Abstract

Flexible bearings are one of the two flexible components in harmonic drives. Under working conditions, they are subjected to follow-up loads, and in addition to the contact fatigue failure of conventional bearings, there is also bending fatigue failure. This paper analyzes the characteristics of symmetric follow-up loading and outer ring distortion of flexible bearings in harmonic drives, points out the technical difficulties in simulating the force and deformation of flexible bearings, reviews the research status of dynamic performance test technologies for flexible bearings, introduces a double flexible bearing dynamic performance testing machine based on flexible cylinder orthogonal antisymmetric deformation follow-up loading, and proposes the future development directions of flexible bearing test technologies, including accelerated life testing, outer ring deformation measurement, performance degradation detection, and test standard formulation.

Introduction

Harmonic drives have the characteristics of small size, large transmission ratio, light weight, and high transmission precision, and are core components of industrial robot arms and humanoid robots. As shown in Figure 1, a harmonic drive is mainly composed of a wave generator, flexible bearing, flexspline, and rigid spline. The flexible bearing and flexspline are the two major flexible components and main failure parts of the harmonic drive. The core principle of the harmonic drive is to use the controllable elastic deformation of the flexible bearing and flexspline to form harmonic motion, thereby achieving the speed change requirement of a large transmission ratio.

Flexible bearings are symmetrically and follow-up loaded in harmonic drives, and their outer rings will undergo torsional deformation. The dynamic performance test technology for flexible bearings is a difficult point in the research of such bearings. Therefore, this paper analyzes the force and deformation of flexible bearings, summarizes the advantages and disadvantages of existing flexible bearing test technologies based on this, proposes a double flexible bearing dynamic performance testing machine based on flexible cylinder orthogonal antisymmetric deformation follow-up loading, and prospects the future development direction of flexible bearing test technologies.

Force and Deformation Analysis of Flexible Bearings

The structure of a flexible bearing is shown in Figure 2a. Under normal conditions, it is circular. Compared with ordinary bearings, the inner and outer rings of a flexible bearing are very thin. After embedding the wave generator into the inner ring of the flexible bearing, as shown in Figure 2b, the flexible bearing becomes non-circular like the wave generator, forming a long axis and a short axis. At this time, the flexible bearing is subjected to the pre-deformation force of the wave generator. After installing the combination of the flexible bearing and the wave generator into the flexspline, as shown in Figure 2c, the flexspline also deforms, causing the external teeth at the long axis end of the flexspline to mesh with the internal teeth of the rigid spline to transmit force and motion. At this time, the flexspline will generate a force that resists deformation on the flexible bearing. Since one end of the flexspline is open and the other end is provided with a cup bottom or 外翻边 (flange) for round-keeping output, the open end of the flexspline expands outward in the long axis direction and shrinks inward in the short axis direction, further causing the outer ring of the flexible bearing to undergo torsional deformation.

The load diagram of the flexible bearing is shown in Figure 3. In addition to bearing the loads from the wave generator and flexspline, it also bears the torque load of the harmonic drive transmitted through the meshing of the external teeth at both ends of the flexspline long axis and the rigid spline. The meshing degree of the flexspline and rigid spline is high, and finally, it acts on the flexible bearing as a distributed load. The position of the long axis in harmonic transmission is determined by the wave generator. Therefore, the force direction of the flexible bearing follows the wave generator to rotate at high speed synchronously, that is, follow-up loading. During the follow-up loading process, the outer ring of the flexible bearing bears alternating bending stress, leading to risks such as bending fatigue fracture failure.

Based on the above analysis, the force and deformation characteristics of the flexible bearing in the harmonic drive are summarized as follows:

1. Symmetric force at both ends of the long axis;
2. Subjected to distributed load;
3. Follow-up loading;
4. Torsional deformation of the outer ring.

When ordinary rolling bearings are working normally, the circle of the inner and outer rings basically does not change, and they rarely bear alternating bending stress. They usually only bear centrifugal load and static or dynamic external loads with fixed directions. Therefore, the performance test device for ordinary bearings cannot achieve the characteristics of follow-up loading and outer ring torsional deformation. Therefore, a special testing machine must be used for testing flexible bearings alone.

Research Status of Dynamic Performance Test Technology for Flexible Bearings

The test technologies for flexible bearings are divided into the whole harmonic drive test and the single test of flexible bearings. The whole machine test can simulate the actual loading conditions of flexible bearings, but in addition to the failure of flexible bearings, there are many failure forms in the harmonic drive, such as flexspline cylinder cracking, tooth damage, flexspline inner wall wear, and poor lubrication of the flexspline-rigid spline tooth surface, which is not conducive to analyzing the failure mechanism of flexible bearings. In addition, the load-bearing capacity of the flexspline is limited, and accelerated tests cannot be carried out, resulting in a long test cycle. Therefore, this paper elaborates on the single test technologies for flexible bearings in recent years in detail.

• By fixing the cam wave generator, a load is applied to the outer ring of the bearing using a lever, and a spring dynamometer is connected to a steel ball through a thin rope to measure the relationship between the maximum torque received by the steel ball and the external load. The device applies a unilateral point load to the flexible bearing, which is inconsistent with the actual working conditions, and measures the static characteristics of a single steel ball of the flexible bearing.
• A special testing machine for the fatigue life of flexible bearings is designed. Its principle is that the flexible bearing is installed on the wave generator, but the wave generator is fixed on the frame. The flat belt is symmetrically tensioned to apply loads to both ends of the long axis of the flexible bearing, and the motor drives the flat belt to drive the outer ring of the bearing to rotate. No failure was found after 7 stress cycles. This testing machine can simulate the characteristic that the flexible bearing is subjected to symmetric distributed loads at both ends of the long axis, but it is different from the actual working conditions where the inner ring of the flexible bearing rotates at high speed and the outer ring rotates at low speed in the opposite direction. It cannot realize the torsional deformation of the outer ring of the flexible bearing, and the loading capacity of the flat belt is limited, which cannot reach the actual bearing level of the bearing.
• A testing machine for detecting the operation stability and rotation accuracy of flexible bearings is designed. The top of the testing machine is provided with a servo motor, which first transmits power to the loading cam through a speed reducer. The radial size of the cam changes periodically during rotation, which is transmitted to the slider-link mechanism in contact with the cam profile, and the other end of the slider-link mechanism is connected to a spring, so that the spring produces periodic deformation, thereby applying a dynamic load to the flexible bearing. On this basis, a multi-station flexible bearing accelerated life test bench is designed. The device uses bolts and springs to load the flexible bearing, and can carry out 4 sets of flexible bearing tests at a time. Although symmetric loading of flexible bearings is realized, neither can simulate the follow-up loading and outer ring torsional deformation of flexible bearings.
• The testing machine can use the auxiliary motor to drive the flexspline and drive the outer ring of the bearing to rotate, simulating the actual working conditions of the flexible bearing in the harmonic drive, and realizing the characteristics of symmetric force, follow-up loading, and outer ring torsional deformation of the flexible bearing. Using this testing machine, the fatigue life test of the flexible bearing was carried out, and the common failure forms of the flexible bearing in the harmonic drive were reproduced, such as outer ring fatigue fracture, pitting corrosion at the long axis of the inner ring, and fretting wear between the inner ring of the bearing and the wave generator at the long axis. However, the load applied to the flexible bearing is not a distributed load, and the loading block is affected by centrifugal force at high speed, resulting in deviations in the final load acting on the flexible bearing.
• On the basis of the above, it is proposed to use the friction torque generated by the friction bearing to balance the torque load applied by the follow-up loading system, and apply tangential load to the flexspline through the elastic loading gear to measure the dynamic performance of the flexible bearing under distributed load. However, the loading device is complex, and the friction bearing is prone to slipping and heating.
• The speed, load, torque, temperature rise, and life of the flexible bearing of the harmonic drive were tested, but the flexible bearing was still placed in the harmonic drive, which still belongs to the category of the whole machine test, and the measured torque and temperature rise are those of the whole harmonic drive, not the flexible bearing.

The summary of the functions and disadvantages of the existing testing machines for flexible bearings in harmonic drives is shown in Table 1. The technical difficulties of the single test technology for flexible bearings lie in the application of follow-up loads and the simulation of outer ring deformation. The current single-component testing machines for flexible bearings cannot completely simulate the actual working conditions. To a certain extent, the operating conditions and failure forms of flexible bearings are reproduced, but the testing machines have large power consumption and low efficiency, and only single sets of bearings can be tested each time. They cannot simulate the distributed load applied to flexible bearings from the rigid spline. In addition, the dynamic components simulating rigid spline loading at high speed will reduce the follow-up load due to their centrifugal load. Although the whole harmonic drive test can simulate the follow-up loading and outer ring deformation of flexible bearings, the measured dynamic performance parameters are those of the harmonic drive, not the flexible bearings.

Double Flexible Bearing Dynamic Performance Testing Device Based on Flexible Cylinder Follow-up Loading

According to the previous analysis, the force sources of flexible bearings include the pre-deformation force of the wave generator, the reaction force of the flexspline, and the meshing force of the gear. Studies have found that the structural parameters of the flexspline, such as the cylinder length and wall thickness, will affect the force of the flexible bearing. The shorter the cylinder length and the thicker the wall thickness, the greater the force on the flexible bearing. Aiming at the force characteristics of the flexible bearing, an equal-diameter flexible cylinder is used to replace the flexspline, and a double flexible bearing dynamic performance testing device based on flexible cylinder follow-up loading is designed, as shown in Figure 10. In this test device, a set of flexible bearings is pressed into both ends of the equal-diameter flexible cylinder, wave generators with the same structure are embedded in the two flexible bearings respectively, the long axes of the two wave generators are perpendicular to each other, and they are installed on the rotating shaft through the two wave generators. The two wave generators are positioned by a sleeve. Under the action of the wave generators perpendicular to each other, the flexible cylinder is forced to undergo orthogonal antisymmetric deformation, as shown in Figure 11. This deformation is used to apply the same size and vertical direction loads to the two flexible bearings. The loaded areas of the two flexible bearings are all at the long axis ends of the respective wave generators, which can truly simulate the deformation of the flexible bearings in the harmonic drive.

When the wave generator rotates at high speed, the loaded areas of the two flexible bearings rotate synchronously with the wave generator, but the loaded areas are always located at the long axis ends of the wave generators, realizing follow-up loading. This test device can test two sets of flexible bearings at the same time, improving the test efficiency, and can simulate the actual working conditions such as symmetric follow-up loading and outer ring torsional deformation of flexible bearings.

Future Development Directions of Flexible Bearing Test Technology

• Accelerated Life Testing: At present, the test cycle of flexible bearings is long. Carrying out accelerated life testing to obtain the life data of bearings in a short time is helpful to quickly evaluate the bearing performance, optimize the bearing design, and shorten the R&D cycle. Accelerated life testing can be realized by improving the test conditions such as load and speed, combined with appropriate accelerated life test theories, such as the Arrhenius model.
• Outer Ring Deformation Measurement: The torsional deformation of the outer ring of flexible bearings is one of their important characteristics. Accurately measuring the outer ring deformation is crucial for in-depth understanding of the bearing working state and failure mechanism. In the future, advanced measurement technologies such as laser measurement technology and strain gauge measurement technology can be used to real-time and accurately measure the deformation of the outer ring under different working conditions.
• Performance Degradation Detection: Study the performance degradation law of flexible bearings during operation, establish a performance degradation model by monitoring parameters such as bearing vibration, temperature, and noise, realize the early warning of bearing faults, and improve the reliability and safety of equipment operation.
• Test Standard Formulation: At present, the test technology for flexible bearings lacks unified standards, resulting in poor comparability between different test results. Formulating unified test standards, standardizing test methods, test conditions, and performance evaluation indicators, etc., is helpful to promote the development and application of flexible bearing technology and promote the standardization and regularization of the bearing industry.

Conclusion

This paper analyzes the force and deformation characteristics of flexible bearings in harmonic drives, such as symmetric follow-up loading and outer ring torsional deformation, and points out the technical difficulties in simulating their force and deformation. The research status of existing dynamic performance test technologies for flexible bearings is reviewed, and a double flexible bearing dynamic performance testing machine based on flexible cylinder orthogonal antisymmetric deformation follow-up loading is introduced, which can better simulate the actual working conditions of flexible bearings. At the same time, the future development directions of flexible bearing test technologies in accelerated life testing, outer ring deformation measurement, performance degradation detection, and test standard formulation are proposed. The research results have important theoretical and engineering application values for the design, R&D, and application of flexible bearings.