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Rolling bearing check calculation

Rolling bearing check calculation


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 can be up to dozens of times, we must use the statistical method to deal with. 

2.Basic rated life: refers to 90% reliability, common materials and processing quality, life under normal operating conditions, expressed by the symbol L10 (r) or L10h (h). 

3.Basic rated dynamic load (C) : the bearing can bear a constant load when the basic rated life is one million RPM (106).In other words, under the action of the basic rated dynamic load, the bearing can work 106 to avoid pitting failure, and its reliability is 90%.The basic rated dynamic load is large, and the bearing capacity against fatigue 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 maximum bearing load when the rolling body and raceway contact center cause the following contact stress. 

Three basic parameters of rolling bearing are often 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 values C, C0, N0 can be consulted the relevant manual. 

Life check calculation formula

The life of rolling bearing decreases with the increase of load. The curve of the relationship between life and load is shown in FIG. 17-6, and its 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 1 million RPM);- life index, =3 for ball bearings, =10/3 for roller bearings. 

The basic rated dynamic load C obtained from the manual is based on L10=1 and reliability is 90%.Therefore, when the equivalent dynamic load of the bearing is P, the basic rated life L10 is based on the unit of rotating speed

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 is greater than or equal to l prime.Lh prime is the expected service life of the bearing.The expected service life of the machine is usually referred to 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 formula, which must meet the requirements of the following formula with the C value of the selected bearing model

N (17.8)

Equivalent dynamic load

In actual working conditions, rolling bearings are often subjected to combined radial and axial loads at the same time. In order to compare the basic rated dynamic load and 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 life of the bearing is the same as that under the actual combined 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 coefficients and axial dynamic load coefficients, 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 there is a radial force action will generate derived S, should be considered in the calculation. 

1.The assembly must be 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, as shown in figure 17-7b. 

2. The action point of bearing force on the shaft

The fulcrum on the shaft 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 figure 17-8.O in the figure, the distance from the outer end face is a, this value can be found in the manual. 

3. Calculation of axial force

When analyzing the axial load of angular contact bearing, the additional axial force caused by radial force and other working axial force acting on the shaft should be considered at the same time. 

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 the 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 "compression" end is equal to the algebraic sum of all the axial forces except the additional axial forces themselves;3) the axial force of the other end bearing is equal to its own additional axial force. 

Formula for calculating static load and limit speed

1.Static load calculation

Static load refers to the load 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.Select the bearing according to the rated static load, and its basic formula is

C0 acuity C0 '= S0P0

Where, C0- basic rated static load, N;C0 '- calculate the rated static load, N;P0- equivalent static load, N;S0- safety factor. 

For static bearings, slow oscillating bearings or bearings with extremely low speed, the safety coefficient can be selected according to table 17-9. 

If the speed of the bearing is low and the requirements for operating accuracy and friction torque are not high, it is allowed to have a large contact stress, which is desirable.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 destroy the oil film, resulting in the failure of rolling tempering or component gluing. 

The ultimate speed N0 of the rolling bearing refers to the speed value when the bearing can bear the highest thermal equilibrium temperature under certain working conditions.The working speed of the bearing shall be below 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 combined load, the loaded rolling body will increase, which will increase the friction between the bearing contact surfaces and make the lubrication state worse.At this point, 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 the bearing, r/min;F1 - load coefficient (FIG. 17-13);F2 - load distribution coefficient.

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