scholarly journals Flutter Instability Speeds of Guided Splined Disks: An Experimental and Analytical Investigation

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Ahmad Mohammadpanah ◽  
Stanley G. Hutton
Keyword(s):  
Degrees Of Freedom ◽  
Lateral Displacement ◽  
Outer Boundary ◽  
Linear Equations ◽  
Experimental Tests ◽  
Travelling Wave ◽  
Transverse Motion ◽  
Flutter Instability ◽  
Spinning Disk ◽  
Lateral Constraint

“Guided splined disks” are defined as flat thin disks in which the inner radius of the disk is splined and matches a splined arbor that provides the driving torque for rotating the disk. Lateral constraint for the disk is provided by space fixed guide pads. Experimental lateral displacement of run-up tests of such a system is presented, and the flutter instability zones are identified. The results indicate that flutter instability occurs at speeds when a backward travelling wave of a mode meets a reflected wave of a different mode. Sometimes, the system cannot pass a flutter zone, and transverse vibrations of the disk lock into that flutter instability zone. The governing linear equations of transverse motion of such a spinning disk, with assumed free inner and outer boundary conditions, are derived. A lateral constraint is introduced and modeled as a linear spring. Rigid body translational and tilting degrees of freedom are included in the analysis of the total motion of the spinning disk. The eigenvalues of the system are computed numerically, and the flutter instability zones are defined. The results show that the mathematical model can predict accurately the flutter instability zones measured in the experimental tests.

Dynamics Behavior of a Guided Spline Spinning Disk, Subjected to Conservative In-Plane Edge Loads, Analytical and Experimental Investigation

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Ahmad Mohammadpanah ◽  
Stanley G. Hutton
Keyword(s):  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Linear Equations ◽  
Transverse Motion ◽  
Stable Operation ◽  
Lateral Direction ◽  
Critical Speeds ◽  
Spinning Disk ◽  
Inner Radius ◽  
Work Done

The governing linear equations of transverse motion of a spinning disk with a splined inner radius and constrained from lateral motion by guide pads are derived. The disk is driven by a matching spline arbor that offers no restraint to the disk in the lateral direction. Rigid body translational and tilting degrees-of-freedom are included in the analysis of total motion of the spinning disk. The disk is subjected to lateral constraints and loads. Also considered are applied conservative in-plane edge loads at the outer and inner boundaries. The numerical solution of these equations is used to investigate the effect of the loads and constraints on the natural frequencies, critical speeds, and stability of a spinning disk. The sensitivity of eigenvalues of spline spinning disk to the in-plane edge loads is analyzed by taking the derivative of the spinning disk's eigenvalues with respect to the loads. An expression for the energy induced in the spinning disk by the in-plane loads, and their interaction at the inner radius, is derived by computation of the rate of work done by the lateral component of the edge loads. Experimental idling and cutting tests for a guided spline saw are conducted at the critical speed, super critical speeds, and at the flutter instability speed. The cutting results at different speeds are compared to show that the idling results of a guided spline disk can be used to predict stable operation speeds of the system during cutting.

Limitation on Increasing the Critical Speed of a Spinning Disk Using Transverse Rigid Constraints, An Application of Rayleigh's Interlacing Eigenvalues Theorem

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Ahmad Mohammadpanah ◽  
Stanley G. Hutton
Keyword(s):  
Rigid Body ◽  
Critical Speed ◽  
Linear Equations ◽  
Experimental Tests ◽  
Original System ◽  
Thin Disk ◽  
Transverse Motion ◽  
Structural Modifications ◽  
Spinning Disk ◽  
Translational Degree

It can be predicted by Rayleigh's interlacing eigenvalue theorem that structural modifications of a spinning disk can shift the first critical speed of the system up to a known limit. In order to corroborate this theorem, it is shown numerically, and verified experimentally that laterally constraining of a free spinning flexible thin disk with tilting and translational degree-of-freedom (DOF), the first critical speed of the disk cannot increase more than the second critical speed of the original system (the disk with no constraint). The governing linear equations of transverse motion of a spinning disk with rigid body translational and tilting DOFs are used in the analysis of eigenvalues of the disk. The numerical solution of these equations is used to investigate the effect of the constraints on the critical speeds of the spinning disk. Experimental tests were conducted to verify the results.

scholarly journals A New Approach of Soft Joint Based on a Cable-Driven Parallel Mechanism for Robotic Applications

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1468
Author(s):  
Luis Nagua ◽  
Carlos Relaño ◽  
Concepción A. Monje ◽  
Carlos Balaguer
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Experimental Tests ◽  
Humanoid Robots ◽  
Inverse Kinematic ◽  
Element Analysis ◽  
New Approach ◽  
Flexible Polymer ◽  
The Mathematical Model

A soft joint has been designed and modeled to perform as a robotic joint with 2 Degrees of Freedom (DOF) (inclination and orientation). The joint actuation is based on a Cable-Driven Parallel Mechanism (CDPM). To study its performance in more detail, a test platform has been developed using components that can be manufactured in a 3D printer using a flexible polymer. The mathematical model of the kinematics of the soft joint is developed, which includes a blocking mechanism and the morphology workspace. The model is validated using Finite Element Analysis (FEA) (CAD software). Experimental tests are performed to validate the inverse kinematic model and to show the potential use of the prototype in robotic platforms such as manipulators and humanoid robots.

Numerical and Experimental Approaches to Investigate the Stability of a Motorcycle Vehicle

2006 ◽  
Author(s):  
Federico Cheli ◽  
Marco Bocciolone ◽  
Marco Pezzola ◽  
Elisabetta Leo
Keyword(s):  
Degrees Of Freedom ◽  
Structural Parameters ◽  
Experimental Tests ◽  
Roll Angle ◽  
Longitudinal Motion ◽  
Reference Trajectory ◽  
Steering Angle ◽  
Steady State Condition ◽  
The Stability ◽  
Linearized Model

The study of motorcycle’s stability is an important task for the passenger’s safety. The range of frequencies involved for the handling stability is lower than 10 Hz. A numerical model was developed to access the stability of a motorcycle vehicle in this frequency range. The stability is analysed using a linearized model around the straight steady state condition. In this condition, the vehicle’s vertical and longitudinal motion are decoupled, hence the model has only four degrees of freedom (steering angle, yaw angle, roll angle and lateral translation), while longitudinal motion is imposed. The stability was studied increasing the longitudinal speed. The input of the model can be either a driver input manoeuvre (roll angle) or a transversal component of road input able to excite the vibration modes. The driver is introduced in the model as a steering torque that allows the vehicle to follow a reference trajectory. To validate the model, experimental tests were done. To excite the vehicle modes, the driver input was not taken into account considering both the danger for the driver and the repeatability of the manoeuvre. Two different vehicle configurations were tested: vehicle 1 is a motorcycle [7] and vehicle 2 is a scooter. Through the use of the validated model, a sensitivity analysis was done changing structural (for example normal trail, steering angle, mass) and non structural parameters (for example longitudinal speed).

scholarly journals State Feedback and Torque Feed Forward Combined Control System for Suppressing Drill-Strings Stick-Slip Vibration

2019 ◽  
Vol 37 (2) ◽  
pp. 291-298
Author(s):  
Meng Fu ◽  
Jianghong Li ◽  
Yafeng Wu ◽  
Shubiao Song ◽  
Aiqi Zhao ◽  
...  
Keyword(s):  
Control System ◽  
Degrees Of Freedom ◽  
State Feedback ◽  
Dynamic Performance ◽  
Experimental Tests ◽  
State Observer ◽  
Lumped Parameter Model ◽  
Stick Slip ◽  
Feed Forward ◽  
Reference Governor

In drilling field, drill-strings stick-slip vibration is a common phenomenon and may lead to a series of drilling accidents. In order to improve drilling efficiency, this paper commits to study a new control system to suppress the undesired stick-slip vibration. In this work, a two degrees of freedom lumped parameter model is established to imitate the drill-strings. A state observer is proposed to estimate the unknown drill-strings states. A reference governor is put forward to optimize drilling parameters. In addition, in order to enhance the anti-interference ability of the closed-loop system, a torque feed forward is introduced into the control system. Based on the state observer and the reference governor, a state feedback and torque feed forward combined controller is designed. The simulation results indicate preliminarily that the designed state feedback and torque feed forward controller, compared with the drilling industry PI controller, has better dynamic performance and stronger ability to eliminate the drill-strings stick-slip vibration. Finally, the control system is applied in the drilling field. The experimental tests demonstrate that the designed controller can effectively suppress the drill-strings stick-slip vibration.

scholarly journals To the Solution of Geometric Inverse Heat Conduction Problems

2021 ◽  
Vol 24 (1) ◽  
pp. 6-12
Author(s):  
Yurii M. Matsevytyi ◽  
◽  
Valerii V. Hanchyn ◽  
Keyword(s):  
Heat Conduction ◽  
Iterative Process ◽  
Regularization Parameter ◽  
Outer Boundary ◽  
Linear Equations ◽  
The Body ◽  
Two Dimensional ◽  
Inverse Heat Conduction ◽  
System Of Linear Equations ◽  
Inverse Heat Conduction Problems

On the basis of A. N. Tikhonov’s regularization theory, a method is developed for solving inverse heat conduction problems of identifying a smooth outer boundary of a two-dimensional region with a known boundary condition. For this, the smooth boundary to be identified is approximated by Schoenberg’s cubic splines, as a result of which its identification is reduced to determining the unknown approximation coefficients. With known boundary and initial conditions, the body temperature will depend only on these coefficients. With the temperature expressed using the Taylor formula for two series terms and substituted into the Tikhonov functional, the problem of determining the increments of the coefficients can be reduced to solving a system of linear equations with respect to these increments. Having chosen a certain regularization parameter and a certain function describing the shape of the outer boundary as an initial approximation, one can implement an iterative process. In this process, the vector of unknown coefficients for the current iteration will be equal to the sum of the vector of coefficients in the previous iteration and the vector of the increments of these coefficients, obtained as a result of solving a system of linear equations. Having obtained a vector of coefficients as a result of a converging iterative process, it is possible to determine the root-mean-square discrepancy between the temperature obtained and the temperature measured as a result of the experiment. It remains to select the regularization parameter in such a way that this discrepancy is within the measurement error. The method itself and the ways of its implementation are the novelty of the material presented in this paper in comparison with other authors’ approaches to the solution of geometric inverse heat conduction problems. When checking the effectiveness of using the method proposed, a number of two-dimensional test problems for bodies with a known location of the outer boundary were solved. An analysis of the influence of random measurement errors on the error in identifying the outer boundary shape is carried out.

scholarly journals Torsion or not torsion, that is the question

2016 ◽  
Vol 25 (12) ◽  
pp. 1644013 ◽  
Author(s):  
Yuri Bonder
Keyword(s):  
General Relativity ◽  
Degrees Of Freedom ◽  
Empirical Support ◽  
Experimental Tests ◽  
Spin Polarized ◽  
Empirical Tests ◽  
New Interactions

A hypothesis of general relativity (GR) is that spacetime torsion vanishes identically. This assumption has no empirical support; in fact, a nonvanishing torsion is compatible with all the experimental tests of GR. The first part of this essay specifies the framework that is suitable to test the vanishing-torsion hypothesis, and an interesting relation with the gravitational degrees of freedom is suggested. In the second part, some original empirical tests are proposed based on the observation that torsion induces new interactions between different spin-polarized particles.

Numerical and experimental performance estimation for a ExoFing - 2 DOFs finger exoskeleton

Robotica ◽  
2021 ◽  
pp. 1-13
Author(s):  
G Carbone ◽  
M Ceccarelli ◽  
C. E. Capalbo ◽  
G Caroleo ◽  
C Morales-Cruz
Keyword(s):  
Degrees Of Freedom ◽  
Experimental Validation ◽  
Index Finger ◽  
Kinematic Model ◽  
Experimental Tests ◽  
Performance Estimation ◽  
Experimental Performance ◽  
Finger Motion ◽  
User Friendly ◽  
Operation Characteristics

Abstract This paper presents a numerical and experimental validation of ExoFing, a two-degrees-of-freedom finger mechanism exoskeleton. The main functionalities of this device are investigated by focusing on its kinematic model and by computing its main operation characteristics via numerical simulations. Experimental tests are designed and carried out for validating both the engineering feasibility and effectiveness of the ExoFing system aiming at achieving a human index finger motion assistance with cost-oriented and user-friendly features.

Hunting Stability Analysis of a New High-Speed Railway Vehicle Model Moving on Curved Tracks

2007 ◽  
Author(s):  
Yung-Chang Cheng ◽  
Sen-Yung Lee
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Lateral Displacement ◽  
Creep Model ◽  
Railway Vehicle ◽  
Nonlinear Creep ◽  
Car Body ◽  
Suspension Parameters ◽  
Virtual Boundary ◽  
Hunting Stability

A new dynamic model of railway vehicle moving on curved tracks is proposed. In this new model, the motion of the car body is considered and the motion of the tuck frame is not restricted by a virtual boundary. Based on the heuristic nonlinear creep model, the nonlinear coupled differential equations of the motion of a fourteen degrees of freedom car system, considering the lateral displacement and the yaw angle of the each wheelset, the truck frame and the car body, moving on curved tracks are derived in completeness. To illustrate the accuracy of the analysis, the limiting cases are examined. In addition, the influences of the suspension parameters on the critical hunting speeds evaluated via the linear and the nonlinear creep models respectively are studied. Furthermore, the influences of the suspension parameters on the critical hunting speeds evaluated via the fourteen degrees of freedom car system and the six degrees of freedom truck system, which the motion of the tuck frame is restricted by a virtual boundary, are compared.

scholarly journals Imaging Noise Suppression: Fourth-Order Partial Differential Equations and Travelling Wave Solutions

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2019
Author(s):  
Sameerah Jamal
Keyword(s):  
Fourth Order ◽  
Noise Suppression ◽  
Linear Equations ◽  
Travelling Wave ◽  
Order Partial Differential Equation ◽  
Travelling Wave Solutions ◽  
Partial Differential ◽  
Total Variation Norm ◽  
Wave Solutions ◽  
Variation Norm

In this paper, we discuss travelling wave solutions for image smoothing based on a fourth-order partial differential equation. One of the recurring issues of digital imaging is the amount of noise. One solution to this is to minimise the total variation norm of the image, thus giving rise to non-linear equations. We investigate the variational properties of the Lagrange functionals associated with these minimisation problems.

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