# Online Condition Monitoring of Gripper Cylinder in TBM Based on EMD Method

- Lin Li
^{1}, - Jian-Feng Tao
^{1}Email author, - Hai-Dong Yu
^{2}, - Yi-Xiang Huang
^{1}and - Cheng-Liang Liu
^{1}

**30**:187

https://doi.org/10.1007/s10033-017-0187-0

© The Author(s) 2017

**Received: **29 November 2016

**Accepted: **29 September 2017

**Published: **31 October 2017

## Abstract

The gripper cylinder that provides braced force for Tunnel Boring Machine (TBM) might fail due to severe vibration when the TBM excavates in the tunnel. Early fault diagnosis of the gripper cylinder is important for the safety and efficiency of the whole tunneling project. In this paper, an online condition monitoring system based on the Empirical Mode Decomposition (EMD) method is established for fault diagnosis of the gripper cylinder while TBM is working. Firstly, the lumped mass parameter model of the gripper cylinder is established considering the influence of the variable stiffness at the rock interface, the equivalent stiffness of the oil, the seals, and the copper guide sleeve. The dynamic performance of the gripper cylinder is investigated to provide basis for its health condition evaluation. Then, the EMD method is applied to identify the characteristic frequencies of the gripper cylinder for fault diagnosis and a field test is used to verify the accuracy of the EMD method for detection of the characteristic frequencies. Furthermore, the contact stiffness at the interface between the barrel and the rod is calculated with Hertz theory and the relationship between the natural frequency and the stiffness varying with the health condition of the cylinder is simulated based on the dynamic model. The simulation shows that the characteristic frequencies decrease with the increasing clearance between the barrel and the rod, thus the defects could be indicated by monitoring the natural frequency. Finally, a health condition management system of the gripper cylinder based on the vibration signal and the EMD method is established, which could ensure the safety of TBM.

## Keywords

## 1 Introduction

Tunnel boring machine (TBM) is widely used for underground construction due to the higher efficiency and better quality of the tunnel in recent decades. However, the TBM suffers strong vibration that could cause failure of its main components, such as fracture of the cutters, leakage of the cylinders, and initiation of cracks on the main bearing. The gripper cylinder providing braced force is used for keeping the TBM stable and direction adjustment. The wear and fracture of the seals or Copper Guide Sleeve (CGS) would cause failure of the gripper cylinder, which result in shutdown of the TBM for lacking sufficient braced force. It takes long time to prepare and change the gripper cylinder, thus early fault diagnosis of the gripper cylinder is important for the safety and efficiency of the tunnel construction.

The dynamic characteristics are the basement for fault diagnosis of different mechanical systems by means of vibration signals. The vibration performance has been analysed for the strength estimation or life prediction of TBM [1–3]. A multi-directional coupling dynamic model was established to analyse the dynamic characteristics of the cutterhead system in TBM. Different working parameters were studied to find out the optimization scheme for the cutterhead structure [1]. Zhang et al. [4] presented a dynamic model for the TBM revolving system considering the periodically varying mesh stiffness of the multiple pinions and the speed-torque characteristics of the variable frequency motor. The result showed the excavation torque could run up to a critical value in the extremely adverse excavation environments, which might result in an unexpected breakdown of TBM and even a failure of the drive motor. A multi-freedom coupling dynamic model for the cutterhead system was established to investigate its natural frequencies and vibration modes [5]. The model laid the foundation for the dynamic performance optimization and fatigue life prediction for the cutterhead system. Zou et al. [6] proposed a dynamic model for the main machine of TBM that included the cutterhead, the driving system, the thrust system, and the interaction between the TBM and the surrounding rocks in terms of the lump parameter method. Different researches show that vibration of TBM could influence the efficiency and the fatigue life of different components, especially the cutterhead and the main drive motor. However, the gripper cylinder is also vulnerable to the vibration which might be neglected. In this paper, the dynamic model of the gripper cylinder is established to analyse its vibration performance with degeneration of health condition.

Vibration signals are the most common monitoring parameters for health management of mechanical system. The traditional signal processing methods, such as Fast Fourier Transformation (FFT) and spectrum analysis, are merely able to obtain the basic frequency of the stationary signal. However, the vibration signals acquired from the working machines that contain complex noises are usually non-stationary and nonlinear. Hence, the frequencies are commonly mixed and the fault features are difficult to be identified from the raw signals. The time–frequency domain analysis methods, such as Short Time Fourier Transform (STFT), Wigner–Ville Distribution (WVD) and Wavelet Transform Analysis (WTA), are proposed to deal with the non-stationary signals [7–9]. In recent years, the Empirical Mode Decomposition (EMD) [10] method has been widely used for fault diagnosis of mechanical systems because it is self-adaptive and no basis is required in advance. Lei et al. [11] concluded that the EMD method was applicable for condition monitoring of numerous rotational components, such as gears, bearings,and motors. The instantaneous frequency could be calculated for fault characteristic frequency detection when the vibration signals are decomposed into a series of Intrinsic Mode Functions (IMFs). The traditional EMD algorithm has several disadvantages, such as the mixing mode, the end effect, and the physical meanings of IMFs are not clear. Thus, researchers proposed several new algorithms to overcome these feedbacks [12–15]. Yan et al. [16] presented a weak signal detection method based on the improved Hilbert-Huang Transform (HHT) by restraining the end effect of the traditional EMD method. The improved HHT method combined with the wavelet analysis had a satisfactory performance for weak signal analysis and it could diagnose the incipient rotor imbalance of the Bently test-rig. An improved Extended EMD (EEMD) method was used for analysing the short hydraulic impact signals besides the application of EMD method in vibration signals. The fault diagnosis approach combining with the improved EEMD method and the Support Vector Machine (SVM) classification algorithm was proved to be propitious for fault diagnosis in hydraulic system [17]. Saidi et al. [18] proposed a Bi-Spectrum based EMD (BSEMD) method to improve the fault diagnosis performance of the traditional EMD method. The outer race bearing defects could be detected with the bi-spectrum analysis of the decomposed IMFs and the health condition of the bearing could be assessed. The studies show that the EMD method is powerful for fault diagnosis in the mechanical system, thus it is chosen to indicate the failure of the gripper cylinder in TBM.

The gripper cylinder is important for balancing the external loads from the cutterhead and keeping the main machine stable. Thus, early fault diagnosis for the gripper cylinder is significant. In this paper, an online condition monitoring system for the gripper cylinder is proposed with the application of the EMD method, which is based on the dynamic model. The remainder of this paper is shown as follows. A lumped mass parameter model of the gripper cylinder is established and the characteristic frequencies are calculated in Section 2. Section 3 illustrates the principle of the EMD method and verifies the accuracy of the algorithm. In Section 4, the EMD method is applied for analysing the nonlinear and non-stationary signal acquired from one type of TBM to indicate the characteristic frequencies. Moreover, the relationship between the equivalent stiffness and the characteristic frequency is simulated. Finally, an online condition monitoring system is established for health condition evaluation of gripper cylinder. The conclusions are drawn in Section 5.

## 2 Dynamic Analysis of the Gripper Cylinder in TBM

### 2.1 Dynamic Model of the Gripper Cylinder in TBM

*x*

_{2}, the radial displacements of the barrel and rod are denoted as \( y_{1} \) and

*y*

_{2}, meanwhile the bending angles are \( \theta_{1} \) and

*θ*

_{2}, respectively. The cylinder barrel and the rod are equivalent as rigid beams with the barycenter in their middle and they are represented with \( m_{b} \) and

*m*

_{ r }. The lengths of the barrel and the rod are \( L_{b} \) and \( L_{r} \). Their bending moments are \( I_{b} = 1/2m_{b} L_{b}^{2} \) and \( I_{r} = 1/2m_{r} L_{r}^{2} \), respectively. The seals and the CGS are regarded as point masses at the end of the piston rod that are denoted as \( m_{s} \) and

*m*

_{ c }. Moreover,

*a*

_{1}represents the distance between the centre of the barrel and the seals, and

*a*

_{2}is the distance between the centre of the rod and the CGS. The interaction between the gripper boots and the rocks is considered as the equivalent stiffness of the rock represented by \( k_{r} \) that is combined with the normal contact stiffness and the tangential contact stiffness. In addition, the equivalent stiffness of the seals, the CGS, the oil, and the bending stiffness of gripper are regarded as \( k_{s} \), \( k_{c} \), \( k_{o} \) and \( k_{g} \), respectively. The external axial forces are represented by \( F_{1} \), \( F_{2} \), the radial forces are denoted as \( F_{3} \), \( F_{4} \) and the torque of the barrel and the rod are \( M_{1} \), \( M_{2} \), respectively.

*V*of the system is

Suppose \(\varvec{q}\;{ = [}x_{1} ,\;y_{1} ,\;\theta_{1} ,\;x_{2} ,\;y_{2} ,\;\theta_{2} ]^{\text{T}}\) is a vector containing the system coordinates, in which \(q_{i}\) are the generalized coordinates of the systems and \(\dot{q}_{i}\) are the generalized velocities, \(Q_{i}\) is the total generalized forces that are not related to the potential energy of the system.

### 2.2 Simulation of the Dynamic Model

Parameters of masses and equivalent stiffness

Equivalent stiffness | Value (GN/m) | Mass | Value (kg) |
---|---|---|---|

Hydraulic Oil | 0.3 | Barrel | 5374 |

Contact stiffness of CGS | 0.2 | Rod | 2810 |

Contact stiffness of seals | 0.1 | Seals | 0.02 |

Contact stiffness of rock | 20 | CGS | 5.01 |

Bending stiffness | 3/rad |

## 3 Principle of EMD Method

*k*times,

*SD*) that is in a range of 0.2–0.3 between two “sieves” is calculated to stop the loop and the

*SD*is expressed as

*SD*reaches the set value and it could be expressed as

*x*with variable frequencies at different time is

*noise*is the random noise in the signal. The signal is decomposed into 7 IMFs with the EMD method and the results are shown in Figure 8(a). The original signal, the reconstructed signal and the reconstructed error are shown in Figure 8(b). The results show that the error between the original signal and the reconstructed signal is near to zero, which means that the IMFs obtained from the EMD method contains the most essence of the signal.

## 4 Design of the Condition Monitoring System

### 4.1 Signal Processing on the Field Data

#### 4.1.1 Frequency Analysis with FFT

#### 4.1.2 Frequency Analysis with EMD Method

### 4.2 Fault Diagnosis Based on the Dynamic Performance

#### 4.2.1 The Equivalent Stiffness for the Contact Elements

*R*

_{1}and

*R*

_{2}are the radii of the barrel and CGS, respectively. The semi width, \(a\), at the contact area could be expressed as [25]

*E*

^{ * }is the equivalent modulus of the elasticity of the two different materials, which is expressed as

*P*is the normal load. In addition, the equivalent stiffness between the seals and the barrel could be calculated with the same method.

#### 4.2.2 Simulation of the Dynamic Performance with Different Equivalent Stiffness

The natural frequency has positive correlation with the equivalent stiffness of the hydraulic oil, the seals, the CGS and the rock. Moreover, the relationships between the natural frequency and the variable equivalent stiffness are nonlinear because the different stiffness is coupled with each other. The natural frequency increases 33.3% with the equivalent stiffness of the seals changing from 0.01 GN/m to 0.15 GN/m and it also increases 33.3% when the equivalent stiffness of the oil changes from 0.3 GN/m to 1.2 GN/m. While the frequency increases 12.8% with the equivalent stiffness of the CGS changing from 0.2 GN/m to 6 GN/m. The nature frequency changes 1.1% when the equivalent stiffness of the rock varies from 20 GN/m to 120 GN/m. It can be concluded that the equivalent of the seals and the oil are the most effective parameters that influence the frequency of the gripper cylinder. The natural frequency of the cylinder that would change when the stiffness varies could be an indicator for fault diagnosis.

The natural frequency of the gripper cylinder would decrease with the degradation of the equivalent stiffness of the seals or the CGS according to the simulation of the lumped mass parameter model with different equivalent stiffness. It means that the natural frequency of the gripper cylinder would reflect the defects of the seals or the CGS. The EMD method could be used for data analysis of the monitoring vibration signals for evaluating the changes of the frequency as it is verified with the test signal. Therefore, failure could be indicated if a decrease of the natural frequency is detected and the online monitoring system based on vibration signals with EMD method could be established for health evaluation of the gripper cylinder.

### 4.3 Online Condition Monitoring System

*x*axial of the accelerator measures the acceleration in the axial direction of the cylinder,

*y*axial is used to monitor the transverse vibration signal of the cylinder and

*z*axial is defined as the tunneling direction. The vibration signals could be acquired through the data acquisition system and stored in computer.

## 5 Conclusions

Online condition monitoring for the gripper cylinder with application of EMD method is the main concern of this paper because the gripper cylinder is vulnerable to the vibration. A lumped mass parameter model with variable stiffness is established to investigate the vibration performance of the gripper cylinder in TBM. The stiffness at the interface between the CGS and barrel are calculated with the Hertz theory and it decreases with the increment of the clearance according to the simulation. Thus, the natural frequency would decrease if the seals or the CGS has defects based on the simulation of the dynamic performance with the decreased stiffness. The EMD method could indicate the characteristic frequencies from the complex vibration signals acquired from the working TBM. Consequently, an online condition monitoring system for the gripper cylinder of TBM based on the EMD method and the vibration signals is established. The failure could timely be detected that could ensure the safety of the TBM project.

## Notes

## Declarations

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

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