Tejas H. Patel

Evaluating the Time-Varying Mesh Stiffness of a Planetary Gear Set Using the Potential Energy Method

Time-varying mesh stiffness is a periodic function caused by the change in the number of contact tooth pairs and the contact positions of the gear teeth. It is one of the main sources of vibration of a gear transmission system. An efficient and effective way to evaluate the time-varying mesh stiffness is essential to comprehensively understand the dynamic properties of a planetary gear set. According to the literature, there are two ways to evaluate the gear mesh stiffness, the finite element method and the analytical method. The finite element method is time-consuming because one needs to model every meshing gear pair in order to know the mesh stiffness of a range of gear pairs. On the other hand, analytical method can offer a general approach to evaluate the mesh stiffness. In this study, the potential energy method is applied to evaluate the time-varying mesh stiffness of a planetary gear set. Analytical equations are derived without any modification of the gear tooth involute curve. The developed equations are applicable to any transmission structure of a planetary gear set. Detailed discussions are given to three commonly used transmission structures: fixed carrier, fixed ring gear and fixed sun gear.

Vibration response of coupled rotor systems with crack and misalignment

Earlier research on the vibration signatures of a crack or misalignment fault have typically been attempted considering one fault at a time. The condition of simultaneous existence of crack and misalignment (in addition to unbalance) was ignored. However, prolonged existence of misalignment preload could develop a fatigue crack in the rotor shaft. The present study aims to investigate the steady-sate vibration response of misaligned coupled rotors with a crack on one of the rotor shafts. This is perhaps the first study where unbalance, crack, and misalignment faults are considered simultaneously. Along with the axial and torsional vibration features, a detailed full spectrum analysis is carried out to reveal the fault-specific whirl signatures. Two new whirl parameters δ1 and δ2 were introduced based on differences in forward and backward whirling 1X and 2X spectral components. The influence of misalignment level and type, crack size, and crack location on these parameters is investigated for examining the effect of growth of one fault on the whirl nature of the vibration motion of the rotors with coexisting faults (i.e. unbalance, crack, and misalignment). The effects of a fault growth on the whirl parameters are found to be typical of a fault for crack and parallel misalignment faults. However, for the angularly misaligned rotors, the increase in misalignment level results in decrease/no change in the parameter δ2 in the presence/absence of a crack. This non-linear trend of the δ2 parameter cannot be related to any single fault, but it is typical of the coexisting faults.

Generating an indicator for pump impeller damage using half and full spectra, fuzzy preference-based rough sets and PCA

Parameters that vary monotonically with damage propagation are useful in condition monitoring. However, it is not easy to find such parameters especially for complex systems like pumps. A method using half and full spectra, fuzzy preference-based rough sets and principal component analysis (PCA) is proposed to generate such an indicator for tracking impeller damage in a centrifugal slurry pump. Half and full spectra are used for extracting features related to pump health status. A fuzzy preference-based rough set model is employed in the process of selecting features reflecting the damage propagation monotonically. PCA is used to condense the features and generate an indicator which represents the damage propagation. The effectiveness of the proposed method is tested using laboratory experimental data. Results show that the indicator generated by the proposed method can clearly and monotonically distinguish the health status of the pump impeller.

Application of Full Spectrum Analysis for Rotor Fault Diagnosis

Machine vibration signal carries abundant information, including the machine health condition. Reliable and foolproof fault detection needs accurate knowledge of the dynamic response features of the faulty system as well as proper method to extract it. The paper presents experimental investigation of steady state vibration response of the rotor bearing system with rotor faults such as unbalance, crack, rotor-stator rub and misalignment at sub-critical rotational speeds. Test rigs are designed and fabricated for the purpose. The conventional Fourier spectrum (i.e., FFT) has limitations in exhibiting the whirl nature (i.e., forward/backward whirl) of the rotor faults. It has been observed in the past that the several other rotor faults generate higher harmonics in the Fourier spectrum. Hence there is always a level of uncertainty in the diagnosis based on FFT when other faults are also suspected. Present work through the use of full spectra has shown possibility of diagnosing these rotor faults through unique vibration features exhibited in the full spectra. The present investigation focuses on the directional nature of higher harmonics, in particular the 2X component. This provides an important tool to separate rotor faults that generate similar frequency spectra (e.g., crack and misalignment) and lead to a more reliable fault diagnosis. Crack, rub and misalignment fault identification through a full spectrum analysis is verified on a laboratory test rotor set-up.

EMD, Ranking Mutual Information and PCA Based Condition Monitoring

Success of any health monitoring system chiefly relies on the effectiveness of condition monitoring parameter. The parameter could be a single or combination of many vibration features. These features are expected to have a monotonic trend with the damage/fault progression. Ranking mutual information technique has the ability to detect the features that have monotonic trend and PCA is a popular and widely accepted multidimensional analysis tool for the feature fusion. A condition monitoring method is presented in this paper by combining EMD, ranking mutual information and PCA. The proposed method is helpful in generation of the indicator that represents the damage progression. This method is tested on the impeller health condition monitoring of a pump.Copyright

Application of fuzzy preference based rough set model to condition monitoring

Parameters that vary monotonically with fault development are useful in condition monitoring, but not easy to find especially for complex systems. A method using fuzzy preference based rough set model and principle component analysis (PCA) is proposed to generate such an indicator. The fuzzy preference based rough set model is employed to evaluate the monotonic trends of features reflecting machinery conditions. PCA is used to condense the informative features and generate an indicator which can represent the development of machine health condition. The effectiveness of the proposed method is tested for damage level detection of an impeller in a slurry pump.

Ordinal semi-supervised k-nearest neighbor algorithm for small training datasets

The traditional k-nearest neighbor (k-NN) algorithms with sufficient training data points seem robust; however, problems, such as decision boundary shift and performance deterioration, occur when the training sets are small. In this paper, a novel algorithm named ordinal semi-supervised k-NN is proposed to handle the cases with small training sets. The method consists of two parts: instance ranking and semi-supervised learning. Using semi-supervised learning techniques, the performance of k-NN can be improved even when the training set is small because they enlarge the training set by including a few high confidence prediction instances. In addition, the performance could be improved further by using an ordinal test set rather than an arbitrary one. Utilizing instance ranking, those instances closer to class boundaries are predicted first, and they are more likely to be the high confidence instances. The semi-supervised learning, thus, benefits from combining with instance ranking. Results for four benchmark datasets show that in the cases with insufficient training data (training ratio≤1/2), the proposed method can greatly improve the classification accuracy and outperform the semi-supervised k-NN and the traditional k-NN methods.