Unequal Angles Research Articles

Sun-tracking commands and reaction wheel sizing with configuration optimization

This paper is composed of two parts. In the first part, two-axis sun-tracking commands for solar arrays articulated to Earth-pointing spacecraft are developed. In the second, the paper deals with optimization of cant angle(s) of reaction wheel pyramids for minimizing power consumption and required torque and momentum capacity of the wheels to deliver a cylindrical momentum envelope and a rectangular parallelepiped torque envelope. The two commonly used four-wheel pyramid configurations and a new one, according to which the wheels are inclined to roll and yaw axes of the spacecraft at unequal angles, are analyzed in depth. The minimum torque and momentum capacity of each wheel in the four-wheel pyramids are compared with the capacity of each wheel in six- and three-wheel pyramids. Both no-wheelfailure and one-wheel-failure cases are considered for all pyramidal configurations. The literal relationships developed in the paper are very useful for quickly determining the optimum cant angle(s) and the torque and momentum capacity of the wheels for given requirements about the spacecraft axes, and for selecting a most suitable wheel configuration from six- and three-wheel pyramids, three four-wheel pyramids of different bases, and six- and three-wheel orthogonal arrangements.

Kinematic Displacement Analysis of a Double-Cardan-Joint Driveline

The input-output displacement relations of two Cardan joints arranged in series on a driveline has been investigated in detail, including the effects of unequal joint angles, the phase angle between the two Cardan joints and also such manufacturing tolerance errors as nonright angle moving link lengths and offset joint axes. A combined Newton-Raphson method and Davidon-Fletcher-Powell optimization algorithm using dual-number coordinate-transformation matrices was employed to perform the analysis. An experiment was conducted to validate the results of the analysis. The apparatus consisted of a double-Cardan-joint driveline whose rotations were measured by optical shaft encoders that were sampled by a computer data-acquisition system. The equipment was arranged so that the phase angle between the joints and the offset angles between the shafts at each of the two joints could be readily varied. The “relative phase angle,” the difference between the phase angle of the two joints and the angle between the planes defined by the input and intermediate and the intermediate and output shafts, was found to be the significant factor. If the offset angles at both Cardan joints are equal, the double-Cardan-joint driveline functions as a constant-velocity coupling when the magnitude of the relative phase angle is zero. If the offset angles at the two Cardan joints are unequal, a condition prevailing in the important front-wheel-drive automobile steering-column application, then fluctuation in output velocity for a constant input velocity is minimized although not eliminated for zero relative phase angle.

Neel wall energy in thin films for unequal magnetization angles

The computer modelling of domain structure and switching in thin magnetic films involves the minimization of an energy functional, one component of which is the domain wall energy. Well-known expressions for this energy have been derived for both Neel and Bloch walls, using the assumption of an elliptically shaped pole distribution in the wall and equal angles of magnetization on either side of it. When a film is subjected to an external field however, the magnetization angles cannot remain the same under all conditions, and an expression is derived for the energy of a Neel wall that takes account of both the dipole and monopole energies present. An approximation to an elliptical distribution of both dipoles and monopoles is utilized to justify separate calculation of the energy contributions. Numerical computation of the wall energy is used to check the accuracy of this procedure. >

Inelastic buckling of single-angle, tee and double-angle struts

Abstract The inelastic flexural and flexural-torsional buckling of axially loaded, pin-ended single-angle, tee and double-angle struts are investigated theoretically. The calculated inelastic buckling loads are based on the tangent modulus concept, assuming idealised residual stress distributions in the strut sections. In the inelastic range, although the elastic flexural-torsional buckling loads for some struts are less than the elastic flexural buckling loads, results show that the inelastic buckling loads of the struts are not at all influenced by nor related to the elastic flexural-torsional buckling loads. It is found that flexural buckling mode is the dominant failure mode for most of the strut shapes, except for single unequal angles and for tees and double angles whose radii of gyration ratios, rx/ry, are greater than 1·0. Experimental results compare well with the ultimate strength curves, except for tee struts in which experimental buckling loads are consistently lower than the theoretical predictions.

An Analysis of Aeroengine Fan Flutter Using Twin Orthogonal Vibration Modes

Flutter prediction methods for aeroengine fans at present typically combine a complex aerodynamic analysis with a simple model of the mechanical behavior of the fan. In this paper a more sophisticated model of the mechanical response is used to investigate flutter and provide additional insight into the physical mechanisms involved. The model incorporates twin orthogonal modes, which are two independent vibration patterns similar in shape and resonant frequency but displaced 1/4 wave circumferentially in space. Flutter can be thought of as a self excited vibration in which the response of each blade in one mode generates aerodynamic forces on the blades which drive the twin mode—and vice versa. The flutter frequency can be determined by considering the phasing between the twin modes; whether flutter does actually occur (at this frequency) depends upon the relationship between the aerodynamic force coefficients and the amplitude response of each mode. The greatest tendency to flutter occurs when the twin modes are identical in frequency. For the more practical case of a frequency split between the modes the tendency to flutter decreases with increased frequency separation, and the vibration pattern becomes non-uniform. The non-uniformities include unequal blade amplitudes, unequal interblade phase angles, variation from blade to blade in the temporal phase between twist and flap within each individual blade, and a deflected shape which is not sinusoidal circumferentially.

Performance of distance protection applied to underground cables alone or mixed with overhead lines

The unequal impedance angles of the positive and zero sequence underground-cable impedances, which are in variance with overhead lines, requires a study to evaluate the appropriate relay residual compnesation factor, which is of paramount importance for earth faults. The problem, in many cases, is provoked when the protected zone consists of a mix of underground cables and overhead lines. This paper shows the importance of having an accurate residual vectorial compensation together with a proper selected comparator characteristic.

Cryptosteady-Flow Energy Separation

The mechanism of cryptosteady-flow energy separation is described and analyzed in its most general form, with full consideration of the effects of bearing friction or other rotor torque, and of such asymmetries as unequal discharge pressures, peripheral velocities, flow losses, prerotation velocities, and discharge angles. Equations are also developed for the proportioning of rotor nozzles in accordance with performance specifications.

The 2750-Å band system of phenol: Part II. Extended vibrational assignments and band contour analysis

Vibrational analysis of the electronic bands of phenol vapor at 2500–2900 Å has been extended to the a 1 modes of phenol- d 5 and the a 2, b 1, and b 2 modes of phenol- h 6, - d 1, and - d 5. The results give an essentially complete set of frequencies for the fundamentals lying below 2000 cm −1 in the excited state. Ground-state fundamentals to about 1000 cm −1 can be identified from “hot” bands in the electronic spectrum and are generally in good agreement with the infrared vapor absorption. The envelopes of A-, B-, and C-type bands have been calculated in the rigid rotor approximation for a range of values of the excited-state inertial constants. Features in the origin band contour are matched in the computed envelope when, and only when, the band is taken as B-type ( y-polarized); therefore the electronic transition is B 2 ← A 1, analogous to the B 2 u ← A 1 g transition of benzene. The changes in rotational constants accompanying the transition are Δ A = −0.0113 5 and Δ B = 0.00116 cm −1. Combined with micro-wave data for the ground state, these constants lead to approximate values for I a and I b in the electronically excited state. While the results are not sufficient for a structure determination, they show that the phenyl ring is almost certainly not a regular hexagon in the B 2 state, though the question whether the distortion is associated with unequal CC bond distances (“quininoid” structure) or unequal angles within the ring, or from a blend of both, cannot be decided. The picture that emerges is consistent qualitatively with the fact that torsional motion in the B 2 state is much more rigid than in the ground state, the torsional barrier being about 3.5 times greater. It therefore appears probable that the phenyl ring has appreciable quininoid character in the B 2 state.

Extrusion through single hole staggered and unequal multi-hole dies

Methods and the results of calculations for the pressure to cause end extrusion through perfectly smooth and rough wedge-shaped dies of small unequal angles are given and an examination is made of the effects on the pressure and obliquity of the emergent sheet of inclining the die orifice to the direction of the punch travel, using approximate methods.End extrusion through three holes of unequal size is considered for two different hypotheses and some calculated results are presented.Some cases of side extrusion through single and then two oppositely situated orifices are examined. Finally, a case of combined end and two side extrusions is considered.

A non-polarising spectrophotometer

The paper deals with a form of spectrophotometer in which uniform monochromatic patches of colour are compared, instead of the more usual arrangement of two portions of a spectrum. A spectrum is arranged so that the upper half has undergone selective absorption by the material under test, and a narrow region of the spectrum is selected by a slit. A split lens then forms two images of the dispersing prism face. These images are brought into juxtaposition by means of a rhomb-like prism with slightly unequal angles, which corrects the divergence of the two beams produced by the split lens. Photometric balance is secured by the partial closure of the lower portion of the selecting slit.