Intermediate cylindrical roller bearings for aero engines
Anti-tilt analysis and optimization design
Abstract In view of the problem that the rollers and the inner ring raceway are spalling due to the inclination of the inner and outer rings of an intermediate cylindrical roller bearing of an aero engine, the anti-tilt ability of the cylindrical roller bearing is evaluated by using the allowable inclination angles of the inner and outer rings, and the allowable inclination angles of the bearings increase with the increase of the roller convexity and the effective width of the inner ring raceway based on this method, so the improvement measures of increasing the roller convexity to 3.2 times of the original structure and increasing the effective width of the inner ring raceway by 6% compared with the original structure are proposed. The allowable inclination angle of the improved bearing is increased to 4~9 times before optimization, and the simulation and test results show that the optimized bearing can avoid stress concentration at one end of the roller and inner ring raceway.
keyword
Rolling bearing; cylindrical roller bearings; aero engines; Fault; Incline; contact stress; trial
1 Overview
Advanced high-thrust aviation gas turbine engines often use a rotor bearing scheme with intermediate cylindrical roller bearings, as shown in Figure 1, there is a set of intermediate bearings between the high-pressure rotor and the low-pressure rotor, and the high-pressure rotor is supported on the low-pressure rotor. The use of intermediate bearings shortens the rotor length and reduces the load-bearing frame by one, thereby significantly reducing the total engine mass and increasing the thrust-to-weight ratio. However, the working condition of the intermediary bearing is bad, and there are many failures of spalling at one end of the roller and raceway in the test run and service, the main reason is the rotor deformation caused by the high-speed operation of the aero engine rotor and the assembly and manufacturing errors, which cause the relative tilt between the inner and outer rings of the intermediate bearing. Therefore, it is necessary to analyze the anti-tilting ability of intermediate cylindrical roller bearings of aero engines and optimize the design accordingly.
Fig.1. Schematic diagram of intermediate cylindrical roller bearing support for aero engine
Fig.1 Diagram of support for intermediate cylindrical roller bearings for aero-engines
Scholars at home and abroad have studied the mechanical properties of bearing rings in the inclined state: in Ref. [1], the differential dynamic equations of roller bearings were established on the basis of static analysis, and the transient motion behavior of rollers, as well as the contact characteristics and motion stability of bearings in the inclined state were analyzed. Considering the radial clearance and roller convexity, the slicing method is used to deal with the linear contact between the inclined roller and the raceway, and the load analysis method of cylindrical roller bearing under the combined action of radial force and moment is proposed. Ref. [3-4] analyzed the contact stress distribution of cylindrical roller bearings in normal and inclined states, and found that roller tilt will change the contact stress distribution between rollers and raceways, and the contact stress distribution can be improved by roller modification.
The above results show that the contact stress distribution of the rollers can be improved through roller modification, thereby improving the fatigue life of the bearing [5-7], but the influence of the raceway width of the inner ring is not considered in the study, and the evaluation method of the anti-tilt ability of cylindrical roller bearings is not established. Therefore, based on the fault characteristics of an intermediate cylindrical roller bearing of an aero engine, this paper proposes an evaluation method for the anti-tilt ability of cylindrical roller bearings, analyzes the influence of roller crown and the effective width of the inner ring raceway on the anti-tilt ability of the bearing, and carries out the corresponding optimization design and experimental verification.
2. Fault characteristics of intermediary cylindrical roller bearings
The typical failure morphology of an intermediary cylindrical roller bearing is shown in Figure 2, where spalling occurs on the same side of the roller near the end face, the spalling pits are annular along the cylindrical surface, and spalling is also present at the same end of the inner ring raceway.
Fig.2. Typical failure profile of an intermediate cylindrical roller bearing
Fig.2 Typical failure morphology of intermediate cylindrical roller bearing
The microscopic morphology of roller spalling is shown in Figure 3, the circumferential unspalled part of the roller is characterized by "extrusion depression", with microcracks distributed along the circumferential direction, and the spalling extends axially along the microcrack onset with tire pattern characteristics, which is a failure mode of high-stress fatigue spalling.
Fig.3. Microscopic morphology of roller spalling
Fig.3 Microscopic morphology of roller spalling
The microscopic morphology of the spalling area of the inner ring raceway is shown in Figure 4: there is a whole circumferential wear at one end of the inner ring raceway, and there is continuous distribution of peeling in about 1/6 of the circumferential area, and the "scratching" marks can be seen in the peeling area, and the peeling starts from the surface of the "scratching" wear traces, which is the fatigue peeling of the surface origin.
Fig.4. Microscopic morphology of inner ring raceway spalling
Fig.4 Microscopic morphology of inner raceway spalling
The spalling position of the roller corresponds to the position of one end of the inner ring raceway, and the cause of bearing failure is: the inner and outer rings are greatly tilted, resulting in a large stress in the spalling area of the roller and the inner ring raceway.
3. Intermediate cylindrical roller bearing anti-tilting ability
3.1 Analysis of contact stress in the inclined state
There are overstep grooves at both ends of the raceway of the intermediate cylindrical roller bearing with flange inner ring, as shown in Figure 5, the β is the correction angle of the inner ring flange, L0 is the width of the inner ring raceway, and Lr is the effective width of the inner ring raceway. The schematic diagram of the locally modified cylindrical roller is shown in Figure 6, the center of the modified arc is on the center line of the roller, Lw is the length of the roller, Lwe is the effective length of the roller, r is the radius of the roller chamfer, R is the radius of the convex arc, and c is the roller convexity.
Fig.5. Schematic diagram of the structure of the inner ring of the intermediate cylindrical roller bearing with flange
Fig.5 Diagram of inner ring structure with rib of intermediate cylindrical roller bearing
Fig.6. Schematic diagram of a locally modified cylindrical roller
Fig.6 Diagram of partially profiled cylindrical roller
Based on the Hertzian contact theory, the contact between the roller and the raceway is a linear contact, and Palmgren established an empirical formula for the load-deformation relationship of the roller-raceway contact based on the test data of the convex roller-raceway contact [8], i.e.,
| | （1） |
The contact zone is divided into k slices along the length of the rollers, each slice is width w, the contact length is kw, and the contact load per unit length is defined as
| | （2） |
Substituting equation (2) into equation (1) and arranging it can be obtained
| | （3） |
where: Q is the normal load of the roller and raceway.
When considering the relative inclination of the inner and outer rings (Fig. 7), the azimuth
The total deformation of the roller-raceway at the nth slice of the roller is
| | （4） |
Fig.7 Schematic diagram of the relative inclination angles of the inner and outer rings
Fig.7 Diagram of relative tilting angle between inner and outer rings
Substituting equation (4) into equation (3) yields the contact stress of the nth slice as
| | （5） |
where Δj is the azimuth
contact deformation of the rollers; θ is the relative inclination angle of the inner and outer rings; kj is the azimuth
The number of slices at the roller. From equation (5), it can be seen that whether each slice is loaded or not depends on the load and inclination angle.
The main parameters of the bearing involved in this calculation are shown in Table 1, the inner ring speed is 10 000 r/min, and the radial load is 12 000 N.
表1 某航空发动机中介圆柱滚子轴承主要参数Tab.1 Main parameters of an intermediate cylindrical roller bearing for aero-engine
Based on the calculation model established by the Romax bearing simulation software, the contact stress between the maximum loaded roller and the inner and outer raceways at the inclination angles of 0, 3', 5' and 10' is obtained respectively, as shown in Fig. 8 (the left side is the inner ring, the right side is the outer ring): when the inclination angle is 0, the contact stress between the inner and outer raceways and the straight section of the roller is the same, and the distribution is relatively uniform; When the inclination angle is 3′, the contact stress between the inner and outer raceways and the straight section of the roller gradually increases along the inclination angle, and the contact stress at the junction of the roller element line and the convexity arc is the largest, which increases by about 14% compared with the inclination angle of 0. When the inclination angle is 5′, the contact stress of the inner and outer raceways increases suddenly, indicating that the contact between the roller and one end of the inner ring raceway produces stress concentration, and the maximum contact stress increases by about 39.6% compared with that at the inclination angle of 0. When the inclination angle is 10′, the stress concentration at one end of the roller and the inner ring raceway is more serious, and the maximum contact stress reaches 4 000 MPa, which is about 228% higher than that at the inclination angle of 0, and reaches the limit of bearing contact stress. The above analysis shows that the relative inclination of the inner and outer rings will cause the change of the contact stress distribution between the roller and the raceway, and the maximum contact stress will increase with the increase of the inclination angle, and the contact position will move to one end of the raceway, and the stress concentration will occur, which will bring great safety risks to the use of aero engines.
Fig.8. Contact stress between rollers and inner and outer raceways
Fig.8 Contact stress between rollers and inner and outer raceways
3.2 Evaluation method of tilt resistance
Considering the characteristics of the spalling position of the roller and one end of the inner ring raceway when the intermediate cylindrical roller bearing fails, the relative inclination angles of the inner and outer rings when the edge of the inner ring raceway is in contact with the rollers are used to evaluate the anti-inclination ability of cylindrical roller bearings, that is, the maximum allowable inclination angle θmax (allowable inclination angle) greater than the inclination angle will aggravate the stress concentration. In addition, the allowable inclination angle should be calculated according to different working conditions, taking into account the load distribution, contact stress, life, etc.
The geometric relationship between the roller and one end of the inner ring raceway is shown in Figure 9, wherein: O is the center of the roller crown arc, Or is the center of the straight section of the roller element, B is the intersection point of the straight section of the roller element line and the crown arc, and A is the contact point of the inner raceway and the roller crown arc.
Fig.9. The geometric relationship between the roller and one end of the inner ring raceway
Fig.9 Geometric relationship between roller and one end of inner ring raceway when in contact
The arc radius of the roller convexity is
| | （6） |
θ can be expressed as
| | （7） |
| |
| |
Under the effective width of different inner ring raceways, the change of the allowable inclination angle of the bearing with the roller crown is shown in Figure 10: when the roller convexity and the effective width of the raceway are taken as the minimum, the allowable inclination angle of the bearing is the smallest, which is 1.3′; When the roller crown and the effective width of the raceway are taken as the maximum, the allowable inclination angle of the bearing is the largest, which is 5.1'; The allowable inclination angle of the bearing increases with the increase of the roller convexity and the effective width of the inner ring raceway, but the influence of the former on the allowable inclination angle is greater than that of the latter.
Fig.10. The variation of the allowable inclination angle of the bearing with the roller crown under different effective widths of the inner ring raceway
Fig.10 Changes in allowable tilting angle of bearings with roller convexity under different effective width of inner ring raceways
4. Optimization design and verification of intermediate cylindrical roller bearings
4.1 Optimize design
With the optimization goal of increasing the anti-tilt ability by more than 4 times, the roller convexity is increased to 3.2 times that of the original structure, the effective width of the inner ring raceway is increased by 6% compared with the original structure, and the allowable inclination angle of the optimized bearing is 4 ~ 9 times that before optimization.
4.2 Simulation verification
Under the same working conditions in Section 3.1, the optimized contact stress between the inner and outer rings of the intermediate cylindrical roller bearing was analyzed based on the Romax software when the inclination angle was 10′, and the results were shown in Fig. 11, and there was no stress concentration caused by edge contact.
Fig.11. Contact stresses between the optimized intermediary cylindrical roller bearing rollers and the inner and outer rings
Fig.11 Contact stress between roller and inner and outer rings of optimized intermediate cylindrical roller bearing
4.3 Test verification
The structure of the double rotor bearing testing machine is shown in Figure 12, the outer ring of the test bearing is connected with the high-pressure simulated rotor through the bearing seat, the inner ring is installed on the low-pressure simulated rotor, and the bearing seat is adjusted through the gasket to form an inclination angle in the inner and outer rings of the bearing. The test conditions are shown in Table 2, a single operation is 1 h, and the whole test is cycled 60 times. The morphology of the inner ring raceway of the bearing after the test is shown in Figure 13: there is spalling at one end of the inner ring raceway of the bearing before optimization; After optimization, there are contact traces on one side of the raceway surface of the inner ring of the bearing, which is due to the relative tilt of the inner and outer rings during the operation of the bearing, but there is no damage such as spalling, which indicates that the anti-tilting ability of the optimized intermediate bearing is improved.
Fig.12. Structure of the double rotor bearing testing machine
Fig.12 Structure of double rotor bearing tester
表2 试验工况Tab.2 Test conditions
Fig.13 Comparison of raceway morphology of bearing inner ring
Fig.13 Morphology comparison of bearing inner ring raceway
5 Concluding remarks
In order to solve the problem of spalling between the rollers and the inner ring raceway caused by the relative inclination of the inner and outer rings of an intermediate cylindrical roller bearing of an aero engine, the anti-tilt ability of the cylindrical roller bearing was evaluated by using the allowable inclination angles of the inner and outer rings, and the variation of the allowable inclination angle of the bearing with the convexity of the rollers and the effective width of the inner raceway was analyzed based on this method, and then the corresponding improvement measures were proposed, and the rationality of the optimized design was verified by simulation and experiment. The quantitative evaluation method of the inclination resistance of intermediate cylindrical roller bearings proposed in this paper can carry out multiple rounds of calculation without the establishment of a finite element model, which can provide a reference for the optimal design of intermediate cylindrical roller bearings for aero engines.