Selection of bearing size

 

Determining bearing size parameters

On many occasions, the inner hole size of bearings has been specifically defined by the structure of machines or devices. No matter whether the working life, static load safety factor and economy meet the requirements, the remaining dimensions and structural forms of bearings must be calculated before they are finally selected. This calculation includes comparing the actual load of the bearing with its load capacity. Static load of rolling bearing means that the bearing is static after loading (there is no relative motion between inner and outer rings) or the rotation speed is very low. In this case, the safety factor of excessive plastic deformation of raceway and roller is calculated. Most bearings are subjected to dynamic load, and the inner and outer rings move relatively. The safety factor of early fatigue damage of raceway and rolling elements is checked by dimensional calculus. Only under special circumstances, the nominal life calculation of the actual working life can be made according to DIN ISO 281. For the design that pays attention to economic performance, it is necessary to make full use of the bearing capacity as much as possible. If we want to make full use of bearings, the more important it is to calculate the accuracy of bearing size selection.

Static load bearing

Calculating the static load safety factor Fs is helpful to determine whether the selected bearing has enough rated static load. FS=CO/PO, where FS static load safety factor, CO rated static load [KN] and po equivalent static load safety factor fs are safety factors to prevent permanent deformation in the contact area of rolling parts. For bearings that must run smoothly and have extremely low noise, the value of FS is required to be high; When only moderate operation noise is required, a smaller FS can be selected; Generally, the following values are recommended: FS=1.5~2.5 is suitable for low noise level FS=1.0~1.5 is suitable for conventional noise level FS=0.7~1.0 is suitable for moderate noise level rated static load CO[KN] has been listed in the table for each type of bearing. The load (radial force for centripetal bearing and axial force for thrust bearing), the theoretical pressure generated at the center of the contact area between the roller and the raceway is: -4600 N/MM2, self-aligning ball bearing -4200 N/MM2, other types of ball bearing -4000 N/MM2, and the total plasticity generated by all roller bearings at the maximum bearing position of the contact area between the roller and the raceway under the action of rated static load Co. The equivalent static load PO[KN] is a theoretical value, which is a radial force for a radial bearing and an axial and centripetal force for a thrust bearing. The stress produced by PO in the center of the maximum bearing contact area between the rolling element and the raceway is the same as that produced by the actual load combination. PO=XO*F r+Ys*Fa[KN], where the equivalent static load of PO, radial load of FR and axial load of Fa are all in kilonewtons, radial coefficient of XO and axial coefficient of YO.

Dynamic load bearing

The standard calculation method of dynamic load bearing specified in DIN ISO 281 is based on material fatigue failure (pits appear), and the life calculation formula is: L10=L=(C/P)P[106 rpm], where L10=L nominal rated life [106 rpm ]C rated dynamic load [KN]P equivalent dynamic load [KN]P life index L10 is the nominal rated life in units of 1 million rpm. For a large group of bearings of the same model, 90% of them should reach or exceed this value. The rated dynamic load C[KN] can be found in the parameter table of each type of bearing. Under this load, the rated life of the bearing can reach 1 million revolutions. Equivalent dynamic load P[KN] is a theoretical value, which is a radial force for radial bearing and an axial force for thrust bearing. Its direction and size are constant. The bearing life under equivalent dynamic load is the same as that under actual load combination. P=X*Fr+Y*Fa, where: P equivalent dynamic load, FR radial load and FA axial load, all in kilonewtons, X radial coefficient and Y axial coefficient. The calculation basis of X,Y values and equivalent dynamic load of different types of bearings can be found in the tables and prefaces of various bearings. The life index p of ball bearing and roller bearing is different. For ball bearings, P=3 for roller bearings, P=10/3.

Variable load and variable speed

If the value and speed of bearing dynamic load change with time, then the equivalent load must be considered accordingly. The continuous load and speed curve will be replaced by piecewise approximation. The calculation formula of equivalent dynamic load becomes:

Minimum load of rolling bearing

Too small load and insufficient lubrication will cause the rolling elements to slip and lead to bearing damage. The minimum load coefficient of cage bearing is P/C=0.02, while the minimum load coefficient of fully loaded bearing is P/C=0.04(P is equivalent dynamic load and c is rated dynamic load).

Accuracy and grade of bearings

The accuracy of rolling bearings can be divided into (mainly) dimensional accuracy and rotational accuracy. The accuracy grade has been standardized and divided into five grades: P0, P6, P5, P4 and P2.

The accuracy increases from 0 level in turn, which is enough for general use, but it needs 5 or higher accuracy when it is used in the conditions or occasions shown in Table 1.

Although the above precision grades are based on ISO standards, their names are different in national standards.

the accuracy grades applicable to various bearing types and the comparison between national standards. Dimensional accuracy (items related to shaft and housing installation)

1. Allowable deviation of inner diameter, outer diameter, width and assembly width

2. Allowable deviation of last contact diameter and last contact diameter in roller group.

3. Allowable limit value of chamfer size

4. Allowable variation of width and rotation accuracy (items related to the jumping of rotating body)

1. Allowable radial runout and axial runout of inner ring and outer ring.

2. Allowable lateral runout of the inner ring

3. Allowable variation of inclination of outer diameter surface

4. Allowable variation of raceway thickness of thrust bearing

5. Allowable deviation and variation of conical hole

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