**3. The influence of geometrical parameters on the friction process in the needle bearing**

The construction of the rolling bearing was initially based on the assumption that the friction loss during the bearing work is significantly smaller than during the sliding. However, during the work of the bearing in the operating conditions there exists both the bearing and the sliding friction. Different factors result in appearance of resistance to motion while the bearing is operating:


36 Performance Evaluation of Bearings

volumes.

surface damage.

the analysis of microstructures.

**Figure 7.** Wear intensity of a shaft neck – energetic criterion: Ntw – relative density of friction power; Wkrw – relative critical density of strain power ; a shaft neck: 1 – 16MnCr5, 2 – 20MoCrS4 + carburising; welding : 3-80G; 4-35X5M1,5; 5-50X10GC1,5; P3 – addition to Acorox 88 oil, needle bearing K 40 x 45x17

The analysis of test data shows that at general resistance to wear criterion for materials at

If chemical reactions, surface-active substance and other factors have significant influence on the processes of creating various secondary structures and products, then determining adequate reliability of criteria of resistance to wear proves to be a difficult problem, for instance at low-intensity oxidizing wear of a tribo-coupling. Resistance criteria in such conditions might be: dislocation density in the thin surface layer of a material, activating

density of strain power) indicates huge variety and complexity of processes of materials

It ought to be noted that the properties which characterize deformed areas of materials at the moment of their destruction (the initial stage of creating wear products) show reactions of these areas to external influence. In order to point those reactions in the desired direction, in this case – to ensure high resistance to abrasion (endurance) of its elements, it is necessary to make the right choice of known materials or produce new ones, having structure of the highest resistance to cracking resulting from the influence of external (exploitation) factors. This means that materials science involving problems of tribotechnology should be based on

The list of materials resistance to wear criteria – invariants of universal criterion Wkr\*

, in worn out

(critical

external friction there occurs average critical density of friction power Wkr\*

energy of chemical reactions and durability characteristics [5 ,9, 10].


When bodies are deformed in the operating conditions, the phenomenon of pure bearing exists if the cooperating elements possess the same diameter, length, the properties of the material and parallel axes. Also, the roughness of the cooperating surfaces should be minimal. In such a case, when there is no lubricant, there appear only some losses caused by hysteresis of deformations [15]. This stems from the fact that the difference between the length of the contact arc and the corresponding arcs before deformations is identical for both bodies. As a result, there is no mutual sliding of the surfaces in the deformation area.

If the curvatures of the cooperating surfaces are different, in the elastic deflection the length of the contact arc for both bodies is identical, whereas before the deflection it was different. Consequently, the deformations in the contact area are accompanied by microsliding; if, however, the speed of both cooperating surfaces is identical, their mutual movement is called "bearing".

In a typical situation, in the process of bearing of two bodies with different peripheral speed there occurs the bearing with sliding; such a situation is the subject of examination here. The aim is to estimate of the extent to which the sliding friction matters in the overall balance of motion resistance.

## **3.1. The analysis of contact areas 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. Figure 8b shows a situation when the axis of the needle and the axis of the shaft neck are parallel. The stresses that occur (Fig. 8 a) are evenly spread along the length of the needle, and the area of contact between the two elements equals the field of the ellipse of the length which is the same as the length of the needle and the width 2b calculated by means of Hertz's solution:

$$b = \sqrt{P \frac{D\_1 \cdot D\_2}{D\_1 + D\_2} \left(\frac{1 - \upsilon\_1^2}{E\_1} + \frac{1 - \upsilon\_2^2}{E\_2}\right)}\tag{14}$$

Performance Evaluation of Rolling Element Bearings Based on Tribological Behaviour 39

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

**Figure 9.** The influence of the needle roller diameter (d) and the shaft neck diameter (D) on the contact

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

The state of the present studies, the information in scientific publications and the catalogues of leading producers of bearings show that the total moment of resistance in the work of a bearing can be understood as the sum of the elemental moments originating in the bearing friction, the sliding friction, the bearing seal friction and the friction occurring in oil

However, in order to estimate the moment of resistance in the friction sliding we suggest the mathematical model in which the total moment of different types of resistance to motion comprises firstly the moment resulting from the bearing friction, calculated as the product of the load – *N* and the rolling friction ratio - *f* , and the moment originating from the sliding friction, taking into account load, the sliding friction - µ and the radius of the roller – *r* (2).

**3.2. The mathematical model of the friction process in the needle bearing** 

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

area (S) of the elements of bearing.

[%].

environment.

where *P* is the strength per each unit of the rollers length; *D1, D2* are the diameters of the shaft neck and the needle respectively; *v1,v2* are Poisson's figures; *E1,E2* are Young's modulus. The indexes *1,2* refer to the roller *1* (the shaft neck) and *2* (the needle roller) respectively.

In the case when the axes of the touching rollers (the shaft neck and the needle) are not parallel (Fig. 8 c), the whole load and the stress connected with it concentrate in a relatively small point [13].

**Figure 8.** The pictorial diagram of the roller bearing: a) the spread of stresses for the connecting rollers with parallel axes, b) the axes of the parallel elements, c) the axes of the elements shifted by an angle

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.

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 [11, 12, 14].

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 motion 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.).

38 Performance Evaluation of Bearings

small point [13].

2 2

(14)

12 1 2 12 1 2

⋅−− = + +

*DD v v* 1 1 *b P DD E E*

where *P* is the strength per each unit of the rollers length; *D1, D2* are the diameters of the shaft neck and the needle respectively; *v1,v2* are Poisson's figures; *E1,E2* are Young's modulus. The

In the case when the axes of the touching rollers (the shaft neck and the needle) are not parallel (Fig. 8 c), the whole load and the stress connected with it concentrate in a relatively

**Figure 8.** The pictorial diagram of the roller bearing: a) the spread of stresses for the connecting rollers with parallel axes, b) the axes of the parallel elements, c) the axes of the elements shifted by an angle

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

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

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

contact area some deformations occur [11, 12, 14].

of motion resistance in the process of bearing.

indexes *1,2* refer to the roller *1* (the shaft neck) and *2* (the needle roller) respectively.

**Figure 9.** The influence of the needle roller diameter (d) and the shaft neck diameter (D) on the contact area (S) of the elements of bearing.

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 [%].

### **3.2. The mathematical model of the friction process in the needle bearing**

The state of the present studies, the information in scientific publications and the catalogues of leading producers of bearings show that the total moment of resistance in the work of a bearing can be understood as the sum of the elemental moments originating in the bearing friction, the sliding friction, the bearing seal friction and the friction occurring in oil environment.

However, in order to estimate the moment of resistance in the friction sliding we suggest the mathematical model in which the total moment of different types of resistance to motion comprises firstly the moment resulting from the bearing friction, calculated as the product of the load – *N* and the rolling friction ratio - *f* , and the moment originating from the sliding friction, taking into account load, the sliding friction - µ and the radius of the roller – *r* (2).

$$M\_{\rm Tc} = \mathbf{N} \cdot f + \mathbf{N} \cdot \boldsymbol{\mu} \cdot \mathbf{r} \tag{15}$$

Performance Evaluation of Rolling Element Bearings Based on Tribological Behaviour 41

by 50 [%], if compared with the durability with the critical slackness. Fig. 10 shows the wear of the shaft neck understood as function of the initial slackness. Point A (Fig. 10 a) as the critical slackness with which the friction pair works in the conditions of normal wear was achieved as a result of crossing the tangents led to the curve of wear in areas I and III

**Figure 10.** Demonstration of the shaft wear: a) the shaft wear in the function of initial slackness where: I is normal wear, II is mechano-chemical wear, III is pathological wear, b) the structure of the worn

[13, 15].

surface of the shaft neck x 300

The recommended examination on a stand (the friction machine SMT-1) makes it possible to obtain the values of the moment of resistance created in the process of sliding friction from the total moment of resistance to motion in the bearing. The needle bearing with the outer ring is mounted directly on the shaft neck which is an interior bearing track for the needles. The outer ring is stationary, and the bearing is loaded with radius force. During the work of the roller turning with the rotational speed of 50-100 rotations per minute there exists only the resistance connected with bearing friction. The observations provided by a torque meter help estimate the moment of bearing friction and the value of the ratio *f*. Then, if the number of rotations of the roller is increased, in the total moment there will appear the already mentioned sliding friction, the value of which can be calculated as the difference between the total moment of resistance obtained in the trail work of the bearing and the value of bearing resistance established earlier.

Such an examination helps to estimate the extent to which the bearing friction and sliding friction matter in the overall balance of motion resistance. The next step in the examination may be to check the influence of load with constant rotational speeds, and the influence of the change in the lubricant environment.

## **3.3. The analysis of the friction process as the function of the initial slackness**

The bearing slackness is a very important geometrical parameter which determines the intensity and the type of wear. In order to estimate the influence of slackness on the process of wear the examination was carried out for the nominal slackness of 0.065 [mm] and other slacknesses achieved as a sum of the nominal one and the value of reduction of the shaft neck diameter. The associations received in this way made it possible to examine the process of friction with slacknesses of 0.1, 0.2, 0.3, 0.4, 0.5 [mm] respectively. A hundred-hour examination was carried out (on the friction machine SMT-1) for each value of slackness in bearing; next, the micro-structure of the friction surface was examined under an optic microscope with magnification X300 (Fig. 10 b). On the basis of the results received it can established that the enlargement of slackness between the elements in the friction pair leads to a considerable enlargement of the intensity in the shaft neck wear, which, in turn, results in the worse durability of the connection.

Fig. 11. shows the kinetic relations between the wear of the shaft neck and different slacknesses in the function of work time. The lines 1 and 2, corresponding to the slacknesses 0,5 [mm] and 0,4 [mm] respectively, indicate the group with a relatively high rate of wear. A significantly smaller rate of wear is represented by the lines 4-7, corresponding to the slacknesses 0,065 [mm] – 0,3 [mm] respectively (Fig. 11). The dotted line 3, typified as the critical slackness *h* = 0,325 [mm] characterizes the shift from the less intensive, mechano-chemical one, to the more intensive one. The increase of the slackness from the critical *h* = 0,325 [mm] to 0,4 [mm] results in the intensity which is approximately twice bigger. With the slackness 0,5 [mm] the durability of the needle bearing decreases by 50 [%], if compared with the durability with the critical slackness. Fig. 10 shows the wear of the shaft neck understood as function of the initial slackness. Point A (Fig. 10 a) as the critical slackness with which the friction pair works in the conditions of normal wear was achieved as a result of crossing the tangents led to the curve of wear in areas I and III [13, 15].

40 Performance Evaluation of Bearings

bearing resistance established earlier.

the change in the lubricant environment.

in the worse durability of the connection.

*M Nf N r Tc* = ⋅+ ⋅⋅

The recommended examination on a stand (the friction machine SMT-1) makes it possible to obtain the values of the moment of resistance created in the process of sliding friction from the total moment of resistance to motion in the bearing. The needle bearing with the outer ring is mounted directly on the shaft neck which is an interior bearing track for the needles. The outer ring is stationary, and the bearing is loaded with radius force. During the work of the roller turning with the rotational speed of 50-100 rotations per minute there exists only the resistance connected with bearing friction. The observations provided by a torque meter help estimate the moment of bearing friction and the value of the ratio *f*. Then, if the number of rotations of the roller is increased, in the total moment there will appear the already mentioned sliding friction, the value of which can be calculated as the difference between the total moment of resistance obtained in the trail work of the bearing and the value of

Such an examination helps to estimate the extent to which the bearing friction and sliding friction matter in the overall balance of motion resistance. The next step in the examination may be to check the influence of load with constant rotational speeds, and the influence of

**3.3. The analysis of the friction process as the function of the initial slackness** 

The bearing slackness is a very important geometrical parameter which determines the intensity and the type of wear. In order to estimate the influence of slackness on the process of wear the examination was carried out for the nominal slackness of 0.065 [mm] and other slacknesses achieved as a sum of the nominal one and the value of reduction of the shaft neck diameter. The associations received in this way made it possible to examine the process of friction with slacknesses of 0.1, 0.2, 0.3, 0.4, 0.5 [mm] respectively. A hundred-hour examination was carried out (on the friction machine SMT-1) for each value of slackness in bearing; next, the micro-structure of the friction surface was examined under an optic microscope with magnification X300 (Fig. 10 b). On the basis of the results received it can established that the enlargement of slackness between the elements in the friction pair leads to a considerable enlargement of the intensity in the shaft neck wear, which, in turn, results

Fig. 11. shows the kinetic relations between the wear of the shaft neck and different slacknesses in the function of work time. The lines 1 and 2, corresponding to the slacknesses 0,5 [mm] and 0,4 [mm] respectively, indicate the group with a relatively high rate of wear. A significantly smaller rate of wear is represented by the lines 4-7, corresponding to the slacknesses 0,065 [mm] – 0,3 [mm] respectively (Fig. 11). The dotted line 3, typified as the critical slackness *h* = 0,325 [mm] characterizes the shift from the less intensive, mechano-chemical one, to the more intensive one. The increase of the slackness from the critical *h* = 0,325 [mm] to 0,4 [mm] results in the intensity which is approximately twice bigger. With the slackness 0,5 [mm] the durability of the needle bearing decreases

μ

(15)

**Figure 10.** Demonstration of the shaft wear: a) the shaft wear in the function of initial slackness where: I is normal wear, II is mechano-chemical wear, III is pathological wear, b) the structure of the worn surface of the shaft neck x 300

Performance Evaluation of Rolling Element Bearings Based on Tribological Behaviour 43

(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

**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

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

2 2

,

12 1 2 12 1 2

⋅−− = + +

*DD v v* 1 1 *b P DD E E*

indexes 1,2 refer to the roller 1 (the shaft neck) and 2 (the needle roller) respectively.

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

of the shaft and the needle, the moment of friction and the heat emitted.

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

the needle and the width 2*b* calculated by means of Hertz's solution:

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

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