CN109520737B - Method for measuring and calculating friction torque of deep groove ball bearing - Google Patents
Method for measuring and calculating friction torque of deep groove ball bearing Download PDFInfo
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- CN109520737B CN109520737B CN201811427816.7A CN201811427816A CN109520737B CN 109520737 B CN109520737 B CN 109520737B CN 201811427816 A CN201811427816 A CN 201811427816A CN 109520737 B CN109520737 B CN 109520737B
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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
Abstract
A method for measuring and calculating the friction torque of deep-groove ball bearing includes fixing the inner ring of ball bearing to be measured on horizontal rotary shaft, loading disc and supporting steel ballWhich provides a radial force; recording the total angular displacement and the total deceleration time of the outer ring deceleration process by a camera to obtain the angular velocity omega of the outer ring deceleration processo(ii) a Using formulas
Calculating the friction torque T acting on the rolling body in the outer ring deceleration processfτ；FhqEquivalent elastic hysteresis rolling resistance of the rolling elements numbered q, MbcIs the friction torque of the cage against the rolling bodies, FfIs the hydrodynamic friction force F under the condition of elastohydrodynamic lubricationτIs the inertial force of the cage in the tangential direction of rotation in the frame of reference of the cage and the rolling elements. The method realizes the measurement and calculation of the friction torque of the deep groove ball bearing, solves the problem of difficulty in calculation of the friction torque of the deep groove ball bearing, and is accurate and reliable in result and simple and easy to implement.
Description
Technical Field
The invention belongs to the field of bearing design and development, and particularly relates to a universal method for measuring and calculating the friction torque of a deep groove ball bearing.
Background
The friction torque of the deep groove ball bearing is an important technical index for evaluating the dynamic performance of the deep groove ball bearing, and the bearing friction torque has direct influence on the temperature rise and energy loss inside the bearing and the friction and abrasion of the bearing. The magnitude of the friction torque of the deep groove ball bearing in actual working conditions is very concerned by industry researchers.
In modern engineering, most common bearing friction torque performance research methods adopt bearing measurement or are based on the traditional theory, the cost required by the bearing measurement is high, and the requirements on operators are high; the traditional theory has larger error and lower application range. Therefore, the method for measuring and calculating the friction torque of the universal deep groove ball bearing by combining the two methods has great theoretical and practical significance.
Disclosure of Invention
The invention provides a method for measuring and calculating the friction torque of a deep groove ball bearing, aiming at the problem that the friction torque of the bearing is difficult to calculate. According to the method, the measuring and calculating of the friction torque of the deep groove ball bearing are realized by means of the establishment of a measuring model and the combination of calculation, the problem that the friction torque of the deep groove ball bearing is difficult to calculate is solved, the calculation result is accurate and reliable, and the method is simple and easy to implement.
In order to achieve the purpose, the invention adopts the specific scheme that:
firstly, establishing a measurement model, fixedly installing an inner ring of a deep groove ball bearing to be measured on a horizontal rotating shaft, wherein a steel retainer is arranged between the inner ring and an outer ring of the deep groove ball bearing, a supporting steel ball is in contact with the upper part of the outer ring, a loading disc is supported above the supporting steel ball, and the loading disc provides radial force for the deep groove ball bearing through the supporting steel ball; then, the rotating shaft drives the inner ring of the deep groove ball bearing to rotate at a constant angular speed, when the rotating speeds of the outer ring and the inner ring of the deep groove ball bearing are equal, the rotating shaft stops rotating, a camera arranged on one side of the deep groove ball bearing records the total angular displacement and the total deceleration time of the outer ring in the deceleration process, and then the angular speed omega of the outer ring in the deceleration process is obtained0；
After the measurement model is established, a formula for calculating the friction torque needs to be obtained, and the method specifically comprises the following steps.
Numbering the rolling bodies in the deep groove ball bearing, wherein the rolling body which is applied to a radial load action line and is loaded to the maximum is No. 0, the two sides of the rolling body are symmetrical and are 1, 2 and 3 … … in sequence, and the position angle psi of the No. 0 rolling body is defined to be 0 degree;
the displacement of the inner ring and the outer ring in the direction of the external force after the deep groove ball shaft bears the radial force is deltarThe rolling elements of number q and inner according to the deformation coordination conditionsThe total elastic deformation between the outer rings is:
δq＝δrcosψq(1)
in the formula: q denotes the rolling element number, #qThe position angle of the rolling element denoted by q is shown.
Delta. as describedrThe height H from the inner surface of the bearing inner ring to the outer surface of the bearing outer ring when no radial force is applied can be measured by recording through a camera arranged on one side of the deep groove ball bearing or by using a caliper1Then measuring the height H from the inner surface of the bearing inner ring to the outer surface of the bearing outer ring when the bearing inner ring is subjected to radial force2Then δr＝H1-H2。
According to the hertzian contact theory, there is the following relationship between contact load and contact deformation:
in the formula: qqThe contact load of the rolling elements with the number q and the roller paths when the inner contact angle and the outer contact angle are equal is shown; knRepresents the total load-deformation constant between the rolling elements and the inner and outer races; for a deep groove ball bearing, n is 1.5.
Obviously, the contact load is the greatest in the radial load application direction, when:
from equations (2) and (3), we can derive:
contact load of the q-th rolling element of
Qq＝Qmaxcosnψq(5)
The outer ring equilibrium equation is expressed as:
in the formula: k represents the serial number of the rolling body with the minimum load;
from equations (5) and (6), we can derive:
due to Fr＝Gd+Gb+Gr(8)
In the formula: gdIndicating the weight of the disc, GbDenotes the weight of the supporting steel ball, GrThe outer ring weight is indicated.
Therefore, the rolling element-raceway contact load Q of any number Q can be determinedq。
In the rolling direction of the steel ball, the force acting on the steel ball has 2 hydrodynamic rolling forces Ffi、Ffo，FfiShowing hydrodynamic rolling force in contact of the steel ball with the inner race groove under lubrication conditions, FfoAnd the hydrodynamic rolling force in the contact of the steel ball and the outer ring channel under the lubrication condition is shown. Since the steel ball and the inner ring and the steel ball and the outer ring have the same geometric angle and load condition, F can be obtainedfi＝Ffo＝FfAccording to Biboulet and Houpert, a fluid dynamic rolling force calculation method under elastohydrodynamic lubrication (EHL) conditions is proposed:
in the formula: u is a speed parameter with dimension one:
w is a load parameter of dimension one:
η is the working temperatureDynamic viscosity of lubricating oil at degree, pas; v ═ v (v)1+v2) 2 is the average tangential velocity of the ball-channel contact area, m/s; v. of1Is the tangential velocity, v, of the rolling element-outer ring raceway contact region2The tangential velocity of the rolling element-inner ring raceway contact region can be calculated from v ═ ω r, where ω represents the angular velocity of the inner and outer rings of the bearing and r represents the distance from the rolling element-raceway contact region to the bearing axis, and for this patent device, v is 0 at the inner ring standstill ω, so v is a constant value2＝0；E*Is the equivalent modulus of elasticity of two contacting bodies, E*＝2.3×1011Pa; k is the radius ratio Ry/Rx；RyIs the equivalent radius of curvature, R, in the principal plane IxIs the equivalent radius of curvature in the principal plane II;
wherein, the principal plane I: an axial plane passing through a contact point between the rolling body and a bearing inner ring channel is defined as a main plane I,
main plane II: the radial plane passing through the contact point between the rolling body and the bearing inner ring channel is defined as a main plane II,
axial plane: a plane passing through the axis of rotation of the bearing,
radial plane: a plane perpendicular to the bearing axis of rotation.
When the center of the rolling body and the arc curvature center of the bearing inner ring channel are on the same side of the contact point of the rolling body and the arc curvature center of the bearing inner ring channel, the equivalent curvature radius R in the main plane IyIs calculated by the formula
Wherein, the radius of curvature R of the circular arc of the bearing inner ring channel1Greater than the radius R of the rolling body2。
When the center of the rolling body and the center of curvature of the circular arc of the bearing inner ring channel are on different sides of the contact point of the rolling body and the circular arc of the bearing inner ring channel, the equivalent radius of curvature R in the main plane IIxIs calculated by the formula
Wherein, the radius of curvature R of the circular arc of the bearing inner ring channel1Greater than the radius R of the rolling body2。
The retainer and the rolling body do decelerating circular motion together, and the acceleration of the retainer and the rolling body consists of two parts: normal acceleration and tangential acceleration, and the inertial force F of the cage in the tangential direction by taking the cage and the rolling bodies as reference systemsτ
In the formula: m iscIs the cage mass; z is the number of bearing rolling elements; m isbIs the rolling element mass; omega0Is the angular velocity of the outer ring; dmIs the bearing pitch circle diameter.
In the rolling process, due to the elastic hysteresis property of materials, the pressure distribution of the front part and the rear part of the contact area is asymmetric, the raceway can generate a rolling friction force on the rolling body, and a false equivalent elastic hysteresis rolling resistance F acting on the center of the rolling body is introducedhThe equivalent elastic hysteresis rolling resistance F of the rolling element numbered q is the same as the effect of the rolling friction forcehq
In the formula: a ishIs the elastic hysteresis loss coefficient; b is the contact ellipse minor semi-axis length; r is the rolling element radius.
The friction torque generated by the retainer to the rolling body is Mbc
In the formula: omegaoAngular velocity of the outer ring; c is the width of the contact area between the rolling element and the cage; r iscIs the cage pocket radius; d is the rolling element diameter; h is0Is the minimum oil film thickness of the lubricating oil;
is the outer ring angular position.
The total tangential resistance f to the largest loaded rolling element in the rolling plane of the rolling elementτ
Friction torque T acting on the rolling bodies during deceleration of the outer ringfτ
So far, the friction torque of the deep groove ball bearing can be obtained, and the method described above is applicable to general deep groove ball bearings.
Has the advantages that:
the measuring and calculating method of the invention can obtain the friction torque of the deep groove ball bearing by calculation according to a corresponding formula after simple equipment measurement, has accurate and reliable calculation result, simple and easy method, lower requirements on equipment investment and operators, can reduce the measurement cost of the traditional pure instrument, and overcomes the defects of larger calculation error and smaller application range of the traditional pure theory.
Drawings
FIG. 1 is a schematic view of a deep groove ball bearing mounted on a rotating table of a friction measuring instrument;
FIG. 2 is a diagram of the forces and moments acting on the loaded largest rolling elements in the rolling direction;
reference numerals: 1-loading the disc; 2-a support ball; 3-deep groove ball bearing; 4-horizontal rotation axis.
Detailed Description
The technical solution of the present invention will be further explained by the following detailed description with reference to the accompanying drawings.
As shown in fig. 1, the auxiliary device for measuring the friction torque of the general deep groove ball bearing comprises a loading disc 1, a supporting steel ball 2, a general deep groove ball bearing 3 to be measured and a horizontal rotating shaft 4. The horizontal rotating shaft 4 is provided with a universal deep groove ball bearing 3 to be tested, a supporting steel ball 2 and a loading disc 1 are arranged above the deep groove ball bearing 3, the loading disc 1 provides radial force for the deep groove ball bearing 3 through the supporting steel ball 2, the loading disc 1 limits the freedom degrees in the front, back, left and right directions through a support, and the loading disc 1 only has the freedom degrees in the upper and lower directions; the middle of the loading disc 1 above the supporting steel ball 2 is provided with a spherical groove which is used for limiting six displacement degrees of freedom of the steel ball, the rotation degree of freedom of the steel ball is not restricted, and the steel ball can freely rotate under the action of the bearing outer ring and transmit the radial force applied to the universal deep groove ball bearing 3 to be tested by the loading disc 1.
The auxiliary device for measuring the friction torque of the general deep groove ball bearing is applied and combined with theoretical calculation to calculate the friction torque of the general deep groove ball bearing, and the method mainly comprises the following two steps: one is to measure the total angular displacement and the total deceleration time of the outer ring in the deceleration process under the action of the loading disc 1, and further obtain the angular velocity omega of the outer ring in the deceleration processo；
And secondly, calculating the friction torque of the deep groove ball bearing through a theoretical formula.
The method comprises the following steps: measuring the total angular displacement and the total deceleration time of the outer ring in the deceleration process under the action of the loading disc 1, and further obtaining the angular velocity omega of the outer ring in the deceleration processo；
Establishing a measurement model shown in figure 1, fixedly installing an inner ring of a deep groove ball bearing to be measured on a horizontal rotating shaft 4, wherein the horizontal rotating shaft 4 can be a rotating shaft on a rotating platform of a friction measuring instrument, a steel retainer is arranged between the inner ring and an outer ring of the deep groove ball bearing, a supporting steel ball 2 is contacted right above the outer ring, a loading disc 1 is supported right above the steel ball, and the loading disc 1 provides radial force for the deep groove ball bearing 3 to be measured through the supporting steel ball 2; then, the rotating shaft 4 drives the inner ring of the deep groove ball bearing to rotate at a constant angular speed, when the rotating speeds of the outer ring and the inner ring of the deep groove ball bearing are equal, the rotating shaft 4 stops rotating, a camera arranged on one side of the deep groove ball bearing 3 records the total angular displacement and the total deceleration time of the outer ring in the deceleration process, and then the outer ring in the deceleration process is obtainedAngular velocity of (a) < omega >o。
Step two: and calculating the friction torque of the deep groove ball bearing through a theoretical formula.
First, the hydrodynamic rolling force F under the elastohydrodynamic lubrication (EHL) condition is calculated by equation (9)f(ii) a Then, the inertial force F in the tangential direction of the cage and the rolling elements is calculated by the formula (10)τ(ii) a Then, the equivalent elastic hysteresis rolling resistance F of the rolling element of number q is calculated by the formula (11)hq(ii) a Then, the formula (12) is used for calculating the friction torque generated by the retainer to the rolling body to be Mbc(ii) a Then, the total tangential resistance f of the individual rolling elements on the rolling plane is calculated from the forces and moments acting on the rolling elements by means of equation (13)τ(ii) a Finally, the friction torque T acting on all the rolling bodies in the outer ring deceleration process is calculated through the formula (14)fτNamely the universal deep groove ball bearing friction torque required by us.
The method can completely realize the measurement and calculation of the friction torque of the general deep groove ball bearing, has simple operation method and convenient operation in the whole process, is clear in the calculation process combining the measurement result, and provides a theoretical basis for the measurement and calculation of the friction torque of the general deep groove ball bearing.
Test examples
The measured bearing is a 6210 deep groove ball bearing, and the friction torque T is known to be 0.058 N.m;
the bearing parameters of the measured bearing are as follows: the diameter d of the rolling body is 9.84mm, and the arc curvature radius R of the raceway1Radius r of cage pocket of 8.4mmc2.05mm, outer ring weight Gr2.389N, lubricating oil viscosity eta 0.08 Pa.S, minimum oil film thickness ho8 μm, elastic hysteresis damage factor ahThe length b of the short semi-axis of the contact ellipse is 3 mu m, and the width c of the contact area between the rolling body and the retainer is 0.5 mm;
in the established measurement model, the weight G of a steel ball is supported on the bearing outer ringb0.04N, disc weight Gd＝0.09N。
The total angular displacement phi of the outer ring deceleration process recorded by the camera is 77.1rad, and the total deceleration time t is 2.57 s.
The parameters are substituted into the formula of the invention to obtain the friction torque T under the conditionfτ0.0562 N.m, and is within the allowable error range compared with the known friction torque of the measured bearing.
Claims (1)
1. A method for measuring and calculating friction torque of a deep groove ball bearing is characterized by comprising the following steps: firstly, establishing a measurement model, fixedly installing an inner ring of a deep groove ball bearing on a horizontal rotating shaft, contacting the top of an outer ring of the deep groove ball bearing with a supporting ball, arranging a loading disc on the supporting ball, and providing radial force for the deep groove ball bearing by the loading disc through a steel ball; then, the rotating shaft drives the inner ring of the deep groove ball bearing to rotate at a constant angular speed, when the rotating speeds of the outer ring and the inner ring of the deep groove ball bearing are equal, the rotating shaft stops rotating, a camera arranged on one side of the deep groove ball bearing records the total angular displacement and the total deceleration time of the outer ring in the deceleration process, and then the angular speed omega of the outer ring in the deceleration process is obtainedo；
Secondly, numbering rolling bodies in the deep groove ball bearing, wherein the rolling body which is loaded most on a radial load action line is No. 0, the two sides of the rolling body are symmetrical and are 1, 2 and 3 … … in sequence, and a position angle psi of the No. 0 rolling body is defined to be 0 degree;
by using the formula (14), the friction torque T acting on the rolling body during the outer ring deceleration is calculatedfτ：
Wherein Z is the number of rolling elements of the bearing, r is the radius of the channel relative to the rotating shaft, d is the diameter of the rolling elements, FhqThe equivalent elastic hysteresis rolling resistance of the rolling elements numbered q,
in formula (11): a ishIs the elastic hysteresis loss coefficient, b is the contact ellipse lengthHalf-axis length, R is rolling element radius, QqContact load of rolling elements and raceways numbered Q when inner and outer contact angles are equal, QqThe method is obtained by combining deformation coordination conditions with a Hertz contact theory;
Mbcis the friction torque of the cage to the rolling body
in the formula (12), η represents the dynamic viscosity of the lubricating oil at the operating temperature, c is the width of the contact region between the rolling element and the cage, and r iscIs the cage pocket radius; d is the rolling element diameter; h is0Is the minimum oil film thickness of the lubricating oil;
is the angular position of the outer ring;
Ffunder the condition of elastic fluid dynamic pressure lubrication, the fluid dynamic pressure friction force,
in the formula (9), U is a speed parameter with a dimension of one, W is a load parameter with a dimension of one, E*Is the equivalent modulus of elasticity of two contacting bodies, E*＝2.3×1011Pa, k is the radius ratio Ry/Rx；RyIs the equivalent radius of curvature, R, in the principal plane IxThe radius of curvature is equivalent to that of a main plane II, the main plane I is an axial plane passing through a contact point between the rolling body and a bearing inner ring channel, and the main plane II is a radial plane passing through the contact point between the rolling body and the bearing inner ring channel;
Fτis the inertial force of the retainer in the tangential direction of rotation in the reference system of the retainer and the rolling body,
in formula (10): m iscIs the cage mass; m isbIs the mass of the steel ball; dmIs the bearing pitch circle diameter.
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| 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 |
| 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 |
| 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 |
| CN113607317B (en) * | 2021-08-04 | 2022-08-16 | 大连理工大学 | Indirect measuring method and system for raceway contact stress |
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