CN113468695A - Convexity optimization design method of roller - Google Patents

Convexity optimization design method of roller Download PDF

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CN113468695A
CN113468695A CN202110834115.0A CN202110834115A CN113468695A CN 113468695 A CN113468695 A CN 113468695A CN 202110834115 A CN202110834115 A CN 202110834115A CN 113468695 A CN113468695 A CN 113468695A
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roller
convexity
profile
design method
formula
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CN113468695B (en
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白雪峰
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Shanghai Renben Group Bearing Technology R & D Co ltd
C&U Co Ltd
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Shanghai Renben Group Bearing Technology R & D Co ltd
C&U Co Ltd
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
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    • 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
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Abstract

The invention provides a convexity optimization design method of a roller, which is based on the traditional formula to establish a convexity design formula of the roller as follows: hc (y) = Zm f (x). Where Zm is the convexity value of the edge of the roller profile and f (x) is a non-dimensionalized convexity profile. According to the convexity optimization design method, only a certain rated dynamic load ratio d, the roller diameter Dwe and the roller length Lwe need to be obtained, so that a large amount of complicated calculation is avoided, the calculation difficulty is reduced, the convexity can be designed without professional designers, meanwhile, the convexity designed by the convexity optimization design method is not weaker than that of a traditional method, and the convexity optimization design method is simpler and more practical.

Description

Convexity optimization design method of roller
Technical Field
The invention relates to the technical field of bearing processing, in particular to an optimal design method for roller convexity.
Background
The straight generatrix roller bearing has inevitable boundary stress concentration at two ends of a rolling body after being loaded, so that the fatigue life of the bearing is greatly reduced due to the generation of a so-called 'edge effect'. The roller surface is designed convex to overcome in subsequent designs.
The traditional roller bearing logarithmic convexity design basic method 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 respectively look up tables to calculate the radial load and the combined load; the contact stress is calculated according to the Hertz contact theory, the calculation modes of the roller, the cylindrical roller and the tapered roller bearing are different, and correction factors such as materials are involved; and finally, calculating by adopting a convexity two-calculation formula shown in the figure 1. Therefore, the design method has many involved parameters and complicated calculation process.
Based on this, the present application is proposed.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a convexity optimization design method of a roller, which solves the problems of complex convexity design process and large calculation amount of the roller in the prior art, and simplifies the convexity design process of the roller so as to be suitable for practical use.
In order to achieve the aim, the convexity optimization design method of the roller comprises the following steps:
firstly, designing a profile curve according to different loads set by a standard curve, then obtaining a convexity numerical value of a roller profile edge related to the diameter and the length of a roller by adopting curve fitting, and finally establishing a roller convexity design formula as follows: hc (y) zmf (x), where Zm is the convexity value of the edge of the roller profile, and f (x) is a non-dimensionalized convexity profile;
wherein Zm is calculated according to the formula Zm ═ a (Dwe + Lwe) + b to obtain the convexity value of the roller contour edge, wherein: a 0.3055 × 3.0175d，b＝(2.3303*d)0.2346/d(ii) a Wherein d is the rated dynamic load (Cr) of the bearing with a certain ratio, Dwe is the diameter of the roller, Lwe is the length of the roller;
wherein f (x) is according to the formula f (x) 3.577 × 10-3*exp([ln(2x)+1.529]20.414) to obtain a convexity profile curve, wherein: where x is the ratio of the distance from a point on the roller profile line to the roller midpoint to the effective length of the roller.
In the present invention, the effective length of the roller means the length over which contact is made and load is borne between the roller and the raceway in use, except for the chamfer.
The invention further provides the following: and d is the ratio of the design load to the rated dynamic load.
The invention further provides the following: the d is 0.2 Cr-0.5 Cr. In the range, the optimal design method provided by the invention has a better effect of smoothing the stress at the edge.
The invention further provides the following: the x needs to satisfy the following condition: 0.15lwe < ═ x < ═ 0.5lwe, and in this value range, the convexity of roller is lower, and the contour curve of roller more tends to be gentle, more adapts to the roller bearing condition in the actual use, also is more convenient for actual processing.
The invention has the following beneficial effects: according to the convexity optimization design method, only a certain rated dynamic load ratio d, the roller diameter Dwe and the roller length Lwe need to be obtained, the number of the known parameters needing to be measured and moved is small, and the calculation steps and the calculation formula are simplified to a greater extent compared with the traditional method, so that the convexity optimization design method based on the roller can obtain results quickly, complex calculation is avoided, the calculation process is simple and convenient, and the convexity of the roller is optimized greatly. In short, the convexity optimization design method is simpler and more practical.
Drawings
FIG. 1 is a comparison of the Lundberg equation with the camber curve of a roller designed by the method of the present invention at an oblique angle of 0.2 Cr.
FIG. 2 is a comparison of the Lundberg equation with the camber curve of a roller designed by the method of the present invention at an oblique angle of 0.3 Cr.
FIG. 3 is a comparison of the Lundberg equation with the camber curve of a roller designed by the method of the present invention at an oblique angle of 0.4 Cr.
FIG. 4 is a comparison of the Lundberg equation with the camber curve of a roller designed by the method of the present invention at an oblique angle of 0.5 Cr.
FIG. 5 is a graph showing the contact stress distribution at 0.5Cr with an inclined angle according to the Lundberg equation and the method of the present invention.
FIG. 6 is a graph showing the contact stress distribution at 0.5Cr with an inclined angle according to the Lundberg equation and the method of the present invention.
FIG. 7 is a graph showing the contact stress distribution at 0.5Cr with an inclined angle according to the Lundberg equation and the method of the present invention.
FIG. 8 is a graph showing the contact stress distribution at 0.5Cr with an inclined angle according to the Lundberg equation and the method of the present invention.
FIG. 9 is a comparison of the Lundberg equation with the camber curve of a roller designed by the method of the present invention at 0.2Cr without a tilt angle.
FIG. 10 is a comparison of the Lundberg equation with the camber curve of a roll designed by the method of the present invention at 0.3Cr without a tilt angle.
FIG. 11 is a comparison of the Lundberg equation with the camber curve of a roll designed by the method of the present invention at 0.4Cr without a tilt angle.
FIG. 12 is a comparison of the Lundberg equation with the camber curve of a roll designed by the method of the present invention at 0.5Cr without a tilt angle.
FIG. 13 is a contact stress distribution diagram of 0.5Cr without an inclined angle designed by the Lundberg formula and the method of the present invention.
FIG. 14 is a graph showing the contact stress distribution at 0.5Cr without any tilt angle according to the Lundberg equation and the method of the present invention.
FIG. 15 is a contact stress distribution diagram of 0.5Cr without an inclined angle designed by the Lundberg formula and the method of the present invention.
FIG. 16 is a contact stress distribution diagram of 0.5Cr without an inclined angle designed by the Lundberg formula and the method of the invention.
Detailed Description
The invention provides a convexity optimization design method of a roller, which is based on the traditional formula to establish a convexity design formula of the roller as follows: hc (y) ═ zmf (x).
In the above formula, where Zm is the crown value of the edge of the roller profile, it is calculated according to the 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*3.0175d (1-2)
b＝(2.3303*d)0.2346/d (1-3)
where d is the ratio of the design load to the dynamic load rating (Cr), which is typically 0.2Cr to 0.5 Cr. In the above formula, f (x) is a non-dimensionalized convexity profile, which is calculated by the formula (2-1):
f(x)＝3.577*10-3*exp([ln(2x)+1.529]2/0.414) (2-1)
in equation (2-1), x is the ratio of the distance from a point on the roller profile to the roller midpoint to the effective length of the roller, and is typically given by the value [0.15lwe,0.5lwe ], which takes into account the roller load conditions and the actual processing where at least 0.3Lwe in the middle of the roller is a straight generatrix, so that a roller convexity sufficient to overcome edge effects can be best achieved for more efficient packaging.
Example 1 a cylindrical roller bearing NU 208: the rated dynamic load Cr is 53.9 kN. The roller diameter Dwe is 10mm, the roller length Lwe is 10mm, the chamfer angle of the roller is 0.5mm, and the inner raceway diameter size is 50 mm.
Using the above data, the roller profile shapes calculated by substituting the above equations with no tilt angle and tilt angle (0.001 radian) as per 0.2Cr, 0.3Cr, 0.4Cr and 0.5Cr respectively are shown in FIGS. 1-4, and the simulation of the test contact stress along the roller length for this roller profile in commercial software is shown in FIGS. 5-8, respectively.
Using the above data, the roller profile shapes calculated by substituting the above equations with no tilt angle in terms of 0.2Cr, 0.3Cr, 0.4Cr and 0.5Cr are shown in fig. 9-12, for which the test contact stresses along the length of the roller were simulated in commercial software as shown in fig. 13-16, respectively.
In the above figures, in fig. 1-4 and 9-12, the X-axis is the effective length position (mm) of the roller and the Y-axis is the amount of convexity (mm); in fig. 5-8 and 13-16, the X-axis is along the roller distance (mm) and the Y-axis is the inner track contact stress (MPa).
Through comparison, in the design of the roller hub shape with or without an inclined angle, the roller profile shape provided by the design method of the invention has different performances on a straight line section and two side edge arc sections compared with a profile curve obtained by using a Lundberg formula. Moreover, under the action load of 0.4Cr, the contact stress calculated according to the formula of the invention is more gradual, the load distribution is uniformly distributed along the length of the middle part of the roller, and the contact stress of the profile curve (shown in figures 2 and 3) obtained by using the Lundberg formula is more gradual in the overall trend. Under the action of 0.3Cr load, the stress distribution obtained by the two curves is completely consistent.
In addition, under the condition of an inclined angle, the contact stress distribution of the convexity curve provided by the design method is more uniform and gentle, the situation of edge stress concentration does not occur, and the design requirement of actual use is met.
It can be concluded from this that the convexity shape designed using the convexity optimization design method of the present invention does not function as weak as the conventional method. Moreover, from the comparison analysis of contact stress, the profile curve of the formula of the invention is more effective.
In conclusion, the invention provides a simple and effective roller convexity optimization design method, the formula model used by the method is very simple, not only is a large amount of complicated calculation avoided, but also the calculation difficulty is reduced, the design can be carried out without professional designers, and the labor and the working time are greatly saved. Meanwhile, the convexity shape of the roller obtained by the optimized design method of the invention has more gentle contour surface stress during bearing and better overcoming effect on edge effect.

Claims (4)

1. A convexity optimization design method of a roller is characterized in that: firstly, designing a profile curve according to different loads set by a standard curve, then obtaining a convexity numerical value of a roller profile edge related to the diameter and the length of a roller by adopting curve fitting, and finally establishing a roller convexity design formula as follows: hc (y) = Zm f (x), where Zm is the convexity value of the edge of the roller profile, f (x) is a non-dimensionalized convexity profile;
wherein Zm is calculated from Zm = a (Dwe + Lwe) + b to obtain the convexity value of the roller profile edge, wherein: a =0.3055 × 3.0175d ，b=(2.3303*d)0.2346/d(ii) a Wherein d is the rated dynamic load (Cr) of the bearing with a certain ratio, Dwe is the diameter of the roller, Lwe is the length of the roller;
wherein f (x) is according to the formula f (x) =3.577 x 10-3*exp([ln(2x)+1.529]20.414) to obtain a convexity profile curve, wherein: where x is the ratio of the distance from a point on the roller profile line to the roller midpoint to the effective length of the roller.
2. The method for optimally designing the convexity of a roller according to claim 1, wherein: and d is the ratio of the design load to the rated dynamic load.
3. The method for optimally designing the convexity of a roller according to claim 1, wherein: and d is 0.2 Cr-0.5 Cr.
4. The method for optimally designing the convexity of a roller according to claim 1, wherein: the x needs to satisfy the following condition: 0.15lwe < = x lwe < =0.5 lwe.
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Citations (3)

* Cited by examiner, † Cited by third party
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

Patent Citations (3)

* Cited by examiner, † Cited by third party
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 (4)

* Cited by examiner, † Cited by third party
Title
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