CN109520737A - A kind of measuring method of deep groove ball bearing moment of friction - Google Patents
A kind of measuring method of deep groove ball bearing moment of friction Download PDFInfo
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- CN109520737A CN109520737A CN201811427816.7A CN201811427816A CN109520737A CN 109520737 A CN109520737 A CN 109520737A CN 201811427816 A CN201811427816 A CN 201811427816A CN 109520737 A CN109520737 A CN 109520737A
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- G—PHYSICS
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- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M13/00—Testing of machine parts
- G01M13/04—Bearings
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Abstract
A method of measuring and calculating deep groove ball bearing moment of friction provides radial force by load disk and support steel ball firstly, the inner ring of deep groove ball bearing to be measured is fixed on horizontal rotation shaft for it；The total angular displacement of outer ring moderating process and total reduction time under camera record by deep groove ball bearing side is arranged in obtain the angular velocity omega of outer ring moderating processo；Then formula is utilizedIt calculates in the moderating process of outer ring and acts on the moment of friction T on rolling elementfτ；FhqThe rolling element equivalent elastic hysteresis rolling resistance for being q for number, MbcFrame is to maintain to the moment of friction of rolling element, FfIt is the hydrodynamic frictional force under Conditions of Elastic Fluid Motive part, FτIt is inertia force of the retainer in rotation tangential direction in the referential of retainer and rolling element.This method realizes the measuring and calculating of deep groove ball bearing moment of friction, solves the problems, such as deep groove ball bearing moment of friction dyscalculia, as a result accurately and reliably, method is simple and easy by the combination of measurement model and calculating.
Description
Technical field
The invention belongs to design bearing development fields, and in particular to the general measuring and calculating deep groove ball bearing moment of friction of one kind
Method.
Background technique
The moment of friction of deep groove ball bearing is to evaluate the important technology index of deep groove ball bearing dynamic property, bearing friction power
Square directly affects Bearing inner temperature rise and energy loss, bearing friction abrasion.Industry research person exists to deep groove ball bearing
Moment of friction size in actual condition is extremely concerned about.
In modern project, common bearing frictional torque performance study method mostly uses greatly bearing measuring or based on tradition
Theory, the higher cost that bearing measuring needs, the requirement to operator are also high；There are biggish errors for traditional theory, are applicable in
Range is also relatively low.Therefore, the method for seeking two methods of a kind of general deep groove ball bearing moment of friction of measuring and calculating of combination has
Great theory and practical significance.
Summary of the invention
The present invention provides a kind of measuring and calculating deep groove ball bearing moment of friction aiming at the problem that bearing frictional torque dyscalculia
Method.This method by measurement model foundation, and combine calculate, realize deep groove ball bearing moment of friction measuring and calculating, solve
The problem of deep groove ball bearing moment of friction dyscalculia, calculated result is accurate and reliable, and method is simple and easy.
To achieve the goals above, the present invention use the specific scheme is that
Firstly, establishing measurement model, the inner ring of deep groove ball bearing to be measured is fixedly mounted on a horizontal rotation shaft,
The retainer of steel is had between deep groove ball bearing inner ring and outer ring, is in contact, is supported with a support steel ball right above outer ring
It is supported by load disk right above steel ball, provides radial force by support steel ball by load disk for deep groove ball bearing；Then, it revolves
Shaft drives the rotation of deep groove ball bearing inner ring with constant angular speed, when the outer ring of deep groove ball bearing and equal inner ring revolving speed,
Stop rotating the rotation of axis, under the camera record by deep groove ball bearing side is arranged in the total angular displacement of outer ring moderating process and
The total reduction time, and then outer ring is obtained in the angular velocity omega of moderating process0；
After completing measurement model foundation, needs to obtain the formula for calculating moment of friction, specifically follow the steps below.
Rolling element in the deep groove ball bearing is numbered, loaded maximum rolling on radial load position is acted on
Kinetoplast is No. 0, and both sides are symmetrical, is followed successively by 1,2,3 ..., and define position angle ψ=0 ° of No. 0 rolling element；
The deep groove ball bearing displacement that inside and outside circle occurs on external force direction after being acted on by radial force is δr, assisted according to deformation
Tune condition, number are total elastic deformation amount between the rolling element of q and Internal and external cycle are as follows:
δq=δrcosψq (1)
In formula: q indicates rolling element serial number, ψqIndicate the position angle for the rolling element that number is q.
The δrIt can be measured by the way that the camera record of deep groove ball bearing side is arranged in, calliper to measure can also be used,
Measurement is not when by radial force first, the height H of bearing inner race inner surface to outer ring outer surface1, then measure by diameter
Height H of the bearing inner race inner surface to outer ring outer surface when to power2, then δr=H1-H2。
There is following relationship according to Hertzian contact theory, between contact load and juxtaposition metamorphose:
In formula: QqIndicate the rolling element and raceway contact load that number is q when inside and outside contact angle is equal；KnIndicate rolling element
Total load displacement constant between Internal and external cycle；For deep groove ball bearing, n=1.5.
Obviously on radial load action direction, contact load is maximum, at this time:
It can be obtained by formula (2) and formula (3):
The contact load of q-th of rolling element is
Qq=Qmaxcosnψq (5)
The equilibrium equation of outer ring indicates are as follows:
In formula: K indicates loaded the smallest rolling element serial number；
It can be obtained by formula (5) and formula (6):
And due to Fr=Gd+Gb+Gr (8)
In formula: GdIndicate disk weight, GbIndicate supporting steel ball weight, GrIndicate outer ring weight.
Therefore, the rolling element and raceway contact load Q that arbitrary number is q can be found outq。
On steel ball rolling direction, the power acted on steel ball has 2 hydrodynamic rolling force Ffi、Ffo, FfiIndicate lubrication
Under the conditions of steel ball contacted with bear inner ring grooved railway in hydrodynamic rolling force, FfoIndicate that steel ball is contacted with outer ring raceway under lubricating condition
In hydrodynamic rolling force.Due to steel ball and inner ring and steel ball and outer ring geometric angle having the same and load-up condition,
It can be concluded that Ffi=Ffo=Ff, proposed according to Biboulet and Houpert and flowed down in elastic hydrodynamic lubrication (EHL) condition
Body dynamic pressure rolling force calculation method:
In formula: U is the speed parameter that dimension is one:
W is the load parameter that dimension is one:
η is the dynamic viscosity of lubricating oil under operating temperature, Pas；V=(v1+v2)/2 are that ball-being averaged for channel contact area is cut
To speed, m/s；v1It is rolling element-outer ring raceway contact area tangential velocity, v2It is rolling element-bear inner ring grooved railway contact area
Tangential velocity can be calculated by v=ω r, and ω indicates that the angular speed of bearing internal external circle, r indicate rolling element-channel contact area in formula
To the distance of bearing axis, for patent device, due to static ω=0 of inner ring at this time, so v2=0；E*It is two contactants
The equivalent elastic modulus of body, E*=2.3 × 1011Pa；K is radius ratio Ry/Rx；RyIt is the equivalent radius of curvature in principal plane I, Rx
It is the equivalent radius of curvature in principal plane II；
Wherein, principal plane I: the axial plane for providing contact point between rolling element and bearing inner race channel is principal plane I,
Principal plane II: the sagittal plane for providing contact point between rolling element and bearing inner race channel is principal plane II,
Axial plane: crossing the plane of bearing rotary axis,
Sagittal plane: the plane vertical with bearing rotary axis.
When rolling element center and bearing inner race channel circular arc curvature center are when the two contact point is ipsilateral, then in principal plane I
Equivalent radius of curvature RyCalculation formula is
Wherein, bearing inner race channel circular arc curvature radius R1Greater than rolling element radius R2。
When rolling element center and bearing inner race channel circular arc curvature center are in the two contact point heteropleural, then in principal plane II
Equivalent radius of curvature RxCalculation formula be
Wherein, bearing inner race channel circular arc curvature radius R1Greater than rolling element radius R2。
Retainer does the circular motion to slow down together with rolling element, and acceleration is made of two parts: normal acceleration and
Tangential acceleration, using retainer and rolling element as referential, then the inertia force F of retainer in the tangential directionτ
In formula: mcIt is to maintain frame quality；Z is bearing roller number；mbIt is to roll weight；ω0It is the angular speed of outer ring；dm
It is bearing pitch diameter.
During scrolling due to the elastic hysteresis property of material, former and later two partial pressures distribution of contact zone is not right
Claim, raceway can generate a force of rolling friction to rolling element, introduce the equivalent elasticity for acting on rolling element center an of illusion
Lag rolling resistance Fh, function and effect are as the function and effect of force of rolling friction, then the equivalent bullet for the rolling element that number is q
Property lag rolling resistance Fhq
In formula: ahIt is elastic hysteresis loss coefficient；B is Contact Ellipse semi-minor axis length；R is rolling element radius.
It is M that retainer, which generates moment of friction to rolling element,bc
In formula: ωoThe angular speed of outer ring；C is the width of contact region between rolling element and retainer；rcIt is to maintain frame pocket hole
Radius；D is rolling element diameter；h0It is the minimum oil film thickness of lubricating oil；It is outer ring Angle Position.
It is rolled in plane in rolling element, total tangential resistance f suffered by loaded maximum rolling bodyτ
In the moderating process of outer ring, the moment of friction T on rolling element is acted onfτ
So far, the moment of friction of deep groove ball bearing can be obtained, and the process described above is suitable for general deep groove ball bearing.
The utility model has the advantages that
Measuring method of the invention calculates you can get it deep-groove ball according to corresponding formula after simple device measuring
The moment of friction of bearing, calculated result is accurate and reliable, and method is simple and easy, and the requirement and operator to equipment investment are wanted
It asks all lower, the cost of traditional simple apparatus measures can be reduced, and overcome that traditional purely theory error is larger, is applicable in model
Enclose lesser defect.
Detailed description of the invention
Fig. 1 is mounted in the deep groove ball bearing schematic diagram on rub measurement instrument turntable；
Fig. 2 is the power and torque schematic diagram that loaded maximum rolling body is acted on rotating direction；
Appended drawing reference: 1-load disk；2-support balls；3-deep groove ball bearings；4-horizontal rotation shafts.
Specific embodiment
With reference to the accompanying drawing, further description of the technical solution of the present invention by specific embodiment.
As shown in Figure 1, the auxiliary device for measuring general deep groove ball bearing moment of friction includes load disk 1, support steel ball
2, general deep groove ball bearing 3 and horizontal rotation shaft 4 to be measured.General deep groove ball bearing 3 to be measured, zanjon are installed on horizontal rotation shaft 4
There are support steel ball 2 and load disk 1 above ball bearing 3, load disk 1 is that deep groove ball bearing 3 provides radial direction by support steel ball 2
Power, load disk 1 limit the freedom degree on four direction all around by bracket, and load 1, disk has upper and lower two sides
Upward freedom degree；It is provided with spherical groove among the load disk 1 of 2 top of support steel ball, the spherical groove is for limiting steel ball
Six displacement freedoms, there is no an effect of contraction to the rotary freedom of steel ball, steel ball can under the action of bearing outer ring from
The radial force of general deep groove ball bearing 3 to be measured is applied to come bootstrap loading disk 1 by rotating and transmitting.
It can be found out using the general deep groove ball bearing moment of friction auxiliary device of above-mentioned measurement and binding isotherm calculating general
Deep groove ball bearing moment of friction, this method are broadly divided into following two step: one is measurement outer ring in the case where load disk 1 acts on
The total angular displacement of moderating process and total reduction time, and then outer ring is obtained in the angular velocity omega of moderating processo；
The second is passing through theoretical formula method deep groove ball bearing moment of friction.
Step 1: the measurement total angular displacement of outer ring moderating process and total reduction time in the case where load disk 1 acts on, and then obtain
Outer ring is obtained in the angular velocity omega of moderating processo；
Measurement model as shown in Figure 1 is established, the inner ring of deep groove ball bearing to be measured is fixedly mounted on a horizontal rotation
In shaft 4, which can be the rotary shaft on rub measurement instrument turntable, deep groove ball bearing inner ring and outer ring it
Between have the retainer of steel, be in contact right above outer ring with a support steel ball 2, be supported by right above steel ball and load disk 1,
Radial force is provided for deep groove ball bearing 3 to be measured by support steel ball 2 by load disk 1；Then, rotary shaft 4 is with constant angle speed
Degree drives the rotation of deep groove ball bearing inner ring, and when the outer ring of deep groove ball bearing and equal inner ring revolving speed, the axis 4 that stops rotating turns
It is dynamic, the total angular displacement of outer ring moderating process and total reduction time under the camera record by 3 side of deep groove ball bearing is arranged in, into
And outer ring is obtained in the angular velocity omega of moderating processo。
Step 2: pass through theoretical formula method deep groove ball bearing moment of friction.
Firstly, calculating hydrodynamic rolling force F under the conditions of elastic hydrodynamic lubrication (EHL) by formula (9)f；So
Afterwards, the inertia force F of retainer and rolling element in the tangential direction is calculated by formula (10)τ；Then, it is calculated by formula (11)
The equivalent elastic hysteresis rolling resistance F for the rolling element that number is qhq；Then retainer is calculated by formula (12) to produce rolling element
Raw moment of friction is Mbc；Then, according to the power and torque acted on rolling element, single rolling element is calculated by formula (13) and is existed
Roll total tangential resistance f suffered in planeτ；It is calculated in the moderating process of outer ring finally by formula (14), acts on institute
There is the moment of friction T on rolling elementfτ, that is, the general deep groove ball bearing moment of friction required by us.
Above as can be seen that the measuring and calculating of general deep groove ball bearing moment of friction, whole process may be implemented in the present invention completely
Operating method it is simple, convenient for operation, the calculating process in conjunction with measurement result is clear, be general deep groove ball bearing frictional force
The measuring and calculating of square provides theoretical foundation.
Test example
Measured bearing is 6210 deep groove ball bearings, it is known that its moment of friction T=0.058Nm；
The bearing parameter of measured bearing are as follows: rolling element diameter d=9.84mm, raceway circular arc curvature radius R1=8.4mm is protected
Hold frame pocket pore radius rc=2.05mm, outer ring weight Gr=2.389N；Lubricating oil viscosity η=0.08PaS, minimum oil film thickness
ho=8 μm, elastic hysteresis Damage coefficient ah=0.2, b=3 μm of length of Contact Ellipse semi-minor axis, connecing between rolling element and retainer
Touch sector width c=0.5mm；
In the measurement model established, supporting steel ball weight G on bearing outer ringb=0.04N loads disk weight Gd=
0.09N。
By total angular displacement φ=77.1rad of the outer ring moderating process under camera record, total reduction time t=2.57s.
It brings above-mentioned parameter into present invention formula, obtains moment of friction T under this conditionfτ=0.0562Nm, and by
It surveys moment of friction known to bearing to compare, in the error range allowed positioned at it.
Claims (1)
1. a kind of measuring method of deep groove ball bearing moment of friction, it is characterised in that: firstly, measurement model is established, by deep-groove ball
Bearing inner race is fixedly mounted in horizontal rotary shaft, is contacted at the top of deep groove ball bearing outer ring with support ball, and on support ball
Setting load disk, loads disk by steel ball and provides radial force for deep groove ball bearing；Then, rotary shaft is with constant angular speed
The rotation of deep groove ball bearing inner ring is driven, when the outer ring of deep groove ball bearing and equal inner ring revolving speed, the rotation for the axis that stops rotating, by
The total angular displacement of outer ring moderating process and total reduction time under the camera record of deep groove ball bearing side are set, and then obtained
Angular velocity omega of the outer ring in moderating processo；
Secondly, the rolling element in the deep groove ball bearing is numbered, act on loaded maximum on radial load position
Rolling element is No. 0, and both sides are symmetrical, is followed successively by 1,2,3 ..., and define position angle ψ=0 ° of No. 0 rolling element；
Using formula (14), the moment of friction T acted on rolling element in the moderating process of outer ring is calculatedfτ:
Wherein, Z is bearing roller number, and r is the channel radius relative to rotary shaft, and d is rolling element diameter, FhqIt is for number
The equivalent elastic hysteresis rolling resistance of the rolling element of q,
In formula (11): ahIt is elastic hysteresis loss coefficient, b is Contact Ellipse semi-minor axis length, and R is rolling element radius, QqIt is inside and outside
The rolling element and raceway contact load that number is q when contact angle is equal, QqIt is obtained by deformation compatibility condition combination Hertzian contact theory
Out；
MbcFrame is to maintain to the moment of friction of rolling element
In formula (12), η is the dynamic viscosity of lubricating oil under operating temperature；C is the width of contact region between rolling element and retainer；
rcIt is to maintain frame pocket pore radius；D is rolling element diameter；h0It is lubricating oil minimum oil film thickness；It is the Angle Position of outer ring；
FfIt is the hydrodynamic frictional force under Conditions of Elastic Fluid Motive part,
In formula (9), U is the speed parameter that dimension is one, and W is the load parameter that dimension is one, E*It is the equivalent bullet of two contact objects
Property modulus, E*=2.3 × 1011Pa, k are radius ratio Ry/Rx；RyIt is the equivalent radius of curvature in principal plane I, RxIt is principal plane II
In equivalent radius of curvature, and principal plane I was the axial plane of contact point between rolling element and bearing inner race channel, main flat
Face II was the sagittal plane of contact point between rolling element and bearing inner race channel；
FτIt is inertia force of the retainer in rotation tangential direction in the referential of retainer and rolling element,
In formula (10): mcIt is to maintain frame quality；；mbIt is steel ball quality；；dmIt is bearing pitch diameter.
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| CN201811427816.7A CN109520737B (en) | 2018-11-27 | 2018-11-27 | Method for measuring and calculating friction torque of deep groove ball bearing |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN111811414A (en) * | 2020-06-15 | 2020-10-23 | 杭州电子科技大学 | Method for detecting thickness of light interference linear oil film of thrust ball bearing |
| CN111811415A (en) * | 2020-06-15 | 2020-10-23 | 杭州电子科技大学 | Thrust ball bearing light interference linear oil film thickness detection test bed and detection method thereof |
| CN112556908A (en) * | 2020-11-26 | 2021-03-26 | 河南科技大学 | Real-time stress detection device and method for rolling friction of elastic rolling ring |
| CN113607317A (en) * | 2021-08-04 | 2021-11-05 | 大连理工大学 | Indirect measuring method and system for raceway contact stress |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111811414A (en) * | 2020-06-15 | 2020-10-23 | 杭州电子科技大学 | Method for detecting thickness of light interference linear oil film of thrust ball bearing |
| CN111811415A (en) * | 2020-06-15 | 2020-10-23 | 杭州电子科技大学 | Thrust ball bearing light interference linear oil film thickness detection test bed and detection method thereof |
| CN111811414B (en) * | 2020-06-15 | 2021-08-10 | 杭州电子科技大学 | Method for detecting thickness of light interference linear oil film of thrust ball bearing |
| CN111811415B (en) * | 2020-06-15 | 2022-03-18 | 杭州电子科技大学 | Thrust ball bearing light interference linear oil film thickness detection test bed and detection method thereof |
| CN112556908A (en) * | 2020-11-26 | 2021-03-26 | 河南科技大学 | Real-time stress detection device and method for rolling friction of elastic rolling ring |
| CN112556908B (en) * | 2020-11-26 | 2022-04-08 | 河南科技大学 | Real-time stress detection device and method for rolling friction of elastic rolling ring |
| CN113607317A (en) * | 2021-08-04 | 2021-11-05 | 大连理工大学 | Indirect measuring method and system for raceway contact stress |
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