Fault Simulation and Experimental Validation of Accessory Transmission System

Abstract

As an important part of the aero-engine, the accessory transmission system affects the operation status of the engine, and it is of great significance to carry out fault mechanism analysis and fault identification. This paper takes a certain type of aero-engine accessory transmission system as the research object, flexes the box using ANSYS, establishes a rigid-flexible coupling model under normal working conditions and fault conditions through ADAMS, and studies the vibration characteristics in single fault and multi-fault combination modes, such as unbalance of the shaft system, gear misalignment and gear broken tooth. Considering different load loading conditions, the dynamic simulation of the transmission system is carried out, the shafting displacement and box acceleration response are extracted, the time–frequency domain feature information of the vibration signal is analyzed, and the fault characteristics and fault types are corresponded one-to-one. The test bench for the principle prototype of the accessory transmission system is designed and built, and the experimental research is carried out. The results show that the simulation results have good consistency with the principle prototype test results, which verifies the rationality of the simulation model.

1 Introduction

The accessory transmission system is a key component of the aero-engine, which works in an environment of high-speed, high-temperature and high-load for a long time, and will be subjected to strong impact. Gears, bearings and other components are prone to fatigue damage. Therefore, the study of vibration characteristics under fault conditions is of great practical application significance.

Domestic and foreign scholars have widely used dynamic modeling methods to study the vibration signal characteristics of gear systems. Hong et al. comprehensively considered the time-varying meshing stiffness, meshing damping, and the integrated error of wheel tooth meshing, and simulated the dynamic characteristics of a multi-stage gear transmission system based on ADAMS [1]. Lu et al. established a rigid-flexible coupling model of the gearbox and compared and analyzed the vibration signal characteristics of the gearbox under normal and broken tooth conditions [2]. Loutas et al. established a two-stage gear system model and investigated the effects of the meshing stiffness and tooth flank clearance on the vibration response of the box [3]. Helsen et al. studied the vibration characteristics of the pure torsion model, the rigid six-degree-of-freedom multi-body dynamics model and the rigid-flexible coupling model of the planetary gearbox, respectively, and concluded that the rigid-flexible coupling model affects the vibration modes and transfer function of the gearbox [4]. Dąbrowski et al. used ADAMS to establish a rigid-flexible coupling model of planetary gearboxes, and studied the vibration response generated by planetary gear transmission errors and manufacturing errors through the meshing force between gear pairs [5]. Chen et al. quantitatively analyzed the effects by time domain indexes for the rigid-flexible coupling model of planetary gearboxes with different tooth root crack degrees [6]. Wu et al. constructed a fixed-axis rigid-flexible coupling model based on LMS Virtual Lab, and studied the vibration response characteristics of the gearbox under normal, broken tooth and eccentric faults [7].

At present, most of the research focuses on the single-stage gear system and the single gear failure condition of the transmission system vibration response. For the multi-stage transmission system, the coupled fault condition of the box vibration response in research is less, and the lack of test. This paper considers the single-fault and multi-fault combination conditions of the accessory transmission system, such as shafting imblance, gear misalignment and gear broken teeth. The rigid-flexible coupling model of the accessory transmission system is established by ANSYS and ADAMS. The signal characteristics are extracted and compared with the vibration response of the box under normal conditions. Finally, the simulation data is compared with test bench data to verify the rationality of the model.

2 Rigid-Flexible Coupling Model of Accessory Transmission System

Taking a certain type of aero-engine accessory transmission system as the research object, its transmission principle is shown in Fig. 1. Using SOLIDWORKS to establish a three-dimensional model including the gear shaft, spline shaft and box, as shown in Fig. 2, and adding the appropriate coordinate system to determine the relative position of various components of the accessory transmission system.

Fig. 1

Transmission principle

Fig. 2

Three-dimensional model

In order to balance simulation accuracy and model complexity, the model of the accessory transmission system is simplified. Retaining the support hole of the box, ignoring the oil hole, through hole and bolt hole; ignoring the smaller steps and chamfers on the gear shaft; ignoring the key slot on the input shaft and output shaft; and fixing the gearbox body and the gearbox cover as a single unit. According to the actual operation characteristics of the accessory transmission system, respectively, set the revolute joint of the gear shaft and spline shaft relative to the box, the fixed joint of the box and the earth, and the solid–solid contact of the gear pair and the spline pair. The contact collision stiffness coefficient K is related to the shape of the contact surface and the material properties, which are calculated by the formula:

$$\left\{ {\begin{array}{*{20}l} {K = \frac{4}{3}\rho^{\frac{1}{2}} E^{*} } \\ {E^{*} = \frac{{1 - \nu_{1}^{2} }}{{E_{1} }} + \frac{{1 - \nu_{2}^{2} }}{{E_{2} }}} \\ {\frac{1}{\rho } = \frac{1}{{\rho_{1} }} + \frac{1}{{\rho_{2} }}} \\ \end{array} } \right.$$

(1)

where ρ is the comprehensive radius of curvature, ${{E}}^{*}$ is the integrated elastic-modulus, ${{v}}_{1} \; \mathrm{ and } \; {{v}}_{2}$ is the Poisson’s ratio of the two meshing gears, E₁ and E₂ is the modulus of elasticity of the two meshing gears, and ρ₁ and ρ₂ is the equivalent radius of curvature of the two meshing gears at the meshing point.

For a pair of spur gears meshing with each other, the radii of curvature of the two tooth profiles at the node are calculated as:

$$\left\{ {\begin{array}{*{20}l} {\rho_{1} = \frac{{d_{1}^{\prime } \sin \alpha^{\prime } }}{2}} \\ {\rho_{2} = \frac{{d_{2}^{\prime } \sin \alpha^{\prime } }}{2}} \\ \end{array} } \right.$$

(2)

$$d_{1}^{\prime } = d_{1} \frac{\cos \;\alpha }{{\cos \;\alpha^{\prime } }}$$

(3)

where d′ is the diameter of the gear pitch circle, d is the diameter of the gear indexing circle, α′ is the pressure angle of the pitch circle, and α is the pressure angle of the indexing circle.

Considering that the bearings can have a great impact on the system performance and the large number of bearings, the contact model would lead to excessive computation, so it is decided to use the bushing force to simulate the bearings [8]. When using the bushing force to simulate the bearing, the stiffness coefficient K and damping coefficient C need to be determined. According to the actual situation, the stiffness and the damping in the direction of the rotational degree of freedom are set to be 0, and the stiffness value of the rest of the five degrees of freedom is 1e5 N/mm, and the damping value is 50 Ns/mm.

Compared with the rigid body, the flexible box is more likely to show the vibration characteristics of gear meshing excitation in the simulation process. Therefore, ANSYS is used to flexible the box, which is imported into ADAMS to replace the rigid body structure in the model, and construct the rigid-flexible coupling model of the accessory transmission system, as shown in Figs. 3 and 4.

Fig. 3

Flexible box

Fig. 4

Rigid flexible coupling mode

3 Simulation Results and Analysis

3.1 Normal Condition

The drive is loaded on the revolute joint at the input end of the internal spline shaft, and the load is added on the end of the output shaft in the form of torque. The simulation end time is 0.3 s, and the simulation steps are 25,000. Simulate the normal condition of the accessory transmission system with a rotational speed of 3000 r/min and a load of 20 Nm, extract the displacement of the output shaft and the input shaft, as well as the acceleration of the three measuring points on the box for the time–frequency domain analysis, and position of the measuring points as shown in Fig. 4.

Through simulation, the output shaft speed is 1843.01 r/min, and the error between the theoretical speed and the simulated speed is 0.023% by calculation, theoretical speed as shown in Table 1. The speed of the accessory transmission system under normal conditions is shown in Fig. 5. Analyze the frequency domain of the output shaft speed, as shown in Fig. 6, the larger spectral line of spectrogram amplitude corresponds to the gear meshing frequency (f_m32 = 644.82 Hz) and its multiple meshing frequencies, which can verify the feasibility of the model.

Table 1 Operating parameters of the accessory transmission system

Fig. 5

Accessory transmission system speed

Fig. 6

Output shaft speed frequency domain diagram

According to Fig. 7, it can be seen that the gear meshing vibration response is relatively smooth, and the spectral lines with larger amplitude in the frequency domain correspond to the meshing frequency and its multiple meshing frequencies of the multi-stage gear transmission system. For example, the spectrum components of measuring point 3 are mainly the meshing frequency of 05 gear shaft and 04 gear shaft (f_m54 = 996.58 Hz), the double meshing frequencies of 06 gear shaft and 05 gear shaft (2f_m65 = 2300 Hz), the double meshing frequencies of 03 gear shaft and 02 gear shaft (2f_m32 = 1289.64 Hz), the triple meshing frequencies (3f_m32 = 1934.46 Hz), quadruple meshing frequencies (4f_m32 = 2579.28 Hz).

Fig. 7

The time–frequency domain diagram of vibration acceleration

3.2 Unbalance of the Shaft System

The instability of the transmission system caused by rotor mass imbalance is one of the typical vibration faults of the aero-engine. The test is realized by installing a balancing disk with threaded holes near the gear end of the output shaft to add the amount of unbalance, and the simulation is set up according to the position of the bolts to simulate the unbalance fault of the shaft system with a solid ball with mass. The mass of the counterweight bolt is 0.79 g, the amount of unbalance is 31.6 g mm, and the drive and load are the same as in the normal condition.

Comparing the output shaft displacement obtained from the normal condition and the unbalanced fault condition as shown in Fig. 10a, the amplitude of the displacement under the fault condition increases in the x and y directions, and the shaft trajectory is elliptical. Extracting the vibration acceleration of the accessory transmission system measuring points 1 and 2 as shown in Fig. 8, compared with the normal condition, the spectral components of the two measuring points are the same as in the normal condition, which are the meshing frequency of the gear drive system and its multiple meshing frequencies.

Fig. 8

Time–frequency domain diagram of vibration acceleration at the measuring point 1 and 2

Due to the small amount of unbalance, the unbalance fault added by the simulation has no obvious effect on the time domain course and spectrogram of the vibration acceleration response of the box. In order to further analyze the fault characteristics, the root mean square (RMS), kurtosis (Ku), waveform factor (WF), crest factor (CF) and impulse factor (IF) of five time-domain indicators are selected to calculate the characteristic differences between the fault condition and the normal condition. The RMS reflects the vibration amplitude, the Ku represents the degree of smoothness of the waveform, and the WF, CF, and IF are used to check whether there is a shock in the signal.

According to the comparison of indicator characteristics at measuring point 1 near the unbalance fault in Fig. 9, when the unbalance fault occurs, other than the RMS, the Ku, WF, CF, and IF of measuring point 1 increase slightly compared with the normal condition.

Fig. 9

Comparison of time-domain indicators of acceleration signals under unbalanced shafting conditions

Fig. 10

The displacement comparison results of normal and fault conditions

3.3 Gear Misalignment

In the gear misalignment fault simulation, the fault is simulated by modifying the position and direction of the Marker point where the revolute joint is located. The 05 gear shaft is deflected in the plane formed by its axis and the axis of the 06 gear shaft. The 05 gear shaft near the gear end bearing is deflected by 1 mm in the direction away from the 06 shaft, and the inclination misalignment between the two shafts is 0.57°.

Comparing the input shaft displacement obtained from the normal condition and the misalignment fault condition as shown in Fig. 10b, the shaft trajectory is still elliptical. According to Fig. 11, the time-domain amplitude of measuring point 3 near the 05 fault shaft decreases compared with the normal condition. The spectrum of measuring point 2 generates the meshing frequency (f_m65 = 1150 Hz) and triple meshing frequencies (3f_m65 = 3450 Hz) of 06 gear shaft and 05 faulty gear shaft on the basis of the spectrum component of the normal condition. The spectrum of measuring point 3 generates the 06 gear shaft and 05 faulty gear shaft triple meshing frequencies (3f_m65 = 3450 Hz) and the triple meshing frequencies (3f_m54 = 2989.74 Hz) of the 05 faulty gear shaft with the 04 gear shaft on the basis of the spectral components of the normal condition.

Fig. 11

Time–frequency domain diagram of vibration acceleration at the measuring point 2 and 3

According to the comparison of indicator characteristics at measuring point 3 near the misalignment fault in Fig. 12, when the misalignment fault occurs, the RMS, Ku, CF, and IF decrease slightly compared with the normal condition.

Fig. 12

Comparison of time-domain indicators of acceleration signals under gear misalignment conditions

3.4 Gear Broken Tooth

Considering the characteristics of processing and assembly, a broken tooth fault is manually set up in the 03 gear shaft, the normal gear in the model is replaced by a broken tooth at the root of one of its gear teeth, and the rigid-flexible coupling model of the accessory transmission system with a broken tooth fault is constructed.

Comparing the output shaft displacement obtained from the normal condition and the gear broken tooth fault condition as shown in Fig. 10c, the amplitude of the displacement under the fault condition increases in the x and y directions, and the shaft trajectory is elliptical. According to Fig. 13, compared with the normal condition of the box vibration time-domain, the broken teeth fault condition of the vibration acceleration has a significant impact, and the impact signal interval time is 0.048 s, which corresponds to the reciprocal of the rotation frequency (f_z3 = 20.8 Hz) of the 03 fault gear shaft. The spectral components of the fault condition are similar to those of the normal condition, and the amplitude corresponding to the meshing frequency and its multiple meshing frequency spectral lines increases. From the refined spectrum near the meshing frequency (3f_m32 = 1934.46 Hz), it can be seen that there exists a faulty shaft rotation frequency (f_z3 = 20.8 Hz) and its frequency doubling modulation at the meshing frequency. The modulation sidebands are asymmetrically distributed.

Fig. 13

Time–frequency domain diagram of acceleration at measuring points 1 and 2

As can be seen from Fig. 14, the values of the indicators at measuring points 1 and 2 close to the fault increase.

Fig. 14

Comparison of time-domain indicators of acceleration signals at measuring points 1 and 2

3.5 Unbalance of the Shaft System and Gear Broken Tooth

When implementing the coupled fault, refer to the single fault implementation mode. A coupled fault rigid-flexible model is constructed by adding a broken 03 gear shaft tooth fault to the accessory transmission system, while a sphere with mass is added to the 02 gear shaft end.

Comparison of normal conditions and coupled fault conditions of the output and input shaft displacement, as shown in Fig. 15, shows that coupled fault conditions of the input and output shaft displacement increase the amplitude in the x and y directions, and the shaft trajectory is elliptical. As can be seen from Fig. 16, due to the small amount of unbalance, the shaft system imbalance and gear broken teeth coupling fault time–frequency domain analysis more intuitively show the characteristics of a broken teeth fault. In order to further explore its fault characteristics, calculate the time-domain indicators. According to Fig. 17, the five indicator values of measuring points 1 and 2 have increased. Compared with the single gear broken fault, the coupling fault adds the unbalance mass, and the increase at measuring point 1 near the shaft system imbalance fault is slightly reduced.

Fig. 15

Output shaft, input shaft displacement

Fig. 16

Time–frequency domain diagram of vibration acceleration at measuring points 1 and 2

Fig. 17

Comparison of time-domain indicators of acceleration signals under coupled fault conditions

4 Experimental Verification

In order to verify the simulation results, the test bench for the accessory transmission system is constructed as shown in Fig. 18. The arrangement of the acceleration sensor on the box is consistent with the position of the measuring point of the simulation model, and the eddy current displacement sensor is set at the end of the output and input shafts, respectively. The loading conditions are the same as in the simulation.

Fig. 18

Test bench sensor installation position

From Fig. 19, it can be seen that the axial trajectory is elliptical, and the amplitude in the x and y directions increases slightly under broken tooth and coupling faults. According to Fig. 20, under normal conditions, the time-domain simulation results of the vibration acceleration of the three measuring points of the box are consistent with the main test results, the main components in the spectrum are the gear shaft meshing frequency and multiple meshing frequencies. Under the fault condition, extracting the acceleration of the measuring points close to the fault shaft for comparison. The gear broken fault and coupling fault in the simulation results of the impact of measuring point 2 is not obvious. The sidebands appear on both sides of the spectrum meshing frequency of the test results, and the comparison results of the remaining measuring points meet the consistency of simulation and test.

Fig. 19

Displacement test results

Fig. 20

Vibration acceleration simulation and test results at measuring points

5 Conclusion

In this paper, by constructing the rigid-flexible coupling model of the accessory transmission system, the time–frequency domain characteristics under fault excitation are studied. The conclusions are as follows:

• (1) Compared with the normal condition, except for the misalignment fault, the amplitude of displacement in the x and y directions increases. The axis trajectory is elliptical.

• (2) Under normal conditions, the main components of the acceleration spectrum of the box measuring point are the gear meshing frequency and its multiple meshing frequencies. Under unbalanced conditions, the vibration acceleration spectrum components are the same as those of normal working conditions; the spectral components of the misalignment conditions produce new spectral lines compared with the normal conditions; the broken tooth condition and coupling fault condition produce side bands on both sides of the mesh frequency and the multiple mesh frequency, which are asymmetrically distributed.

• (3) The simulation results of the accessory transmission system are in good agreement with the experimental results.