Fatigue life experiments and failure analysis of flexible bearings for harmonic gear reducer

Xiao-yang CHEN, En ZHU, Zhao-yan YANG, Hai-chao KANG

(1School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200444, China)(2Beijing CTKM Harmonic Drive Co., Ltd., Beijing 101318, China)

Abstract: Flexible bearing is an important part of a harmonic gear reducer. In order to study the failure characteristics of flexible bearings, a special testing machine performing fatigue life experiments for flexible bearings was developed. The loading device of this testing machine can rotate with the inner ring of the flexible bearing and apply loads at both ends of the major axis of the outer ring synchronously. Several failure phenomena of flexible bearings were observed by the fatigue life experiments with four sets of flexible bearings. The width, depth and surface roughness of the raceways were measured after the experiments. The experimental results showed that wear and fatigue spalling behavior appeared only at the end of the major axis of the inner rings, and fatigue fracture and spalling might occur on the outer rings. Moreover, it was found that the wear of the raceways was not uniform.

Key words: Flexible bearing, Failure characteristics, Fatigue life experiments

1 Introduction

The harmonic gear reducer is composed of three main components: a circular spline(CS), a flexspline (FS) and a wave generator(WG). The structure of a harmonic gear reducer is shown in Fig.1. The WG consists of a flexible bearing and an elliptical cam. When the harmonic reducer works, the inner ring of the flexible bearing is assembled with the cam. Therefore, the rings of the flexible bearing will produce great deformation, which is different from an ordinary bearing [1-3].

Fig.1 Structure of a harmonic gear reducer

The FS produces elastic deformation when the WG rotates in the FS. The teeth of the FS and CS circulate four states: “engaging in, engagement, engaging out and disengagement”. It is called staggered movement. The schematic diagram of staggered movement is shown in Fig.2. It can convert high-speed input rotation to low-speed output rotation. The rotational direction of the inner ring and the outer ring is opposite [4].

Fig.2 Staggered movement

Many experts and scholars have made a large amount of research about flexible bearings. Ostapski [5] established a mathematical model of flexible bearings and introduced a failure mode of flexible bearings. Guan Jian [6] proposed a mixed lubrication model to study the tribological performance of the ball-inner raceway contact region in flexible bearings based on the Hertz contact theory and elastohydrodynamic lubrication theory. They put forward many theoretical calculations on the stress distribution of flexible bearings but no direct experiments on flexible bearings.

Ishida [7] presented a method for measuring the loads on steel balls in a flexible bearing assembled with an elliptical cam and clarified the change of the loads on steel balls during the assembly process. Liu Long [8] proposed a device that can reproduce the working mode of flexible bearings without the disturbance of a FS and CS. Normally, the inner ring of a flexible bearing is rotating at high speed while the outer ring is rotating at low speed. But the working characteristic of the testing machine of Liu was contrary to the actual working model of flexible bearings.

A flexible bearing is one of the most important components for a harmonic gear reducer, so it is necessary to study the performance of flexible bearings [9-10]. A testing machine was developed which can perform the fatigue life experiments for flexible bearings solely. The experiment results for flexible bearing components were collected to study the failure characteristics of flexible bearings.

2 Fatigue life experiment

2.1 Structure of the testing machine

The testing machine of flexible bearings was specially developed, which can reproduce characteristics of the loading region on the outer ring of flexible bearings. The structure of the testing machine in this paper is shown in Fig.3.

1.Gear motor; 2.Coupling; 3.Link rod of FS; 4.Support platform;5.FS;6.Loading wheel;7.Loading arm;8.External shaft;9.Loading device; 10.Motorized spindle;11.Baseboard

The real testing machine is shown in Fig.4. The high-speed motorized spindle can be assembled with an external shaft that has a convex shoulder. The loading device is mounted on the convex shoulder of the external shaft. There are two loading arms symmetrically mounted on the loading device, and the loading wheels mounted at the end of the two loading arms. The flexible bearing is assembled with the elliptical cam that is mounted at the end of the external shaft. The whole flexible bearing is inside of the FS. The gear motor connects with the FS by the coupling and shafts.

Fig.4 Real testing machine

The two loading wheels installed symmetrically can apply radial loads at both ends of the major axis of the FS. The loads can be transferred to the flexible bearing through the FS. The two loading arms can move in radial direction, and the value of the radial load can be changed by adjusting the position of the loading arms with a torque wrench. Different loads adapt to different types of flexible bearings.

The core principle of the testing machine is that the loading device can rotate with the inner ring synchronously. The loading device and the elliptical cam are all fixed on the external shaft that is driven by the motorized spindle. In this way, the loading device can always apply loads at both ends of the major axis of the outer ring. So this loading device is called the follow-up loader.

2.2 Experimental conditions

Some parameters of the testing machine are listed in Table 1. During the experiments, the rotating speed of the motorized spindle was 1350 rpm, and the rotating speed of the gear motor was 13rpm. In this case, the working condition of the deceleration ratio of 100 was simulated. The applied radial loads were 400 N. The lubrication method was grease lubrication, and the experimental temperature was ambient. These parameters remained unchanged during the experiments. The main structural and material parameters of testing flexible bearings are shown in Table 2.

Table 1 Parameters of the testing machine

Table 2 Parameters of the flexible bearings

2.3 Experiment process

Before starting the testing machine, the flexible bearing was assembled with the elliptical cam and then the radial loads of 400 N were applied at both ends of the major axis of the FS symmetrically. After these preparations, the electric spindle and the gear motor could be started up.

During the experiments, it was necessary to detect the vibration and noise of the testing machine in order to monitor the working state of the flexible bearings. If any abnormality was detected, the experiment would be stopped. The downtime conditions were [11]:

(1) Fault feature frequency in the frequency spectrum of vibration signal was found. The value of the failure frequency of flexible bearings in this working condition are shown in Table 3;

Table 3 Failure frequency of flexible bearings

(2) The amplitude of vibration or noise was abnormal.

The vibration velocity was measured by the laser vibration measuring instrument PDV-100, as shown in Fig.5. And the frequency domain was analyzed to obtain the frequency spectrum. The signal of 284.1 Hz would be detected in the spectrum if the inner ring got fault, and the signal of 228.9 Hz would be detected if the outer ring got fault. For example, the amplitude of the signal with a frequency of about 284.1 Hz became prominent when the inner ring of the flexible bearing failed, as shown in Fig.6. When the testing machine stopped, the spalling was found on the inner ring raceway.

Fig.5 Measurement of vibration signals

Fig.6 Fault spectrum of one flexible bearing

The noise signal was collected by the noise sensor MPA231, as shown in Fig.7. If the amplitude of the noise signal increased abnormally, the flexible bearing might get failed. For example, Fig.8 was the time-domain diagram of the noise signal of one flexible bearing during the fatigue life experiment. As can be seen from this figure, the amplitude of the noise signal in normal conditions is about 90 dB, but it increases to 100 dB abnormally when the bearing failed. The outer ring of the flexible bearing was found broken when the testing machine stopped.

Fig.7 Measurement of noise signals

Fig.8 Time-domain diagram of the noise signal

When one of the shutdown conditions was reached, the testing machine should be stopped. The flexible bearing was removed from the cam and then it was cleaned with kerosene. The flexible bearing components were carefully observed and the failure reasons were analyzed.

3 Experiment results

3.1 Failure characteristics

The fatigue life experiments of the four sets of flexible bearings have been carried out. They were named 1#, 2#,3# and 4# in the order of trial time. The failure characteristics of the flexible bearing components are shown in Fig.9 and Fig.10.

Fig.9(a) is the experimental results of the inner rings, in which the inner ring of the 1# bearing is worn at the one end of the major axis, and the inner rings of the 2# and 3# bearings are spalling at the end of the major axis. Fig.9(b) is the experimental results of the outer rings, in which the outer rings of the 1# and 4# bearings are fatigue fracture, and the outer ring of the 3# bearing is spalling.

Fig.9 Failure characteristics of the rings

Fig.10 shows the surface condition of a ball of the 1# bearing observed with a microscope. It can be seen that the surface is black and yellow, but there is no spalling or pitting. These experimental results are summarized in Table 4.

Table 4 Experimental results of the four flexible bearings

Fig.10 Surface of a steel ball of the 1# bearing

Fig.11 and Fig.12 show the characteristics of the inner ring failure region more clearly. Fig.11 shows the wear of the raceway of an inner ring. It is obvious that the surface quality of the inner raceway decreases rapidly at the major axis. Fig.12 shows the fatigue spalling of the inner raceway.

Fig.11 Wear of an inner ring at the one end of the major axis

Fig.12 Spalling of an inner ring at the one end of the major axis

3.2 Wear characteristics of raceways

In Fig.11, the wear of the raceway on the right side is more serious than that on the left side in the wear area. It can be seen that the wear of the raceway is uneven. The cause of this phenomenon is shown in Fig.13. The FS just deforms into oval at the opening after assembling it with the deformed flexible bearing, and the bottom of the FS is still circular due to the bottom constraint. Therefore, the flexible bearing will produce a small contact angleβat the major axis[12]. For clarity, this angle is exaggerated in Fig.13. Due to the existence of this contact angle, the inner ring raceway bears both radial force and axial force[13]. This inclined contact will eventually lead to uneven wear of the inner and outer raceways.

Fig.13 Cause of uneven wear

3.3 Analysis of experimental results

After the experiments, the width, depth, and surface roughness of the raceways of the four flexible bearings were changed. The raceway parameters were measured by a contourgraph, and the surface roughness was measured by a roughness measuring instrument.

The raceway parameters of the inner rings and outer rings were measured at both ends of the major axis and at random positions respectively. The results are shown in Fig.14 and Fig.15. According to the measurement results, the raceway of the 1# bearing changed the most. The width and depth of the inner raceway of the 1# bearing at one end of the major axis increased by 37.6% and 93.2% respectively. These results showed that the 1# bearing was seriously worn during the experiment.

Fig.15 Raceway parameters for the depth of the 1- 4# bearings

Fig.14 Raceway parameters for the width of the 1- 4# bearings

The surface roughness of the inner and outer raceways of the 1#, 2# and 4# bearings was measured but without the 3# bearing, because its inner raceway surface at both ends of the major axis was spalling. The results are shown in Table 5. The surface quality of the raceway of the 1# bearing was the worst. The roughness of the inner and outer raceways of the 1# bearing increased by 660% and 216% respectively. According to the changes of surface roughness of the three sets of bearings, it can be seen that the surface quality of the inner raceways was worse than that of the outer raceways.

Table 5 Surface roughness of the flexible bearing raceways

4 Conclusions

(1) A special device that can perform fatigue life experiments for flexible bearings was developed. The experiments of the four sets of flexible bearings have been carried out with this testing machine.

(2) The experimental results show that wear and fatigue spalling were two typical failure modes of inner rings of flexible bearings, and the failure location was mainly at the ends of the major axis. But for outer rings, spalling and fatigue fracture were two typical failure modes, which were different from the failure modes of ordinary bearings.

(3) It was found that the wear of the raceways of the flexible bearings was uneven. This was due to the inclined contact caused by the assembly of a flexible bearing and a FS.

(4) After the experiments, the width, depth, and surface roughness of the raceways of the four sets of flexible bearings were changed. And the surface quality of the inner raceways was worse than that of the outer raceways.