Abstract

The convexity offset of rollers has a significant effect on the life of tapered roller bearings. Through finite element analysis, this paper discusses the changes in contact stress between rollers and the inner and outer ring raceways of bearings when the convexity center of tapered rollers offsets toward both ends under certain load conditions. The results show that the convexity center of tapered rollers can offset toward the large end of the roller within a certain range; if exceeding this range, a severe stress difference will occur at both ends of the roller, leading to premature bearing failure. Moreover, the convexity center of rollers should not offset toward the small end of the roller. To improve the contact fatigue life of bearings, it is necessary to determine the allowable convexity offset of rollers.

Key words: tapered roller bearing; convexity offset; contact stress; finite element analysis

1 Introduction

Tapered roller bearings have the advantages of withstanding both axial and radial loads simultaneously, large load-carrying capacity, small rolling friction, high rigidity, and easy installation. They are widely used in large mechanical equipment such as automobiles, railways, machine tools, mines, and metallurgy. The convexity offset error during the machining of logarithmic convexity rollers and the roller offset error during assembly have important impacts on their service performance and life. Therefore, it is necessary to determine a reasonable error range.

The determination of the convexity offset has guiding significance for the design and application of tapered roller bearings. Reference uses the finite element method to analyze the stress distribution of cylindrical roller bearings under certain load conditions, and gives the convexity offset to be controlled during the modification of logarithmic curve rollers by analyzing the roller offset. Reference analyzes the life calculation formula applicable to different modified rollers, indicating that logarithmic curve modification has certain significance for improving bearing life. In this paper, the double-row tapered roller bearing 353112 is taken as an example for finite element analysis to study the reasonable range of its convexity offset and its influence on the distribution of contact stress.

2 Finite Element Model of Tapered Roller Bearings

2.1 Roller Convexity Offset

The design and machining of tapered rollers mainly consider the requirements for their working surface characteristics, i.e., the convexity and the spherical base surface of the roller. For logarithmic curve convexity rollers, different convexity amounts at both ends of the roller can be achieved by slightly moving the effective length center of the roller as the coordinate origin toward the large end of the roller. The schematic diagram of the convexity offset of the logarithmic curve roller is shown in Figure 1. The convexity offset error of a tapered roller refers to the offset s between the symmetric point on the modified logarithmic curve roller and the coordinate origin o.

Figure 1: Schematic Diagram of Convexity Offset of Logarithmic Curve Roller

2.2 Modeling

The structural schematic diagram of the double-row tapered roller bearing 353112 for truck wheel hubs is shown in Figure 2, and the main structural parameters are listed in Table 1.

Figure 2: Schematic Diagram of Tapered Roller Bearing Structure

Table 1 Main Structural Parameters of the Bearing

The bearing material is GCr15, the contact friction coefficient between the roller and the inner and outer raceway surfaces is 0.1, the elastic modulus of the material is 206 GPa, and the Poisson's ratio is 0.3. The maximum normal load on the roller is 7,000 N. Due to its symmetrical structure, only a 1/2 finite element model needs to be established.

When establishing the model with finite element software, chamfers and edges that have little influence on bearing stress are ignored, and the effects of axial clearance, radial clearance, and lubricating oil film on contact stress are not considered. The element type adopts an 8-node Solid185 element, with 3 degrees of freedom per node, which can be used to simulate homogeneous solid structures. After cutting the contact positions between the inner and outer ring raceways and the rollers, the overall element size is set for mapped mesh division, and the swept mesh division method is adopted for other parts. The minimum mesh element at the encrypted part is smaller than the contact half-width length, as shown in Figure 3.

Figure 3: Finite Element Model

Contact pairs are created with the inner and outer rings of the bearing as the target surface and the roller surface as the contact surface, with a contact friction coefficient of 0.1. Boundary condition settings: Symmetrical constraints are applied to each section of the bearing, the outer surface of the outer ring is fully constrained due to interference fit with the bearing seat, and the axial degree of freedom of the inner ring is constrained. When loading, the node at the symmetry center of the inner ring is taken as the master node, adjacent nodes are selected as slave nodes, and then all nodes on the inner surface of the inner ring are coupled with the y-direction (radial) degree of freedom, and the load is applied on the master node.

3 Results and Analysis

Without convexity offset, the stress distribution along the roller generatrix direction between the roller and the inner and outer ring raceways is shown in Figure 4. It can be seen that the maximum stress value between the roller and the inner ring is located at the position slightly left of the roller center. However, the maximum stress value between the tapered roller and the outer ring is close to the roller center, and the stress distribution is symmetrical and uniform.

Figure 4: Contact Stress Between Roller and Inner and Outer Rings Without Convexity Offset

When the convexity center of the roller offsets 0.4 mm toward the large end of the roller and 0.2 mm toward the small end of the roller, the distribution of contact stress between the roller and the inner ring raceway along the roller generatrix is shown in Figure 5, and the contact stress is not symmetrically and uniformly distributed.

Figure 5: Contact Stress Between Roller and Inner Raceway When Convexity Center of Roller Offsets

When the convexity center of the roller offsets toward both ends, the changes in contact stress between both ends of the roller and the inner ring raceway are shown in Figure 6. It can be seen from Figure 6a that under the same conditions, as the convexity offset increases, the contact stress at the small end of the roller gradually decreases, while the contact stress at the large end of the roller increases rapidly. When the offset increases to more than 0.2 mm, the difference in contact stress between both ends of the roller increases rapidly. The situation where the convexity center offsets toward the small end of the roller is shown in Figure 6b. As the offset increases, the difference in contact stress between both ends of the roller begins to increase significantly. It can be seen that the convexity offset of the roller generatrix will lead to asymmetry and non-uniformity of contact stress between both ends of the roller and the raceway.

Figure 6: Influence of Convexity Offset on Contact Stress Between Both Ends of Roller and Inner Raceway

Figure 7 is a quantitative assessment of the influence of convexity offset on contact stress at both ends of the roller. As the convexity offset increases, the relative difference in contact stress between both ends of the roller increases non-linearly. When the convexity offset toward the large end is greater than 0.1 mm, the relative difference in contact stress between both ends of the roller increases rapidly, indicating that 0.1 mm offset toward the large end is a turning point. At this time, the relative difference between both ends of the roller is about 20%, which meets the maximum allowable relative error of 25% in engineering. However, when the convexity center offsets toward the small end, the relative difference in contact stress between both ends of the roller is large and does not meet engineering conditions. Therefore, to meet the uniformity and symmetry of stress distribution of the 353112 tapered roller bearing, the convexity center of the logarithmic curve roller should be controlled within 0.1 mm offset toward the large end, and should not offset toward the small end.

Figure 7: Relationship Between Convexity Center Offset and Relative Stress Difference Between Both Ends of Roller)

4 Conclusion

When modifying logarithmic curve rollers, the offset of the roller convexity center should be strictly controlled; otherwise, the contact stress will exhibit complex asymmetry. The convexity center can offset moderately toward the large end. For the 353112 bearing, the convexity center of the roller should be controlled within 0.1 mm offset toward the large end, and the convexity center should not offset toward the small end of the roller.

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