**4. The analysis of friction surfaces of the needle bearing elements**

This part gives an analysis of the change in the contact area of elements cooperating under static load in dry environment when two rollers with parallel axes – the needle rollers and the shaft neck – work against each other [16, 17]. Since the nominal contact areas are relatively small – especially when compared with the overall dimensions of the aforementioned elements – pressure in contact areas are significant and accompanied by concentration of stresses. Hertz's solution made it possible to establish the nature of mutual interaction between the bodies, namely the width of contact area and maximum pressure. Next, the area of contact surface was measured, taking into consideration various diameters of the needle and the shaft, various values of Young's modulus and Poisson's ratio and diversified load. The above mentioned will be borne in mind while examining the wear of bearing elements in the energetic perspective. Deformed areas of friction surfaces are characterised by specific features which directly influence the durability of the elements of a friction pair. This, in turn, means that it is essential to choose appropriate friction materials and to analyse their geometry.

## **4.1. Description of the stand**

The examination stand (Fig. 12) consists of an apparatus responsible for loading *F* the bearing, the electric motor (1) with a fluent regulation of rotation speed 0 – 1500 rpm, the torque meter (2) responsible for constant measurement of the friction moment, the rotation sensor: the shaft (7), the needle roller around the axis of the shaft (6) and its axis of symmetry (5), the thermovisional camera (8), the converter processing the above-mentioned parameters (9) and the computer for recording data (10). The needle bearing with a fixed, immobile outer ring is placed on the shaft neck and loaded with radius force *F*. The motor drives the shaft neck up to a certain speed and then the rotation sensors, the torque meter and the camera record the rotation speed of the shaft and the needle, the moment of friction and the heat emitted.

**Figure 12.** The examination stand: 1 – the source of energy, 2 – the torque meter, 3 – the shaft neck of diameter *D*, 4 – the needle roller of diameter d, 5 – the rotation sensor n2 of the needle against the symmetry axis, 6 – the rotation sensor n3 of the needle around the axis of the roller, 7 – the rotation sensor n1 of the roller, 8 the thermo-visional camera, 9 – the converter, 10 – the computer for processing data

#### **4.2. The analysis of contact areas of friction elements**

42 Performance Evaluation of Bearings

different slacknesses in association)

and to analyse their geometry.

**4.1. Description of the stand** 

**Figure 11.** The kinetic relations in the wear of the needle bearing elements ( the operating conditions,

In real conditions, when the surfaces of the bodies in direct contact are uneven, and anisotropy of top layer occurs, the problem of body contact becomes a more complicated one. Further examination will focus on the analysis of friction surface of the needle bearing

This part gives an analysis of the change in the contact area of elements cooperating under static load in dry environment when two rollers with parallel axes – the needle rollers and the shaft neck – work against each other [16, 17]. Since the nominal contact areas are relatively small – especially when compared with the overall dimensions of the aforementioned elements – pressure in contact areas are significant and accompanied by concentration of stresses. Hertz's solution made it possible to establish the nature of mutual interaction between the bodies, namely the width of contact area and maximum pressure. Next, the area of contact surface was measured, taking into consideration various diameters of the needle and the shaft, various values of Young's modulus and Poisson's ratio and diversified load. The above mentioned will be borne in mind while examining the wear of bearing elements in the energetic perspective. Deformed areas of friction surfaces are characterised by specific features which directly influence the durability of the elements of a friction pair. This, in turn, means that it is essential to choose appropriate friction materials

The examination stand (Fig. 12) consists of an apparatus responsible for loading *F* the bearing, the electric motor (1) with a fluent regulation of rotation speed 0 – 1500 rpm, the torque meter

elements in real conditions, in the lubricated environment and under kinematic load.

**4. The analysis of friction surfaces of the needle bearing elements** 

In the place of contact of two elastic bodies pressed against each other with some force, some contact stresses within a certain field of mutual contact occur. They reach significant values even in the situation when the pressing force is relatively small, which, as a consequence, may lead to exceeding the acceptable limit of the material effort. This is of paramount importance during the work of needle bearings which are under considerable load. Needle bearing requires an adequate positioning of the needles in relation to the shaft neck; in the right position – i.e. when the axes of the elements are parallel – the contact area of these bodies equals the area of the ellipse of the length which is the same as the length of the needle and the width 2*b* calculated by means of Hertz's solution:

$$b = \sqrt{P \frac{D\_1 \cdot D\_2}{D\_1 + D\_2} \left(\frac{1 - \upsilon\_1^2}{E\_1} + \frac{1 - \upsilon\_2^2}{E\_2}\right)} / \tau$$

where *P* is the strength per each unit of the rollers' length, *D*1*, D*2 are the diameters of the shaft neck and the needle respectively, *v*1*,v*2 are Poisson's *E*1*,E*<sup>2</sup> are Young's modulus. The indexes 1,2 refer to the roller 1 (the shaft neck) and 2 (the needle roller) respectively.

The area of the friction surface of the elements of bearing is influenced not only by the adequate mutual positioning of the cooperating elements, but also by the changeable relation of the diameters of the needle and the roller, changeable values of Young's modulus, Poisson's ratio of the materials used, and the change of load.

Performance Evaluation of Rolling Element Bearings Based on Tribological Behaviour 45

**Figure 13.** The influence of Young's modulus – *E* of the material, Poisson's ratio – *v*, the diameter of the

Assuming that the task of loading is an indispensable factor in creating stresses and deformations in the needle roller and the shaft neck, the influence of radius strength *P* on

From the analysis of the diagram in Fig. 13 it is clear that the increase in the area *S* is directly proportional to the growing strength *P*. In the test a needle roller of 2 [mm] in diameter (*E* = 210 [GPa], *v* = 0.3) was used as well as a set of four rollers of 10, 20, 30, 40 [mm] (*E* = 200 [GPa], *v* = 0.25) in diameter. The diagram of the increase in the contact area with the load of bearing by radius force ranging from 200 to 450 [N/mm] is reflected by power function (Fig. 14) which is connected z hardening of the contact area under the influence of growing force.

**Figure 14.** The influence of load (*P*) and the diameter of the shaft neck (*D*) on the contact area of the

To model the process of friction, to calculate the rotational speed of the shaft and the needle roller, and to estimate the importance of slide resistance in the overall process of friction, the

shaft neck (*D*) on the contact area of the elements of bearing (*S*)

the contact area becomes obvious.

elements of bearing (*S*)

following examination stand was used [18,19].

The basic theoretical perspective assumed while calculating contact stresses and the width of the contact area between co-working bodies was based on Hertz's theory, drawing on the following premises: the contacting elements are made from a homogenous, isotopic material; they are limited by the smooth surfaces with a regular curvature; and within the contact area some deformations occur (Dietrich, 2003). The analysis of the change in the contact area of the elements of needle bearing presented below was prepared on the basis of all the premises of Hertz's theory concerning the work of two rollers (the shaft neck, the needle roller) with parallel axes, working under static load in dry environment. In the examination of the factors which have an impact on the measure of contact area of the elements cooperating in the form of "the shaft neck – the needle roller" interaction is particularly important as the contact area influences the change in the moment of movement resistance in the process of bearing.

In the first test eight different needles of 1,4 [mm] up to 2,5 [mm] in diameter were juxtaposed with four rollers of 10, 20, 30, 40 [mm] in diameter. The contact area of the cooperating elements was calculated taking as an assumption the constant load of 200 [N/mm]. Different combinations of elements (needles and rollers) were tested. The bigger the diameter of the needle, the bigger the contact area becomes – this tendency can be measured by means of power equations (Fig. 9).

In the case demonstrated above, the biggest changes in the contact area can be observed while putting together the needles of bigger diameters with the given set of rollers, i.e. for the needle of 1,4 [mm] in diameter cooperating with the rollers of 10 and 40 [mm] in diameter the contact area increased by approximately 5 [%], while for the needle of 2,5 [mm] in diameter cooperating with the same rollers the contact area increased by approximately 9 [%].

Fig. 13. shows the influence of Young's modulus *E*, Poisson's ratio *v* and the roller diameter *D* on the area *S* under a constant load. The range of Young's modulus assumed in the test was identical with the one meant for the materials used in the construction of shafts and bearings. The increase in the contact area of cooperating elements when *E* and *v* are changed is not significant; in the situation illustrated in Fig. 13, the increase approximates to mere 0.8 [%] when *E* is doubled. This is connected with the assumed load which is transmitted onto the whole length of the needle (the axes of the shaft and the needle roller are parallel). In case of materials that are characterized by Young's modulus of 200 [GPa] and more, the assumed load of 200 [N/mm] does not enforce any deformation in the cooperating elements, i.e. the needle of 2 [mm] in diameter and a set of rollers of 20, 30, 40 [mm] in diameter.

resistance in the process of bearing.

approximately 9 [%].

[mm] in diameter.

measured by means of power equations (Fig. 9).

The area of the friction surface of the elements of bearing is influenced not only by the adequate mutual positioning of the cooperating elements, but also by the changeable relation of the diameters of the needle and the roller, changeable values of Young's

The basic theoretical perspective assumed while calculating contact stresses and the width of the contact area between co-working bodies was based on Hertz's theory, drawing on the following premises: the contacting elements are made from a homogenous, isotopic material; they are limited by the smooth surfaces with a regular curvature; and within the contact area some deformations occur (Dietrich, 2003). The analysis of the change in the contact area of the elements of needle bearing presented below was prepared on the basis of all the premises of Hertz's theory concerning the work of two rollers (the shaft neck, the needle roller) with parallel axes, working under static load in dry environment. In the examination of the factors which have an impact on the measure of contact area of the elements cooperating in the form of "the shaft neck – the needle roller" interaction is particularly important as the contact area influences the change in the moment of movement

In the first test eight different needles of 1,4 [mm] up to 2,5 [mm] in diameter were juxtaposed with four rollers of 10, 20, 30, 40 [mm] in diameter. The contact area of the cooperating elements was calculated taking as an assumption the constant load of 200 [N/mm]. Different combinations of elements (needles and rollers) were tested. The bigger the diameter of the needle, the bigger the contact area becomes – this tendency can be

In the case demonstrated above, the biggest changes in the contact area can be observed while putting together the needles of bigger diameters with the given set of rollers, i.e. for the needle of 1,4 [mm] in diameter cooperating with the rollers of 10 and 40 [mm] in diameter the contact area increased by approximately 5 [%], while for the needle of 2,5 [mm] in diameter cooperating with the same rollers the contact area increased by

Fig. 13. shows the influence of Young's modulus *E*, Poisson's ratio *v* and the roller diameter *D* on the area *S* under a constant load. The range of Young's modulus assumed in the test was identical with the one meant for the materials used in the construction of shafts and bearings. The increase in the contact area of cooperating elements when *E* and *v* are changed is not significant; in the situation illustrated in Fig. 13, the increase approximates to mere 0.8 [%] when *E* is doubled. This is connected with the assumed load which is transmitted onto the whole length of the needle (the axes of the shaft and the needle roller are parallel). In case of materials that are characterized by Young's modulus of 200 [GPa] and more, the assumed load of 200 [N/mm] does not enforce any deformation in the cooperating elements, i.e. the needle of 2 [mm] in diameter and a set of rollers of 20, 30, 40

modulus, Poisson's ratio of the materials used, and the change of load.

**Figure 13.** The influence of Young's modulus – *E* of the material, Poisson's ratio – *v*, the diameter of the shaft neck (*D*) on the contact area of the elements of bearing (*S*)

Assuming that the task of loading is an indispensable factor in creating stresses and deformations in the needle roller and the shaft neck, the influence of radius strength *P* on the contact area becomes obvious.

From the analysis of the diagram in Fig. 13 it is clear that the increase in the area *S* is directly proportional to the growing strength *P*. In the test a needle roller of 2 [mm] in diameter (*E* = 210 [GPa], *v* = 0.3) was used as well as a set of four rollers of 10, 20, 30, 40 [mm] (*E* = 200 [GPa], *v* = 0.25) in diameter. The diagram of the increase in the contact area with the load of bearing by radius force ranging from 200 to 450 [N/mm] is reflected by power function (Fig. 14) which is connected z hardening of the contact area under the influence of growing force.

**Figure 14.** The influence of load (*P*) and the diameter of the shaft neck (*D*) on the contact area of the elements of bearing (*S*)

To model the process of friction, to calculate the rotational speed of the shaft and the needle roller, and to estimate the importance of slide resistance in the overall process of friction, the following examination stand was used [18,19].
