LIU Xin(劉 鑫), JIA Yun-xian(賈云獻), FAN Zhi-teng(范智滕), ZHOU Jie(周 杰), ZOU Xiao(鄒 效)

1 Department of Equipment Command and Management， Mechanical Engineering College， Shijiazhuang 050003，China2 Northwest Institute of Nuclear Technology, Xi’an 710024, China

Analysis and Simulation for Planetary Gear Fault of Helicopter Based on Vibration Signal

LIU Xin(劉 鑫)1*, JIA Yun-xian(賈云獻)1, FAN Zhi-teng(范智滕)2, ZHOU Jie(周 杰)1, ZOU Xiao(鄒 效)1

1DepartmentofEquipmentCommandandManagement，MechanicalEngineeringCollege，Shijiazhuang050003，China2NorthwestInstituteofNuclearTechnology,Xi’an710024,China

Fault diagnosis for helicopter’s main gearbox based on vibration signals by experiments always requires high costs. To solve this problem, a helicopter’s planetary gear system is taken as an example. Firstly, a simulation model is established by McFadden, and analyzed under ideal condition. Then this model is developed and improved as the delay-time model of the vibration signal which determines the phase-change of sidebands when the system is running. The cause and change-rules of planetary gear system’s vibration signal are analyzed to establish the fault diagnosis model. At the same time, the vibration signal of fault condition is simulated and analyzed. This simulation method can provide a reference for fault monitoring and diagnosis for planetary gear system.

planetarygear;thephaseofsideband;vibrationsignal;faultdiagnosis

Introduction

With the development of aviation technology, helicopters are more and more complex, and aviation maintenance methods are constantly reforming and innovating. Due to helicopter’s unique configuration, the retarder of existing driveline is usually designed without redundancy, the failure often causes plane crash[1]. As an important part of the helicopter’s reducer, gear is the most prone to failure. By installing sensors on the system of the planet gear transmission and monitoring its vibration signal, the health of various components in system can be inferred, in order to provide a basis for maintenance decisions.

Huangetal. proposed a method for extracting signal feature of fault gear based on simulation[1]. Xueetal. provided a method for determining life and reliability of complex systems based on series-to-parallel reliability model of the system[2]. Shenetal. proved that different characteristic signals could be separated by empirical mode decomposition(EMD) under a sufficient condition[3]. These studies were based on classical model established by McFadden, but the classical model was restricted under ideal conditions, and could not fully consist with engineering practice. In this paper, the helicopter’s planetary gear system of main retarder is studied. Firstly, the vibration signal characteristics of a planetary gear system during operation are analyzed, and then McFadden’s model is improved based on the analysis results. Finally, the gear fault signal is simulated and the vibration signal delay-time model of a planetary gear system is established.

1 Vibration Model of Planetary Gear System

In the ideal case, assuming that the planetary gears are equally spaced along the circumference of the planetary carrier plate, the sensor is fixed on the fixed-annulus-gear configuration whose vibrations are measured at a fixed point in the annulus gear. Among the vibration signal acquired by sensor, there will be harmonic of the tooth meshing frequency in a time domain of the vibration spectrum, which contains multiple frequency components, known as sidebands. These are centered at integer multiples of the tooth meshing frequency, which is quantified asm·Nt·f, withNtbeing the number of teeth in the annulus gear,fthe planetary carrier rotation frequency, andman index designating the harmonic number.

In the ideal case, the vibration regions of the planetary gears are centered at integer multiples of the planetary carrier rotation frequencyf, and sidebands can exist only at frequencies that arem·Nt+nmultiples of the planetary carrier frequencyf, wherenis an index designating multiple of the carrier rotation frequency.

The tooth meshing vibration signal of a single planet gear, as seen from a fixed point in the planetary carrier, is generated by the engaging of teeth of this gear with the teeth of both the sun gear and the annulus gear. It is assumed that all the teeth behave similarly and such that their vibration components have uniform amplitude. This signal, whose amplitude is defined asβ1, is expected to show harmonics, with amplitudes ofβ2for the second,β3for the third and so on.

This rule will be represented by a Fourier transform. The coefficients are represented with indices of the letterα. Note that eachαnis shown at bothn=-kandn=kfor any integerk.

Therefore, we get the classic model of gear vibration proposed by McFadden[3]:

(1)

whereMis the total number of harmonics of the tooth meshing frequency andNis multiples of the rotation frequency to consider in a given vibration analysis.φp.m.nis a phase angle dependent upon the geometric position of the planet gears and is evaluated as

φp.m.n=(m·Nt+n)θp.

(2)

whereθpis the angle between the planetary gear and sensor locations.

DefineTpas the time it takes for planet gearPto reach the sensor within one revolution of the planetary carrier. Because the planetary off, and because planet gearPis located atθpin the instant where timet=0[4], we have

θp=2πfTp.

(3)

The vibration signatures of individual planet gears can be described as a sum of sinusoids given by

(4)

Substituting Eqs.(2) and (3) into Eq.(4) and regrouping we obtain that

(5)

Assuming that the first planer gear is aligned with the sensor att=0, yieldingθ1=T1=0, and because of thet+Tpfactor in Eq. (5), the vibration of any planet gear may be expressed as a delayed version of the first planet gear’s vibration，

yp=y1(t-Tp).

(6)

Ideally, the movements of the planetary gear and the annulus gear are similar. If the planet gears are spaced equally, the vibration of the entire system can be considered as a model ofNptimes delay for the first planetary gear vibration signal, the time-delay model is shown as follows:

(7)

If the gears are not evenly distributed, the vibration of each planetary gear is still similar. In this case, each of the planet gears has their own specific delay timeTp, which requires separation of the vibration signal of each gear. This complex situation will not be discussed in this article.

2 Vibration Analysis of Planetary Gear Model

For planetary gears are equally spaced along the circumference of the planetary carrier plate, shown in Fig.1, we can define the angleθp,

(8)

Fig.1 A schematic figure of the planetary gear system

Assuming a planetary gearPmoves a certain angleδprelative to theθp. As we know, the phase of the sidebands is determined by the geometry position of the planetary gear. When a planetary gear moved fromθptoθp+δp, the phase of the sidebands will change accordingly. Equation (2) becomes

(9)

(10)

(11)

(12)

In the planetary gear system, if the sidebands changed, then the adjacent gear is likely to be failure. Assuming a partial failure occurs to a certain gear, the fault will change the stiffness of the gear[8]. During the fault teeth meshing with the other tooth, the vibration signal will be changed correspondingly. This process can be defined as the amplitude modulation and phase modulation for harmonics frequency[9].

When the vibrations between the gears are coupled, the vibration signal will be shown below:

(13)

3 The Simulation of Vibration Signal Characteristic

In the ideal case, based on the classical model of gear vibration established by McFadden, vibration signals should be a sinusoidal curve. However, the meshing gears which include a harmonic of the meshing frequency, and the random noise will be unavoidable.

When the gear fails, the vibration signal will be coupled[11]. The difference between coupled amplitude and the normal condition is shown in Fig.2, as we can see, the cycle of vibration becomes unobvious and the dispersion degree of vibration becomes larger. The difference between coupled phase and the normal condition is shown in Fig.3. We can see that the cycle change of the vibration is unobvious and there is no obvious impact on the vibration signal[9]. The difference between coupled amplitude and phase and the normal condition is shown in Fig.4, we cannot see obviously cycle anymore and the amplitude increases, at the same time, the time-domain characteristic of the signal is not obvious[12].

Fig.2 The difference between coupled amplitude and the normal condition

Fig.3 The difference between coupled phase and the normal condition

Fig.4 The difference between the fault and the normal condition

4 Conclusions

Based on analysis and simulation results for the movement of the helicopter planetary gear system, we get the time-domain characteristics under gears working or breaking down, and the time-domain characteristics under both failed state and normal state are analyzed. Through monitoring the vibration signal and analyzing the sidebands, we can determine the current operating status of each component and detect potential failures immediately. This work has some significance for helicopter maintenance and can reduce the accident rate of planetary gear system.

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TH17 Document code: A

1672-5220(2015)01-0148-03

Received date: 2014- 08- 08.

*Correspondence should be addressed to LIU Xin, E-mail: lmh19901228@126.com