CN105241407A - Prediction method for radial runout of inner ring of cylindrical roller bearing - Google Patents

Abstract

The invention relates to a prediction method for radial runout of an inner ring of a cylindrical roller bearing. The method includes the steps: calculating a coordinate of the center of each of rollers below an X-axis according to a given bearing parameter, translating an inner ring of a bearing, calculating the shortest distance between the surface of each roller and the contour of the rolling path of the inner ring according to the coordinate of the center of each roller below the X-axis and a coordinate of the center of the inner ring of the bearing, recording the position angles of all the rollers that contact the inner ring of the bearing, finding out the most stable contact state on the basis of a bearing stable contact state criterion, and calculating a radial runout value of the inner ring according to the corresponding coordinate of the center of the inner ring of the bearing in the contact state. In this way, the precision grade of an assembled finished product bearing is predicated according to the precision grade of bearing elements. The method provides a theoretical basis for distribution and control for the precision of bearing elements, plays an active role in research and development of high-precision rolling bearing products, and can be used for production guidance.

Description

Cylinder roller bearing inner ring diameter run-out Forecasting Methodology

Technical field

The invention belongs to cylinder roller bearing kinematic accuracy electric powder prediction, be specifically related to a kind of cylinder roller bearing inner ring diameter run-out Forecasting Methodology.

Background technology

At present, bearing rotation precision is the key parameter weighing bearing dynamic property, the index evaluating rolling bearing running accuracy comprises bearing inner race diameter run-out, outside lane runout and face runout etc., existing cylinder roller bearing radial pulsation measurement method can only be measured the complete cylinder roller bearing after process and assemble, but can not can not predict bearing diameter run-out value according to given bearing element shape error.

Summary of the invention

The invention provides cylinder roller bearing inner ring diameter run-out Forecasting Methodology, how to measure bearing inner race diameter run-out accurately according to given bearing element shape error be worth problem to solve.

For solving the problems of the technologies described above, cylinder roller bearing inner ring diameter run-out Forecasting Methodology of the present invention comprises the steps:

1) given bearing parameter, comprises bearing outer ring ball track diameter, bearing inner race raceway diameter, roller diameter, roller number N, bearing outer ring ball track contour curve, bearing inner race raceway contour curve and roller surface contour curve;

2) bearing inner race rotates and presets step-length angle;

3) with the center of circle of bearing outer ring be initial point, horizontal direction sets up rectangular coordinate system for X-axis, judges the number Z of the roller be positioned at below X-axis;

4) along the direction of the roller center of circle and outer ring circle center line connecting to outer ring raceway respectively movement be positioned at the roller below X-axis, until roller contacts with outer ring raceway, record the central coordinate of circle o of now roller _rj, j=1,2,3 ..., Z;

5) according to presetting translating step, translation bearing inner race, records the central coordinate of circle of now bearing inner race;

6) according to the roller central coordinate of circle be positioned at below X-axis, calculate the bee-line of the roller surface below X-axis to inner ring raceway profile, and then judge under the central coordinate of circle of this bearing inner race, whether have roller and bearing inner race raceway contact, if do not have, return step 5), if have, record the position angle of all rollers contacted with bearing inner race;

7) judge whether the central coordinate of circle of bearing inner race exceeds setting range of translation, if do not have, returns step 5), otherwise, enter step 8);

8) contact condition criterion is stablized according to bearing, to exist and roller contact all bearing inner races central coordinate of circle under bearing touch state differentiate, find out contact condition the most stable under wherein only considering Action of Gravity Field, the Y-coordinate of bearing inner race central coordinate of circle corresponding under this contact condition is exactly inner ring diameter run-out value.

According to step 2) ~ 8) obtain inner ring diameter run-out value under bearing inner race different rotary angle, thus obtain bearing inner race diameter run-out course.

Step 4) in judge that the method whether roller and outer ring raceway contact is: calculate the bee-line of roller surface to outer ring raceway profile, when bee-line is less than setting value, roller contacts with outer ring raceway; Wherein, roller surface to the computing method of the bee-line AB of outer ring raceway profile is: calculate the distance L of roller surface to outer ring raceway profile _e, AB is for work as θ _eat [0,2B _e/ d _e] in scope during change, make L _eminimum value, wherein,

$L_e=\sqrt{{\mathrm{AO}}^2+{{\mathrm{Oo}}_{rj}}^2-2AO\×{\mathrm{Oo}}_{rj}\×cos\left({\mathrm{\θ}}_e\right)}-d_e/2-\underset{m_e=2}{\overset{n_e}{\mathrm{\Σ}}}\[A_{m_e}cos(m_e{\mathrm{\θ}}_B-m_e{\mathrm{\α}}_e)+B_{m_e}sin(m_e{\mathrm{\θ}}_B-m_e{\mathrm{\α}}_e)\]$

AO is the distance of 1 A and the center of circle, outer ring O on outer ring raceway, Oo _rjfor the center of circle, outer ring and roller center of circle o _rjdistance, θ _efor the line of A point and O point and O point and o _rjthe angle of some line; θ _bfor the position angle of roller surface B point, d _efor the desirable radius of outer ring raceway; m _efor outer ring raceway harmonic order; n _efor the maximum harmonic order of outer ring raceway; with be respectively harmonic component sine and cosine coefficient; B _efor default outer ring search width; α _efor the angle of outer ring rotating.

Described step 6) in roller surface below X-axis to the computing method of the bee-line of inner ring raceway profile be: calculating roller surface is to the distance L of inner ring raceway profile _i, CD is for work as θ _iat [0,2B _i/ d _i] in scope during change, make L _iminimum value, wherein,

$L_e=\sqrt{{{\mathrm{Co}}_i}^2+o_i{o_{rj}}^2-2{\mathrm{Co}}_i\×o_i{o}_{rj}\×\cos \left({\mathrm{\θ}}_i\right)}-d_i/2-\underset{m_i=2}{\overset{n_i}{\mathrm{\Σ}}}\[A_{m_i}\cos \left(m_i{\mathrm{\θ}}_D-m_i{\mathrm{\α}}_i\right)+B_{m_i}\sin \left(m_i{\mathrm{\θ}}_D-m_i{\mathrm{\α}}_i\right)\]$

Co _ifor 1 C on outer ring raceway and inner ring center of circle o _idistance, o _io _rjfor the inner ring center of circle and roller center of circle o _rjdistance, θ _ifor A and o _iline and o _iwith o _rjthe angle of line; θ _dfor the position angle of roller surface D point, d _ifor the desirable radius of inner ring raceway; m _ifor inner ring raceway harmonic order; n _ifor the maximum harmonic order of inner ring raceway; with be respectively harmonic component sine and cosine coefficient; B _ifor default inner ring search width; α _ifor the angle that inner ring rotates.

Step 6) under the central coordinate of circle of this bearing inner race, there is roller and bearing inner race raceway is interfered, namely this roller surface is negative to the bee-line of inner ring raceway profile, and its absolute value is greater than convergence error, returns step 5).

Described step 8) in bearing stablize contact condition criterion and be: the number of the roller 1. contacted with bearing inner race is at least two; 2. roller and bearing inner race raceway are without interference; 3. a pair roller is had at least to lay respectively at Y-axis both sides; 4. to bear semiaxis angle minimum for roller contact district center line and Y-axis.

Method of the present invention is after the inside and outside circle raceway of given bearing and roller surface shape error, all roller central coordinate of circle contacted with outer ring raceway below X-axis can be calculated, then outer ring and roller central coordinate of circle is fixed, translation inner ring, obtain the different inner ring raceway central coordinate of circle with the roller contacted with inner ring raceway, contact criteria is stablized according to bearing, judge best inner ring central coordinate of circle, then calculate bearing inner race diameter run-out value, the method only just need can realize the measurement of bearing diameter run-out value according to given bearing element shape error.

The present invention can also pass through mobile bearing inner race, obtain the inner ring diameter run-out course of inner ring within the scope of certain angle, bearing diameter run-out course then can represent more running accuracy behavioral characteristics in bearing rotary process preferably, thus the accuracy class realized according to bearing finished products after bearing element accuracy class prediction assembling, for bearing element precision distribution and control provide theoretical foundation, to development high-precision rolling bearing product, there is positive role, and can be used for Instructing manufacture.

Accompanying drawing explanation

Fig. 1 is the cylinder roller bearing reduced graph of the present embodiment;

Fig. 2 (a) is when on outer ring raceway profile, any is above the roller center of circle and outer ring raceway circle center line connecting, roller surface profile and outer ring raceway profile geometric relationship figure;

Fig. 2 (b) is when on outer ring raceway profile, any is below the roller center of circle and outer ring raceway circle center line connecting, roller surface profile and outer ring raceway profile geometric relationship figure;

Fig. 3 (a) is when on inner ring raceway profile, any is above the roller center of circle and inner ring raceway circle center line connecting, roller surface profile and inner ring raceway profile geometric relationship figure;

Fig. 3 (b) is when on inner ring raceway profile, any is below the roller center of circle and inner ring raceway circle center line connecting, roller surface profile and inner ring raceway profile geometric relationship figure;

Fig. 4 (a) is the first inner ring contact stabilization view of the present embodiment;

Fig. 4 (b) is the second inner ring contact stabilization view of the present embodiment;

Fig. 5 is the inner ring diameter run-out course curve of the present embodiment.

Embodiment

Below in conjunction with accompanying drawing, technical scheme of the present invention is described in further detail.

As shown in Figure 1, the present embodiment centre bearer inner ring raceway, outer ring raceway and roller surface all have shape error to bearing arrangement, and outer ring is fixed, and inner ring rotates.The bearing inner race diameter run-out Forecasting Methodology of the present embodiment is based on following hypothesis:

(1) only consider the geometrical constraint of bearing, do not consider the load restraint of bearing, namely only consider bearing element running accuracy under idle condition, do not consider the elastic deformation of bearing element.

(2) do not consider the impact of retainer, suppose that between adjacent rollers, angle is equal.

(3) only consider that roller geometric error is on the impact of bearing rotation precision below bearing.

(4) do not consider relative sliding between roller and lasso, namely think between roller and lasso to be pure rolling.

(5) impact of bearing lubrication on bearing rotation precision is not considered.

Concrete performing step comprises:

1) given bearing parameter, comprises bearing outer ring ball track diameter, bearing inner race raceway diameter, roller diameter, roller number N, bearing outer ring ball track contour curve, bearing inner race raceway contour curve and roller surface contour curve;

2) bearing inner race rotates and presets step-length angle;

3) with the center of circle of bearing outer ring be initial point, horizontal direction sets up rectangular coordinate system for X-axis, judges the number Z of the roller be positioned at below X-axis;

4) along the direction of the roller center of circle and outer ring circle center line connecting to outer ring raceway respectively movement be positioned at the roller below X-axis, until roller contacts with outer ring raceway, record the central coordinate of circle o of now roller _rj, j=1,2,3 ..., Z;

5) according to setting step-length, translation bearing inner race, records the central coordinate of circle of now bearing inner race;

6) according to the roller central coordinate of circle be positioned at below X-axis, calculate the bee-line of the roller surface below X-axis to inner ring raceway profile, and then judge under the central coordinate of circle of this bearing inner race, whether have roller and bearing inner race raceway contact, if do not have, return step 5), if have, record the position angle of all rollers contacted with bearing inner race;

7) judge whether the central coordinate of circle of bearing inner race exceeds setting range of translation, if do not have, returns step 5), otherwise, enter step 8);

8) contact condition criterion is stablized according to bearing, to exist and roller contact all bearing inner races central coordinate of circle under bearing touch state differentiate, find out contact condition the most stable under wherein only considering Action of Gravity Field, the Y-coordinate of bearing inner race central coordinate of circle corresponding under this contact condition is exactly inner ring diameter run-out value.

Below above-mentioned steps is described in detail:

1, given bearing parameter: outer ring raceway diameter, inner ring raceway diameter, roller diameter, roller number N, outer ring raceway contour curve, inner ring raceway contour curve, roller surface contour curve, as shown in Figure 1, roller is on bearing pitch diameter bearing original state, inner ring and outer ring concentric;

2, inner ring rotates a step-length angle;

3, the position angle of a jth roller is calculated, judge whether a jth roller is positioned at below X-axis by position angle, if, then enter next step, otherwise, make j=j+1, namely continue the position angle calculating next roller, the position angle of roller refers to that the angle of semiaxis is born in the roller center of circle and outer ring circle center line connecting and Y-axis;

4, below X-axis a jth roller radially, namely the roller center of circle and circle center line connecting direction, outer ring, move a preseting length to outer ring raceway, calculate the jth roller surface bee-line to outer ring raceway profile;

5, judge whether a jth roller contacts with outer ring raceway, if a jth roller contacts with outer ring raceway, then enter next step, otherwise, return the 4th step;

The radial distance of movement when 6, being contacted with outer ring raceway by a jth roller, calculates a central coordinate of circle when jth roller contacts with outer ring raceway, the central coordinate of circle of a record jth roller and position angle;

7, judge whether j is less than roller number N, if be less than N, then return the 3rd step, calculate next roller central coordinate of circle, otherwise statistics is positioned at total number Z of the roller below X-axis, enters next step;

8, now raceway outer ring and be positioned at the center of circle of the roller below X-axis and number fixing, only translation inner ring, the central coordinate of circle of roller is the roller central coordinate of circle that above-mentioned steps calculates, and sets inner ring range of translation in x and y direction and translating step respectively according to bearing parameter;

9, bearing inner race is divided into some parts in X-direction and Y-direction range of translation by translating step, define a dot matrix, that is, by in range of translation in units of translating step mobile inner ring, multiple bearing inner race central coordinate of circle can be obtained, bearing inner race central coordinate of circle value get wherein arbitrary point value time, carry out following steps correlation computations;

10, the bee-line of q roller surface to inner ring raceway profile is calculated below X-axis, this seasonal q=1;

11, judge whether q roller contacts with inner ring raceway, if q roller contacts with inner ring raceway, record contact roller number and roller position angle, if q roller and inner ring raceway are interfered, then think has roller and inner ring to interfere under this translating step, and the inner ring central coordinate of circle under this translating step is unreasonable, stops the calculating of follow-up roller, return the 9th step, obtain a new bearing inner race central coordinate of circle and calculate; Described roller and inner ring raceway are interfered and are referred to: roller surface is negative to the bee-line of inner ring raceway profile, and its absolute value is greater than convergence error,

12, judge whether q is less than roller sum Z below X-axis, if be less than, makes q=q+1, then returns the 10th step, carry out the correlation computations of next roller, otherwise, enter step 13;

13, record inner ring central coordinate of circle, contact roller position angle under this translating step, enter step 14;

14, judge whether bearing inner race central coordinate of circle exceeds its range of translation, if do not exceed its scope, then return the 9th step, change inner ring central coordinate of circle, carry out 10th ~ 13 step correlation computations, otherwise, enter step 15;

15, contact condition criterion is stablized according to bearing, all step-length lower bearing contact conditions are differentiated, find out contact condition the most stable under wherein only considering Action of Gravity Field, central coordinate of circle corresponding to it is final inner ring rotation center coordinate, and then the inner ring diameter run-out value obtained under this step-length, i.e. the Y-coordinate in the bearing inner race center of circle;

16, judge whether inner ring rotational angle exceeds the angular range of setting, if not, return the 2nd step, repeat the computation process of step 2 ~ 15, otherwise record inner ring diameter run-out course, calculates inner ring diameter run-out, terminate program.

Wherein, roller surface is as follows to the computing method of the bee-line of outer ring raceway profile:

Inner ring rotates α _iangle, when p roller moves to a certain position, supposes center of circle o _rjdistance to the center of circle, outer ring O is D _ej, roller and outer ring raceway geometric relationship are as shown in Fig. 2 (a).From geometric relationship, outer ring raceway is put the distance L of A and roller surface point B _efor:

L _e＝Ao _rj-Bo _rj(1)

In formula, at Δ Ao _rjin O, Ao can be obtained by the cosine law _rj, calculated by formula (2); Bo _rjfor roller rotation α _rafter angle, B dot profile radius, is calculated by formula (3).

${\mathrm{Ao}}_{rj}=\sqrt{{\mathrm{AO}}^2+{{\mathrm{Oo}}_{rj}}^2-2AO\×{\mathrm{Oo}}_{rj}cos\left({\mathrm{\θ}}_e\right)}---\left(2\right)$

In formula, AO is the profile radius of outer ring raceway A point, is calculated by formula (5); Oo _rjfor the center of circle, outer ring is to the distance of a jth roller centre, Oo _rj=D _ej; θ _efor AO and Oo _rjangle.

${\mathrm{Bo}}_{rj}=r_e\left({\mathrm{\θ}}_B\right)=d_e/2+\underset{m_e=2}{\overset{n_e}{\mathrm{\Σ}}}\[A_{m_e}cos(m_e{\mathrm{\θ}}_B-m_e{\mathrm{\α}}_e)+B_{m_e}sin(m_e{\mathrm{\θ}}_B-m_e{\mathrm{\α}}_e)\]---\left(3\right)$

In formula, θ _bfor the position angle of roller surface B point, when A point is at Oo _rjtime above straight line, θ _b=β _j-π+γ _j, otherwise, θ _b=π-γ _j+ β _j, as shown in Fig. 2 (b), wherein, γ _j=arccos ((Ao _rj ²+ Oo _rj ²-AO ²)/(2Ao _rj× Oo _rj)); d _efor the desirable radius of outer ring raceway; Me is outer ring raceway harmonic order; n _efor the maximum harmonic order of outer ring raceway; with be respectively harmonic component sine and cosine coefficient, α _efor the angle of outer ring rotating.

A given θ _evalue, can obtain A point distance L on roller surface B point to outer ring raceway profile _e, sparse its scope that arranges according to roller and outer ring raceway waveform is 0≤θ _e≤ 2B _e/ d _e, wherein, B _efor default outer ring search width.Work as θ _ewhen changing within the scope of this, a series of L can be obtained _evalue, therefrom finds out minimum L _evalue is the bee-line AB of roller surface to outer ring raceway profile.

The preferred said method of the present embodiment calculates the bee-line of roller surface to outer ring raceway profile, certainly, as other embodiments, also can by calculating outer ring raceway surface any point and the distance in the center of circle, outer ring and the center of circle, the outer ring difference to the distance of roller surface, using the minimum value of this difference as bee-line, can convert accordingly computing formula according to above-mentioned computing method, introduce computation process no longer in detail here.

Roller surface is as follows to the computing method of the bee-line of inner ring raceway profile:

Inner ring rotation alpha _iangle, when p roller moves to a certain position, supposes center of circle o _rjdistance to inner ring center of circle O is D _ij, roller and inner ring raceway geometric relationship are as shown in Fig. 3 (a).From geometric relationship, distance outer ring raceway being put C and roller surface point D is:

CD＝Co _rj-Do _rj(4)

In formula, Co _rjfor the roller center of circle is to the distance of inner ring raceway C point, is calculated by formula (5) and obtain; Do _rjfor roller rotation α _rthe profile radius of D point after angle, is calculated by formula (6) and obtains.

${\mathrm{Co}}_{rj}=\sqrt{{{\mathrm{Co}}_i}^2+o_i{o_{rj}}^2-2{\mathrm{Co}}_i\×o_i{o}_{rj}\×cos\left({\mathrm{\θ}}_i\right)}---\left(5\right)$

In formula, Co _ifor the profile radius of C point on inner ring raceway, calculated by formula (5) and obtain; o _io _rjfor the inner ring center of circle is to the distance of a jth roller centre; θ _ifor Co _iwith o _io _rjangle.

${\mathrm{Do}}_{rj}=r_i\left({\mathrm{\θ}}_D\right)=d_i/2+\underset{m_i=2}{\overset{n_i}{\mathrm{\Σ}}}\[A_{m_i}\cos \left(m_i{\mathrm{\θ}}_D-m_i{\mathrm{\α}}_i\right)+B_{m_i}\sin \left(m_i{\mathrm{\θ}}_D-m_i{\mathrm{\α}}_i\right)\]---\left(6\right)$

In formula, θ _dfor the position angle of roller surface D point, when D point is at o _io _rjtime above straight line, otherwise, wherein, γ _ij=arccos ((Co _rj ²+ o _io _rj ²-Co _i ²)/(2Co _rj× o _io _rj)); d _ifor inner ring raceway diameter; m _ifor inner ring raceway harmonic order; n _ifor the maximum harmonic order of inner ring raceway; with be respectively inner ring raceway harmonic component sine and cosine coefficient, α _ifor the angle that inner ring rotates.

A given θ _ivalue, can obtain D point distance CD on roller surface C point to inner ring raceway profile, sparse its scope that arranges according to roller and inner ring raceway waveform is 0≤θ _i≤ 2B _i/ d _e, wherein, B _efor default inner ring search width.Work as θ _iwhen changing within the scope of this, a series of CD value can be obtained, therefrom find out minimum CD value and be the bee-line of roller surface to inner ring raceway profile.

The preferred said method of the present embodiment calculates the bee-line of roller surface to inner ring raceway profile, certainly, as other embodiments, also can by calculating inner ring raceway surface any point and the distance in the inner ring center of circle and the inner ring center of circle difference to the distance of roller surface, using the minimum value of this difference as bee-line, can convert accordingly computing formula according to above-mentioned computing method, introduce computation process no longer in detail here.

Contact condition criterion stablized by bearing:

Only consider that gravity is to the effect of bearing, when being positioned at the multiple rollers below X-axis and contacting with inner ring, inner ring contact condition reaches steady state (SS), need meet following condition simultaneously:

1. contact roller number at least two

When only having a roller to contact with inner ring raceway, inner ring contact condition is unstable, and at least two rollers contact with inner ring and just likely make inner ring be in steady state (SS).

2. roller and inner ring are without interference

When having roller and inner ring is interfered, no matter there are how many rollers to contact with inner ring, this inner ring contact condition is non-steady state.

3. a pair contact roller is had at least to lay respectively at Y-axis both sides

When there being multiple roller to contact with inner ring, have at least a roller to contact with inner ring in the every side of Y-axis, otherwise this contact condition is non-steady state.

4. to bear semiaxis angle minimum for roller contact district center line and Y-axis

When have multiple meet more than the inner ring contact condition of 3 conditions time, an inner ring contact condition the most rational need be found out.Suppose that each roller to inner ring force direction all radially, because gravity is along Y-axis negative direction, only have when roller contact district center line and Y-axis bear semiaxis angle little as far as possible time more easily could make bearing semiaxis with Y-axis with joint efforts and overlapping of acting force suffered by inner ring, namely inner ring is more easily made to reach steady state (SS), as shown in Figure 4, Fig. 4 (a) is the first contact condition, Fig. 4 (b) is the second contact condition, the angle that the second contact condition roller contact district center line and Y-axis bear semiaxis angle more stable than the first contact condition is little, therefore, the second contact condition is the most reasonable.The definition of contact region center line: contact region refers to the camber line region in the roller that all and inside and outside circle raceway all contacts between the leftmost roller center of circle and the rightmost roller center of circle, the line of the center of circle, outer ring camber line mid point is therewith contact region center line.

Provide a kind of embodiment below, set forth the detailed process that above-mentioned Forecasting Methodology obtains cylinder roller bearing inner ring diameter run-out course and diameter run-out thereof.

Given bearing parameter: outer ring raceway diameter is 75.032mm, inner ring raceway diameter is 54.991mm, and roller diameter is 10mm, and roller number is 14.Inner ring raceway profile is oval, and outer ring raceway profile is oval, calculates inner ring rotating 360 degrees inner ring diameter run-out course.Arranging inner ring rotation step-length is 1 degree, and inner ring range of translation is :-0.0355≤X≤0.0355 ,-0.0355≤Y≤0.Adopt this Forecasting Methodology, implementation step is as follows:

First according to this Forecasting Methodology the 1st step, provide bearing parameter: outer ring raceway diameter is 75.032mm, inner ring raceway diameter is 54.991mm, and roller diameter is 10mm, and roller number is 14.Inner ring raceway profile polar equation is: r _i(θ)=d _i/ 2+0.002cos (3 θ)+0.002sin (3 θ), outer ring raceway profile polar equation is: r _e(θ)=d _e/ 2+0.002cos (3 θ)+0.002sin (3 θ), roller surface profile polar equation is: r (θ)=D _w/ 2+0.002cos (3 θ)+0.002sin (3 θ).

2nd step, the scope of setting inner ring rotational angle is 360 degree, and rotating step-length is 1 degree, first inner ring rotation center coordinate during calculating inner ring rotation 1 degree; By the 3rd, 4 steps to calculate below all X-axis roller after they move a step-length by initial position to outer ring raceway, their roller surfaces are to the bee-line of outer ring raceway profile, and judge whether this roller contacts with outer ring raceway by the 5th, if do not contacted, then return the 4th step, continue slide roller step-length, restart the 4th, 5 step correlation computations again, if roller contacts with outer ring raceway, by the 6th step, calculate the distance that roller radially moves to outer ring raceway, the coordinate figure of roller under global coordinate system can be calculated;

7th step, roller number below statistics X-axis, the 3rd carried out to next roller, 4,5, the correlation computations of 6 steps.Until central coordinate of circle when calculating that below all X-axis, roller contacts with outer ring raceway;

8th step, setting inner ring range of translation in x and y direction and step-length, be 1/2nd end-plaies at X to moveable maximal value according to the known bearing inner race of bearing end-play value, consider bearing inner race raceway again, outer ring raceway and roller surface have shape error, according to national standard, bearing element shape error amplitude is all within 5 μm, therefore, inner ring mobile ultimate range can increase 0.015mm again in X-direction on the basis of 1/2nd end-plaies, final inner ring is 0.0355mm in the ultimate range of X forward and negative sense moving range, therefore, inner ring is [-0.0355 at X to moving range height, 0.0355], the ultimate range in like manner setting inner ring movement is in the Y direction 0.0355mm, consider that inner ring moves from Y-direction zero position to Y negative direction, therefore inner ring is set in Y-direction moving range as [-0.0355, 0], the step-length of inner ring translation is little as much as possible, such precision of this Forecasting Methodology that can make is higher, 1nm is to the moving step length with Y-direction at this setting X, this is because bearing element shape error is micron number magnitude, to shape error be reflected in correlation computations, need the step-length exceeding the several quantity of micron order effectively could reflect the impact of shape error on bearing diameter run-out.

9th ~ 15 steps give several inner ring central coordinate of circle values, when inner ring gets any one coordinate figure, all will carry out 10th ~ 14 step correlation computations, by calculating below each X-axis roller surface to the bee-line of inner ring raceway, to judge under some inner ring central coordinate of circle that whether each roller contacts with inner ring raceway or interfere, if interfered, then think that this step-length is unreasonable, stop the calculating of follow-up roller, return the 9th step, reselect next inner ring central coordinate of circle value, carry out 10th ~ 14 step correlation computations, if contact, then record the position angle of this roller, and contact roller number increases by 1 under making this step-length.

15th step, stablizes contact condition criterion according to bearing, finds out that central coordinate of circle value making inner ring the most easily reach stable, is the central coordinate of circle value of inner ring under this anglec of rotation.By that analogy, every inner ring can be calculated and rotate arbitrarily angled lower central coordinate of circle value, thus the inner ring diameter run-out course of acquisition inner ring within the scope of certain angle, as shown in Figure 5, because inner ring moves along Y-axis negative direction, therefore, inner ring diameter run-out value is negative value.Maximum radial jitter values in inner ring diameter run-out course is 0.02605mm, and smallest radial jitter values is 0.01897mm, and both differences are inner ring diameter run-out, and its value is 0.007086mm.

Be presented above concrete embodiment, but the present invention is not limited to described embodiment.Basic ideas of the present invention are above-mentioned basic scheme, and for those of ordinary skill in the art, according to instruction of the present invention, designing the model of various distortion, formula, parameter does not need to spend creative work.The change carried out embodiment without departing from the principles and spirit of the present invention, amendment, replacement and modification still fall within the scope of protection of the present invention.

Claims (6)

1. cylinder roller bearing inner ring diameter run-out Forecasting Methodology, it is characterized in that, the method comprises the steps:

1) given bearing parameter, comprises bearing outer ring ball track diameter, bearing inner race raceway diameter, roller diameter, roller number N, bearing outer ring ball track contour curve, bearing inner race raceway contour curve and roller surface contour curve;

2) bearing inner race rotates and presets step-length angle;

3) with the center of circle of bearing outer ring be initial point, horizontal direction sets up rectangular coordinate system for X-axis, judges the number Z of the roller be positioned at below X-axis;

4) along the direction of the roller center of circle and outer ring circle center line connecting to outer ring raceway respectively movement be positioned at the roller below X-axis, until roller contacts with outer ring raceway, record the central coordinate of circle o of now roller _rj, j=1,2,3 ..., Z;

5) according to presetting translating step, translation bearing inner race, records the central coordinate of circle of now bearing inner race;

6) according to the roller central coordinate of circle be positioned at below X-axis, calculate the bee-line of the roller surface below X-axis to inner ring raceway profile, and then judge under the central coordinate of circle of this bearing inner race, whether have roller and bearing inner race raceway contact, if do not have, return step 5), if have, record the position angle of all rollers contacted with bearing inner race;

7) judge whether the central coordinate of circle of bearing inner race exceeds setting range of translation, if do not have, returns step 5), otherwise, enter step 8);

8) contact condition criterion is stablized according to bearing, to exist and roller contact all bearing inner races central coordinate of circle under bearing touch state differentiate, find out contact condition the most stable under wherein only considering Action of Gravity Field, the Y-coordinate of bearing inner race central coordinate of circle corresponding under this contact condition is exactly inner ring diameter run-out value.

2. cylinder roller bearing inner ring diameter run-out Forecasting Methodology according to claim 1, it is characterized in that, according to step 2) ~ 8) obtain inner ring diameter run-out value under bearing inner race different rotary angle, thus obtain bearing inner race diameter run-out course.

3. cylinder roller bearing inner ring diameter run-out Forecasting Methodology according to claim 1, it is characterized in that, step 4) in judge that the method whether roller and outer ring raceway contact is: calculate the bee-line of roller surface to outer ring raceway profile, when bee-line is less than setting value, roller contacts with outer ring raceway; Wherein, roller surface to the computing method of the bee-line AB of outer ring raceway profile is: calculate the distance L of roller surface to outer ring raceway profile _e, AB is for work as θ _eat [0,2B _e/ d _e] in scope during change, make L _eminimum value, wherein,

$L_e=\sqrt{{\mathrm{AO}}^2+{{\mathrm{Oo}}_{rj}}^2-2AO\×{\mathrm{Oo}}_{rj}\×\cos \left({\mathrm{\θ}}_e\right)}-d_e/2-\underset{m_e=2}{\overset{n_e}{\mathrm{\Σ}}}\[A_{m_e}\cos (m_e{\mathrm{\θ}}_B-m_e{\mathrm{\α}}_e)+B_{m_e}\sin (m_e{\mathrm{\θ}}_B-m_e{\mathrm{\α}}_e)\]$

AO is the distance of 1 A and the center of circle, outer ring O on outer ring raceway, Oo _rjfor the center of circle, outer ring and roller center of circle o _rjdistance, θ _efor the line of A point and O point and O point and o _rjthe angle of some line; θ _bfor the position angle of roller surface B point, d _efor the desirable radius of outer ring raceway; m _efor outer ring raceway harmonic order; n _efor the maximum harmonic order of outer ring raceway; with be respectively harmonic component sine and cosine coefficient; B _efor default outer ring search width; α _efor the angle of outer ring rotating.

4. cylinder roller bearing inner ring diameter run-out Forecasting Methodology according to claim 1, it is characterized in that, described step 6) in roller surface below X-axis to the computing method of the bee-line of inner ring raceway profile be: calculating roller surface is to the distance L of inner ring raceway profile _i, CD is for work as θ _iat [0,2B _i/ d _i] in scope during change, make L _iminimum value, wherein,

$L_e=\sqrt{{{\mathrm{Co}}_i}^2+o_i{o_{rj}}^2-2{{\mathrm{Co}}_i}^2\×o_i{o}_{rj}\×\cos \left({\mathrm{\θ}}_i\right)}-d_i/2-\underset{m_i=2}{\overset{n_i}{\mathrm{\Σ}}}\[A_{m_i}\cos (m_i{\mathrm{\θ}}_D-m_i{\mathrm{\α}}_i)+B_{m_i}\sin (m_i{\mathrm{\θ}}_D-m_i{\mathrm{\α}}_i)\]$

for 1 C on outer ring raceway and inner ring center of circle o _idistance, o _io _rjfor the inner ring center of circle and roller center of circle o _rjdistance, θ _ifor A and o _iline and o _iwith o _rjthe angle of line; θ _dfor the position angle of roller surface D point, d _ifor the desirable radius of inner ring raceway; m _ifor inner ring raceway harmonic order; n _ifor the maximum harmonic order of inner ring raceway; with be respectively harmonic component sine and cosine coefficient; B _ifor default inner ring search width; α _ifor the angle that inner ring rotates.

5. cylinder roller bearing inner ring diameter run-out Forecasting Methodology according to claim 1, it is characterized in that, step 6) under the central coordinate of circle of this bearing inner race, there is roller and bearing inner race raceway is interfered, namely this roller surface is negative to the bee-line of inner ring raceway profile, and its absolute value is greater than convergence error, returns step 5).

6. cylinder roller bearing inner ring diameter run-out Forecasting Methodology according to claim 4, is characterized in that, described step 8) in bearing stablize contact condition criterion and be: the number of the roller 1. contacted with bearing inner race is at least two; 2. roller and bearing inner race raceway are without interference; 3. a pair roller is had at least to lay respectively at Y-axis both sides; 4. to bear semiaxis angle minimum for roller contact district center line and Y-axis.