Vector bending sensors based on fibre Bragg gratings inscribed by infrared femtosecond laser

A novel, direction-sensitive bending sensor based on an asymmetric fiber Bragg grating (FBG) inscribed by an infrared femtosecond laser was demonstrated. The technique is based on tight transverse confinement of the femto-inscribed structures and can be directly applied in conventional, untreated singlemode fibers. The FBG structure was inscribed by an amplified, titanium sapphire laser system. The grating cross-section was elongated along the direction of the laser beam with the transverse dimensions of approximately 1 by 2 μm. It was suggested that the sensitivity of the device can be improved by inscribing smaller spatial features and by implementing more complex grating designs aimed at maximizing the effect of strain.

Symmetric and asymmetric evaluation of the Tokamap in comparison with direct symplectic integration

Comparing the Poincaré plots of the Tokamap and the underlying Hamiltonian system reveals large differences. This stems from the particular choice of evaluation of the singular perturbations present in the system (a series of δ functions). A symmetric evaluation approach is proposed and shown to yield results that almost perfectly match the Hamiltonian system. © 2005 The American Physical Society.

Bending and orientational characteristics of long period gratings written in D-shaped optical fiber

Long period gratings (LPGs) were written into a D-shaped single-mode fiber. These LPGs were subjected to a range of curvatures, and it was found that as curvature increased, there was increasingly strong coupling to certain higher order cladding modes without the usual splitting of the LPGs stopbands. A bend-induced stopband yielded a spectral sensitivity of 12.55 nm·m for curvature and 2.2×10-2 nm°C-1 for temperature. It was also found that the wavelength separation between adjacent bend-induced stopbands varied linearly as a function of curvature. Blue and red wavelength shifts of the stopbands were observed as the sensor was rotated around a fixed axis for a given curvature; thus, in principle, this sensor could be used to obtain bending and orientational information. The behavior of the stopbands was successfully modeled using a finite element approach.

Risk, seasonality and the asymmetric behaviour of stock returns

For some time there has been a puzzle surrounding the seasonal behaviour of stock returns. This paper demonstrates that there is an asymmetric relationship between systematic risk and return across the different months of the year for both large and small firms. In the case of both large and small firms systematic risk appears to be priced in only two months of the year, January and April. During the other months no persistent relationship between systematic risk and return appears to exist. The paper also shows that when systematic risk is priced, the size of the systematic risk premium is higher for large firms than for small firms and varies significantly across the months of the year.

Directional bend sensor based on an asymmetric modification of the fiber cladding by femtosecond laser

A femtosecond laser was used to modify a part of the cladding of a standard LPG bend sensor. The device produced wavelength shifts depending upon the direction of bend, thus making a shape sensor.

Long period grating directional bend sensor based on asymmetric index modification of cladding

A long period grating (LPG) written in a standard optical fibre was modified by using a femtosecond laser to induce an asymmetric change in the cladding's refractive index. This device produced blue and red wavelength shifts depending on the orientation of applied curvature, with maximum sensitivities of -1.6 nm m and +3.8 nm m, suggesting that this type of LPG may be useful as a shape sensor.

Bending characteristics of fiber long-period gratings with cladding index modified by femtosecond laser

A femtosecond laser has been used to asymmetrically modify the cladding of fiber containing long-period gratings. Following modification, devices in single-mode fiber are shown to be capable of sensing the magnitude and direction of bending in one plane by producing blue and red wavelength shifts depending upon the orientation of the bend. The resulting curvature sensitivities were -1.62 and +3.82 nm&middotm. Devices have also been produced using an elliptical core fiber to study the effects of the cladding modification on the two polarization eigenstates. A cladding modification applied on the fast axis of the fiber is shown to affect the light in the fast axis much more significantly than the light in the orthogonal state; this behavior may ultimately lead to a sensor capable of detecting the direction of bending in two dimensions for applications in shape sensing.

Vector bending sensors based on fiber bragg gratings inscribed by an infrared femtosecond laser

A direction-sensitive bend sensor in standard single-mode fiber is demonstrated for the first time based on an axially-offset fiber Bragg grating, directly written by an infrared femtosecond laser.

The mechanics of continuous roller bending of plates

This research initiates a study of the mechanics of four roll plate bending and provides a methodology to investigate the process experimentally. To carry out the research a suitable model bender was designed and constructed. The model bender was comprehensively instrumented with ten load cells, three torquemeters and a tachometer. A rudimentary analysis of the four roll pre-bending mode considered the three critical bending operations. The analysis also gave an assessment of the model bender capacity for the design stage. The analysis indicated that an increase in the coefficient of friction in the contact region of the pinch rolls and the plate would reduce the pinch resultant force required to end a plate to a particular bend radius. The mechanisms involved in the four roll plate bending process were investigated and a mathematical model evolved to determine the mechanics of four roll thin plate bending. A theoretical and experimental investigation was conducted for the bending of HP30 aluminium plates in both single and multipass bending modes. The study indicated that the multipass plate bending mechanics of the process varied according to the number of bending passes executed and the step decrement of the anticipated finished bend radius in any two successive passes (i.e. the bending route). Experimental results for single pass bending indicated that the rollers normally exert a higher bending load for the steady-continous bending with the pre-inactive side roll oper?tive. For the pre-bending mode and the steady-continous bending mode with the pre-active side roll operative, the former exerted the higher loads. The single pass results also indicated that the force on the side roll, the torque and power steadily increased as the anticipated bend radius decreased. Theoretical predictions for the plate internal resistance to accomplish finished bend radii of between 2500mm and 500mm for multipass bending HP30 aluminium plates, suggested that there was a certain bending route which would effectively optimise the bender capacity.

The mechanics of ultrasonic tube bending

The technology of precision bending of tubes has recently increased in importance and is widely demanded for many industrial applications. However, whilst attention has been concentrated on automation and increasing the production rate of the bending machines, it seems that with one exception very little work has been done in order to understand and therefore fundamentally improve the bending process. A new development for the process of draw-bending of tubes, in which the supporting mandrel is axially vibrated at an ultrasonic frequency, has been perfected. A research programme was undertaken to study the mechanics of tube• bending under both vibratory and non-vibratory conditions. For this purpose, a conventional tube-bending machine was modified and equipped with an oscillatory system. Thin-walled mild steel tubes of different diameter to thickness ratios were bent to mean bend radii having various values from 1.5 to 2.0 times the tube diameter. It was found that the application of ultrasonic vibration reduces the process forces and that the force reduction increases with increasing the vibration amplitude. A reduction in the bending torque of up to 30 per cent was recorded and a reduction in the maximum tube-wall thinning of about 15 per cent was observed. The friction vector reversal mechanism as well as a reduction in friction account for the changes of the forces and the strains. Monitoring the mandrel friction during bending showed, in some cases, that the axial vibration reverses the mandrel .mean force from tension to compression and, thus, the mandrel is assisting the tube motion instead of resisting it. A theory has been proposed to describe the mechanics of deformation during draw-bending of tubes, which embodies the conditions of both "with" and "without" mandrel axial vibration. A theoretical analysis, based on the equilibrium of forces approach, has been developed in which the basic process parameters were taken into consideration. The stresses, the strains and the bending torque were calculated utilising this new solution, and a specially written computer programme was used to perform the computations. It was shown that the theory is in good agreement with the measured values of the strains under vibratory and non-vibratory conditions. Also, the predicted bending 'torque showed a similar trend to that recorded experimentally.

Bending and orientational characteristics of long period gratings written in D-shaped optical fiber

Long period gratings (LPGs) were written into a D-shaped single-mode fiber. These LPGs were subjected to a range of curvatures, and it was found that as curvature increased, there was increasingly strong coupling to certain higher order cladding modes without the usual splitting of the LPGs stopbands. A bend-induced stopband yielded a spectral sensitivity of 12.55 nm · m for curvature and 2.2 × 10-2 nm°C-1 for temperature. It was also found that the wavelength separation between adjacent bend-induced stopbands varied linearly as a function of curvature. Blue and red wavelength shifts of the stopbands were observed as the sensor was rotated around a fixed axis for a given curvature; thus, in principle, this sensor could be used to obtain bending and orientational information. The behavior of the stopbands was successfully modeled using a finite element approach.