Mathematical formulation of the film thickness in a multi-pad externally adjustable hydrodynamic bearing using the transformation technique

Instability problem of a hydrodynamic plain journal bearing at higher speeds is conventionally resolved by using the non-circular bearings. High speed precision rotating shafts demands accurate positioning of the journal centres. A multi-pad adjustable bearing is a non-circular bearing, provides a fine-tuning option of the journal centre by continuously changing the bearing profile. In the present study, the bearing has a configuration of four bearing pads that are adjustable both in the radial and tilt directions. The fluid film thickness profile is conventionally obtained using the trigonometric relations, which has computational limitations, especially in multi-pad adjustable bearings. In this investigation, the film thickness profile of a multi-pad adjustable bearing is mathematically formulated using the transformation technique. The results obtained are compared with those available in the literature for a similar bearing. The observation shows that transformation technique eliminates the projection approximation error present in the conventional technique.

Rastreador recursivo de subespaços e ordem do modelo aplicado à estimação adaptativa do número de componentes harmônicos e inter-harmônicos em sinais elétricos

Em muitas aplicações se faz necessário conhecer previamente o número exato de componentes senoidais presentes em um sinal, como é o caso dos métodos paramétricos de alta resolução de frequência para estimação de parâmetros de componentes em sinais elétricos na presença de ruído. Este trabalho propõe a utilização de um método para estimação do número de componentes harmônicos e inter-harmônicos em sinais elétricos baseado em técnicas de subespaços e em teoria da informação. Trata-se de um método recursivo que se utiliza do rastreador de subespaços PASTd (Projection Approximation Subspace Tracking with deflation), que apresenta complexidade computacional baixa de ordem O(mr), onde m denota o tamanho do vetor de entrada e r a dimensão do subespaço de sinal. Além disso, o método utiliza um detector de ordem baseado nos critérios advindos da teoria da informação AIC (Akaike Information Criterion) e MDL (Minimum Description Length). Resultados de diversos testes de simulação serão gerados e discutidos com o intuito de caracterizar o método e identificar possíveis pontos fortes e fracos.

Identification of the time-varying modal parameters of a spacecraft with flexible appendages using a recursive predictor-based subspace identification algorithm

This study focuses on the recursive identification of the time-varying modal parameters of on-orbit spacecraft caused by structural configuration changes. For this purpose, an algorithm called recursive predictor-based subspace identification is applied as an alternative method to improve the computational efficiency and noise robustness, and to implement an online identification of system parameters. In the existing time-domain identification methods, the eigensystem realization algorithm and subspace identification methods are usually applied to obtain the on-orbit spacecraft modal parameters. However, these approaches are designed based on a time-invariant system and singular value decomposition, which require a significant amount of computational time. Thus, these methods are difficult to employ for online identification. According to the adaptive filter theory, the recursive predictor-based subspace identification algorithm can not only avoid the singular value decomposition computation but also provide unbiased estimates in a general noisy framework using the recursive least squares approach. Furthermore, in comparison with the classical projection approximation subspace tracking series recursive algorithm, the recursive predictor-based subspace identification method is more suitable for systems with strong noise disturbances. By establishing the dynamics model of a large rigid-flexible coupling spacecraft, three cases of on-orbit modal parameter variation with time are investigated, and the corresponding system frequencies are identified using the recursive predictor-based subspace identification, projection approximation subspace tracking, and singular value decomposition methods. The results demonstrate that the recursive predictor-based subspace identification algorithm can be used to effectively perform an online parameter identification, and the corresponding computational efficiency and noise robustness are better than those of the singular value decomposition and projection approximation subspace tracking series approaches, respectively. Finally, the applicability of this method is also verified through a numerical simulation.