to satisfy the following conditions: in the value range, the convexity of the roller is lower, the contour curve of the roller is flatter, the roller is more suitable for the bearing condition of the roller in actual use, and the actual processing is more convenient, wherein 0.15lwe < = x < = 0.5lwe.
The beneficial effects of the invention are as follows: the convexity optimization design method only needs to know a certain rated dynamic load ratio d, the roller diameter Dwe and the roller length Lwe, the number of known parameters required to be measured and moved is small, and the calculation steps and the calculation formulas are simplified to a greater extent compared with the traditional method, so that the convexity optimization design method based on the roller can quickly obtain results, complicated calculation is avoided, the calculation process is simple and convenient, and the convexity of the roller is greatly optimized. In short, the convexity optimization design method is simpler and more practical.
Drawings
FIG. 1 is a graph comparing the Lundberg equation with the convexity curve of a roller designed by the method of the present invention at 0.2Cr with an inclination angle;
FIG. 2 is a graph comparing the Lundberg equation with the convexity curve of a roller designed by the method of the present invention at 0.3Cr with an inclination angle;
FIG. 3 is a graph comparing the Lundberg equation with the convexity curve of a roller designed by the method of the present invention at 0.4Cr with an inclination angle;
FIG. 4 is a graph comparing the Lundberg equation with the convexity curve of a roller designed by the method of the present invention at 0.5Cr with an inclination angle;
FIG. 5 is a graph showing the contact stress distribution of the Lundberg formula and 0.2Cr with an inclination angle designed by the method of the present invention;
FIG. 6 is a graph showing the contact stress distribution of the Lundberg formula and 0.3Cr with an inclination angle designed by the method of the present invention;
FIG. 7 is a graph showing the contact stress distribution of the Lundberg formula and 0.4Cr with an inclination angle designed by the method of the present invention;
FIG. 8 is a graph showing the contact stress distribution of the Lundberg formula and 0.5Cr with an inclination angle designed by the method of the present invention;
FIG. 9 is a graph comparing the Lundberg equation with the convexity curve of a roller at 0.2Cr without an angle of inclination, as designed by the method of the present invention;
FIG. 10 is a graph comparing the Lundberg equation with the convexity curve of a roller at 0.3Cr without an angle of inclination as designed by the method of the present invention;
FIG. 11 is a graph comparing the Lundberg equation with the convexity curve of a roller at 0.4Cr without an angle of inclination as designed by the method of the present invention;
FIG. 12 is a graph comparing the Lundberg equation with the convexity curve of a roller at 0.5Cr without an angle of inclination as designed by the method of the present invention;
FIG. 13 is a graph showing the contact stress distribution of the Lundberg formula with 0.2Cr without an angle of inclination as designed by the method of the present invention;
FIG. 14 is a graph showing the contact stress distribution of the Lundberg formula with 0.3Cr without an angle of inclination as designed by the method of the present invention;
FIG. 15 is a graph showing the contact stress distribution of the Lundberg formula with 0.4Cr without an angle of inclination as designed by the method of the present invention;
FIG. 16 is a graph showing the contact stress distribution of the Lundberg formula with 0.5Cr without an angle of inclination as designed by the method of the present invention.
Detailed Description
The invention provides a convexity optimization design method of a roller, which is based on a traditional formula to establish a roller convexity design formula as follows: hc (y) =zm×f (x).
In the above formula, where Zm is the convexity value of the roller profile edge, calculated according to formula (1-1):
Zm=a(Dwe+Lwe)+b （1-1）
wherein Dwe is the roller diameter and Lwe is the roller length.
In the formula (1-1):
a=0.3055*3.0175 d （1-2）
b=(2.3303*d) 0.2346/d （1-3）
where d is the ratio of the design load to the rated dynamic load (Cr), which is typically 0.2Cr to 0.5 Cr.
In the above formula, f (x) is a non-dimensionalized convexity contour curve, and is calculated by the formula (2-1):
f(x)=3.577*10 -3 *exp([ln(2x)+1.529] 2 /0.414) （2-1）
in formula (2-1), x is the ratio of the distance from a point on the roller contour to the midpoint of the roller to the effective length of the roller, and is typically a value of [0.15lwe,0.5lwe ], which takes into account the roller load bearing condition and the fact that at least 0.3Lwe of the middle of the roller is a straight busbar, so that the convexity of the roller best obtained for more efficient packaging is sufficient to overcome the edge effect.
Example 1 some cylindrical roller bearing NU208: the rated dynamic load Cr is 53.9kN. The roller diameter Dwe is 10mm, the roller length Lwe is 10mm, the chamfer angle of the roller is 0.5mm, and the diameter size of the inner race is 50mm.
Using the above data, the roller profile shapes calculated according to the above formulas with no tilt angle and tilt angle (0.001 radian) and substituting 0.2Cr, 0.3Cr, 0.4Cr, and 0.5Cr into the above formulas are shown in fig. 1-4, and the test contact stresses along the length of the roller for the roller profile simulated in commercial software are shown in fig. 5-8, respectively.
Using the above data, the roller profile shapes calculated according to the above formulas with no tilt angles of 0.2Cr, 0.3Cr, 0.4Cr, and 0.5Cr are shown in fig. 9-12, and test contact stresses along the length of the roller for the roller profile simulated in commercial software are shown in fig. 13-16, respectively.
In the upper diagrams, in fig. 1-4 and 9-12, the X axis is the effective length position (mm) of the roller, and the Y axis is convexity (mm); in fig. 5 to 8 and 13 to 16, the X-axis is the distance along the roller (mm) and the Y-axis is the inner race contact stress (MPa).
By comparison, the roller contour shape provided by the design method of the invention has different performances on the straight section and the arc sections at the two side edges compared with the contour curve obtained by using the Lundberg formula in the design of the roller hub shape with or without the inclination angle. In addition, under the action load of 0.4Cr, the contact stress calculated according to the formula of the invention is more gentle, the load distribution is uniformly distributed along the length of the middle part of the roller, and the contact stress of the invention is more gentle compared with the contact stress of a profile curve obtained by using the Lundberg formula (shown in figures 2 and 3) on the whole trend. Under the load of 0.3Cr, the stress distribution obtained by the two curves is completely consistent.
Moreover, under the inclined condition with an inclined angle, the contact stress distribution of the convexity curve provided by the design method is more uniform and flatter, the situation of edge stress concentration is avoided, and the design requirement of practical use is met.
It can be deduced from this that the convexity shape designed by the convexity optimization design method of the present invention is not weaker in function than the conventional method. Moreover, the profile curve of the formula of the invention is more effective from the comparison analysis of contact stress.
In summary, the invention provides a simple and effective optimal design method for roller convexity, and the formula model used by the invention is very simple, so that not only is a great deal of complicated calculation avoided, but also the calculation difficulty is reduced, the design can be realized without professional designers, and the manpower and the working time are greatly saved. Meanwhile, the convexity shape of the roller obtained by the optimal design method is flatter in profile surface stress during bearing, and has better effect of overcoming edge effect.
Claims (1)
1. A convexity optimization design method of a roller is characterized in that: firstly, setting different loads according to a standard curve to design a contour curve, then adopting curve fitting to obtain convexity values of the contour edge of the roller related to the diameter and the length of the roller, and finally establishing a roller convexity design formula as follows: hc (y) =zm×f (x), where Zm is the convexity value of the roller profile edge and f (x) is the dimensionless convexity profile;
wherein Zm is calculated to obtain the convexity value of the edge of the roller profile according to the formula zm=a (Dwe + Lwe) +b, wherein: a=0.3055×3.0175 d ，b=(2.3303*d) 0.2346/d The method comprises the steps of carrying out a first treatment on the surface of the Wherein d is the ratio of the design load to the rated dynamic load, the rated dynamic load of the bearing is Cr, dwe is the roller diameter, and Lwe is the roller length;
wherein f (x) is according to formula f (x) =3.577×10 -3 *exp([ln(2x)+1.529] 2 0.414) calculating to obtain a convexity profile curve, wherein: wherein x is the distance from a point on the roller contour line to the midpoint of the roller and the rollerRatio of effective length;
d is 0.2 Cr-0.5 Cr;
the x is required to satisfy the following conditions: 0.15Lwe < = x Lwe < = 0.5Lwe.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110834115.0A CN113468695B (en) | 2021-07-20 | 2021-07-20 | Convexity optimization design method for roller |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110834115.0A CN113468695B (en) | 2021-07-20 | 2021-07-20 | Convexity optimization design method for roller |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN113468695A CN113468695A (en) | 2021-10-01 |
| CN113468695B true CN113468695B (en) | 2023-08-25 |
Family
ID=77881933
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110834115.0A Active CN113468695B (en) | 2021-07-20 | 2021-07-20 | Convexity optimization design method for roller |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN113468695B (en) |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103810354A (en) * | 2014-03-11 | 2014-05-21 | 大连交通大学 | Optimal design method for logarithm shaping curve of cylindrical roller bearing |
| CN107657122A (en) * | 2017-09-29 | 2018-02-02 | 无锡三立轴承股份有限公司 | Machine tool chief axis Design of Cylindrical Roller Bearing method |
| CN111188838A (en) * | 2020-03-26 | 2020-05-22 | 洛阳Lyc轴承有限公司 | Logarithmic contour roller and manufacturing method thereof |
-
2021
- 2021-07-20 CN CN202110834115.0A patent/CN113468695B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103810354A (en) * | 2014-03-11 | 2014-05-21 | 大连交通大学 | Optimal design method for logarithm shaping curve of cylindrical roller bearing |
| CN107657122A (en) * | 2017-09-29 | 2018-02-02 | 无锡三立轴承股份有限公司 | Machine tool chief axis Design of Cylindrical Roller Bearing method |
| CN111188838A (en) * | 2020-03-26 | 2020-05-22 | 洛阳Lyc轴承有限公司 | Logarithmic contour roller and manufacturing method thereof |
Non-Patent Citations (1)
| Title |
|---|
| 圆柱滚子轴承凸度设计及其对疲劳寿命影响;崔立;何亚飞;蔡池兰;;机械设计与研究(05);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN113468695A (en) | 2021-10-01 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN104801921B (en) | The method of major diameter cylinder body inner sleeve stainless steel sleeve | |
| CN103810354B (en) | The Optimization Design of cylinder roller bearing logarithm modification curve | |
| CN113468695B (en) | Convexity optimization design method for roller | |
| CA2405335A1 (en) | Gas turbine engine compressor blade restoration | |
| CN111475895B (en) | End arc shape-modifying method for spherical roller | |
| CN108220782B (en) | Continuous oil pipe with online continuous production and dynamically adjustable performance and preparation method thereof | |
| CN107931797A (en) | A kind of welding method of H profile steel component | |
| CN105803453B (en) | A kind of device and method of engine crankshaft fatigue crack laser repairing and reinforcing | |
| CN110773685A (en) | Preparation method of thick and large variable-section Ti-6242 alloy blisk forging | |
| CN108160903A (en) | A kind of spherical roller forming process of roll milling and its Roller compaction device | |
| CN112069627A (en) | Rolling stress calculation method and device of rolling wheel and application of rolling stress calculation method and device | |
| CN110883285A (en) | Local continuous plastic rolling device for bolt ball double-pair roller ball body | |
| CN109933889A (en) | A kind of more curved section repairing type methods of railway bearing rolling element | |
| CN112877621B (en) | Cold bulging method for regulating residual stress of aluminum alloy ring piece and improving mechanical property | |
| CN107511644A (en) | A kind of high intensity, the green intelligence of super abrasive cylinder sleeve make method | |
| CN207288454U (en) | A kind of dedicated tool of hollow pipe correction | |
| JP6750595B2 (en) | Method for processing lap fillet welded joint and method for manufacturing lap fillet welded joint | |
| CN107609264B (en) | Method for determining radial critical geometric feed amount of mandrel-free rotary swaging | |
| CN1285900C (en) | Real time detecting method for gas carburization three dimension concentration field of complicate shape workpiece | |
| CN207918926U (en) | Roll the pull-out mechanism of reinforcing bar | |
| JPS63220939A (en) | Forging method | |
| Vasechkin et al. | Increasing the strength of welded thin-walled axisymmetric vessels made of corrosion-resistant steel | |
| CN106891084A (en) | A kind of automatic Welding Process of the typical weld seam of front frame for loader | |
| CN115139158B (en) | Roller repairing method for double-row aligning spherical roller bearing | |
| CN109290735A (en) | Improve the repair process of compression roller wearability |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |