# Dynamic Analysis Method for Fault Propagation Behaviour of Machining Centres
## 1 Introduction  
CNC technology and CNC machine tools are enabling the development of technologies and basic equipment towards emerging high-technology and cutting-edge industries [1]. Numerical control technology is extensively used in many countries worldwide to improve the capacity and level of the equipment manufacturing industry, and to improve market adaptability and competitiveness [2]. Machining centres are widely used because of their strong flexible processing capabilities. They have a strong technical advantage in the manufacturing field and have become the main processing equipment for various manufacturing enterprises. A machining centre is a complex system composed of multiple components. Given the influence of system structure, working environment, human factors, and maintenance level, the usage of a machining centre becomes more complex. The system fault is not only related to the independent fault of the component but also to the propagation faults [3]. If the fault cannot be eliminated in a timely manner, it will affect the progress of the entire production and even cause the contract to fail to be performed as scheduled, resulting in irreparable economic losses to a company [4]. Currently, many companies have low levels of fault diagnosis and maintenance in their machining centres, especially in the fault diagnosis of a machining centre [5]. The cost [6] and time [7] spent on locating a fault source of a machining centre cannot be ignored and when the cause of the fault is determined, the time for troubleshooting will be significantly shortened. Therefore, clarifying the real-time faultpropagation behaviour of a machining centre is crucial for the prediction and elimination of faults. The current fault diagnosis methods can be summarized into four categories [8; 9]: knowledge-based fault diagnosis [10; 11; 12], model-based fault diagnosis [13; 14; 15], signal-based fault diagnosis [16; 17; 18], and hybrid method-based fault diagnosis (a method that combines two or more methods) [19; 20; 21; 22]. Fault diagnosis for machining centres mainly include diagnosis methods based on fault information monitoring, training models, and fault trees. The diagnosis method based on fault information monitoring is concerned with monitoring information characteristics of each system component of a machining centre by means of sensors [23]. Through the test analysis software and the corresponding model, the fault information feature extraction is realized and the fault location is determined [24]. However, because the sensor is highly susceptible to the influence of the surrounding environment, the collected signal is not accurate enough and leads to a certain deviation of the diagnosis results. This method cannot detect all the usage information of a system; hence, it is mostly used for the fault diagnosis of system components and cannot realize the fault diagnosis of an entire system. The diagnosis method based on training model is concerned with training models such as support vector machines [25; 26; 27] and neural networks [28; 29; 30] on the basis of constructing a machine fault information database. Then, on the basis of the input information that represents the fault symptom, the output information that reflects the fault cause is directly derived to realize the judgment of the machine fault; However, this method cannot accurately determine the fault location of a machine. Concurrently, when the machine is very expensive, establishing test samples is difficult, hence collecting numerous samples to train a model is impossible. The diagnosis method based on fault trees is concerned with listing all the possible causes of machine faults successively from top to bottom [31]. By establishing the fault tree of a machining centre, faults can be checked individually [32]. However, this method uses the dependency of each fault mode to construct the fault tree and realizes the fault diagnosis on the basis of the simple logic gate and the average fault rate of the bottom event.