Computational Issues Associated with Gear Rattle Analysis

1995 ◽  
Vol 117 (1) ◽  
pp. 185-192 ◽  
Author(s):  
C. Padmanabhan ◽  
R. C. Barlow ◽  
T. E. Rook ◽  
R. Singh
Keyword(s):  
Mathematical Formulation ◽  
Evaluation Criteria ◽  
Numerical Algorithms ◽  
Order Reduction ◽  
Simulation Models ◽  
Reduction Gear ◽  
Contact Ratio ◽  
Model Order ◽  
Domain Integration ◽  
Gear Rattle

This paper proposes a new procedure for formulating the gear rattle type problem analytically before attempting a numerical solution. It also outlines appropriate evaluation criteria for direct time domain integration algorithms used to solve such problems. The procedure is necessary due to the non-analytical nature of the mathematical formulation describing vibro-impacts, which can lead to numerical “stiffness” problems. The method is essentially an “intelligent” pre-processing stage and is based on our experience in simulating such systems. Important concepts such as model order reduction, gear or clutch stiffness contact ratio, appropriate choice of non-dimensionalization parameters are illustrated through examples. Several case studies of increasing complexity are solved using various well known numerical algorithms; solutions are compared qualitatively and quantitatively using the proposed evaluation criteria, and specific numerical problems are identified. Some of the simulation models have also been validated by comparing predictions with experimental data.

Computational Issues Associated With Gear Rattle Analysis: Part I — Problem Formulation

1992 ◽  
Author(s):  
C. Padmanabhan ◽  
T. E. Rook ◽  
Rajendra Singh
Keyword(s):  
Numerical Solution ◽  
Mathematical Formulation ◽  
Order Reduction ◽  
Problem Formulation ◽  
Reduction Gear ◽  
Type Problem ◽  
Contact Ratio ◽  
Processing Stage ◽  
Gear Contact ◽  
Gear Rattle

Abstract This paper proposes a new procedure for formulating the gear rattle type problem analytically before attempting a numerical solution. This step is necessary due to the nature of the mathematical formulation with vibro-impacts, which is non-analytical and hence causes numerical “stiffness”. The procedure is essentially an “intelligent” pre-processing stage and is based on our vast experience in simulating such systems. Important concepts such as order reduction, gear contact ratio, appropriate choice of non-dimensionalization parameters are illustrated through several examples.

Computational Issues Associated With Gear Rattle Analysis: Part II — Evaluation Criteria for Numerical Algorithms

1992 ◽  
Author(s):  
R. C. Barlow ◽  
C. Padmanabhan ◽  
Rajendra Singh
Keyword(s):  
Linear Model ◽  
Evaluation Criteria ◽  
Numerical Algorithms ◽  
Simulation Models ◽  
Physical Systems ◽  
Non Linear ◽  
Integration Algorithms ◽  
Domain Integration ◽  
Gear Rattle ◽  
Reliable Methods

Abstract The main focus of this study is to establish evaluation criteria for direct time domain integration algorithms used to solve gear rattle type problems. Such criteria may be used to identify specific numerical problems encountered. The ultimate goal obviously is to find reasonably accurate and reliable methods of solution for such physical systems. Six case studies of increasing complexity, linear to highly non-linear, are solved using well known algorithms. The solutions to the linear model are verified by using analytical results. Non-linear model solutions as yielded by different algorithms are compared qualitatively and quantitatively. Several non-linear simulation models have been validated by comparing predictions with experimental data and results available in the literature.

Fast Harmonic MEMS Simulation With Arnoldi Model Order Reduction

2009 ◽  
Author(s):  
David Binion ◽  
Xiaolin Chen
Keyword(s):  
Model Order Reduction ◽  
Krylov Subspace ◽  
Order Reduction ◽  
Simulation Models ◽  
Original Model ◽  
Computational Time ◽  
Mems Devices ◽  
Element Analysis ◽  
Model Order ◽  
Similar Accuracy

Recent years has witnessed a large increase in the use of vibrating Micro-Electro-Mechanical-Systems (MEMS) especially in the expanding wireless telecommunication industry. In particular, the use of microresonators to generate or filter signals has facilitated a reduction in the size of many popular cell phones. Advances in microfabrication have increased the ability to create complex MEMS devices. Finite Element Analysis (FEA) has widely been used in the design of these devices. To obtain accurate simulations of complex MEMS devices, a dense FEA mesh is required resulting in computationally demanding simulation models. Arnoldi Model Order Reduction has been investigated and implemented to improve the computational efficiency of MEMS simulations. Using ANSYS, a popular FEA program, a micro resonator model was created. With Arnoldi, a Krylov subspace was extracted from the model and the model was projected onto the subspace reducing the model size. A harmonic simulation over normal operating frequencies was performed on the reduced model and compared with a simulation of the original model. It was found that the computational time was drastically reduced through the use of Arnoldi while achieving similar accuracy as compared to the original model.

Optimal projection methods for model order reduction of discrete-time systems

2018 ◽  
Vol 36 (4) ◽  
pp. 1105-1131 ◽  
Author(s):  
Salim Ibrir
Keyword(s):  
Discrete Time ◽  
Model Order Reduction ◽  
Numerical Algorithms ◽  
Order Reduction ◽  
Order System ◽  
Model Order ◽  
Reduced Order ◽  
Discrete Time Systems ◽  
Optimal Projection ◽  
Time Systems

AbstractNumerical algorithms are developed for model order reduction of discrete-time systems using both optimal projection and $H_2$-norm minimization. The state-space matrices of the reduced-order system are obtained via the solution of a convex optimization problem. Subsequently, the results are exploited for the design of non-linear reduced-order systems verifying the input-to-state stability property. Proofs of stability and error approximation bounds are provided along with numerical simulations to highlight the strengths and the validity of the theoretical results.

THE NEW ALGORITHM OF SOLVING HARMONIC BALANCE EQUATIONS

2019 ◽  
Author(s):  
Vladimir Lantsov ◽  
A. Papulina
Keyword(s):  
Harmonic Balance ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Balance Equations ◽  
Model Order ◽  
Cad Systems ◽  
Computational Costs ◽  
Reduction Methods ◽  
Model Equations

The new algorithm of solving harmonic balance equations which used in electronic CAD systems is presented. The new algorithm is based on implementation to harmonic balance equations the ideas of model order reduction methods. This algorithm allows significantly reduce the size of memory for storing of model equations and reduce of computational costs.

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