Design and optimization of push-pull-shear lateral support of thin meniscus mirror

Influence of rheological properties of stirred liquids on the axial and tangential forces in a vessel with a PMT impeller

Primary mirror is an important component of collimator. The surface figure error of primary mirror is a critical factor affecting the imaging quality of collimator. Besides, the support system of primary mirror of collimator must be steady, while collimator need be moved safely as an elementary optical measuring tool. The support system of the primary mirror is composed of axial support and lateral support. Due to the axis of the primary mirror is horizontal when collimator working, the lateral support of the primary mirror has a far greater impact on the figure error of the primary mirror. In this paper, static structure analysis with finite element method is carried out for a 5m collimator primary mirror with V-block support under gravity load. With the analysis, the relationship between the structure parameters in primary mirror V-block support and the deformation of the primary mirror is built. With this relationship, the optimization parameters are found out to reduce the gravity deformation of the primary mirror.

In the context of the NASA CNES FIREBALL balloon borne experiment, we present the design of a semi-kinematic mount to hold the 1 meter class mirrors of this mission. To maintain these large optics in a reasonable mass and price budgets we choose thin ULE mirrors with a thickness over diameter ratio of 1/16. Such thin mirrors require a multi support mount to reduce self weight deflection. Classical multi support mount used for ground based telescope would not survive the level of shock observed in a balloon experiment either at parachute opening or landing. To firmly maintain these mirrors in several points without noticeably deforming them we investigated the design of a two stages semi-kinematic mount composed of 24 monopods. We present the detailed design of this innovative mirror mount, the finite element modeling with the deduced optical wavefront deformation. During the FIREBALL integration and flight campaign in July 2007 at CSBF, we confirmed the validity of the mechanical concept by obtaining an image quality well within the required specifications. Variants of this approach are potentially applicable to large thin mirrors on ground-based observatories.

In this paper, the radial and axial forces due to inrush and short circuit currents on both inner and outer surfaces of low voltage (LV) and high voltage (HV) windings are calculated. Static and dynamic aspects of these forces which are related to the variation of forces versus winding height and time are analyzed. Power transformer in the start-up mode and under short circuit fault is modeled using two-dimensional (2D) time stepping finite element method (TSFEM). This approach leads to the precise determination of the required signals including current, magnetic flux density, radial and axial forces. Calculated forces are analyzed significantly to compare impacts of the mechanical forces due to inrush and short circuit currents on the windings of the transformer. Three-dimensional (3D) TSFEM is utilized to evaluate aforementioned forces and compare with 2D TSFEM results. In the 3D TSFEM, geometrical and physical characteristics of the all components of the transformer, nonlinearity of the core materials and distribution of the primary and secondary windings are taken into account. 2D TSFEM results are verified by 3D TSFEM results.

A research pump intended for both flow visualization studies and direct measurement of hydrodynamic radial and axial forces has been developed. The impeller and the volute casing are constructed from Plexiglas which facilitates optical access for laser velocimetry measurements of the flow field both inside the impeller and in the volute casing. The pump housing is designed for flexibility allowing for each interchange of impellers and volute configurations. The pump rotor is supported by three radial magnetic bearings and one double acting magnetic thrust bearing. The magnetic bearings have been calibrated to characterize the force versus coil current and air gap relationship for each bearing type. Linear calibration functions valid for rotor eccentricities of up to 2/3 of the nominal bearing clearances and force level of ±58 N (13 lbf) and ±267 N (60 lbf) for the radial and axial bearings, respectively, were found. A detailed uncertainty analysis of the force calibration functions was conducted such that meaningful uncertainty bounds can be applied to in situ force measurements. Hysteresis and eddy current effects were quantified for each bearing such that their effect on the in situ force measurements could be assessed. By directly measuring the bearing reaction forces it is possible to determine the radial and axial hydraulic loads acting on the pump impeller. To demonstrate the capability of the magnetic bearings as active load cells representative hydraulic force measurements for a centered 4 vane 16 degree log spiral radial flow impeller operating in a single tongue spiral volute casing were made. At shut-off a nondimensional radial thrust of 0.084 was measured. A minimum nondimensional radial thrust of about 0.007 was observed at the nominal design flow. The nondimensional radial thrust increased to about 0.019 at 120 percent of design flow. The nondimensional axial thrust had a maximum at shut-off of 0.265 and decreased steadily to approximately 0.185 at 120 percent of design flow. Two regions of increasing axial thrust, in the flow range 75 to 100 percent of design flow, were observed. The measurements are compared to radial and axial force predictions using classical force models. The direct radial force measurements are compared to a representative set of radial force measurements from the literature. In addition, the directly measured radial force at design flow is compared to a single representative radial force measurement (obtained from the literature) calculated from the combination of static pressure and net momentum flux distribution at the impeller exit.

<div class="section abstract"><div class="htmlview paragraph">Presently, the automotive industry is being renovated with the help of an electrical machine, batteries, and power electronic components. In this technological shift, permanent magnet machines (PMSM) are mainly preferred for traction, because of their high efficiency and power density. The noise, vibration, and harshness (NVH) performance of the electrical machine is one of the main challenges, due to the tangential and radial electromagnetic forces. In this research study, a geometrical and electrical approach has been executed to reduce the radial force, which has a larger impact on vibration and noise. Initially, a permanent magnet synchronous motor with a V-shaped magnet configuration has been designed and the output performances are analyzed. The base structure (V-shaped magnet without duct) highlights that the radial force in the 12/3 and 12/12 order is higher, which will increase the vibration and noise of the motor. In this proposed geometrical approach, a duct has been introduced in the rotor outer periphery, which will reduce the airgap permeance and minimize the radial force. Different duct-shaped rotor configuration has been simulated using finite element analysis. The effectiveness of different duct shapes (like circle, rectangle, and ellipse) is analyzed and compared. The radial electromagnetic forces of a motor without duct and with duct have been provided. After placing the duct, the radial force was reduced which minimizes the vibration and noise. The ellipse duct rotor configuration shows better electromagnetic performance compared with rectangle and circle-shaped ducts. An electrical approach has been proposed to minimize the radial electromagnetic forces by injecting harmonic current and current angle on <i>d-</i>axis and <i>q-</i>axis. Finite element analysis with various results ensures the improved structure with an ellipse-shaped duct can reduce the radial force of the motor by around 36%.</div></div>

The Gemini primary mirror support incorporates a system of hydraulic whiffletrees to carry the mirror weight and define its position. The six orthogonal kinematic degrees of freedom are controlled by six hydraulic zones--three axial, two lateral, plus a transverse lateral. By varying the fluid volumes in these hydraulic zones the mirror position can be adjusted in all six degrees of freedom. Because of the finite lengths of the linkages that connect the mirror to the lateral supports, any shift in mirror position changes the amplitudes and directions of the applied forces with a resulting effect on the static balance and mirror figure. These effects have been calculated for mirror translations and rotations in all six degrees of freedom, resulting in predictions of the changes in the axial and lateral support forces and in the mirror figure. This paper describes the modeling as well as experimental verification of the results.

The accuracy and reliability of instrumented bicycle crank systems (i.e. power meters) is an important consideration for sport scientists who evaluate cycling performance and pedalling biomechanics. Many crank systems report power and or force/s on the left and right crank arms separately, or indexes of pedalling effectiveness, although crank systems that have genuinely independent force transducers on the left and right crank arms are rare. There is a need to be able to evaluate the accuracy and reliability of the measurements of power meters without the requirement for expensive and or complex instrumentation. The present study describes a relatively simple and novel method of assessing the accuracy and reliability of measures of crank angle, radial force and tangential force. The method is demonstrated in its application to an instrumented crank system (Axis Cranks ™). Reported crank forces were compared with actual applied forces to determine accuracy and some procedures used to assess the measurement of force were duplicated to determine reliability. The crank system measured crank angle with an average RMS error of 1.84 degrees across pedalling rates of 30-150 r/min. The absolute error of radial and tangential force measurements were 6% and 3.2% respectively (RMSE) and the relative error (accuracy of change in force) of radial and tangential force were 1.48% and 0.25% respectively (RMSE). Repeated measurements of force were found to be highly reliable (intra-class coefficient > 0.998). The method presented in this report could be used to evaluate the accuracy and reliability of other power meters and instrumented crank systems.

The actuator is a critical component of the micromanipulator. By utilizing the properties of expansion and contraction, the piezoelectric actuator enables the manipulator to handle and grasp miniature objects during micromanipulation. However, in piezoelectric ceramic disc actuators with conventional surface electrode configurations, the actuating force generated in the radial direction is relatively limited. When used as the actuation element of the manipulator, achieving regulation over a wide range of operating strokes becomes challenging. Therefore, altering the electrode structure is necessary to generate a greater radial force, thus enhancing the positioning and grasping capabilities of the operating arm. This paper investigates a piezoelectric actuator with interdigitated spiral electrodes, featuring a constant pitch between adjacent electrodes. The radial force was tested under mechanical clamping conditions, and the influence of the electrical signal was examined. The characteristics of the electrode structure were described, and the working principles of the piezoelectric actuators were analyzed. Theoretical equations were derived for the macroscopic characterization of the radial clamping force of the actuator, based on the piezoelectric constitutive equation, geometric principles, and Bond matrix transformation relationships. A finite element model was developed, reflecting the features of the electrode structure, and finite element simulations were employed to verify the theoretical equations for radial force. To prepare the samples, encircled interdigitated spiral electrode lines were printed on the PZT-52 piezoelectric ceramic disc using a screen printing method. The clamping force experimental platform was established, and experiments on the clamping radial force were conducted with electrical signals of varying waveforms, frequencies, and voltages. The experimental results show that the piezoelectric ceramic disc actuator with an interdigitated spiral electrode line structure, when excited by a stable sine wave operating at 200 V and 0.2 Hz, generated a peak force of 0.37 N. It was 1.76 times greater than that produced by a previously utilized piezoelectric disc with conventional electrode structures.

Simply by push-pull shear action at their outer edge, large circular telescope mirrors can be laterally supported free from bending distortion, if the upright mirror is kept in balance by a cosine distribution of weak axial forces applied at its outer rim and possibly also at the central hole. The flexure-induced comalike wave-front aberration of a thin 8-m meniscus mirror was reduced to an rms value of 0.5 nm over the full aperture; the largest path difference was reduced to 2.4 nm. A comparable result has also been calculated for a meniscus mirror of different geometry and a material with different elastic constants. Realizing such possibilities in practice demands accurate engineering. A helpful artifice is investigated for the correct application of the tangential supporting forces.

There are axial and radial electromagnetic forces between the stator and rotor of axial flux disk motor besides the useful torque. The electromagnetic forces act on the rotor and are crucial to the stable operation in magnetic levitation applications driven by disk motor. This article concerns the behaviors of axial and radial electromagnetic forces of disk motor using for cryogenic submersible pump. It is measured experimentally that the electromagnetic properties of motor materials, including the electrical conductor and magnetic conductor materials, in room temperature (RT) and liquid nitrogen (LN <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) environment. Then, the 3D finite element model (FEM) of the three-phase asynchronous disk motor in RT environment is built which is also validated by the RT experimental tests. Finally, the behaviors of axial and radial electromagnetic forces in LN <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> environment are investigated using the modified FEM taking account of the effect of cryogenic environment on the motor material. It is concluded that the axial electromagnetic force decreases monotonously with the increasing air-gap thickness or the decreasing rotating speed. When the rotor exhibits radial eccentricity, there is a restoring radial electromagnetic force, trying to pull the rotor back to the central position. The radial electromagnetic force increases with the increasing rotational speed and radial eccentric displacement.

When steel moment frames are subjected to seismic forces, H-shaped beams carry the gradient flexural moment. Large cross-section beams are used as main beams to design structural members effectively in real large space structures. Long span beams may not possess the plastic strength due to lateral buckling, so that many lateral braces along the beams should be set up to prevent the lateral bucking deformation (AIJ 1998). Most oy beams in frames are connected by continuous braces such as folded-roof plates, which are effective to prevent the lateral buckling oy beams. However, in the Japanese design code, non-structural members are not considered as the braces. On the other hands, there have been many moment resisting frames with dampers to prevent damages oy main frames recently, and then H-shaped beams connected with dampers are subjected to compressive axial forces in addition to gradient flexural moment. If the beam carries the large axial force induced by the damper during earthquake, the lateral-torsional buckling behavior oy H-shaped beam becomes more unstable than that under flexural moment only. The axial force which the beams carry is possible to exceed 30% oy yield load oy the beam. Therefore, in this paper, the lateral buckling behavior for H-shaped beams with continuous braces under gradient flexural moment and compressive axial force is clarified and elasto-plastic lateral buckling stress oy the beams or lateral stiffing force and rotational stiffing moment oy continuous braces are evaluated by the energy method and numerical analyses. In this study, for H-shaped beams with continuous braces subjected to gradient flexural moment and compressive axial force, two types oy loading conditions and two types oy bracing rigidities are considered. One oy the loading conditions, which is called as Type A, is the case that the upper flange's compressive load is larger than the lower flange's one in the left side oy beam as shown in Fig. 3(a), and another, which is called as Type B, is that the upper flange's compressive load is smaller than the lower flange's one in the left side oy beam as shown in Fig. 3(b). Furthermore, the ratio oy the compressive axial force, P2 to P1 is represented as an axial force ratio ‘p’ in equation oy elastic lateral buckling load. The continuous braces are divided into the lateral braces, ku, and rotational braces, kβ, as shown in Fig. 1. In the case oy TypeA, ku is effective for preventing lateral deformation oy compressive upper flange, whereas in the case oy TypeB, kβ, is effective for preventing torsional deformation. This study is conducted by the following procedures: 1. The equations oy lateral buckling loads oy H-shaped beams with continuous braces under gradient flexural moment and compressive axial force are derived by energy method. To simplify the equations by energy method, the new equations oy lateral buckling loads are suggested with reference to the terms oy the flexural and torsional rigidities oy beams, the rigidities oy braces, and condition oy the loads. 2. The elasto-plastic buckling behaviors oy the beams are simulated by elasto-plastic large deformation analysis. The lower bound oy the elasto-plastic buckling stress oy the beams can be evaluated with the interpolated buckling curve between those oy bending member and compression member, which are provided by Recommendation for Limit State Design oy Steel Structure (AIJ), depending on the axial force ratio. 3. The upper bound oy moment and lateral force which continuous braces carry at the lateral buckling oy beams is evaluated based on the ratio oy the flexural and torsional rigidities oy beams, the rigidities oy braces, the axial force ratio, and the gradient oy flexural moment.

A theoretical analysis of the lateral force as measured with a scanning force microscope is performed, showing that the lateral force signal contains a topography-induced component which is proportional to the slope of the surface, in addition to the signal arising from the tangential force. Measurements carried out on corrugated samples (gold, indium-tin-oxide, diamond) are analysed within the framework of this theory on the basis of a simple physical model for the forces, taking into account a repulsive normal force, a tangential friction force, and an adhesion force. The correlation between the lateral force and the topography is confirmed quantitatively. Furthermore, friction coefficients are determined and the influence of the adhesion force on the data is discussed.

The operation of a switched reluctance machine with eccentric rotor positions creates asymmetrical airgap flux distributions and results in unbalanced magnetic pull. This paper comprehensively investigates the static and dynamic radial force characteristics of an 18/12 switched reluctance machine with unbalanced operation. A powerful magnetic equivalent circuit (MEC) modelling approach is developed and allow fast and accurate force predictions with arbitrary excitation and position. The model calculates the instantaneous radial and tangential forces on the individual poles as well as the net forces on the rotor. The method is validated with finite element analysis (FEA) and against experimental results from a 12/8 machine. Static radial force characteristics are first developed. The MEC is then coupled with a time stepping algorithm to calculate the simultaneously varying electrical, mechanical, and magnetic variables for dynamic operation of the complete SR motor drive. Dynamic radial force behavior is examined, where parallel connected windings are found to naturally and significantly reduce the unbalanced magnetic pull. Variations of radial force with torque-speed operating point are also examined.

This paper is based on the theoretical analysis designs of a dry cutting orthogonal test in order to study a phenomenon that the radial force is larger than the main cutting force when a PCBN (polycrystalline cubic boron nitride) tool hard turns GCr15. Finite element modelling and cutting tests show the cutting depth and the spindle speed having an impact on the main cutting force, the radial force, and the axial force. In this study, due to the shear function of the cutting process, the squeezing effect between the tool and the workpiece, and the metal softening effect of the workpiece material, the different cutting depth and the spindle speed bring about different cutting force changes, and also different spindle speeds have different effects on the three components of the total cutting force. The research result provides a basis for further study on dry turning of hardened bearing steel.