**3.5. Conclusions of the analysis**

The conclusions of the analysis [10] are as follows:


weight will also be decreased, and this fact will allow an increase in the maximum revolving speed.

 The number of bearings in bearing arrangement "i" is the significant factor which can favourably influence stiffness. But the increased number of bearings will reduce the maximum revolving frequency and therefore it is possible to use this solution only for low speed spindle-bearing systems.

66 Performance Evaluation of Bearings

and

When 1 2 

value *Fp*.

**3.5. Conclusions of the analysis** 

will be smaller.

The conclusions of the analysis [10] are as follows:

and decreases when *"a"* is prolonged, (Figure 10).

and substituting the equation in brackets

2

*i*

*<sup>i</sup> <sup>T</sup>*

1 2

*<sup>i</sup> <sup>T</sup>*

3 2 1/3 22 1

cos sin <sup>1</sup> in equation

 

(35)

(36)

(37)

(38)

 

3 2 1/3 11 2

cos sin

2 5

*i*

*r*

*r K*

*K*

*K*

will be equal to 1 and the relation (37) will be simplified. Thus

5 <sup>3</sup> <sup>2</sup> <sup>2</sup>

sin <sup>1</sup> in equation

2 <sup>1</sup> <sup>1</sup>

in a nodal point with bearings arranged according to shape, or i = 0 in nodal

<sup>1</sup> . . 2 2 *a*

points with bearings arranged according to direction, the quotient of the constants T1, T2

<sup>1</sup> . 2 2 *a*

Taking equations (32) and (34) into consideration, it is evident that the stiffness of the bearing arrangement depends on the number of bearings (*i1* and *i2*) in the arrangement, the dimensions of the bearings (*z1, dw1* and *z2, dw2*), the contact angle (*α1* and *α2*) and the preload

Radial stiffness increases proportionally with increasing values of *"z", "dw", "i", "Fp"*

 The parameters *"z"* and *"dw"* must be evaluated in mutual interaction because they characterize the size and dimensions of the bearings. Increasing both of these parameters, and producing the consequent increase of stiffness of the bearing arrangement, can be achieved by increasing the inner bearing diameter. The disadvantage here is that maximum revolving speed will be reduced. A more suitable solution is to decrease the width of the bearing, e.g. from B72 to B70, B719 or B718. In this case the number of rolling elements "*z*" will be increased and their diameter *"dw"* 

 Considering equations (31), (32) and (34), it is evident that *"z"* has a more important influence on stiffness than *"dw"*. If the diameter of the rolling elements is smaller, their

*tg* 

*K T*

*tg T* 

<sup>3</sup> <sup>1</sup> <sup>1</sup>

sin

the dependence between the axial and radial stiffness can be expressed by the relation

