Added Stability Lobes in Machining Processes That Exhibit Periodic Time Variation, Part 1: An Analytical Solution

2004 ◽  
Vol 126 (3) ◽  
pp. 467-474 ◽  
Author(s):  
William T. Corpus ◽  
William J. Endres
Keyword(s):  
Numerical Simulation ◽  
Analytical Solution ◽  
Closed Form ◽  
High Speed ◽  
Stability Limit ◽  
Second Order ◽  
Machining Processes ◽  
Stability Lobes ◽  
Time Varying Systems ◽  
Computationally Intensive

An added family of stability lobes, which exists in addition to the traditional stability lobes, has been identified for the case of periodically time varying systems. An analytical solution of arbitrary order is presented that identifies and locates multiple added lobes. The stability limit solution is first derived for zero damping where a final closed-form symbolic result can be realized up to second order. The un-damped solution provides a mathematical description of the added lobes’ locations along the speed axis, an added-lobe numbering convention, and the asymptotes for the damped case. The derivation for the damped case permits a final closed-form symbolic result for first-order only; the second-order solution requires numerical evaluation. The easily computed analytical solution is shown to agree well with the results of the computationally intensive numerical simulation approach. An increase in solution order improves the agreement with numerical simulation; but, more importantly, it allows equivalently more added lobes to be predicted, including the second added lobe that cuts into the speed regime of the traditional high-speed stability peak.

A High-Order Solution for the Added Stability Lobes in Intermittent Machining

2000 ◽  
Author(s):  
William T. Corpus ◽  
William J. Endres
Keyword(s):  
Closed Form ◽  
High Speed ◽  
Higher Order ◽  
Second Order ◽  
Machining Processes ◽  
Analytical Technique ◽  
First Order ◽  
Order Solution ◽  
Order Case ◽  
Speed Stability

Abstract An earlier work by the authors presented a solution for the added ultrahigh-speed stability lobe that has been shown to exist for intermittent and other periodically time varying machining processes. That earlier first-order solution was not clearly extendible to a higher order. A more general analytical technique presented here does permit higher-order results. The solution is developed first for the case of zero damping for which a final closed-form symbolic result can be realized up to second order. More important than improved accuracy, the higher-order nature of the result confirms that there exist multiple added lobes and permits a mathematical description of their locations along the spindle-speed axis. A solution is then derived for the structurally damped case, where the first-order case permits a final closed-form symbolic result while the second-order case requires computational evaluation. The first-order result matches perfectly the previously published one, as expected. The second-order result improves accuracy, measured relative to numerical simulation results, and, more important, permits a second added lobe to be predicted. The second added lobe tends to cut into the region of the high-speed stability peak that is predicted under traditional zero-frequency (time-averaged) analyses. The damped solutions also indicate that structural damping of the dominant mode becomes virtually unimportant at ultrahigh speeds.

scholarly journals Numerical Simulation Analysis of an Oversteer In-Wheel Small Electric Vehicle Integrated with Four-Wheel Drive and Independent Steering

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Muhammad Izhar Ishak ◽  
Hirohiko Ogino ◽  
Yoshio Yamamoto
Keyword(s):  
Numerical Simulation ◽  
Steady State ◽  
Critical Velocity ◽  
High Speed ◽  
Simulation Analysis ◽  
Stability Limit ◽  
Conventional Vehicle ◽  
Wheel Drive ◽  
On The Road ◽  
Four Wheel Drive

Similar to conventional vehicle, most in-wheel small EVs that exist today are designed with understeer (US) characteristic. They are safer on the road but possess poor cornering performance. With recent in-wheel motor and steer-by wire technology, high cornering performance vehicle does not limit to sport or racing cars. We believe that oversteer (OS) design approach for in-wheel small EV can increase the steering performance of the vehicle. However, one disadvantage is that OS vehicle has a stability limit velocity. In this paper, we proposed a Four-Wheel Drive and Independent Steering (4WDIS) for in-wheel small EV with OS characteristic. The aim of implementing 4WDIS is to develop a high steer controllability and stability of the EV at any velocity. This paper analyses the performance of OS in-wheel small EV with 4WDIS by using numerical simulation. Two cornering conditions were simulated which are (1) steady-state cornering at below critical velocity and (2) steady-state cornering over critical velocity. The objective of the simulation is to understand the behavior of OS in-wheel small EV and the advantages of implementing the 4WDIS. The results show that an in-wheel small EV can achieve high cornering performance at low speed while maintaining stability at high speed.

Integration of Drill Torsional-Axial Coupling in Spindle-Vibratory Drilling Head Model for Stability Analysis

2013 ◽  
Author(s):  
Said Mousavi ◽  
Vincent Gagnol ◽  
Pascal Ray
Keyword(s):  
High Speed ◽  
Design Parameters ◽  
Head Model ◽  
Machining Processes ◽  
Alternative Response ◽  
Analytical Stability ◽  
Stability Lobes ◽  
Excited Vibration ◽  
The Stability ◽  
Industrial Solutions

The drilling of deep holes with small diameters remains an unsatisfactory technology, since its productivity is rather limited. The main limit to an increase in productivity is directly related to the poor chip evacuation, which induces frequent tool breakage and poor surface quality. Retreat cycles and lubrication are common industrial solutions, but they induce productivity and environmental drawbacks. An alternative response to the chip evacuation problem is the use of a vibratory drilling head, which enables the chips to be fragmented thanks to the axial self-excited vibration. Contrary to conventional machining processes, axial drilling instability is sought, thanks to an adjustment of head design parameters and appropriate conditions of use. In this paper, self-vibratory cutting conditions are established through a specific stability lobes diagram. A dynamic high-speed spindle / drilling head / tool system model is elaborated on the basis of rotor dynamics predictions. The model-based tool tip FRF is integrated into an analytical stability approach. The torsional-axial coupling of the twist drill is investigated and consequences on drilling instability are established. Specific stability lobes are established and indicate modifications of self-excited operating zones. This approach allows refining the stability prediction of the global system during a drilling operation.

Numerical Modeling of Kites for Power Generation

2014 ◽  
Author(s):  
Alireza Mahdavi Nejad ◽  
David J. Olinger ◽  
Gretar Tryggvason
Keyword(s):  
Numerical Simulation ◽  
Flow Field ◽  
High Speed ◽  
Stokes Equations ◽  
Second Order ◽  
Staggered Grid ◽  
Immersed Boundary ◽  
Uniform Mesh ◽  
Two Dimensional ◽  
Time Step

A computational model of a massless kite that produces power in an airborne wind energy system (AWE) is presented. AWE systems use tethered kites at high altitudes to extract energy from the wind, and are being considered as an alternative to wind turbines since the kites can move in high-speed cross-wind motions over large swept areas to increase power production. In our model the kite completes successive power-retraction cycles where the kite angle of attack is altered as required to vary the resultant aerodynamic forces on the kite. The numerical simulation models the flow field in a two-dimensional domain near the flexible kite by solving the full Navier-Stokes equations. Eulerian grid points for the flow domain together with a Lagrangian representation of the kite are employed. The flow field is determined through a second-order finite difference projection method using a non-uniform mesh on a staggered grid. A corrector-predictor technique is employed to ensure the second-order accuracy in time of the numerical simulation. The two-dimensional kite shape is modeled as a slightly cambered immersed boundary that evolves with the flow. The flexible kite surface is modeled with a set of linear springs following Hooke’s law. The unstretched length of each elastic tether at a given time step is controlled using periodic triangular wave shapes to achieve the required power-retraction phases. A study was conducted in which the wave shape amplitude, frequency, and phase (between two tethers) was adjusted to achieve a suitably high net power output with very good agreement to predictions for Loyd’s simple kite in two-dimensional motion. Aerodynamic coefficients for the kite, tether tensions, tether reel-out and reel-in speeds, and vorticity flowfields in the kite wake are also determined.

Numerical simulation of high-speed civil transport inlet operability with angle of attack

AIAA Journal ◽  
1998 ◽  
Vol 36 ◽  
pp. 1223-1229
Author(s):  
Ge-Cheng Zha ◽  
Doyle Knight ◽  
Donald Smith ◽  
Martin Haas
Keyword(s):  
Numerical Simulation ◽  
High Speed ◽  
Angle Of Attack

Numerical Simulation of High-Speed Crack Propagating and Branching Phenomena

2016 ◽  
Vol 37 (7) ◽  
pp. 729-739
Author(s):  
GU Xin-bao ◽  
◽  
ZHOU Xiao-ping ◽  
XU Xiao ◽  
Keyword(s):  
Numerical Simulation ◽  
High Speed

scholarly journals The Hydromechanical Interplay in the Simplified Three-Dimensional Limit Equilibrium Analyses of Unsaturated Slope Stability

Geosciences ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 73
Author(s):  
Panagiotis Sitarenios ◽  
Francesca Casini
Keyword(s):  
Analytical Solution ◽  
Slope Stability ◽  
Slope Failure ◽  
Failure Modes ◽  
Pore Water Pressure ◽  
Limit Equilibrium ◽  
Water Pressure ◽  
Three Dimensional ◽  
Stability Limit ◽  
Smooth Transition

This paper presents a three-dimensional slope stability limit equilibrium solution for translational planar failure modes. The proposed solution uses Bishop’s average skeleton stress combined with the Mohr–Coulomb failure criterion to describe soil strength evolution under unsaturated conditions while its formulation ensures a natural and smooth transition from the unsaturated to the saturated regime and vice versa. The proposed analytical solution is evaluated by comparing its predictions with the results of the Ruedlingen slope failure experiment. The comparison suggests that, despite its relative simplicity, the analytical solution can capture the experimentally observed behaviour well and highlights the importance of considering lateral resistance together with a realistic interplay between mechanical parameters (cohesion) and hydraulic (pore water pressure) conditions.

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