# Noise Source Identification of a Ring-Plate Cycloid Reducer Based on Coherence Analysis

Authors: Bing Yang; Yan Liu
Journal: Mathematical Problems in Engineering
 (2013)

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## Abstract

A ring-plate-type cycloid speed reducer is one of the most important reducers owing to its low volume, compactness, smooth and high performance, and high reliability. The vibration and noise tests of the reducer prototype are completed using the HEAD acoustics multichannel noise test and analysis system. The characteristics of the vibration and noise are obtained based on coherence analysis and the noise sources are identified. The conclusions provide the bases for further noise research and control of the ring-plate-type cycloid reducer.


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## Body

## 1. Introduction

Speed reducers are used in various fields for the purposes of speed and torque conversion. Speed reducers have many kinds such as worm reducer, crane reducer, cycloid reducer, planetary gear reducer, and ring-plate-type reducer. A ring-plate-type cycloid speed reducer is one of the most important reducers owing to its low volume, smooth and high performance, and high reliability. The internal transmission structure of the ring-plate-type cycloid speed reducer is shown in Figure1 [1–3]. The input shaft equipped with a driving involute gear is supported by the reducer. Two driven gears are mounted on two driven cranks. Four ring plates with pin gears are connected to the two driven cranks. Two cranks have the same length. Thus, ring plate and two cranks become a parallel four-bar mechanism. When the input shaft rotates, it causes the two cranks to rotate. The four ring plates mounted to the cranks rotate. Then the cycloidal gear rotates. The output shaft rotates since the cycloidal gear is mounted to the output shaft [4].Figure 1
Crank ring-plate-type cycloid speed reducer.At present, the application of the reducer is limited to some extent because of the noise level. So, it has practical significance to research the vibration and noise of the reducer [5–10]. The vibration and noise tests of the reducer are completed using the HEAD acoustics multichannel noise test and analysis system. The characteristics of the vibration and noise are obtained based on coherence analysis and the noise sources of the double crank ring-plate-type pin-cycloid gear reducer are identified.


## 2. Noise Source Identification Methods

Mechanical equipment noise control is mainly in three areas: sound source control, transmission route control, and recipient protection. And the control of the noise source is the most fundamental and effective method. The premise is identifying the main sources of the equipment [11–13]. There are many noise source identification methods such as subjective evaluation, respectively run, and lead cover. The following are frequency spectrum and coherence analysis methods.


### 2.1. Frequency Spectrum

The data measured are time-domain signal in general. In order to obtain the frequency characteristics of the noise source, frequency spectrum analysis is often made. The frequency spectrum can be generated via a Fourier transform of the signal, into a single harmonic component to study, to thereby obtain the frequency structure of the signal, and the amplitude and phase information of the harmonic and the resulting are usually presented as frequency spectrum diagrams [14–16]. The peak values of the frequency spectrum diagrams are closely but not necessarily related to the main source of noise. A peak in the noise and vibration frequency spectrum diagram may come from several noise sources, and sometimes a noise source may produce more than one peak in the frequency spectrum diagram.


### 2.2. Coherence Analysis

A coherence function is the description of the relevance of the two signals in a system [17, 18]. Let x(t) and y(t) be the signals; the Autocorrelation function is defined as
(1)Rx(τ)=E[x(t+τ)x(t)].The cross-correlation function is defined as(2)Rxy(τ)=E[x(t+τ)y(t)].The correlation coefficient betweenx(t) and y(t) can be expressed as
(3)ρxy=∑t=0∞x(t)y(t)[∑t=0∞x2(t)∑t=0∞y2(t)]0.5.The inputs of a system are the noise or vibration; the only linear output is thaty(t). y(t) is the sum of the linear outputs. The coherence function between an input and the output can be expressed as
(4)γiy2(ω)=|Giy(ω)|2Gii(ω)Gyy(ω).


## 2.1. Frequency Spectrum

The data measured are time-domain signal in general. In order to obtain the frequency characteristics of the noise source, frequency spectrum analysis is often made. The frequency spectrum can be generated via a Fourier transform of the signal, into a single harmonic component to study, to thereby obtain the frequency structure of the signal, and the amplitude and phase information of the harmonic and the resulting are usually presented as frequency spectrum diagrams [14–16]. The peak values of the frequency spectrum diagrams are closely but not necessarily related to the main source of noise. A peak in the noise and vibration frequency spectrum diagram may come from several noise sources, and sometimes a noise source may produce more than one peak in the frequency spectrum diagram.


## 2.2. Coherence Analysis

A coherence function is the description of the relevance of the two signals in a system [17, 18]. Let x(t) and y(t) be the signals; the Autocorrelation function is defined as
(1)Rx(τ)=E[x(t+τ)x(t)].The cross-correlation function is defined as(2)Rxy(τ)=E[x(t+τ)y(t)].The correlation coefficient betweenx(t) and y(t) can be expressed as
(3)ρxy=∑t=0∞x(t)y(t)[∑t=0∞x2(t)∑t=0∞y2(t)]0.5.The inputs of a system are the noise or vibration; the only linear output is thaty(t). y(t) is the sum of the linear outputs. The coherence function between an input and the output can be expressed as
(4)γiy2(ω)=|Giy(ω)|2Gii(ω)Gyy(ω).


## 3. Vibration and Noise Tests

### 3.1. Test Equipment

The vibration and noise tests of the reducer prototype are completed using the HEAD acoustics test and analysis system in an ordinary laboratory. The HEAD acoustics multichannel noise test and analysis system is selected for the measurement. The system is made of SQLab II data acquisition recorder, G. R. A. S. microphones and KISTLER acceleration sensors, and Artemis software. The data collection and analysis process of the HEAD acoustics multichannel noise test and analysis system is shown in Figure2. The signals are collected from reducer through sensors to the front end. The analog signal is converted into a digital signal through SQLab. At last, the digital signals are analyzed by Artemis software with different analysis methods.Figure 2
Signal collection and analysis process.


### 3.2. Test Point Position

The ring-plate cycloid reducer noise comes mainly from structural noise. Structural noise is generated by the imbalance, the mechanical collision, and structural resonance and propagates to the space propagation through the shaft, the bearing, and the block. Structural noise mainly comes from the following two sections. The first, section, machinery parts produces sound when they rotate. Such as shaft, gear, motor and so on. The other section comes from components engagement and sound.The main noise sources of the ring-plate cycloid reducer are the following aspects through experiences: (1) the noise generated by ring plates and cycloidal gear when they mesh, (2) the noise generated by involute spur gears when they mesh, (3) the noise caused by driving motor, and (4) the noise caused unbalanced installation of ring plates. According to the possible noise sources, three vibration test points and one noise test point were positioned in the test procedure Figure3. The location of the test points is shown in Figure 4. The detailed information of test points is shown in Table 1.Table 1
Test point location explanation.
Point  name
Test  point location
1
Vibration  test point, near the input shaft, on the surface of the reducer
2
Vibration  test point, near the cycloid gear, on the surface of the reducer
3
Vibration  test point, near the output shaft, on the surface of the reducer
5
Noise  test point, 1 meter above the reducerFigure 3
Test points position.Figure 4
Multi-input single-output linear system.


## 3.1. Test Equipment

The vibration and noise tests of the reducer prototype are completed using the HEAD acoustics test and analysis system in an ordinary laboratory. The HEAD acoustics multichannel noise test and analysis system is selected for the measurement. The system is made of SQLab II data acquisition recorder, G. R. A. S. microphones and KISTLER acceleration sensors, and Artemis software. The data collection and analysis process of the HEAD acoustics multichannel noise test and analysis system is shown in Figure2. The signals are collected from reducer through sensors to the front end. The analog signal is converted into a digital signal through SQLab. At last, the digital signals are analyzed by Artemis software with different analysis methods.Figure 2
Signal collection and analysis process.


## 3.2. Test Point Position

The ring-plate cycloid reducer noise comes mainly from structural noise. Structural noise is generated by the imbalance, the mechanical collision, and structural resonance and propagates to the space propagation through the shaft, the bearing, and the block. Structural noise mainly comes from the following two sections. The first, section, machinery parts produces sound when they rotate. Such as shaft, gear, motor and so on. The other section comes from components engagement and sound.The main noise sources of the ring-plate cycloid reducer are the following aspects through experiences: (1) the noise generated by ring plates and cycloidal gear when they mesh, (2) the noise generated by involute spur gears when they mesh, (3) the noise caused by driving motor, and (4) the noise caused unbalanced installation of ring plates. According to the possible noise sources, three vibration test points and one noise test point were positioned in the test procedure Figure3. The location of the test points is shown in Figure 4. The detailed information of test points is shown in Table 1.Table 1
Test point location explanation.
Point  name
Test  point location
1
Vibration  test point, near the input shaft, on the surface of the reducer
2
Vibration  test point, near the cycloid gear, on the surface of the reducer
3
Vibration  test point, near the output shaft, on the surface of the reducer
5
Noise  test point, 1 meter above the reducerFigure 3
Test points position.Figure 4
Multi-input single-output linear system.


## 4. Noise Source Identification

The double-crank four ring-plate-type cycloid reducer internal-noise-source-related parameters can be expressed as(5)k=ffs,
where f is the main frequency and fs is the shaft frequency, and the shaft frequency can be expressed as
(6)fs=n60,
where n is the rotation speed of the gears.The data collected from three vibrations test points are supposed asx1(t), x2(t), x3(t), and the signal received from the noise test point is y(t). The multi-input single-output linear system model is shown in Figure 4. The collected vibration acceleration signals x1(t), x2(t), x3(t) are the inputs of the system; the collected sound pressure level signal y(t) is the output of the linear outputs. The four test point data are collected synchronously through the front end. The collected data are analyzed through the Artemis software.In order to grasp the noise distributing laws of the reducer, three different speeds and three different loads were selected. They are 750 rotations per minute, 1000 rotations per minute, and 1250 rotations per minute. The three different loads are 40%, 60%, and 80% of the full load. Figure5 shows the vibration acceleration spectrum diagram of test point 1 with the input shaft rotation of 1250 rpm. The frequency spectrum diagrams of the other speeds are not given here due to limited space.Figure 5
Vibration acceleration of test point 1.Figure5 shows that the vibration acceleration of test point 1 shakes a little bit in the low frequency range. Figure 6 shows the noise frequency spectrum diagram of test point 5 with the input shaft rotation of 1250 rpm.  Figure 6 shows that the sound pressure lever of test point 5 is 86.4 dB. The frequencies corresponding to the four peaks are 584 Hz, 1168 Hz, 1744 Hz, and 2360 Hz, respectively.Figure 6
SPL of test point 5.Figure7 shows the Autocorrelation frequency spectrum diagram of test point 1. The frequencies corresponding to the three peaks are 584 Hz, 1768 Hz, and 2320 Hz, respectively. Figure 8 shows the Autocorrelation frequency spectrum diagram of test point 2. The frequencies corresponding to the peaks are 1752 Hz and 2336 Hz.Figure 7
Autocorrelation of test point 1.Figure 8
Autocorrelation of test point 2.Figure9 shows the cross-spectrum analysis diagram of between test point 5 and test point 1. Figure 10 shows the cross-spectrum analysis diagram of between test point 5 and test point 2. From the analysis we know the following conclusions. The contribution of the noise from the position of the ring plates is the biggest. The involute spur gears’ contribution to the noise is not too high. So the noise reduction measures should be taken.Figure 9
Cross-spectrum between 5 and 1.Figure 10
Cross-spectrum between points 5 and 2.


## 5. Conclusions

Double-crank four ring-plate cycloid speed reducer is one of the most important reducers owing to its low volume, smooth and high performance, and high reliability. In this paper, the characteristics of the vibration and noise are obtained after the vibration and noise tests. The noise sources are identified as the ring plates. To reduce the noise of the reducer, the structure of the ring plates or the unbalance of installation may be taken into consideration.



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*Source: 875929-2013-03-28.xml*