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od for Calculating the Fatigue Life of Bearings Taking into Account Wearing of Rolling Elements V. B. Balyakina, *, E. P. Zhilnikova, and K. K. Pillaa aSamara

National Research University, Samara, 443086 Russia *e-mail: [email protected]

Received June 21, 2019; revised April 27, 2020; accepted April 29, 2020

Abstract—Experimental data on the wear of rolling elements are used to develop a method developed for determining the fatigue life of rolling bearings taking into account their wear. The results of calculating the fatigue life of a bearing taking into account the wear of rolling elements are given. It is shown that wear of rolling elements reduces the fatigue life of bearings. Keywords: rolling bearing, bearing, roller, wear, fatigue life DOI: 10.3103/S1068366620040029

INTRODUCTION Rolling bearings are increasingly used in modern mechanical engineering. Trends in the development of rolling bearings are due to an increase in the tactical and technical requirements of products, namely, an increase in rotational speeds, dimensions, temperatures, and other parameters. For example, the rotor bearings of modern aircraft gas turbine engines operate at high speeds dn = 3–3.5 × 106 mm rpm and temperatures up to 200°C. The evolution of rolling bearing design (Fig. 1) is the result of these trends. Ensuring the reliability and cost-effectiveness of products

requires continuous improvement of methods for calculating rolling bearings. In some cases, during the operation of rolling bearings, sliding bodies slip, which causes sliding friction at the contact with races [1]. This leads to wear of the rolling elements during operation and an increase in the radial clearance in the bearing [2]. Theoretical [3, 4] and experimental [5] studies have shown that the geometric parameters significantly influence the durability and other characteristics of rolling bearings. In addition, an increase in the clearance in rolling bearings affects the stiffness of the rotor bearings and, as a consequence, the eigenfrequencies of the system

dn × 106, mm rpm

Sensor

Bearing design evolution

6 5 4 3 2 1 1960

1970

1980

1990

2000

2010

2020

Fig. 1. Evolution of bearing bearing design.

359

2030 Year

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BALYAKIN et al.

αi

D

A

α1

Rext

αi

Xi

O C

B

Rint Calculated cross section Fig. 2. Diagram of contact between bearing bearing with tracks of rings. Here АB = Rint + Rext − DW + δint + δext ; BО = S0; AО = Rint + Rext − DW − gi 2 , where δint and δext are deformation at contacts between bearing and rings.

[6]. Therefore, it is very important to know the true value of the radial clearance in rolling bearings, which changes during operation. Objective—To develop a method for calculating the durability of bearings taking into account the wear of rolling elements and study the effect of wear on the performance characteristics of the bearings.

Then, taking into account (1) and (2), we obtain the following expressions:

FORMULATION OF THE PROBLEM Figure 2 shows a view of the bearing assembly. Neglecting the centrifugal forces of th