1. Basic concepts
1.Bearing life: the total number of revolutions or working hours at a certain speed before any component in the bearing shows signs of fatigue spalling and expansion.
Mass production of components, due to the uneven material, the bearing life has a great dispersion, the longest and shortest life up to dozens of times, we must use statistical methods to deal with.
2.Basic rated life: refers to the life of 90% reliability, commonly used materials and processing quality, and under normal operating conditions, expressed by the symbol L10 (r) or L10h (h).
3.Basic rated dynamic load (C) : constant load that the bearing can bear when the basic rated life is one million revolutions (106).That is, under the action of the basic rated dynamic load, the bearing can work 106 to do not occur pitting failure, its reliability is 90%.The basic rated dynamic load is large, and the anti-fatigue bearing capacity of the bearing is relatively strong.
4.Basic rated static load (radial C0r, axial C0a) : it refers to the imaginary radial load or central axial static load equivalent to the following contact stress caused by the contact center between the maximum bearing load rolling body and raceway.
Three basic parameters of rolling bearing are commonly used in the design: the basic rated dynamic load Cr (radial) or Ca (axial) that meets certain fatigue life requirements, the basic rated static strength C0r (radial) or C0a (axial) that meets certain static strength requirements, and the limit speed N0 that controls bearing wear.All kinds of bearing performance index value C, C0, N0, can check the relevant manual.
2. Calculation formula of life checking
The life of rolling bearing decreases with the increase of load. The relationship curve between life and load is shown in FIG. 17-6, and the curve equation is
P epsilon L10 = constant
Where, P- equivalent dynamic load, N;L10- basic rated life, usually in units of 106r (L10=1 when life is one million revolutions);- life index, ball bearing =3, roller bearing =10/3.
The basic rated dynamic load C obtained by the manual is based on L10=1 and reliability is 90%.Therefore, the basic rated life L10 in unit of rotational speed can be obtained when the equivalent dynamic load of the bearing is P
C epsilon * 1 = P epsilon * L10
L10 = (C/P) epsilon 106 r (17.6)
If the working speed of the bearing is n r/min, the basic rated life in hours can be obtained
H (17.7)
L10 should be greater than or equal to l prime.Lh 'is the expected service life of the bearing.The expected service life of the machine is usually referred to as the overhaul period.
If the equivalent dynamic load P and expected service life Lh 'of the bearing are known, the corresponding calculated rated dynamic load C' can be obtained according to the following equation, which must meet the requirements of the following equation with the C value of the selected bearing model
N (17.8)
3 equivalent dynamic load
In the actual working condition, the rolling bearing is often subjected to combined radial and axial loads at the same time. In order to compare the basic rated dynamic load with the actual load under the same conditions, the actual working load should be converted into equivalent dynamic load.Under the action of equivalent dynamic load, the bearing life is the same as that under the actual joint load.The formula for calculating the equivalent dynamic load P is
P = XFr + YFa
Where, fr-radial load, N;Fa- axial load, N;X, Y- radial dynamic load coefficient and axial dynamic load coefficient, as shown in table 17-7.
Load calculation of angular contact bearing
For "3" and "7" bearings, due to the characteristics of their own structure, when the radial force will produce derived S, should be considered in the calculation.
1.The assembly form must be installed in pairs: formal (or "face to face") - the distance between the two fulcrum is short;As shown in figure 17-7 a.Reverse mounting (or "back to back") - long distance between two points, suitable for cantilever mounting of transmission bearings, see figure 17-7b.
2. The action point of bearing force on the shaft
The pivot point on the axis is at the intersection of the normal line and the axis at the contact point between the rolling body and the raceway, as shown in FIG. 17-8.In the figure, the distance from the outer end is a, which can be found in the manual.
3. Calculation of axial force
The additional axial force caused by radial force and other working axial force on the shaft should be considered simultaneously when analyzing the axial load of angular contact bearing.
FR and FA are radial and axial loads acting on the shaft respectively, the radial reaction forces of the two bearings are Fr1 and Fr2, and the additional axial forces generated correspondingly are Fs1 and Fs2.The axial forces acting on the axis are shown in FIG. 17-10.
According to the balance relationship of shaft bearing Ⅰ, according to the following two cases analysis Ⅱ by axial force:
- if FS1 + FA>Fs2 (figure 17-11), shaft has a tendency to move to the right, make the bearing Ⅱ "pressure", right in the shaft bearing Ⅱ by a balanced reaction Fs2 ', from which the axial force of the bearing Ⅱ for
Fa2 = Fs2 + Fs2 '= Fs1 + FA
By bearing Ⅰ only additional axial force, reason
Fa1 = FS1
- if FS1 + FAs2 (figure 17-12), the shaft has a tendency to move to the left, make the bearing Ⅰ "pressure", this time the left end of the shaft will by a bearing Ⅰ balance reaction FS1 ', which can calculate both the axial force on the bearing, respectively
Fa1 = Fs1 + Fs1 '= Fs2 - FA
Fa2 = Fs2
The method to calculate the axial force of angular contact bearing can be summarized as follows: 1) determine the direction of the resultant force of all the axial forces on the shaft (including external load and additional axial force of the bearing), and determine the bearing at the "compression" end;2) the axial force of the bearing at the "compaction" end is equal to the algebraic sum of all the axial forces except the additional axial forces of the bearing itself;3) the axial force of the other bearing is equal to the additional axial force of the bearing itself.
Formula for calculating static load and limit speed
1.Static load calculation
Static load refers to the load applied on the bearing when the relative speed of the bearing ring is zero.In order to limit excessive contact stress and permanent deformation of rolling bearing under static load, static load calculation is needed.The bearing is selected according to the rated static load, and the basic formula is
C0 acuity C0 '= S0P0
Where, C0- basic rated static load, N;C0 '- calculation of rated static load, N;P0- equivalent static load, N;S0- safety factor.
For stationary bearings, slow oscillating bearings or bearings with very low speed, the safety coefficient can be selected according to table 17-9.
If the bearing speed is low and the requirements for running accuracy and friction torque are not high, it is allowed to have a large contact stress.1.Thrust centering roller bearing, whether rotating or not, should be S0≥4.
2.Limit speed
If the speed of rolling bearing is too high, high temperature will be generated between the friction surfaces, which will affect the performance of lubricant and damage the oil film, which will result in the failure of rolling body tempering or component bonding.
The ultimate speed N0 of rolling bearing refers to the speed value when the bearing reaches the maximum thermal equilibrium temperature under certain working conditions.The working speed of the bearing shall be lower than its limit speed.
Rolling bearing performance given in the table limit speed values are established in the grease lubrication and oil lubrication conditions, and applies only to a level 0 tolerance, lubrication cooling normal, cooperate with rigid bearing and shaft, bearing load P 0.1 C or less (C for bearing the basic dynamic load rating, centripetal bearing only by radial load, thrust bearing only by axial load) of the bearing.
When rolling bearing loads P>At 0.1c, the contact stress will increase;When the bearing bears the joint load, the load bearing rolling body will increase, which will increase the friction between the bearing contact surface and make the lubrication state bad.At this time, the limit speed value should be revised, the actual allowable speed value can be calculated according to the following formula
N = f1f2N0
Where, N- actual allowable speed, r/min;N0- ultimate speed of bearing, r/min;F1 - load coefficient (FIG. 17-13);F2 - load distribution coefficient.