CN101523068A - Designing method for roller bearing and crowning - Google Patents
Designing method for roller bearing and crowning Download PDFInfo
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- CN101523068A CN101523068A CNA200780038432XA CN200780038432A CN101523068A CN 101523068 A CN101523068 A CN 101523068A CN A200780038432X A CNA200780038432X A CN A200780038432XA CN 200780038432 A CN200780038432 A CN 200780038432A CN 101523068 A CN101523068 A CN 101523068A
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Abstract
The invention provides a roller bearing that can facilitate inspection of a crowning and a method of designing a crowning in which time and labor required for designing can be significantly reduced are provided. An optimal value z m [[mu]m] of a drop amount of a crowning at an end of an effective length of a roller (13) is determined using Equation (1), below, from a diameter d[mm] of the roller (13) and an effective length L[mm] of the roller (13). In addition, whether drop amounts at a plurality of positions in a bus-line direction of the crowning are within an allowable range in Table (1), below, is judged. As a result, product inspection can be easily performed on a production line. 0.40 (d+L)+0.66 <= z[m]<=0.46(d+L)+1.03 ...(1).
Description
Technical field
The present invention relates to form on a kind of at least one face in inner race track face, outer race track face and roller rolling surface the roller bearing of crowning and the design method of crowning.
Background technique
All the time, in roller bearing, on inner race track face, outer race track face or roller rolling surface, form crowning, prevent the generation of edge load of end of the contacting part of plane of trajectory orbital and rolling surface, realize the prolongation of the fatigue life of roller bearing.
Shape for the crowning that is formed at roller bearing is used the curve of representing with logarithmic function, as the crowning curve of representing with this logarithmic function, the curve that proposes according to Lundberg is well-known (with reference to non-patent literature 1:Lundberg, G., Elastic Contact Between Two Semi-Infinite Bodies, Forschung auf den Gebiete des Ingenieurwesen, 5 (1939), pp.201-211.).In addition, as with the improvement curve of this crowning curve in practicality, the formula that is Johns-Gohar as can be known is (with reference to non-patent literature 2:Johns, P.M.and Gohar, R., Rollerbearing under radial and eccentric loads, Tribology International, 14 (1981), pp.131-136.).
But the crowning curve of the formula of Johns-Gohar has the contact pressure of the plane of trajectory orbital of end of the formation part that improves crowning to a certain extent and rolling surface and can not fully prevent the tendency of edge load.
Therefore, at present the present inventor proposed for the homogenization that makes the contact pressure between plane of trajectory orbital and the rolling surface in the formula of Johns-Gohar, imported new design parameter the crowning curve (with reference to patent documentation 1: 2006-No. 52790 communiques of TOHKEMY).In the design of the roller bearing of having used this crowning curve, determine that the initial value of above-mentioned design parameter is explored scope and cut apart number, obtain objective function for exploring scope according to initial value and cutting apart the combination of counting the design parameter that obtains.The combination of the optimal design parameter of this objective function is adopted as initial value,, determined the crowning curve, the crowning of design roller bearing according to the further tight optimization of optimal method of mathematical computations.In addition, other crowning curve is proposed by patent documentation 2.
Non-patent literature 1:Lundberg, G., Elastic Contact Between Two Semi-Infinite Bodies, Forschung auf den Gebiete des Ingenieurwesen, 5 (1939), pp.201-211.
Non-patent literature 2:Johns, P.M.and Gohar, R., Roller bearing under radial andeccentric loads, Tribology International, 14 (1981), pp.131-136.
Patent documentation 1: 2006-No. 52790 communiques of TOHKEMY
Patent documentation 2: No. 3731401 communiques of patent
In fact there is the problem that need spend a large amount of labours to the inspection of crowning in existing roller bearing in the inspection of goods.Specifically, since above-mentioned existing roller bearing determine the design parameter of crowning curve therefore, in this design parameter, to be set with tolerance with optimization computation.Thereby, carry out in the inspection of crowning curve, need to measure the shape of generatrix of having implemented crowning, calculate design parameter from determination data, and the value of calculating of judging this design parameter is whether in tolerance.Carrying out such operation on the manufacturing line of reality, is unpractical from the viewpoint in man-hour.
Summary of the invention
Therefore, first purpose of the present invention is, a kind of roller bearing that can carry out the inspection of crowning easily is provided.
In addition, in the design method of the crowning of above-mentioned present roller bearing, be used for determining that the optimization computation of the initial value of design parameter is undertaken by computer.But the condition that this optimization computation is explored scope for the initial value that is contained in design parameter needs a large amount of computings.Therefore, there is the problem that needs plenty of time and labour in above-mentioned design methods existing.
Therefore, second purpose of the present invention is, the design method of crowning of the roller bearing of the time and labor that can significantly subdue designs consume is provided.
In order to solve described problem, first aspect present invention provides a kind of roller bearing, it is provided with a plurality of rollers between inner race track face and outer race track face, and be formed with crowning at least one face in described inner race track face, outer race track face and roller rolling surface, it is characterized in that the optimum value z of the breakage of the crowning of the end of effective length
mThe diameter d (mm) of (μ m), roller, the effective length L (mm) of roller satisfy following formula (3), and the breakage of a plurality of positions of the generatrix direction of described crowning is in the allowed band of following table 3 simultaneously.
[formula 3]
0.40(d+L)+0.66≤z
m≤0.46(d+L)+1.03…(3)
[table 3]
| Generatrix direction position (nondimensional number) | The allowed band of breakage (nondimensional number) |
| ±0.7 | 0～0.1 |
| ±0.9 | 0.6～0.8 |
| ±1.0 | 1.25～1.75 |
The present inventor has used the optimization computation of objective function of the design parameter of regulation for the crowning curve of existing logarithmic function, found that between the breakage of crowning of end of effective length of the nominal size of roller and design load and roller to have correlation.Find to form the present invention based on this.
That is, the roller bearing of a plurality of sizes is set a plurality of load-up conditions and carried out the optimization computation of objective function, its result obtains the such relation of following formula (4).
[formula 4]
z
m＝(0.0051x+0.2721)·(d+L)+(0.0415x-0.3443)…(4)
Wherein, z
m(μ m) is the optimum value of breakage of crowning of end of the effective length of roller, and x (%) is the ratio of design load with respect to basic dynamic load rating, and d (mm) is the diameter of roller, and L (mm) is the effective length of roller.
At this, under the service condition of reality, design load seldom has 35% the situation that surpasses with respect to the ratio of basic dynamic load rating.On the other hand, when the ratio of design load hangs down than 25%, can not fully prevent the generation of edge load.Therefore, for formula (4), when the scope of the value of x more than 25 and 35 when following, the breakage of the crowning of the end of the effective length of roller is suitable for the condition that reality is used.That is, can be judged as the optimum value z of breakage of crowning of the end of effective length
mThe diameter d (mm) of (μ m), roller, the effective length L (mm) of roller satisfy under the situation of described formula (4), and the crowning with these values is applicable to actual use.
Further, breakage for a plurality of locational crownings of generatrix direction, give to the breakage error and calculate the increment rate of the equivalent stress of Mi Saisi, consequently, the permissible range of the breakage of the increment rate of this equivalent stress below specified value is as described shown in the table 3.In described table 3, the value of generatrix direction position be by the change of the value of half of the effective length of roller (L/2) zero dimension value, with the central authorities of the effective length of roller as 0.The value of the permissible range of breakage is the optimum value (z by the breakage of the end of this effective length
m) the zero dimension change value.Under the situation of breakage in described permissible range of the crowning of described generatrix direction position, the size that is judged as described crowning is in tolerance.Therefore, owing to roller bearing of the present invention need not to measure the crowning shape and calculates design parameter as at present, can be than the easier inspection of carrying out crowning at present.
Second aspect present invention provides a kind of design method of crowning of roller bearing, this method is for being provided with in the roller bearing of a plurality of rollers between inner race track face and the outer race track face, be formed on described inner race track face, the design method of the crowning at least one face in outer race track face and the roller rolling surface, it is characterized in that, based on the nominal size of described roller size and design load and obtain the breakage of crowning of end of the effective length of described roller, the breakage of the end of the effective length of described roller is applied to represent with nondimensional number the chart of a plurality of breakages corresponding with a plurality of positions of generatrix direction, determine a plurality of breakages of a plurality of positions of generatrix direction, be formed on the outer race track face according to the described a plurality of breakage decisions that are determined, the profile line of the crowning at least one face in inner race track face and the roller rolling surface.
The present inventor has used the optimization computation of objective function of the design parameter of regulation for the crowning curve of present logarithmic function, it found that between the breakage of crowning of end of effective length of the nominal size of roller and design load and roller to have correlation.Find to form the present invention based on this.
According to second aspect, based on the nominal size of described roller and design load and obtain the breakage of crowning of end of the effective length of described roller, be applied to described chart by breakage, can determine a plurality of breakages of a plurality of positions of generatrix direction the end of the effective length of described roller.By this breakage that is determined, can determine to be formed on the profile line of the crowning at least one face in outer race track face, inner race track face and the roller rolling surface.Like this, according to the present invention, need not the value of carrying out a large amount of parameters is carried out optimization computation.Thereby, the time and labor of the designs consume of the crowning of this roller bearing with compare at present and can significantly reduce.
In addition, so-called " breakage of described crowning " is meant the distance from the bus of the plane of trajectory orbital of implementing crowning or rolling surface to the bus orthogonal direction of crowning face.
Third aspect present invention provides a kind of design method of crowning of roller bearing on the basis of second aspect, it is characterized in that, uses following formula (5) to obtain the breakage of crowning of end of the effective length of described roller.
[formula 5]
z
m＝(0.0051x+0.2721)·(d+L)+(0.0415x—0.3443)…(5)
Wherein, z
m(μ m) is the breakage of crowning of end of the effective length of roller, and x (%) is the ratio of design load with respect to basic dynamic load rating, and d (mm) is the diameter of roller, and L (mm) is the effective length of roller.
According to the third aspect, as long as will be, just obtain the breakage z of crowning of end of the effective length of roller easily as the diameter d of the nominal size of roller and effective length L sum, as the ratio x substitution with respect to the design load of basic dynamic load rating of design load
m
Fourth aspect present invention provides a kind of design method of crowning of roller bearing on the basis of second aspect, it is characterized in that, described chart comprises the value of record in the following table 4.
[table 4]
| Generatrix direction position (nondimensional number) | Breakage (nondimensional number) |
| 0-0.50 | 0 |
| 0.55 | 0.002 |
| 0.60 | 0.015 |
| 0.65 | 0.043 |
| 0.70 | 0.086 |
| 0.75 | 0.147 |
| 0.80 | 0.229 |
| 0.85 | 0.340 |
| 0.90 | 0.489 |
| 0.95 | 0.696 |
| 1.00 | 1.000 |
According to fourth aspect, only need zero dimension value with the breakage of the breakage of the end of the effective length of roller and described table 4 to multiply each other and to determine the locational breakage of each generatrix direction.
In addition, in the described table 4, the value of generatrix direction position be with the change of the value of half of the effective length of roller (L/2) zero dimension value, the value of breakage is the breakage (z with the end of the effective length of roller
m) the zero dimension change value.
Fifth aspect present invention is on the basis of the third aspect, a kind of design method of crowning of roller bearing is provided, it is characterized in that, the value of the x of described formula (5) is made as more than 25 and 35 following and obtain the breakage of crowning of end of the effective length of described roller.
According to the 5th aspect, can design crowning curve corresponding to the user mode of the reality of roller bearing.At this, when the value of x than 25 hours, can not fully prevent the generation of the edge load that the crowning curve causes.On the other hand, when the value of x was bigger than 35, the amount of finish the during making of crowning increased and causes the increase of manufacture cost.
Sixth aspect present invention is on the basis of second aspect, a kind of design method of crowning of roller bearing is provided, it is characterized in that, by the described a plurality of breakages that are determined are distributed to the breakage of described inner race track face or outer race track face and the breakage of described roller rolling surface, thereby decision is formed on the profile line of the crowning on described inner race track face or outer race track face and the described roller rolling surface.
According to the 6th aspect, the described a plurality of breakages that are determined are distributed to inner race track face or the breakage of wheel track face and the breakage of roller rolling surface of each position of generatrix direction.According to the breakage of this distribution, can determine to be formed on inner orbit face or outer race track face crowning profile line and be formed on the profile line of the crowning on the roller rolling surface.Thus, can be formed on the design of inner race track face or outer race track face and described this two side's of roller rolling surface crowning.
According to roller bearing of the present invention, for for the roller bearing that is formed with crowning at least one face in inner race track face, outer race track face and the roller rolling surface, at the optimum value z of the breakage of the crowning of the end of effective length
mThe diameter d (mm) of (μ m), roller, the effective length L (mm) of roller satisfy the formula of regulation, and the breakage of the crowning of a plurality of generatrix direction position of described crowning the regulation allowed band in the time, can be judged as the suitable crowning that can prevent the edge load, therefore, can be than carrying out at present the inspection of crowning easily.
According to design method of the present invention, based on the nominal size of roller and design load and obtain the breakage of crowning of end of the effective length of roller, and zero dimension chart by this breakage is applied to stipulate, decide the profile line of crowning, therefore, need not a large amount of parameter values is carried out optimization computation, thereby, the time and labor of designs consume of the crowning of this roller bearing can be reduced.
Description of drawings
Fig. 1 is the sectional drawing of the cylindrical roller bearing of expression embodiments of the present invention;
Fig. 2 is the figure of the profile of the crowning of expression cylinder roller on y-z system of coordinates;
Fig. 3 is the end of effective length is selected in expression from the result of optimization computation breakage z
mThe figure that represents;
Fig. 4 is the breakage z of the end of expression effective length
mConstant a, the b of vague generalization formula and design load with respect to the figure of the relation of the ratio x of basic dynamic load rating;
Fig. 5 A is that the expression design load is the figure of optimized results of crowning shape of 25% situation of basic dynamic load rating;
Fig. 5 B is that the expression design load is the figure of optimized results of crowning shape of 30% situation of basic dynamic load rating;
Fig. 5 C is that the expression design load is the figure of optimized results of crowning shape of 35% situation of basic dynamic load rating;
Fig. 5 D is that the expression design load is the figure of optimized results of crowning shape of 40% situation of basic dynamic load rating;
Fig. 5 E is that the expression design load is the figure of optimized results of crowning shape of 50% situation of basic dynamic load rating;
Fig. 6 extracts the curve of peaked curve of expression in whole crowning curve of Fig. 5 A～Fig. 5 E and expression minimum value the figure of expression out;
Fig. 7 is with K
1And z
mAs parameter, the figure of the peaked distribution of expression Mi Saisi equivalent stress;
Fig. 8 is the chart that the breakage of crowning of the goods of the breakage of crowning of the present invention and existing other companies compares.
The reference numeral explanation
11 inner rings
11a inner race track face
12 outer rings
12a outer race track face
13 cylinder rollers
13a cylinder roller rolling surface
13b, 13c cut crowning
Embodiment
Below, be elaborated with reference to the mode of execution of accompanying drawing to the design method of roller bearing of the present invention and crowning.
Fig. 1 is the sectional drawing of the cylindrical roller bearing of expression embodiment of the present invention.As shown in Figure 1, this cylindrical roller bearing possesses inner ring 11, outer ring 12, rolling is installed in a plurality of cylinder roller 13,13 to each other of inner race track face 11a and outer race track face 12a freely ..., keep cylinder roller 13,13 along the interval of bearing circumferentially spaced regulation ... retainer 14.In this embodiment, at each cylinder roller 13,13 ... rolling surface 13a, 13a ... cutting crowning 13b, 13c are set, and it is planar that the plane of trajectory orbital 12a of the plane of trajectory orbital 11a of inner ring 11 and outer ring 12 forms cylinder respectively.
Fig. 2 is that the bearing of trend that is illustrated in the bus of cylinder roller 13 is the y axle, and bus orthogonal direction (roller radially) is the figure of the crowning of expression cylinder roller 13 on the y-z system of coordinates of z axle.This y-z system of coordinates is initial point O with the central authorities of effective contacting part of the inner ring on the bus of cylinder roller 13 11 or outer ring 12 and cylinder roller 13.So-called " effectively contacting part ", be hypothesis under the situation that forms cutting crowning 13b, 13c on the cylinder roller 13 inner ring 11 or the contact position of outer ring 12 and cylinder roller 13.In addition, because cylinder roller 13,13 ... each crowning 13b, 13c on the z axle of the central authorities by effective contacting part, be line usually and be symmetrically formed, therefore, in Fig. 2, only represent a side crowning 13b.
Above-mentioned crowning 132b can use logarithmic function figure to represent as following formula (6).
[formula 6]
Wherein, k
1It is the parameter of degree of the curvature of expression crowning.A is with 2Q/ π LE ' expression, and Q is a load, and L is the generatrix direction length of effective contacting part, and E ' is an equivalent elastic modulus.In addition, z
mBe the optimum value of breakage of crowning of end of the effective length of roller, the meaning is meant the optimum value of the maximum loss amount of crowning 13b.P among Fig. 2
1Point is the optimum value z of the maximum loss amount of expression crowning 13b
mThe position.A is the length of the end from initial point O to effective contacting part.K
2Be the parameter of expression crowning length with respect to the ratio of above-mentioned a.On the crowning 13b of Fig. 2, because initial point O is the central authorities of effective contacting part, so a=L/2.In addition, because the initial point O of crowning 13b
1Coordinate be (a-k
2A, 0), so the scope of the y in the formula (6) is y〉and (a-k
2A).
The z (y) of formula (6) is the breakage of crowning 13b of the generatrix direction position y of cylinder roller 13.In formula (6), the value of Q, L, E ' and a is given as design condition.In addition, the zone of the initial point O1 from initial point O to crowning 13b is to form the planar line part of cylinder, therefore, and as 0≤y≤(a-k
2A) time, z (y)=0.In addition, work as k
2=1 o'clock, initial point O
1O is consistent with initial point, and therefore, formula (6) expression does not have the full crowning of line part.
In the design method of existing roller bearing and even crowning, by the design condition of formula (6) being given load Q etc., suitable design parameter k
1, k
2, z
m, determine the crowning curve.At definite this design parameter k
1, k
2, z
mThe time, in the desirable scope of each parameter, carry out the optimization computation of objective function.Therefore, need carry out a large amount of optimization computation, need a large amount of labour and time each cylindrical roller bearing that designs.
Relative therewith, in the present embodiment, use the nominal size of roller and design load function as parameter, obtain the optimum value z of breakage of crowning of end of the effective length of above-mentioned roller
m, by optimum value z with this breakage
mThe chart that is applied to stipulate is determined the shape of crowning integral body.
Above-mentioned function is as described below tries to achieve.
At first, by the above-mentioned parameter of the optimal method optimization of mathematical technique.In the optimization of this parameter, under the situation of giving the roller inclination, under most condition, k
2=1, approaching more full crowning, face pressure or Mi Saisi equivalent stress are more little.On the other hand, the cylinder roller is because manufacture view is preferably the line part that has at least 50% degree with respect to total length.Therefore, in the present embodiment, optimization K not
2, and the fixing K of the mode that accounts for total length 50% with line part
2
Next, for roller that is of a size of φ 5 * 5～φ 24 * 38 and the optimization computation of similarly carrying out the crowning curve at present.In optimized objective function, adopted near the maximum value of the Mi Saisi equivalent stress of contacting part.For design condition, the inclination of roller was decided to be for 1/1000 (being equivalent to 2/1000 value in the misalignment of inner ring and outer ring).Design load is that one the roller and the contact load of inner ring are set.This contact load be set at the load that acts on bearing basic dynamic load rating Cr more than 25% and 50% maximum rolling body load when following.Below, the maximum rolling body load in the time of will acting on the load of x% of basic dynamic load rating Cr on bearing is called the x%Cr design as the design condition of design load.In addition, as carrying out optimized objective function, can use the maximum contact pressure that inner race track face, outer race track face or roller rolling surface be subjected to, the maximum value of Mi Saisi equivalent stress, the maximum value of bending Leix card (tresca) equivalent stress, at least one in the rolling fatigue life.Block under maximum value situation of equivalent stress at maximum value or in the wrong this, so that the minimum mode of these values determines design parameter as objective function with maximum contact pressure, Mi Saisi equivalent stress.Under with the situation of rolling fatigue life, so that the longest mode of rolling fatigue life determines design parameter as objective function.
Fig. 3 is that expression is from carrying out the optimum value z of breakage that optimized result select the end of effective length with the Mi Saisi equivalent stress as objective function to each design condition
mThe figure of result of calculation.Among Fig. 3, transverse axis is the diameter d (mm) and effective length L (mm) sum of roller, and the longitudinal axis is the optimum value z of breakage of the end of effective length
m(μ m).Among Fig. 3, the optimized results of the roller of 64 kinds of sizes below 24 to 25%Cr design and 35%Cr design expression φ is to the optimized results that 30%Cr designs, 40%Cr designs, the roller of 20 kinds of sizes in 64 kinds of sizes of φ below 24 is represented in the 50%Cr design alternative.As can be seen from Figure 3, under any load-up condition, the diameter d of roller and effective length L sum, with the optimum value z of the breakage of the end of the effective length of roller
mBetween all exist correlation coefficient in the linear dependence more than 0.997.
According to result of calculation shown in Figure 3, (d+L) in each load-up condition (mm) and z
mRelation formula described as follows (7)～(11) of (μ m) are represented like that.
[formula 7]
z
m＝0.3983(d+L)+0.6600…(7)
[formula 8]
z
m＝0.4313(d+L)+0.8945…(8)
[formula 9]
z
m＝0.4560(d+L)+1.0270…(9)
[formula 10]
z
m＝0.4654(d+L)+1.5259…(10)
[formula 11]
z
m＝0.5330(d+L)+1.6352…(11)
At this, formula (7) is for 25%Cr designs, and formula (8) is for 30%Cr designs, and formula (9) is for 35%Cr designs, and formula (10) is for 40%Cr designs, and formula (11) designs for 50%Cr.
Further, think above-mentioned formula (7)～(11) are generalized to z
mWhen a of constant portion the during form of=a (d+L)+b and b were load and linear dependence, it is approximate that works a and b formula described as follows (12) and (13).
[formula 12]
a＝0.0051x+0.2721…(12)
[formula 13]
b＝0.0415x+0.3443…(13)
To be expression overlap figure on the coordinate with above-mentioned formula (12) and (13) to Fig. 4.In Fig. 4, transverse axis is the ratio x (%) of design load with respect to basic dynamic load rating, and the longitudinal axis is a and b.When using above-mentioned formula (12) and (13) vague generalization formula (7)～(11), shown in the formula described as follows (14).
[formula 14]
z
m＝(0.0051x+0.2721)·(d+L)+(0.0415x-0.3443)…(14)
By above-mentioned formula (14), can be from as the d+L (mm) of the nominal size of roller with respect to the ratio x (%) of design load, and obtain z
mThe optimum value of (μ m).
Next, make the chart of the global shape that is used for definite crowning.
At first,, remove the value of generatrix direction position and carry out zero dimensionization, simultaneously with the optimum value z of the breakage of the end of effective length with half of effective length L as the result of the optimization computation of crowning curve
mRemove each generatrix direction position breakage value and carry out zero dimensionization.Fig. 5 A～5E is the figure that each load-up condition is represented the crowning curve after the zero dimensionization.In Fig. 5 A～5E, transverse axis is zero dimension generatrix direction position, and the longitudinal axis is the zero dimension breakage.The center of the position 0 expression roller of zero dimension generatrix direction.
Fig. 5 A～5E repeats to represent that relevant diameter is the figure of optimized results of the roller of 64 kind the design size of φ below 24, and the design condition beyond the design load is mutually the same.As design condition, Fig. 5 A is 25%Cr, and Fig. 5 B is 30%Cr, and Fig. 5 C is 35%Cr, and Fig. 5 D is 40%Cr, and Fig. 5 E is 50%Cr.
By Fig. 5 A～Fig. 5 E as can be known, the crowning curve of any load-up condition carries out zero dimensionization when representing, all is expressed as roughly the same shape.Fig. 6 selects the figure that the curve of peaked curve of expression and expression minimum value is represented in whole crowning curve with Fig. 5 A～Fig. 5 E.As can be known from Fig. 6, regardless of the size and the load-up condition of roller, can determine to design crowning to non dimensional curve from narrower and small zone.
Fig. 7 is that expression is with K
1And z
mAs parameter and represent that the objective function of optimization computation is the figure of the peaked distribution of Mi Saisi equivalent stress.As can be seen from Figure 7, the tendency this point from the maximum value of Mi Saisi equivalent stress reduces preferably makes parameter K
1Value bigger than optimum line Lb (representing) to leak white line.At this, work as parameter K
1During increase, the curvature of crowning curve reduces.Therefore, if be preferably the crowning curve of selecting to be fit to the big condition of width from the maximum value and the zone between the minimum value of curve shown in Figure 6, then selecting breakage in whole generatrix direction positions is peaked curve.When the point on such curve is represented by the nondimensional number of generatrix direction position and breakage, shown in the table 5 described as follows.
[table 5]
| Generatrix direction position (nondimensional number) | Breakage (nondimensional number) |
| 0-0.50 | 0 |
| 0.55 | 0.002 |
| 0.60 | 0.015 |
| 0.65 | 0.043 |
| 0.70 | 0.086 |
| 0.75 | 0.147 |
| 0.80 | 0.229 |
| 0.85 | 0.340 |
| 0.90 | 0.489 |
| 0.95 | 0.696 |
| 1.00 | 1.000 |
In above-mentioned table 5, can be by using the breakage z that tries to achieve by above-mentioned formula (14)
mDetermine the shape of crowning integral body.That is, the nondimensional number on the hurdle of generatrix direction position multiply by the value as the L/2 of half of the effective length of roller, and simultaneously, the nondimensional number on the hurdle of breakage multiply by above-mentioned breakage z
mThus, can determine point on y-z system of coordinates that generatrix direction (y axle) and bus orthogonal direction (z axle) by roller form.By setting curve, can determine the crowning curve by this point.
The roller bearing of present embodiment and even the design method of crowning need not to carry out the optimization computation of crowning curve at every turn when designing.Thereby, owing to need not present so selectable condition of design parameter is carried out a large amount of computings, can effectively subdue labour and the time of expending in the crowning design.
In addition, in the above-described embodiment, under the situation of high loading, edge load prevent effect this on the one hand, z
mBe the bigger the better, but breakage z
mWhen excessively increasing, the processing quantitative change when crowning is made causes uneconomical greatly.In addition, under the general service condition of reality, load is at basic below 25% of dynamic load rating, and the situation above 35% is very rare.Therefore, be preferably x in the formula (14) more than 25 and below 35.
Next, for the roller bearing of present embodiment, the inspection method of the goods after the life-span makes.
In the roller bearing of present embodiment, the optimum value z of the breakage of the effective length end of roller
m(μ m) designs with following formula (15) according to the diameter d (mm) of roller and the effective length L (mm) of roller.
[formula 15]
0.40(d+L)+0.66≤z
m≤0.46(d+L)+1.03…(15)
Above-mentioned formula (15) is tried to achieve as following mode.That is, under the actual service conditions of roller bearing, design load surpasses 35% situation seldom with respect to the ratio x of basic dynamic load rating.On the other hand, when the ratio of design load hangs down than 25%, can not fully prevent the generation of edge load.Therefore, for formula (14),, then be suitable for the service condition of reality if the breakage of the crowning of the end of the effective length of the roller of goods satisfies the scope of value of x in the condition below 35 more than 25.That is, at the optimum value z of the breakage of the end of effective length
mThe diameter d (mm) of (μ m), roller, the effective length L (mm) of roller satisfy under the situation of above-mentioned formula (15), can be judged as the crowning with these values and be suitable for actual use.
Select the generatrix direction position of the crowning of goods, measure the breakage of this position, can judge that this breakage is whether in the scope of the tolerance of regulation.
Show that shown in above-mentioned formula (6) the crowning curve is by three design parameter K
1, K
2, z
mDecide.Therefore, under the situation that the breakage of the crowning of selecting goods is checked, select these 3 needs to take into full account.In this case, should select the point of direct representation design parameter as far as possible, determine z
mIntersection point and definite K of the facial and chamfered section of protuberance
2Line part and these 2 facial at intersection point of protuberance can select easily.On the other hand, because K
1Not the parameter of the point of determining of expression crowning, so need to select other representative point.As other a example of representative point, can select breakage is z
m1/2 point.
In addition, because selecteed point is to be measured by the inspection operation on the manufacturing line of roller bearing, so must be the point of measuring easily.At this, on plane of trajectory orbital or rolling surface, near the scope internal loss amount of the ratio broad on generatrix direction of the intersection point that line part and protuberance are facial is roughly 0.Therefore, be envisioned in design the line part and the breakage of the facial intersection point of protuberance when giving tolerance, become minimum tolerance.Therefore, as this replacement point, be preferably the service wear amount at z
mAbout 1/10 point.
The generatrix direction position and the breakage that become determination object also can carefully be tried to achieve from above-mentioned table 5, if but consider to certainly exist the easness of error and mensuration in the actual goods, then be preferably with the such point of following table 6 as object.
[table 6]
| Generatrix direction position (nondimensional number) | Breakage (nondimensional number) |
| 0.7 | 0.1 |
| 0.9 | 0.5 |
| 1.0 | 1.0 |
In above-mentioned table 6, the value of generatrix direction position be with the value of half of the effective length of roller (L/2) carry out the zero dimension change value, the value of breakage is the optimum value (z with the breakage of the end of the effective length of roller
m) carry out the zero dimension change value.
At this, 3 kinds of concrete roller bearings are carried out the tolerance of optimization computation and research breakage.The roller bearing that calculates is selected following bearing.
Bearing A: the diameter of roller and length ratio are near 1:1, and the roller footpath is little;
Bearing B: the diameter of roller and length ratio are near 1:1, and the roller footpath is big;
Bearing C: the diameter and the length ratio of roller are big, and the roller footpath equates with bearing B;
During model routine of expression bearing, bearing A can adopt NU304E, and bearing B can adopt NU312E, and bearing C can adopt NU2312E.
For the roller of bearing A～C, during the peaked increment rate of the Mi Saisi equivalent stress when the zero dimension axle direction position calculation at table 6 gives error, obtain the such result in following table 7～9.When carrying out this calculating, be to calculate the crowning curve that has carried out careful design by optimum as the crowning shape of benchmark.On the other hand, the crowning shape of having considered error is to carry out the resulting simple and easy curve of interpolation between each point with three times natural spline curve his-and-hers watches 6.Therefore, even the error of each point is 0, also do not have big differently with optimum shape, owing to carefully inconsistently, so the increment rate of the equivalent stress in table 7～9 can not be 0.
[table 7]
The relation of the peaked increment rate (%) of the sum of errors Mi Saisi equivalent stress of the breakage of table 7 expression bearing A.
[table 8]
The relation of the peaked increment rate (%) of the sum of errors Mi Saisi equivalent stress of the breakage of table 8 expression bearing B.
[table 9]
The relation of the peaked increment rate (%) of the sum of errors Mi Saisi equivalent stress of the breakage of table 9 expression bearing C.
In addition, in table 7～table 9, a is the breakage error (μ m) of generatrix direction position 0.9, and b is the breakage error (μ m) of generatrix direction position 1.0.
According to table 7～9, when the increment rate that allows equivalent stress according to the mode that becomes tolerance that can volume production to 20% the time, each bearing A to B is set at the such tolerance of following table 10.
[table 10]
Table 10 is the tolerances of situation that allow the increment rate to 20% of Mi Saisi equivalent stress.
As optimum value z with the breakage of the end of the effective length of each bearing
mWhen removing the tolerance of table 10 and carrying out zero dimension, become the such tolerance of following table 11.
[table 11]
Table 11 is the optimum value z with the breakage of the end of effective length
mAfter the zero dimensionization and tolerance breakage.
Show that from table 11 regardless of the size of bearing, the tolerance of each generatrix direction position all is roughly the same degree.
From as can be known above-mentioned, we can say size regardless of bearing, the tolerance of crowning curve (allowed band) can use summary value table 12 described as follows to set like that.
[table 12]
| Generatrix direction position (nondimensional number) | The allowed band of breakage (nondimensional number) |
| ±0.7 | 0～0.1 |
| ±0.9 | 0.6～0.8 |
| ±1.0 | 1.25～1.75 |
Table 12 is tolerances of crowning curve.
With reference to the table 12 of trying to achieve like this, whether the crowning of judging goods is in tolerance range.That is, for the crowning of goods, selection is equivalent to the position of 3 zero dimension generatrix direction positions of table 12, measures the breakage of this position, calculates the nondimensional number of this breakage.Under the situation of this nondimensional number in the allowed band of table 12, the size that can judge this crowning is in tolerance.More than be the narration that the generatrix direction position is carried out at the crowning of positive side because crowning is a bilateral symmetry in the cylinder roller, so for generatrix direction for negative zone, also can similarly check.
Like this, roller bearing of the present invention is measured the crowning shape and is calculated design parameter in the inspection of goods as at present, need not to judge that this design parameter is whether in the scope of tolerance.Therefore, can be than the easier inspection of carrying out crowning at present.
In the above-described embodiment, crowning can be arranged on any face of plane of trajectory orbital of the rolling surface of roller and outer ring or inner ring.Forming under the situation of crowning on this two side of plane of trajectory orbital of the rolling surface of roller and outer ring or inner ring,, determining that the crowning curve that is formed at each face gets final product as long as the breakage of above-mentioned each generatrix direction position is distributed to rolling surface side and plane of trajectory orbital side.In addition, in the inspection of the goods of roller bearing, as long as calculate the breakage sum of the crowning of the breakage of crowning of rolling surface side and plane of trajectory orbital side, judge this and value whether satisfy table 12 and get final product.
In addition, in the table 5 of the nondimensional number of expression above-mentioned generatrix direction position and breakage, represent the generatrix direction position every 0.05, but definite interval of generatrix direction position also can be other values beyond 0.05.
At last, Fig. 8 represents the comparison of breakage of the crowning of the breakage of crowning of the present invention and existing other company's goods (A, B, C corporate system roller bearing).In figure, transverse axis is zero dimension axle direction (generatrix direction) position, and the longitudinal axis is breakage (μ m).The center of zero dimension axle direction position 0 expression roller.Show that from Fig. 8 the breakage of crowning of the present invention (zero dimension axle direction position=0.7,0.9,1.0) is with the breakage of the crowning of goods is all obviously different at present arbitrarily.In addition, also illustrate the scope of the breakage of first aspect invention regulation in the patent documentation 2 (No. 3731401 communiques of patent) in the lump.
Claims (6)
1, a kind of roller bearing, it is provided with a plurality of rollers between inner race track face and outer race track face, and is formed with crowning at least one face in described inner race track face, outer race track face and roller rolling surface, it is characterized in that,
The optimum value z of the breakage of the crowning of the end of effective length
m(μ m) obtained with following formula (1) by the diameter d (mm) of roller and the effective length L (mm) of roller,
When with the central authorities of the effective length of roller as initial point, remove the generatrix direction position and carry out zero dimensionization with L/2, with z
mWhen removing the breakage of crowning and carrying out zero dimension,
The breakage of the crowning of a plurality of positions of the generatrix direction of described crowning is in the allowed band that following table 1 puts down in writing,
[formula 1]
0.40(d+L)+0.66≤z
m≤0.46(d+L)+1.03…(1)
[table 1]
2, a kind of design method of crowning of roller bearing, this method is for being provided with in the roller bearing of a plurality of rollers between inner race track face and the outer race track face, be formed on the design method of the crowning at least one face in described inner race track face, outer race track face and the roller rolling surface, it is characterized in that
Based on the nominal size of described roller and design load and obtain the breakage of crowning of end of the effective length of described roller,
The breakage of the end of the effective length of described roller is applied to represent with nondimensional number the chart of a plurality of breakages corresponding with a plurality of positions of generatrix direction, determines a plurality of breakages of a plurality of positions of generatrix direction,
Be formed on the profile line of the crowning at least one face in outer race track face, inner race track face and the roller rolling surface by the described a plurality of breakages decision that is determined.
3, the design method of the crowning of roller bearing as claimed in claim 2 is characterized in that,
Use following formula (2) to obtain the breakage of crowning of end of the effective length of described roller,
[formula 2]
z
m＝(0.0051x+0.2721)·(d+L)+(0.0415x—0.3443)…(2)
Wherein, z
m(μ m) is the breakage of crowning of end of the effective length of roller, and x (%) is the ratio of design load with respect to basic dynamic load rating, and d (mm) is the diameter of roller, and L (mm) is the effective length of roller.
4, the design method of the crowning of roller bearing as claimed in claim 2 is characterized in that,
Described form comprises the value of record in the following table 2,
[table 2]
5, the design method of the crowning of roller bearing as claimed in claim 3 is characterized in that,
The value of the x of described formula (2) is made as more than 25 and 35 following and obtain the breakage of crowning of end of the effective length of described roller.
6, the design method of the crowning of roller bearing as claimed in claim 2 is characterized in that,
By the described a plurality of breakages that are determined are distributed to the breakage of described inner race track face or outer race track face and the breakage of described roller rolling surface, thereby decision is formed on the profile line of the crowning on described inner race track face or outer race track face and the described roller rolling surface.
Applications Claiming Priority (5)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP305426/2006 | 2006-11-10 | ||
| JP2006305426A JP4980031B2 (en) | 2006-11-10 | 2006-11-10 | Rolling bearing crowning design method |
| JP2006309598A JP5037094B2 (en) | 2006-11-15 | 2006-11-15 | Roller bearing |
| JP309598/2006 | 2006-11-15 | ||
| PCT/JP2007/071083 WO2008056563A1 (en) | 2006-11-10 | 2007-10-30 | Designing method for roller bearing and crowning |
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| CN101523068A true CN101523068A (en) | 2009-09-02 |
| CN101523068B CN101523068B (en) | 2011-09-28 |
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|---|---|---|---|
| CN200780038432XA Active CN101523068B (en) | 2006-11-10 | 2007-10-30 | Designing method for roller bearing and crowning |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102853948A (en) * | 2012-09-10 | 2013-01-02 | 西安交通大学 | Load calculation method for paired tapered roller bearings |
| CN105940191A (en) * | 2013-11-29 | 2016-09-14 | 蒂森克虏伯普利斯坦技术中心股份公司 | Adjustable camshaft |
| CN108884864A (en) * | 2016-04-01 | 2018-11-23 | Ntn株式会社 | Tapered roller bearing |
| CN111188838A (en) * | 2020-03-26 | 2020-05-22 | 洛阳Lyc轴承有限公司 | Logarithmic contour roller and manufacturing method thereof |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2013002567A (en) * | 2011-06-17 | 2013-01-07 | Ntn Corp | Cylindrical roller bearing |
| JP7191762B2 (en) | 2019-04-17 | 2022-12-19 | 東日本旅客鉄道株式会社 | Temporary snow fence |
Family Cites Families (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP3731401B2 (en) * | 1999-08-31 | 2006-01-05 | 日本精工株式会社 | Roller bearing |
| JP2001124089A (en) * | 1999-10-28 | 2001-05-08 | Ntn Corp | Cylindrical roller bearing |
| CN1610798A (en) * | 2001-12-28 | 2005-04-27 | 日本精工株式会社 | Roller bearing |
| JP2004353744A (en) * | 2003-05-28 | 2004-12-16 | Nsk Ltd | Roller bearing |
| JP4429842B2 (en) * | 2004-08-11 | 2010-03-10 | Ｎｔｎ株式会社 | Roller bearing |
-
2006
- 2006-11-10 JP JP2006305426A patent/JP4980031B2/en active Active
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2007
- 2007-10-30 CN CN200780038432XA patent/CN101523068B/en active Active
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102853948A (en) * | 2012-09-10 | 2013-01-02 | 西安交通大学 | Load calculation method for paired tapered roller bearings |
| CN105940191A (en) * | 2013-11-29 | 2016-09-14 | 蒂森克虏伯普利斯坦技术中心股份公司 | Adjustable camshaft |
| US9926815B2 (en) | 2013-11-29 | 2018-03-27 | Thyssenkrupp Presta Teccenter Ag | Adjustable camshaft |
| CN108884864A (en) * | 2016-04-01 | 2018-11-23 | Ntn株式会社 | Tapered roller bearing |
| CN111188838A (en) * | 2020-03-26 | 2020-05-22 | 洛阳Lyc轴承有限公司 | Logarithmic contour roller and manufacturing method thereof |
Also Published As
| Publication number | Publication date |
|---|---|
| CN101523068B (en) | 2011-09-28 |
| JP4980031B2 (en) | 2012-07-18 |
| JP2008121769A (en) | 2008-05-29 |
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