CN111188838B - Quasi-logarithmic contour roller and manufacturing method thereof - Google Patents
Quasi-logarithmic contour roller and manufacturing method thereof Download PDFInfo
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- CN111188838B CN111188838B CN202010220813.7A CN202010220813A CN111188838B CN 111188838 B CN111188838 B CN 111188838B CN 202010220813 A CN202010220813 A CN 202010220813A CN 111188838 B CN111188838 B CN 111188838B
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- 238000004519 manufacturing process Methods 0.000 title claims abstract description 11
- 238000012545 processing Methods 0.000 claims abstract description 24
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- 238000013461 design Methods 0.000 claims abstract description 11
- 238000000034 method Methods 0.000 claims description 20
- 238000005457 optimization Methods 0.000 claims description 6
- 238000012216 screening Methods 0.000 claims description 6
- 238000001514 detection method Methods 0.000 abstract description 12
- 238000005096 rolling process Methods 0.000 abstract description 11
- 238000009826 distribution Methods 0.000 description 5
- 238000005516 engineering process Methods 0.000 description 3
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- 208000014674 injury Diseases 0.000 description 1
- 238000003754 machining Methods 0.000 description 1
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C33/00—Parts of bearings; Special methods for making bearings or parts thereof
- F16C33/30—Parts of ball or roller bearings
- F16C33/34—Rollers; Needles
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Abstract
The invention discloses a quasi-logarithmic contour roller and a manufacturing method thereof we Within the range, the roller main body comprises a first arc and a second arc, and the radius of the first arc is R 1 What is meant byThe radius of the second arc is R 2 . The logarithmic contour roller has the advantages that the logarithmic contour is only composed of two arcs, the occupation ratios of the two arcs on the length of the roller are different (obtained by calculation), curve fitting is carried out based on geometry to enable calculation to be simpler, the two arcs enable processing and detection to be more convenient and rapid, unification of design, processing, detection and application in the true sense can be realized, due to the fact that the similar logarithmic curve enables line contact with a rolling bearing, internal edge stress concentration cannot occur in application, and early failure is avoided.
Description
Technical Field
The invention relates to the technical field of rolling bearings, in particular to a logarithmic contour roller and a manufacturing method thereof.
Background
The rolling bearing is an industrial basic part, is almost used in all running machines, and plays an important role in national economy.
Cylindrical roller bearings and tapered roller bearings are common and very important types in rolling bearing families, and because the inner rollers are in a line contact form, the bearings can bear large loads, and therefore the cylindrical roller bearings and the tapered roller bearings are generally applied to the fields of railways, wind power, engineering machinery, metallurgy, mines and the like.
Starting from the 1882 hz contact stress, the contact problem inside the rolling bearing is attracting attention, and in the linear contact cylindrical roller bearing and the conical roller bearing, the stress concentration phenomenon occurs at the roller edge of the linear contact, which leads to the early failure of the bearing. Until 1939 Lundberg proposed a logarithmic curve profile to make the stress on the line contact entity evenly distributed, effectively solving the problem of edge stress concentration, and able to make the life of the rolling bearing improved by more than several times. Subsequently, stress-life theory was developed and specified within the ISO standard. This forms the basic theoretical system of the field of rolling bearings.
However, due to the limitation of processing technology, the Lundberg logarithmic theory is not capable of processing a roller with a perfect logarithmic curve profile for a long time. Therefore, on the basis of the roller, various modified linear contour rollers are developed, wherein the contour is a middle straight line and arcs at two ends. The arc may be tangential or tangential to a straight line. The ratio of the arc to the roller length is also a fixed value, that is, the length of the arc segment is uniformly specified to be a fixed value (different from each bearing manufacturer) such as 15% or 20% of the effective length of the roller, regardless of the size of the roller. However, until now, most of the linear contact rolling bearings still use modified linear profile rollers, and only a few rolling bearings use logarithmic curve profile rollers, so that even if the control is strict, the quality of the processed logarithmic curve and the uniformity of the same batch still do not achieve the expected results.
For this situation, people are always exploring better choices. The invention patent (without right) with patent number CN 102644663 a discloses a multi-arc variable curvature convex engineering simulation method, which divides a logarithmic curve into n segments, calculates the contact stress distribution of different numbers of multi-arcs based on contact mechanics, and finally selects a proper number n of multi-arcs. Theoretical calculation shows that stress distribution which is very similar to the logarithmic convex type stress distribution can be obtained when n is less than or equal to 10. The basis of the invention is contact stress distribution, and the calculation is more complicated and is difficult to be mastered by engineering technicians. In addition, a multi-section variable-curvature arc simulation method is applied to the processing technology. In the aspect of processing, the logarithmic curve profile is based on n-segment circular arc combined profiling processing. And the fitting method of the multi-segment circular arc usually selects each segment to be equal in length. Therefore, the method for fitting the multi-segment equal-length circular arcs does not have practical value, namely the actual results of designing the rollers into the multi-segment equal-length circular arc curves and the logarithmic curves are the same, and the problems of complex calculation, inconvenient processing and large detection workload also exist. Therefore, we propose a logarithmic contour roller and a manufacturing method.
Disclosure of Invention
The invention aims to overcome the existing defects and provides a logarithmic contour roller and a manufacturing method thereof, wherein the logarithmic contour only consists of two arcs, the proportions of the two arcs on the length of the roller are different (obtained by calculation), curve fitting is carried out based on geometry so that the calculation is simpler, the two arcs enable the processing and detection to be more convenient and faster, the unification of design, processing, detection and application in the true sense can be realized, because the similar logarithmic curve enables the line to contact with a rolling bearing, the stress concentration of the inner edge can not occur in the application, the condition of early failure is avoided, and the problems in the background technology can be effectively solved.
In order to achieve the purpose, the invention provides the following technical scheme: a kind of logarithmic contour roller, including the roller body, the roller generatrix of the said roller body is in the effective length L of the roller we Within the range, the roller main body comprises a first arc and a second arc, wherein the radius of the first arc is R 1 The radius of the second arc is R 2 And the curve central points of the first arc and the second arc are both at the center of the roller body and are perpendicular to the axial line direction of the roller body.
As a preferable technical solution of the present invention, both ends of the roller main body are provided with chamfered sections.
As a preferred technical scheme of the invention, the generatrix equation of the roller main body is
The invention also provides a manufacturing method of the logarithmic contour roller, which comprises the following steps:
1) inputting parameters required by calculation of load, bearing and the like;
2) defining a curve equation;
3) definition of R 1 With arc segments half-length of rollermDoubling, respectively takingmA number of values of =0.5~0.9, then the intersection pointcIs composed of
；
4) In that
Segment optimization calculation solution R 1 The objective function is:
5) known as R 1 Then, at
Segment optimization solution R 2 The objective function is:
6) using Newton iteration method to solve to obtain optimal solution R 2 At this time, the sum of the total differences of the two curves is calculated
；
7) Calculate a set of parametersc、R 1 、R 2 、fThen, the next one is iteratedmReturning to the step three, and storing the result into an array after each iteration;
8) screening out the result arrayfAnd screening out the correspondingm、c、R 1 、R 2 A value;
9) and substituting the obtained optimal result into an equation Y to design and process the roller, firstly processing an arc R2 and then processing an arc R1 during processing, and smoothly transitioning at an arc intersection point c to obtain the logarithm-like contour roller.
Compared with the prior art, the invention has the beneficial effects that: the invention discloses a logarithmic contour roller, which is characterized in that a logarithmic contour is only composed of two arcs, the occupation ratios of the two arcs on the length of the roller are different (obtained by calculation), curve fitting is carried out based on geometry to ensure that the calculation is simpler, the two arcs ensure that the processing and the detection are more convenient and rapid, the unification of design, processing, detection and application can be realized in a real sense, and the linear contact rolling bearing cannot generate internal edge stress concentration in application because of similar logarithmic curves, so that the condition of early failure is avoided.
Drawings
FIG. 1 is a schematic structural view of the present invention;
FIG. 2 is a flow chart of a fitting method of the present invention;
FIG. 3 is a graph of a fit of a first embodiment of the present invention;
FIG. 4 is a graph of a fit of a second embodiment of the present invention;
FIG. 5 is a first step in the process of manufacturing a roller according to the present invention;
FIG. 6 is a second step of the roller processing of the present invention.
In the figure: 1 roller main body, 2 arc I, 3 arc II and 4 chamfer sections.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
Referring to fig. 1, the present invention provides the following technical solutions: roller bus comprising roller body 1 and roller body 1At the effective length L of the roller we Within the scope, the roller body 1 comprises a first arc 2 and a second arc 3, the radius of the first arc 2 is R 1 The radius of the circular arc II 3 is R 2 The curve central points of the first arc 2 and the second arc 3 are both at the center of the roller main body 1 and are vertical to the axis of the roller main body 1, the arc profile is infinitely close to a logarithmic curve, which is called a logarithmic profile-like roller, both ends of the roller main body 1 are provided with chamfer sections 4,
the generatrix equation of the roller body 1 is
R of generatrix of logarithmic contour roller 1 And R 2 The optimal value is obtained by solving after fitting with a Lundberg logarithmic equation. c is the intersection point of the two circular arc curves and is also the optimal point obtained after the curve is fitted.
The Lundberg logarithmic equation is:
referring to fig. 2, the present invention further provides a method for manufacturing a roller with logarithmic contour, comprising the following steps:
1) inputting parameters required by calculation of load, bearing and the like;
2) defining a curve equation;
3) definition of R 1 With arc segments half-length of rollermDoubling, respectively takingmA number of values of =0.5~0.9, then the intersection pointcIs composed of
；
4) In that
Segment optimization calculation solution R 1 The objective function is:
in the equation onlyR 1 Is an unknown number; the unconstrained minimization optimization problem can be calculated by using a Newton's traumatic injury method, and the calculation steps are as follows: setting a convergence precision eps; assigned an initial value R 1 0; the value of equation f1 is calculated and compared to eps if f1 < eps, R 1 0 is the optimal solution; if f1 > eps, let
R 1 k= R 1 0- f1’/f1’’
Will calculate the R 1 k is assigned to R 1 0; and f1 is calculated again, and judgment is carried out again until f1 < eps is finally obtained, wherein R is 1 0 is the optimum value R 1 。
5) Known as R 1 Then, at
Segment optimization solution R 2 . The objective function is:
in the equation onlyR 2 Is an unknown number.
6) Using Newton iteration method to solve, the iteration method is not repeated, and obtaining optimal solution R 2 At this time, the sum of the total differences of the two curves is calculated
。
7) Calculate a set of parametersc、R 1 、R 2 、fThen, the next one is iteratedmReturning to the step three, and storing the result into an array after each iteration;
8) screening out the result arrayfAnd screening out the correspondingm、c、R 1 、R 2 A value;
9) and substituting the obtained optimal result into an equation Y to design and process the roller, firstly processing an arc R2 and then processing an arc R1 during processing, and smoothly transitioning at an arc intersection point c to obtain the logarithm-like contour roller.
The invention is illustrated below by means of two examples.
In one embodiment, referring to FIG. 3, for a bearing, the effective length L of the roller is we =47mm, calculated Lundberg logarithmic equation:
setting convergence accuracy eps =1X10 -10 mm, the whole iteration process only needs less than 1 second, and the fitted curve is shown in figure 3. The optimal result obtained after calculation is as
m=0.86，c=20.21mm，R 1 =57160mm，R 2 =9276mm，f=2.963X10 -5 mm
In the second embodiment, referring to fig. 4, to verify the universality of the bearing, taking another bearing as an example, the effective length of the roller is Lwe =39mm, and the Lundberg logarithmic equation is calculated as:
the fitted curve is shown in fig. 4. The optimal result obtained after calculation is as
m =0.88，c=17.16mm，R1=48685mm，R2=6684mm，f=1.656X10-5mm
As can be seen from fig. 3 and 4, the circular arc curve and the logarithmic curve highly coincide. The fitted curve has the characteristic of a logarithmic curve, and is favorable for uniform stress distribution of the roller in the working process. The length proportion m of the two sections of arcs after fitting in the two cases is different obviously from that of the traditional design method, in the design of the profile of the corrected line, the proportion of the length of the end arc of a bearing product produced by a specific manufacturer is fixed, and the arc algorithm is also a design method which is completely independent of the logarithmic curve.
Referring to fig. 5, the basic process of the arc curve profile of the quasi-logarithmic profile roller of the present invention. Firstly, the grinding wheel is dressed to be R 2 Performing circular arc, and performing profiling grinding on the roller; then dressing the grinding wheel to R 1 Performing circular arc, and performing profiling grinding on the roller; and finally, smoothly polishing the intersection point of the circular arcs. The profiling machining of only two sections of arcs enables the manufacturing process to be simpler, the machined arc is completely matched with the designed arc, and the detection can be carried out completely according to the designed arc during the detection. The simulation processing and detection of the multi-section equal-length arc curves are not needed any more, and the unification of design, processing and detection is realized.
In conclusion, the logarithmic contour roller has a logarithmic curve outline with high coincidence, is beneficial to uniform distribution of internal stress of a bearing in application, can realize unified design, processing, detection and application, has a simple algorithm, and has a great engineering application value.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (1)
1. A logarithmic profile-like roller comprising a roller body (1), characterized in that: the roller bus of the roller main body (1) has an effective length L in the roller we Within the range, the roller main body (1) comprises a first arc (2) and a second arc (3), and the radius of the first arc (2) is R 1 The radius of the second circular arc (3) is R 2 Radius R of arc one (2) 1 And radius R of arc two (3) 2 The optimal value is obtained by solving after the Lundberg logarithmic equation is fitted, the intersection point of the arc I (2) and the arc II (3) is c, the c is the optimal point obtained after the Lundberg logarithmic equation is fitted with a curve, and the curve central points of the arc I (2) and the arc II (3) are both in the center of the roller main body (1) and perpendicular to the axis direction of the roller main body (1); two of the roller main body (1)The end is provided with a chamfer section (4);
the manufacturing method of the logarithmic contour roller comprises the following steps:
1) input load Q, modulus of elasticity E of the bearing material, Poisson's ratio v, and bearing roller effective length L we The parameters of (1);
2) defining a curve equation, equation Y
3) Definition of R 1 The arc segment occupies m times of half the length of the roller, and m is 0.5-0.9, so that the intersection point c is
4) The optimal calculation solution R is obtained in the section of x being more than or equal to 0 and less than c 1 The objective function is:
5) known as R 1 Then, x is more than or equal to c and less than L we Optimization solution R of/2 section 2 The objective function is:
6) using Newton iteration method to solve to obtain optimal solution R 2 When the sum of the total differences f of the two curves is calculated to be f1+ f 2;
7) a set of parameters c and R are calculated 1 、R 2 After f, iterating the next m value, returning to the step three, and storing the result into an array after each iteration;
8) screening out the minimum value of f from the result array, and screening out corresponding m, c and R 1 、R 2 A value;
9) substituting the obtained optimal result into equation Y to design and process the roller, and firstly processing an arc R during processing 2 Then, R is further processed 1 And smoothly transiting at the arc intersection point c to obtain the quasi-logarithmic contour roller.
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| CN113468695B (en) * | 2021-07-20 | 2023-08-25 | 人本股份有限公司 | Convexity optimization design method for roller |
| CN113464550B (en) * | 2021-08-06 | 2023-02-28 | 中车大连机车研究所有限公司 | Double-row cylindrical roller bearing for urban rail transit axle box |
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| JP3731401B2 (en) * | 1999-08-31 | 2006-01-05 | 日本精工株式会社 | Roller bearing |
| CN100366932C (en) * | 2006-02-24 | 2008-02-06 | 马家驹 | Cylindrical roller with logarithmic curve |
| JP4980031B2 (en) * | 2006-11-10 | 2012-07-18 | Ｎｔｎ株式会社 | Rolling bearing crowning design method |
| JP5056115B2 (en) * | 2007-03-29 | 2012-10-24 | 日本精工株式会社 | Roller bearing |
| JP2009197904A (en) * | 2008-02-21 | 2009-09-03 | Ntn Corp | Rolling mechanical element |
| CN102287450B (en) * | 2011-08-05 | 2012-10-03 | 福建省永安轴承有限责任公司 | Structure-optimized long-life tapered roller bearing |
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Address after: 471039 No. 96, Jianxi, Luoyang District, Henan, Jianshe Road Patentee after: Luoyang Bearing Group Co.,Ltd. Country or region after: China Address before: 471039 No. 96, Jianxi, Luoyang District, Henan, Jianshe Road Patentee before: LUOYANG LYC BEARING Co.,Ltd. Country or region before: China |
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