**4. Conclusion**

48 Mechanical Engineering

*d* and *<sup>d</sup>* + 

This model of the spall assumes that the rolling element will lose contact suddenly once it enters the spall region, and will regain contact instantly when exiting from that area (Figure-3.4.2 (a)). The abrupt change in the rolling element positions at the entry and exit of the spall results in very large impulsive forces in the system, which is not quite realistic. An modification on the previous model was introduced in [28] in which the depth of the fault

to represent more realistic trajectory of the rolling element movement based on the relative size of the rolling element and the depth of the spall. Although, the profile of the trajectory appears much less abrupt than the earlier version; and apears to have only one position that may result in impulse, it still resulted in two impulses which does not agree with the

Careful observation of the interaction between the rolling element and spall leads to the trajectory is shown in Figure-3.4.3. The entry path of the rolling element has been represented as having a fixed radius of curvature (equal to that of the rolling element); entry of the rolling element in to the spall is therefore somewhat smoother. The smoother change in curvature at the entry would then represent a step in acceleration. On exiting the spall, the centre of the rolling element would have to change the direction suddenly, this representing a step change in velocity or an impulse in acceleration. This has been modelled as a sudden change (i.e. similar to the original model [28]). The resulting acceleration signal

*<sup>d</sup>* . This normally occurs in

*<sup>j</sup>* ), Figure-3.4.2 (b). The improvement on the model is

*<sup>d</sup>* = *c do dt* 

Fig. 3.4.2. Modified model of a spall based on a more realistic ball trajectory. [66]

the load zone. An inner race spall rotates at the same speed as the rotor, i.e.

Fig. 3.4.3. A correlated model of a spall based on experimental data.

The outer race spall is fixed in location between

*do* : initial starting location of the spall).

(*Cd* ) was modelled as a function of (

experimental observation.

( The techniques for modelling the effect of gearbox faults: tooth fillet cracks, tooth face spalls and bearing spalls, were presented and discussed in this chapter. The main purpose of the damage modelling is to simulate the effect of the faults on the dynamics of a geared transmission system that can be used in improving the understanding of the diagnostic information that manifest in the vibration signal mix from a gearbox.

The fault detection and diagnostic techniques based on vibration signal analysis are the ideal non-destructive machine health monitoring method, that can be applied in a minimally intrusive manner; i.e. by attaching an accelerometer on a gearbox casing. However, the dynamic interaction amongst the machine elements of a gearbox is often complex and the vibration signals measured from the gearbox is not easy to interpret. The diagnostic information that directly related to an emerging fault in a gear or a bearing is typically buried in the dominating signal components that are driven by the mechanisms of the transmission system themselves: For example, gear meshing signals.

Traditionally, the researchers worked on development of a signal processing technique for the gearbox diagnosis have embarked on their endeavours by making educated assumptions on the properties of the diagnostic information of the faults. These assumptions are often based on their careful observation of a measured vibration signals. However, the relevance of this approach is often somewhat limited by the simple fact that it's not easy to observe the key details of the fault signals from the signal mix.

It was demonstrated in this chapter how simulation models can be put to effective uses for studying the properties of the fault signals in greater details. A method of isolating the fault signals from the simulated gearbox signal mix was described in the section 3.3. The residual signals obtained from this process showed how the faults manifested in the resulting vibration signals in the "cleaned" state. The observation of the simulated residual signals has led to an improved understanding of the characteristics of impulses caused by the faults and the distorting effect of the transmission path (from the origin of the fault signal to the measurement location). The improved understanding of the fault signal obtained from the simulation studies led to the development of more effective signal processing techniques [34, 35, 62, 66].

The models of the gearbox faults presented in this work require further refinement. Some of the areas of future improvement aforementioned in the main body of the chapter include; improving the understanding of; the effect of plastic deformation in gear TFC, the effect of spall shapes and the effect of non-linear dynamic interaction of the gears and bearings. Improving the correlation between the simulated and the measured signals is a good way to demonstrate the understanding of the effect of faults in a geared transmission system. This

Gearbox Simulation Models with Gears and Bearings Faults 51

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**6. References** 

knowledge compliments the design and development efforts in vibration signal analysis based machine condition monitoring technologies. In the near future, accurately simulated signals of a faulty gearbox can aid the machine learning process of fault diagnosis algorithms based on neural networks. Performing this task in experiments are time consuming and costly exercise; simulation model based approach appears much more desirable.

The authors hope that the work presented in this chapter will stir the thoughts and the new ideas in readers that will contribute to the advancement of the gear engineering and the technologies in detecting and diagnosing the incipient faults in geared transmission systems.
