scholarly journals FAST NUMERICAL IMPLEMENTATION OF THE MDR TRANSFORMATIONS

2018 ◽  
Vol 16 (2) ◽  
pp. 127 ◽  
Author(s):  
Justus Benad
Keyword(s):  
Hertzian Contact ◽  
Uniform Grid ◽  
Numerical Implementation ◽  
Axially Symmetric ◽  
Central Difference ◽  
Central Difference Scheme ◽  
The Past ◽  
Standard Tool ◽  
Implementation Method ◽  
Implementation Technique

In the present paper a numerical implementation technique for the transformations of the Method of Dimensionality Reduction (MDR) is described. The MDR has become, in the past few years, a standard tool in contact mechanics for solving axially-symmetric contacts. The numerical implementation of the integral transformations of the MDR can be performed in several different ways. In this study, the focus is on a simple and robust algorithm on the uniform grid using integration by parts, a central difference scheme to obtain the derivatives, and a trapezoidal rule to perform the summation. The results are compared to the analytical solutions for the contact of a cone and the Hertzian contact. For the tested examples, the proposed method gives more accurate results with the same number of discretization points than other tested numerical techniques. The implementation method is further tested in a wear simulation of a heterogeneous cylinder composed of rings of different material having the same elastic properties but different wear coefficients. These discontinuous transitions in the material properties are handled well with the proposed method.

Design and High Accuracy Numerical Implementation of Fractional Order PI Controller for a PMSM Speed System

2021 ◽  
Author(s):  
Baokun Wang ◽  
Shaohua Wang ◽  
Ying Luo
Keyword(s):  
Fractional Order ◽  
Permanent Magnet Synchronous Motor ◽  
High Accuracy ◽  
System Control ◽  
Numerical Implementation ◽  
Implementation Method ◽  
Improved Performance ◽  
Fractional Order Pi Controller ◽  
Discretization Orders ◽  
Fopi Controller

Abstract In this paper, a systematic design and high accuracy implementation of fractional order proportional integral (FOPI) controller is proposed for a permanent magnet synchronous motor (PMSM) speed system, and the numerical implementation performance of the fractional order operator is evaluated with comprehensive investigation using different implementation methods. Three commonly used numerical implementation methods of fractional operators are investigated and compared in this paper. Futhermore, for the impulse response invariant method, the effects of different discretization orders on the system control performance are compared. The simulation results show that the high accuracy numerical implementation method of the designed high-order FOPI controller has improved performance over normal accuracy fractional order operation implementation.

The numerical algorithms for discrete Mittag-Leffler functions approximation

2019 ◽  
Vol 22 (1) ◽  
pp. 95-112 ◽  
Author(s):  
Ang Li ◽  
Yiheng Wei ◽  
Zongyang Li ◽  
Yong Wang
Keyword(s):  
Transition Matrix ◽  
State Transition ◽  
Numerical Algorithms ◽  
The State ◽  
State Transition Matrix ◽  
Numerical Implementation ◽  
Science And Engineering ◽  
Implementation Method ◽  
Theoretical Results

Abstract Motivated essentially by the success of the applications of the discrete Mittag-Leffler functions (DMLF) in many areas of science and engineering, the authors present, in a unified manner, a detailed numerical implementation method of the Mittag-Leffler function. With the proposed method, the overflow problem can be well solved. To further improve the practicability, the state transition matrix described by discrete Mittag-Leffler functions are investigated. Some illustrative examples are provided to verify the effectiveness of the proposed theoretical results.

The role and application of entropy terms for acoustic wave modeling by the finite‐difference method

Geophysics ◽  
1984 ◽  
Vol 49 (9) ◽  
pp. 1457-1465 ◽  
Author(s):  
M. A. Dablain
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Acoustic Wave ◽  
Difference Scheme ◽  
Acoustic Wave Propagation ◽  
Central Difference ◽  
Central Difference Scheme ◽  
One Dimensional ◽  
The Finite Difference Method

The significance of entropy‐like terms is examined within the context of the finite‐difference modeling of acoustic wave propagation. The numerical implications of dissipative mechanisms are tested for performance within two very distinct differencing algorithms. The two schemes which are reviewed with and without dissipation are (1) the standard central‐difference scheme, and (2) the Lax‐Wendroff two‐step scheme. Numerical results are presented comparing the short‐wavelength response of these schemes. In order to achieve this response, the linearized version of an exploding one‐dimensional source is used.

scholarly journals Stress Tensor and Gradient of Hydrostatic Pressure in the Contact Plane of Axisymmetric Bodies Under Normal and Tangential Loading

2020 ◽  
Author(s):  
Emanuel Willert ◽  
Fabian Forsbach ◽  
Valentin L. Popov
Keyword(s):  
Hydrostatic Pressure ◽  
Stress Tensor ◽  
Normal Component ◽  
Hertzian Contact ◽  
Von Mises Stress ◽  
Axially Symmetric ◽  
Principal Stresses ◽  
Contact Plane ◽  
Stress Components ◽  
Von Mises

The Hertzian contact theory, as well as most of the other classical theories of normal and tangential contact, provides displacements and the distribution of normal and tangential stress components directly in the contact surface. However, other components of the full stress tensor in the material may essentially influence the material behaviour in contact. Of particular interest are principal stresses and the equivalent von Mises stress, as well as the gradient of the hydrostatic pressure. For many engineering and biomechanical problems, it would be important to find these stress characteristics at least in the contact plane. In the present paper, we show that the complete stress state in the contact plane can be easily found for axially symmetric contacts under very general assumptions. We provide simple explicit equations for all stress components and the normal component of the gradient of hydrostatic pressure in the form of one-dimensional integrals.

scholarly journals On the determination of the dissipation rate of turbulence kinetic energy

2021 ◽  
Vol 62 (7) ◽  
Author(s):  
James M. Lewis ◽  
Timothy W. Koster ◽  
John C. LaRue
Keyword(s):  
Kinetic Energy ◽  
Difference Scheme ◽  
Dissipation Rate ◽  
Hot Wire ◽  
Central Difference ◽  
Time Resolved ◽  
Central Difference Scheme ◽  
Derivative Spectra ◽  
Velocity Derivative ◽  
Velocity Spectra

Abstract The paper presents a comparison of the dissipation rate obtained from numerical differentiation of the time-resolved velocity, analog differentiation of the hot-wire signal, integration of the velocity derivative spectra obtained from the velocity spectra, and the application of a power decay law. Hot-wire measurements downstream of an active-grid provide the time-resolved velocity with a Taylor Reynolds number in the range of 200–470, turbulence intensities in the range of 5.8–11%, and nominal mean velocities of 4, 6, and 8 m s$$^{-1}$$ - 1 . The dissipation rate calculated using a ninth-order central-difference scheme differs at most by $${\pm }$$ ±  4% from the value obtained by analog differentiation. For comparison, a 23rd-order central-difference scheme offers negligible (0.02%) difference relative to the ninth-order scheme. Correction for an apparent uncertainty in the calibration of the analog differentiator reduces the difference to $${\pm }$$ ±  2.5%. In contrast, integration of the velocity derivative spectra obtained from the velocity spectra leads to a dissipation rate 14–45% larger than the corresponding values obtained using analog differentiation. Results obtained from the application of a power decay law of turbulence kinetic energy with a nonzero virtual origin to determine the dissipation rate deviate by 1.7%, 1.6%, and 3.6% relative to the corresponding values obtained from the analog differentiator based on the ensemble average of downstream locations with a $${\pm }$$ ± 5.6% scatter about the ensemble average. Graphic abstract

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