CN116150916A - Method for determining position and polishing amount of bearing soft belt and bearing - Google Patents

Method for determining position and polishing amount of bearing soft belt and bearing Download PDF

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Publication number
CN116150916A
CN116150916A CN202310403631.7A CN202310403631A CN116150916A CN 116150916 A CN116150916 A CN 116150916A CN 202310403631 A CN202310403631 A CN 202310403631A CN 116150916 A CN116150916 A CN 116150916A
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bearing
soft belt
displacement
contact force
polishing amount
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王燕霜
王明伟
刘方正
许树辉
王子君
栗文彬
于长鑫
袁锡铭
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Qilu University of Technology
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
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    • Y02E10/72—Wind turbines with rotation axis in wind direction

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  • Rolling Contact Bearings (AREA)

Abstract

The invention discloses a method for determining the position and polishing amount of a bearing soft belt and a bearing, wherein the method comprises the following steps of (1) calculating contact force and inner ring normal deformation vector under two working conditions according to radial and axial loads and moment acting on a Y-axis under fatigue load working conditions and extreme load working conditions; (2) Searching two rolling body position angles with contact forces being approximately equal under two working conditions, wherein if one of the contact forces is smaller than the other, the rolling body position angle is the position angle of the soft belt region; (3) And taking the maximum normal deformation vector of the inner ring as the minimum soft belt polishing amount. According to the method, the contact force and the normal deformation vector of the inner ring under two working conditions are calculated through the radial and axial loads acting on the bearing and the moment acting on the Y shaft under the fatigue load working condition and the limit load working condition, so that the contact force and the normal deformation vector under the two working conditions are obtained, and then the soft belt area and the polishing amount are obtained.

Description

Method for determining position and polishing amount of bearing soft belt and bearing
Technical Field
The invention belongs to the technical field of mechanical equipment, and particularly relates to a method for determining the position and polishing amount of a bearing soft belt and a bearing.
Background
During induction hardening of the raceway, a blank area appears between the starting point and the end point of the hardening head, which is called a soft belt because the raceway is low in surface strength and hardness due to the fact that the raceway is not hardened. During operation of the bearing, the soft belt region needs to be placed in a position where the force is small and must not be in contact with the rollers. The bearing service life is seriously influenced by the bearing soft belt placement area and the polishing depth of the soft belt, if the roller is contacted with the soft belt area, the position of the soft belt is damaged, and then the whole bearing raceway is damaged. At present, the soft belt is placed at a position with smaller stress by experience, and the polishing depth is a certain depth by experience.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a method for determining the position and the polishing amount of a bearing soft belt.
The invention is realized by the following technical scheme:
in the above-mentioned technical scheme, the method comprises the steps of,
a method for determining the position and polishing amount of a bearing soft belt comprises the following steps,
(1) According to radial and axial loads acting on the bearing under the fatigue load working condition and the limit load working condition and the moment acting on the Y shaft, calculating the contact force and the normal deformation vector of the inner ring under the two working conditions;
(2) Searching two rolling body position angles with the contact force being approximately equal under two working conditions, and if one rolling body position angle contact force is smaller than the other rolling body position angle contact force, setting the rolling body position angle as the position angle of the soft belt region;
(3) And taking the maximum normal deformation vector of the inner ring as the minimum soft belt polishing amount.
Wherein, the equation for determining the contact force in the step (1) is:
Figure SMS_1
；
when the external load under the fatigue load working condition and the limit load working condition is determined, the numerical solution of the equation set is used for solving to obtain the axial displacement
Figure SMS_2
And radial displacement->
Figure SMS_3
And angular displacement->
Figure SMS_4
Substituted into the following formula,
Figure SMS_5
；
obtaining contact force on any two contact pairs
Figure SMS_6
Axial displacement of the inner ring->
Figure SMS_7
And radial displacement
Figure SMS_8
And angular displacement->
Figure SMS_9
Is substituted into the formula of the product,
Figure SMS_10
；
obtaining normal deformation vector of inner ring of any two contact pairs
Figure SMS_11
；
wherein ,
Figure SMS_14
for the load displacement coefficient>
Figure SMS_17
Is the curvature radius of the inner race->
Figure SMS_21
Is the distance between the curvature centers of the inner ring groove and the outer ring groove at any rolling body, +.>
Figure SMS_15
For the distance between the centers of curvature of the grooves at 0 play before loading, < >>
Figure SMS_16
For the original contact angle of the bearing, +.>
Figure SMS_19
For the position angle +.>
Figure SMS_22
For any rolling element position angle i=1, 2, 3..z, Z is the total number of rolling elements, +.>
Figure SMS_12
For radial displacement +.>
Figure SMS_18
For axial displacement>
Figure SMS_20
For angular displacement->
Figure SMS_23
and />
Figure SMS_13
The radial and axial loads acting on the bearing, respectively, M being the moment acting on the Y axis.
In the technical scheme, the bearing is a yaw ball bearing or a pitch ball bearing for wind power.
A bearing prepared by adopting the method for determining the position and the polishing amount of the bearing soft belt.
The invention has the advantages and beneficial effects that:
according to the invention, the contact force and the normal deformation vector of the inner ring under the two working conditions are calculated through the radial and axial loads acting on the bearing under the fatigue load working condition and the limit load working condition and the moment acting on the Y axis, so that the contact force and the normal deformation vector under the two working conditions are obtained, then the soft belt area and the polishing amount are obtained, the actual working condition is combined for calculation, the result is accurate, the experience defect is overcome, and the product design quality standard is ensured.
Drawings
FIG. 1 is a ball-race contact geometry model after loading;
FIG. 2 is a geometric model of the displacement of the inner ring (outer ring stationary) under the combined action of radial, axial and moment;
FIG. 3 is a geometric model of the center of curvature trajectory of the trench before loading;
FIG. 4 is a geometric model of the curvature center trajectory of the post-displacement groove.
In the figure:
Figure SMS_26
is the rolling element-raceway load,/->
Figure SMS_30
Is the distance between the curvature center tracks of the inner and outer raceway grooves,/>
Figure SMS_35
Is the distance between the centers of curvature of the raceway grooves, +.>
Figure SMS_27
Is the initial contact angle, +.>
Figure SMS_31
Is the working contact angle +.>
Figure SMS_34
、/>
Figure SMS_37
Is the displacement of the inner and outer rollaway nest,
Figure SMS_24
is relative axial displacement, ++>
Figure SMS_29
Is relative radial displacement, & lt & gt>
Figure SMS_33
Is relative angular displacement, θ is the relative angular displacement of the inner and outer rings, and +.>
Figure SMS_36
Is the curvature radius of the outer race, < >>
Figure SMS_25
Is the curvature radius of the inner race, < > and>
Figure SMS_28
is the initial inner circle center,/->
Figure SMS_32
Is the center of the inner ring after loading.
Other relevant drawings may be made by those of ordinary skill in the art from the above figures without undue burden.
Detailed Description
In order to make the person skilled in the art better understand the solution of the present invention, the following describes the solution of the present invention with reference to specific embodiments.
The invention relates to a method for determining the position and polishing amount of a soft belt of a bearing, in particular to a large-scale bearing, which comprises the following steps,
(1) According to radial and axial loads acting on the bearing under the fatigue load working condition and the limit load working condition and the moment acting on the Y shaft, calculating the contact force and the normal deformation vector of the inner ring under the two working conditions; wherein X and Y are radial. Taking fig. 3 and 4 as an example, Z is the horizontal axis, that Y is the vertical downward radial, X is the outward radial perpendicular to the paper,
(2) Searching two rolling body position angles with the contact force being approximately equal under two working conditions, and if one rolling body position angle contact force is smaller than the other rolling body position angle contact force, setting the rolling body position angle as the position angle of the soft belt region; the two contact forces are equal or the difference value is minimum at two different position angles in a whole circumferential range, and then the position angle at which the two contact forces are minimum is regarded as a soft bag polishing position;
(3) And taking the maximum normal deformation vector of the inner ring as the minimum soft belt polishing amount.
Specifically, the equation for determining the contact force in the step (1) is:
Figure SMS_38
；
when the external load under the fatigue load working condition and the limit load working condition is determined, the numerical solution of the equation set is used for solving to obtain the axial displacement
Figure SMS_39
And radial displacement->
Figure SMS_40
And angular displacement->
Figure SMS_41
Substituted into the following formula,
Figure SMS_42
；
obtaining the contact force on any two contact pairs of two rows of rolling bodies
Figure SMS_43
，/>
Figure SMS_44
For any rolling element position angle i=1, 2, 3..z, Z is the total number of rolling elements, the axial direction of the inner ring is taken as the axis direction of the inner ringDisplacement->
Figure SMS_45
And radial displacement->
Figure SMS_46
And angular displacement->
Figure SMS_47
Is substituted into the formula of the product,
Figure SMS_48
；
obtaining normal deformation vector of inner ring of any two contact pairs
Figure SMS_49
；
wherein ,
Figure SMS_53
for the load displacement coefficient>
Figure SMS_55
Is the curvature radius of the inner race->
Figure SMS_59
Is the distance between the curvature centers of the inner ring groove and the outer ring groove at any rolling body, +.>
Figure SMS_52
For the distance between the centers of curvature of the grooves at 0 play before loading, < >>
Figure SMS_56
For the original contact angle of the bearing, +.>
Figure SMS_58
For the position angle +.>
Figure SMS_61
For any rolling element position angle +.>
Figure SMS_50
For radial displacement +.>
Figure SMS_54
For axial displacement>
Figure SMS_57
For angular displacement->
Figure SMS_60
and />
Figure SMS_51
Radial and axial loads acting on the bearing, respectively; m is the moment acting on the Y axis.
In practice, given a wind power bearing fatigue load condition
Figure SMS_62
，/>
Figure SMS_69
，/>
Figure SMS_71
And +.>
Figure SMS_63
，
Figure SMS_68
，/>
Figure SMS_73
Respectively obtaining the contact force +.>
Figure SMS_74
and />
Figure SMS_64
Comparison->
Figure SMS_67
and />
Figure SMS_72
Finding the position angle of the rolling element with contact force approximately equal under two working conditions generally results in two rollingThe contact forces at the corners of the moving body being equal, i.e
Figure SMS_75
，/>
Figure SMS_65
If->
Figure SMS_66
The P-th rolling element position angle +.>
Figure SMS_70
Is the position angle at which the soft zone is placed. Under the extreme load working condition and the fatigue load working condition, the maximum normal deformation vector of the inner ring is that
Figure SMS_76
The minimum soft belt polishing amount.
Wherein, the above-mentioned deriving process is as follows,
position angle of each rolling element of four-point contact ball bearing
Figure SMS_77
Can be expressed as:
Figure SMS_78
（1）
z is the total rolling element number, i=1, 2, 3..Z, wherein Z represents the total rolling element number, two groups of channels are arranged on the inner ring and the outer ring of the four-point contact ball bearing, the rolling elements, namely steel balls, can form two contact pairs, and the distance A between the curvature centers of the inner ring and the outer ring grooves at any rolling element is before the bearing is loaded
Figure SMS_79
（2）
Distance between groove centers of curvature at 0 play before load
Figure SMS_80
The following are provided:
Figure SMS_81
（3）
Figure SMS_82
，/>
Figure SMS_83
，/>
Figure SMS_84
and />
Figure SMS_85
The curvature coefficient of the inner ring groove, the curvature coefficient of the outer ring groove, the spherical diameter and the play are respectively.
The radius of the circle in which the center of curvature of the inner channel groove is located can be expressed as
Figure SMS_86
（4）
Figure SMS_87
For the original contact angle of the bearing, +.>
Figure SMS_88
The pitch diameter of the finger bearing. When the rolling element is loaded, the distance between the curvature centers of the inner and outer raceways is +.>
Figure SMS_89
To vary with the amount of radial approach between the raceways. As can be seen from fig. 1
Figure SMS_90
（5）
Figure SMS_91
（6）
Figure SMS_92
，/>
Figure SMS_93
，/>
Figure SMS_94
The contact deformation of the rolling bodies and the inner ring, the contact deformation of the rolling bodies and the outer ring and the total deformation of the bearing are respectively adopted. When a load is applied to the bearing, as shown in fig. 2, if the outer race of the bearing is considered to be spatially fixed, radial displacement, axial displacement and angular displacement of the inner race will occur, while the center distance of curvature of the inner and outer race grooves changes due to the displacement of the inner race. As can be seen from fig. 4, the angle +_ is at any rolling element position>
Figure SMS_95
Groove curvature center distance of two contact pairs>
Figure SMS_96
Is->
Figure SMS_97
（7）
Figure SMS_98
（8）
in the formula ,
Figure SMS_99
radial displacement is given in mm; />
Figure SMS_100
Axial displacement is given in mm; />
Figure SMS_101
The unit is angle displacement, 1 and 2 are the left and right rows of rolling bodies, and the following is the same;
bringing formulae (7) and (8) into formula (6)
Figure SMS_102
（9）
Figure SMS_103
(10）
According to the load-displacement relation of the rolling element rollaway nest:
Figure SMS_104
（11）
in the formula (11), a=3/2 for the ball bearing and a=10/9 for the roller bearing. Bringing the formula (9), the formula (10) into the formula (11), and obtaining the contact force on the two contact pairs as
Figure SMS_105
（12）
Figure SMS_106
（13）
I.e.
Figure SMS_107
（14）
Figure SMS_108
（15）
At any rolling element position angle
Figure SMS_109
Where, working contact angle +.>
Figure SMS_110
Can be determined as
Figure SMS_111
（16）
Figure SMS_112
（17）
Figure SMS_113
（18）
Figure SMS_114
（19）
Equation (11) gives the normal load acting on the raceway along the contact angle, which can be resolved into the following axial and radial components:
Figure SMS_115
（20）
Figure SMS_116
（21）/>
if the radial and axial loads acting on the bearing are respectively
Figure SMS_117
and />
Figure SMS_118
Then the static equilibrium equation is
Figure SMS_119
（22）
Figure SMS_120
（23）
For static equilibrium, the moment M acting on the Y-axis must be equal to the sum of the moments of each rolling element on the Y-axis
Figure SMS_121
（24）
Substituting equations (14) - (19) into (22), (23) and (24) yields the equation for determining contact force described above.
Particular embodiments wherein fatigue loading of wind bearings is designed
Figure SMS_122
=1583KN，/>
Figure SMS_123
=380KN，/>
Figure SMS_124
=1650 kn·m, limit load +.>
Figure SMS_125
=2487KN，/>
Figure SMS_126
=1170KN，/>
Figure SMS_127
=4642 KN ·m. And calculating to obtain the maximum relative displacement under the limiting working condition of 0.547mm and the maximum relative displacement under the fatigue working condition of 0.352mm. And obtaining curves of contact forces at different position angles through a calculation model, wherein the abscissa of a coordinate system where the curves are positioned is the position angle of the rolling body, and the ordinate is the contact force. The two curves are the corresponding relation between the position angle and the contact force under the fatigue working condition and the limit working condition respectively. The two curves are intersected, and an intersecting point is found, so that the abscissa of the intersecting point is the polishing position of the soft belt. If the curves intersect many times, the position angle of the point with the smallest ordinate value (contact force) is taken as the soft band position. The two curves intersect at the 149 deg. position angle, the bearing soft belt should be placed at the 149 deg. position angle of the bearing, and the polishing amount is more than 0.547mm to ensure that the soft belt does not contact with the rolling bodies.
The polishing position and the polishing amount of the soft belt of the large four-point contact ball bearing can be obtained through the method, so that the soft belt position is ensured not to be contacted with the roller in the actual operation process of the wind power bearing, and the service life of the variable pitch bearing is prolonged.
Meanwhile, the bearing prepared by the method for determining the position and the polishing amount of the soft belt of the large bearing is also disclosed. The general large-scale bearing is a bearing with the outer diameter larger than 440mm, and the model is a yaw bearing or a pitch bearing which are commonly used for wind power by ball bearings.
The foregoing has described exemplary embodiments of the invention, it being understood that any simple variations, modifications, or other equivalent arrangements which would not unduly obscure the invention may be made by those skilled in the art without departing from the spirit of the invention.

Claims (4)

1. A method for determining the position and polishing amount of a bearing soft belt is characterized by comprising the following steps,
(1) According to radial and axial loads acting on the bearing under the fatigue load working condition and the limit load working condition and the moment acting on the Y shaft, calculating the contact force and the normal deformation vector of the inner ring under the two working conditions;
(2) Searching two rolling body position angles with the contact force being approximately equal under two working conditions, and if one rolling body position angle contact force is smaller than the other rolling body position angle contact force, setting the rolling body position angle as the position angle of the soft belt region;
(3) And taking the maximum normal deformation vector of the inner ring as the minimum soft belt polishing amount.
2. The method for determining the position and the polishing amount of the bearing soft belt according to claim 1, wherein the method comprises the following steps: the equation for determining the contact force in the step (1) is as follows:
Figure QLYQS_1
；
when the external load under the fatigue load working condition and the limit load working condition is determined, the numerical solution of the equation set is used for solving to obtain the axial displacement
Figure QLYQS_2
And radial displacement->
Figure QLYQS_3
And angular displacement->
Figure QLYQS_4
Substituted into the following formula,
Figure QLYQS_5
；
obtaining contact force on any two contact pairs
Figure QLYQS_6
Axial displacement of the inner ring->
Figure QLYQS_7
And radial displacement->
Figure QLYQS_8
And angular displacement->
Figure QLYQS_9
Substituted formula->
Figure QLYQS_10
；
Obtaining normal deformation vector of inner ring of any two contact pairs
Figure QLYQS_11
；
wherein ,
Figure QLYQS_15
for the load displacement coefficient>
Figure QLYQS_18
Is the curvature radius of the inner race->
Figure QLYQS_21
Is the distance between the curvature centers of the inner ring groove and the outer ring groove at any rolling body, +.>
Figure QLYQS_14
For the distance between the centers of curvature of the grooves at 0 play before loading, < >>
Figure QLYQS_17
Is a bearingOriginal contact angle,/->
Figure QLYQS_20
For the position angle +.>
Figure QLYQS_23
For any rolling element position angle i=1, 2, 3..z, Z is the total number of rolling elements, +.>
Figure QLYQS_12
For radial displacement +.>
Figure QLYQS_16
For axial displacement>
Figure QLYQS_19
For angular displacement->
Figure QLYQS_22
and />
Figure QLYQS_13
The radial and axial loads acting on the bearing, respectively, M being the moment acting on the Y axis.
3. The method for determining the position and the polishing amount of the bearing soft belt according to claim 1, wherein the method comprises the following steps: the bearing is a yaw ball bearing or a pitch ball bearing for wind power.
4. A bearing prepared by the method for determining the position and polishing amount of a bearing soft belt according to any one of claims 1 to 3.
CN202310403631.7A 2023-04-17 2023-04-17 Method for determining position and polishing amount of bearing soft belt and bearing Pending CN116150916A (en)

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Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102819635A (en) * 2012-08-02 2012-12-12 河南科技大学 Method for establishing statics model of extra-large double-row four-point contact ball bearing
CN112329305A (en) * 2020-11-05 2021-02-05 中车株洲电力机车研究所有限公司 Method for determining position and polishing amount of soft belt of variable-pitch bearing of wind turbine generator

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102819635A (en) * 2012-08-02 2012-12-12 河南科技大学 Method for establishing statics model of extra-large double-row four-point contact ball bearing
CN112329305A (en) * 2020-11-05 2021-02-05 中车株洲电力机车研究所有限公司 Method for determining position and polishing amount of soft belt of variable-pitch bearing of wind turbine generator

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
王燕霜 等: "负游隙对特大型双排四点接触球轴承载荷分布的影响", 《机械工程学报》, vol. 48, no. 21, pages 110 - 115 *
贾晨鹤 等: "风电机组双列圆锥滚子主轴承热分析", 《HTTPS://KNS.CNKI.NET/KCMS/DETAIL//41.1148.TH.20221206.1335.003.HTML》, pages 1 - 10 *

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Application publication date: 20230523