Paul A. Meehan

Vertical Wall Formation and Material Flow Control for Incremental Sheet Forming by Revisiting Multistage Deformation Path Strategies

In this article, multistage deformation path strategies for single point incremental forming (SPIF) are revisited with the purpose of controlling material flow (improving sheet thickness distribution) and forming a vertical wall surface for cylindrical cups. It is noted that stretching and thinning are two main deformation modes during SPIF. How to control material flow in an optimal way is a key point for successful forming. Multistage incremental forming shows more advantages than single-stage forming, especially dealing with shapes with steep walls. In this study, three basic multistage deformation path strategies have been proposed, that is: A. incremental part diameter; B. incremental draw angle; and C. incremental part height and draw angle. Those strategies and their combinations have been evaluated in terms of formability and compared in order to understand the material allocation mechanism and optimize the multistage forming process. In addition, approximate plane-strain analysis models have been given to provide formability predictions between single-stage and multistage strategies, and between strategies B and C, respectively. The prediction results show good agreement with the experimental results. It is demonstrated that the strategic combination A + B is the optimal way to achieve the forming target.

ANALYSIS OF CHAOTIC INSTABILITIES IN A ROTATING BODY WITH INTERNAL ENERGY DISSIPATION

Melnikovs method is used to analytically predict the onset of chaotic instability in a rotating body with internal energy dissipation. The model has been found to exhibit chaotic instability when a harmonic disturbance torque is applied to the system for a range of forcing amplitude and frequency. Such a model may be considered to be representative of the dynamical behavior of a number of physical systems such as a spinning spacecraft. In spacecraft, disturbance torques may arise under malfunction of the control system, from an unbalanced rotor, from vibrations in appendages or from orbital variations. Chaotic instabilities arising from such disturbances could introduce uncertainties and irregularities into the motion of the multibody system and consequently could have disastrous effects on its intended operation. A comprehensive stability analysis is performed and regions of nonlinear behavior are identified. Subsequently, the closed form analytical solution for the unperturbed system is obtained in order to identify homoclinic orbits. Melnikovs method is then applied on the system once transformed into Hamiltonian form. The resulting analytical criterion for the onset of chaotic instability is obtained in terms of critical system parameters. The sufficient criterion is shown to be a useful predictor of the phenomenon via comparisons with numerical results. Finally, for the purposes of providing a complete, self-contained investigation of this fundamental system, the control of chaotic instability is demonstated using Lyapunovs method.

Control of chaotic instabilities in a spinning spacecraft with dissipation using Lyapunov's method

Control of chaotic instability in a simplified model of a spinning spacecraft with dissipation is achieved using an algorithm derived using Lyapunovs second method. The control method is implemented on a realistic spacecraft parameter configuration which has been found to exhibit chaotic instability for a range of forcing amplitudes and frequencies when a sinusoidally varying torque is applied to the spacecraft. Such a torque, may arise in practice from an unbalanced rotor or from vibrations in appendages. Numerical simulations are performed and the results are studied by means of time history, phase space, Poincare map, Lyapunov characteristic exponents and bifurcation diagrams

Vibration Instability in Rolling Mills: Modeling and Experimental Results

Models for the occurrence of the vibrational instability during rolling known as third octave chatter are presented and discussed. An analysis of rolling mill chatter was performed for the purpose of identifying characteristics of the vibrations and to determine any dependency on the rolling schedule. In particular, a stability criterion for the critical rolling speed is used to predict the maximum rolling speed without chatter instability on schedules from a 5 stand tandem mill rolling thin steel product. The results correlate well with measurements of critical speed occurring on the mill using a vibration monitor: This research provides significant insights into the chatter phenomena and has been used to investigate control methods for suppression of the instability.

Modeling and Optimization of Surface Roughness in Incremental Sheet Forming using a Multi-objective Function

As a critical product quality constraint, surface roughness is regarded as a weak point in incremental sheet forming (ISF). It is of great importance to identify the impact of forming parameters on the surface roughness and optimize the surface finish at the production stage. This paper proposes a systematic approach to modeling and optimizing surface roughness in ISF. The quantitative effects of four parameters (step down, feed rate, sheet thickness, and tool diameter) on surface roughness are analyzed using the response surface methodology with Box–Behnken design. The multi-objective function is used to evaluate the overall surface roughness in terms of the tool-sheet contact surface roughness, i.e., internal surface roughness and the noncontact surface roughness, i.e., external surface roughness. Additionally, the average surface roughness (R a) on each surface is measured along the tool-path step-down direction taking the impact of sheet roll marks into account. The optimal conditions for the minimization of overall surface roughness are determined as step down (0.39 mm), feed rate (6000 mm/min), sheet thickness (1.60 mm), and tool diameter (25 mm). This study shows that Box–Behnken design with a multi-objective function can be efficiently applied for modeling and optimization of the overall surface roughness in ISF.

Control of Chaotic Motion in a Spinning Spacecraft with a Circumferential Nutational Damper

Control of chaotic vibrations in a simplified model of a spinning spacecraft with a circumferential nutational damper is achieved using two techniques. The control methods are implemented on a realistic spacecraft parameter configuration which has been found to exhibit chaotic instability when a sinusoidally varying torque is applied to the spacecraft for a range of forcing amplitude and frequency. Such a torque, in practice, may arise in the platform of a dual-spin spacecraft under malfunction of the control system or from an unbalanced rotor or from vibrations in appendages. Chaotic instabilities arising from these torques could introduce uncertainties and irregularities into a spacecrafts attitude and consequently could have disastrous affects on its operation. The two control methods, recursive proportional feedback (RPF) and continuous delayed feedback, are recently developed techniques for control of chaotic motion in dynamical systems. Each technique is outlined and the effectiveness of the two strategies in controlling chaotic motion exhibited by the present system is compared and contrasted. Numerical simulations are performed and the results are studied by means of time history, phase space, Poincaré map, Lyapunov characteristic exponents and bifurcation diagrams.

Chaotic Motion in a Spinning Spacecraft with Circumferential Nutational Damper

The dynamics of a simplified model of a spinning spacecraft with a circumferential nutational damper is investigated using numerical simulations for nonlinear phenomena. A realistic spacecraft parameter configuration is investigated and is found to exhibit chaotic motion when a sinusoidally varying torque is applied to the spacecraft for a range of forcing amplitude and frequency. Such a torque, in practice, may arise in the platform of a dual-spin spacecraft under malfunction of the control system or from an unbalanced rotor or from vibrations in appendages. The equations of motion of the model are derived with Lagranges equations using a generalisation of the kinetic energy equation and a linear stability analysis is given. Numerical simulations for satellite parameters are performed and the system is found to exhibit chaotic motion when a sinusoidally varying torque is applied to the spacecraft for a range of forcing amplitude and frequency. The motion is studied by means of time history, phase space, frequency spectrum, Poincaré map, Lyapunov characteristic exponents and Correlation Dimension. For sufficiently large values of torque amplitude, the behaviour of the system was found to have much in common with a two well potential problem such as a Duffing oscillator. Evidence is also presented, indicating that the onset of chaotic motion was characterised by period doubling as well as intermittency.

Simulation and Experimental Observations of Effect of Different Contact Interfaces on the Incremental Sheet Forming Process

Incremental sheet forming (ISF) is a promising forming process perfectly suitable for manufacturing customized products with large plastic deformation by using a simple moving tool. Up to now, however, the effects of contact conditions at the sheet interface are not well understood. The aim of this work is to study the effect of tool type and size on the formability and surface integrity during the forming process. Experimental tests were carried out on aluminum sheets of 7075-O to create a straight groove with four different tools (ϕ 30,ϕ25.4,ϕ20 andϕ10mm). One tool tip was fitted with a roller ball (ϕ 25.4mm) while the other three were sliding tips. The contact force, friction and failure depth were evaluated. A finite element (FE) model of the process was set up in an explicit code LS-DYNA and the strain behavior and thickness distribution with different tools were evaluated and compared with the experimental results. This study provides important insights into the relatively high formability observed in the ISF process. Microscopic observations of the surface topography revealed that a rolling tool tip produced better surface integrity as compared with a sliding tool tip, wherein, distinct scratch patterns in the tool traverse direction were evident.

Investigation of the effect of lateral adhesion and rolling speed on wheel squeal noise

In order to validate prediction models of wheel squeal, a rolling contact test rig is used to investigate fundamental squeal behaviour. The vibration characteristics of the wheel are investigated using analytical and finite element methods, and by experimental impact hammer analysis, respectively. Accordingly, the lateral resonant frequencies and mode shapes of the wheel are determined. A dominant mode is identified based on this as the primary peak in the sound spectrum of squeal and is used as an indicator of the occurrence and magnitude of squeal. The lateral creep curves and amplitudes of wheel vibration at various rolling speeds are measured using a strain gauge technique and predicted. A simplified model including the interaction between lateral force and transverse vibration of the dominant mode is developed, and the experimental and simulated results show the sound pressure level and vibration velocity of the wheel increases substantially as the angle of attack reaches and exceeds the value around 8 mrad. The phenomenon of double peaks in the sound spectrum of wheel squeal is also investigated. It is found that the cause of double peaks is due to the wheel rotation and the frequency divergence of double peaks increases with rolling speed as predicted theoretically.

Control of chaotic motion in a dual-spin spacecraft with nutational damping

Control of chaotic vibrations in a dual-spin spacecraft with an axial nutational damper is achieved using two techniques. The control methods are implemented on two realistic spacecraft parameter configurations that have been found to exhibit chaotic instability when a sinusoidally varying torque is applied to the spacecraft for a range of forcing amplitudes and frequencies. Such a torque, in practice, may arise under malfunction of the control system or from an unbalanced rotor. Chaotic instabilities arising from these torques could introduce uncertainties and irregularities into a spacecrafts attitude motion and, consequently, could have disastrous effects on its operation. The two control methods, recursive proportional feedback and continuous delayed feedback, are recently developed techniques for control of chaotic motion in dynamic systems. Each technique is outlined and the effectiveness on this model compared and contrasted. Numerical simulations are performed, and the results are studied by means of time history, phase space, Poincare map, Lyapunov characteristic exponents, and bifurcation diagrams.