Inertia Torque Research Articles

Organizing principles for single-joint movements. I. A speed-insensitive strategy.

1. Normal human subjects made discrete elbow flexions and extensions in the horizontal plane from a stationary initial position to visually defined targets at different distances with a constant inertial load or made flexions to a visually defined target with different inertial loads. We measured joint angle, acceleration, and electromyograms (EMGs) from two agonist and two antagonist muscles. 2. Subjects were instructed to move their limbs accurately but quickly to the targets. Movements of greater distances or lesser loads were performed at higher velocities. 3. Peak inertial torque, acceleration and velocity, movement time, and integrated, rectified EMG were all highly correlated with the task variables, distance and inertial load. We show that peak inertial torque can be used as a linking variable that is almost sufficient to explain all correlations between the tasks, the EMG, and movement kinematics. 4. The rate at which subjects initially developed torque to accelerate their movements was invariant over changes in the value of either task variable. The rising phase of the agonist EMG was also independent of the distance or load moved. 5. Two components were distinguished in the antagonist EMG. The first had a relatively constant latency and amplitude. It terminated on the onset of the second and larger component at a latency that was delayed as both distance and load increased. 6. The integrated, rectified antagonist EMG was proportional to inertial load and peak decelerating torque for changes in inertial load. When target distance varied, proportionality between peak decelerating torque and antagonist EMG could be found if correction was made for the effects of muscle length on the torque-EMG relationship. 7. We propose organizing principles for the control of single-joint human movements in which tasks are performed by one of two strategies. These are called speed-insensitive and speed-sensitive strategies. 8. A model is described in which movements made under a speed-insensitive strategy are executed by controlling the duration and the relative timing of amplitude invariant patterns of activation to the spinal motoneuron pools.

Inertial and Aerodynamic Torques on the Wings of Diptera in Flight

ABSTRACT The magnitude and distribution of the torques caused by inertial and aerodynamic forces on the wings of Diptera in flight are calculated. The bending torque at stroke reversal due to the inertia of the virtual mass of air bound to the wing is only slightly less than the torque due to the inertia of the wing mass itself. The maximum inertial torque due to both wing mass and virtual mass is usually slightly greater than the maximum aerodynamic torque encountered by the wings. Bending torques decrease rapidly away from the wing base. Pitching torques are much smaller than bending torques at the wing base, but do not decrease much until near the tip. The pattern of loading affects the wing design. Wings are thicker nearer the base to resist bending, but thin and light near the tip to minimize inertial energy expenditure. Their open, corrugated structure resists bending, while allowing them to be twisted as a result of the weak pitching moments.

Inertia, Viscous and Elastic Load Torque Simulator Using DC Separately Excited Generator Controlled by Microprocessor

The position and the speed control systems used in the industrial robots or the autonomous vehicles have to be developed for the load torque changing with time. However, it is difficult to set the load touque as a function of time by use of passive load, suth as the friction and the inertia mass.This paper describes the principle and the performance of a load torque simulator which is constructed by a dc generator and a current type dc amplifier and controlled by a micropocessor. The simulator is able to produce some kinds of torque such as inertia viscous and elastic load torque which has arbitrary magnitude and is set as a function of time. The responses of the dc motor coupled to the simulator are measured to verify the availability of this simulator. Furthermore, the responses calculated theoretically are also shown.

Inertial effects in rotating lyotropic liquid crystals

Abstract The orientation of the director of a lyotropic liquid crystal with negative anisotropy of the diamagnetic susceptibility is studied when the sample is spun at various speeds and angles from the magnetic field. Different behaviours is observed at low and high spinning speeds where the orientation is governed by the magnetic and the inertial torques, respectively. At intermediate frequencies it is possible to reach an equilibrium between these two torques. The evolution of this equilibrium with the average magnetic torque allows one to form a conclusion on the inertial nature of this effect.

Mathematical modeling and simulation of stepping motor systems

A mathematical model is developed for a variable reluctance stepping motor and then a numerical simulation is provided in view of studying the behaviour of the motor chiefly in dynamic start regime. The voltage equations are written considering the magnetic circuit unsaturated and the torque equation contains inertia, viscous friction and load torque components. The six first order differential equations of the model are solved using Basic language programs for a Wang 2200 computer. The motor is tested by numerical simulation in dynamic start regime with constant frequency of input pulses and also with different laws for varying this frequency determing the optimal law for motor acceleration. The method presented here for this aim is generally valid for a wide range of VR stepping motors.

Reflex and mechanical contributions to head stabilization in alert cats.

Five alert cats were tested for their responses to rotation in a device that allowed rotation of the head on the trunk about a vertical axis passing through the C1-C2 vertebral joint. Electrodes were implanted to record the horizontal and vertical electrooculogram and electromyographic (EMG) activity of the dorsal neck muscles splenius, biventer cervicus, and complexus. Head rotation and torque acting on the head were recorded in the horizontal plane during rotations in the 0.05-5.0 Hz frequency range. Responses were interpreted with reference to a closed-loop dynamic model of the head-neck system. Whole-body rotation (WBR) with no neck movement elicited a vestibulocollic reflex (VCR). Neck muscle EMG lagged the sinusoidal platform rotation by approximately 120 degrees at low frequencies, which represents a 60 degrees lead relative to a perfectly compensatory 180 degrees lag. This phase lead was related to the cumulative eye position of the accompanying horizontal vestibular nystagmus as reported by Vidal et al. Horizontal head torque exhibited a similar low-frequency behavior. At high frequencies, EMG exhibited a progressively increasing phase lead and gain increase typical of a second-order lead system as described in decerebrate cats. Torque, however, showed much less lead and gain increase, presumably because of the low-pass filter properties of the process coupling muscle excitation to torque. Head torque did exhibit a steep increase in gain with frequency and a phase approaching that of platform acceleration at high frequencies when weights were attached to the head to increase its moment of inertia. The same +40 dB/decade gain slope and phase approaching 0 degree was observed during WBR rotation of the anesthetized cat in which head inertia is the only factor contributing to the torque. This dynamic behavior was predicted by the inertial component of the model. In the alert unweighted cat, the inertial torque was smaller than VCR-generated torque at frequencies below 4 Hz. Rotation of the neck with the head held fixed in space (HFS rotation) elicited a cervicocollic reflex (CCR). Neck EMG response was very similar to that observed during WBR, both in dynamic behavior and overall gain. Torque, however, was consistently greater than that generated by WBR and showed a steady increase of 8 dB/decade as frequency rose. The added torque can be attributed to the viscoelastic properties of neck muscles. Driven rotation of the head on the fixed body elicited torques that could be closely approximated by a vector sum of torques observed during WBR and HFS rotations.(ABSTRACT TRUNCATED AT 400 WORDS)

The Diagnosis of Cylinder Power Faults in Diesel Engines by Flywheel Speed Measurement

A technique for estimating the power contribution of each cylinder in a multi-cylinder diesel engine is developed as an engine diagnostic capability. Robust magnetic sensors are used to obtain a waveform of engine speed fluctuations over one engine cycle under steady state operating conditions. Adopting a simplified model of engine dynamics, a computer processes the time history by application of the discrete Fourier transform to reproduce the crankshaft torque waveform. Subtracting the engine inertia torque provides an estimate of the gas pressure torque waveform, from which the power contribution of individual cylinders can be determined.

Research on Two-stroke Cycle Single Cylinder Vibrationless Reciprocating Engine Chain Saw Utilizing an Internal Gearing System : 1st Report, Analysis of This Engine and Numerical Computation

Forestry workers who use the chain saw, daily in their works are susceptible to vascular disease disorders of the fingers and hands, due to exposure to the severe vibration. This paper presents the structure, design, dynamics of machinery and numerical computation of the equivalent moment of inertia and loads acting on each portion of a new vibrationless chain saw. The perfect balance for this chain saw engine utilizing internal gearing system are theoretically analysed. The dynamic analyses of moving parts in this chain saw engine are explained. The output torque consists of gas pressure torque, minues the friction loss torque and inertia torque resulting from unevenness of rotation. The equation for output torque is the same as that or a conventional chain saw. However, the equivalent moment of inertia acting on the crankshaft is constant, regardless of crack angle, and is about 10 percent larger than that for a convential chain saw. The values of the moment of inertia, load conditions on each portion and the tooth force are obtained by numerical computations.

Adaptive microprocessor control of a linear helical reluctance motor

It has been shown previously that open-loop control, using a dedicated microprocessor, achieves a very satisfactory dynamic and static performance. However, this performance is only valid provided that output inertia and load torque do not vary.This paper extends the work to closed-loop operation in which a nonlinear sampled-data feedback controller is proposed. It is found that the resulting system resolution is inferior to that achieved with open-loop control and leads to the concept of two-mode control with open-loop control operating at input displacement demands below ±1°, to achieve good resolution. Finally an adaptive controller is implemented to cope with wide variation of load mass of about three times the rotor mass. Optimum dynamic resolution is of the order of ±0.25° (≡ ± 3× 10−3m).

The rotation of the Earth's inner core

The inner core rotates under the influence of inertial, frictional, electromagnetic and gravity torques. When its symmetry axis is inclined by an angle to the mantle symmetry axis, calculation shows the gravity restoring torque to be 2.50 x 1024cos01sin01N m, several orders of magnitude larger than the other torques combined. Investigation of its rotational dynamics under this torque shows that it can have two modes of steady precession. One mode involves a slow precession in space and is presumably ruled out because of the nearly diurnal relative motion required with respect to the outer core. The second steady precessional mode involves a rapid, nearly diurnal prograde motion in space and hence is slow in the mantle frame. Because the inner core is a good electrical conductor and because of its large rotational energy it is likely to have a strong interaction with the main magnetic field. In particular, if it is in the second steady precessional mode it may be carrying magnetic fields bodily for periods of several thousand years (its magnetic diffusion time) and the ‘dipole wobble’ of the main field, seen in historical measurements, and apparently extending into the palaeomagnetic record, may be a reflection of the influence of this motion on the outer core dynamo.

Mass and Angular Momentum Diagnostics of Cyclones within Numerically Simulated Linear Baroclinic Waves

The mass and angular momentum budgets of extratropical cyclones within three numerically simulated adiabatic linear baroclinic waves are investigated through quasi-Lagrangian diagnostics. The waves analyzed, wavenumbers 5, 11 and 17, were chosen to represent a range of baroclinically active horizontal scales observed in the atmosphere within which cyclonic circulations develop. Results are compared with diagnostics of an observed atmospheric cyclone in order to examine the extent to which linear baroclinic instability theory explains extratropical cyclone development in the real atmosphere. Diagnostics are computed in both isobaric and isentropic coordinates. In the isobaric framework, inward mass and angular momentum transport occurs in the lower troposphere of the linear cyclones while the transport is outward in the upper troposphere Upward transport of these quantities throughout the troposphere redistributes these quantities vertically. Within isobaric coordinates the mass and angular momentum budgets of the cyclones within linear waves resemble results from actual cyclones. Analysis of these linear model cyclones in isentropic coordinates shows that the mass and angular momentum transport is inward in upper isentropic layers and outward below. Angular momentum is transferred from upper to lower isentrople layers by pressure and inertial torques within the baroclinic structure. The vertical distribution of transport process and torques within linear baroclinic wave is in general agreement with the results occurring during the dry-baroclinic phase of development in a 1971 Alberta cyclone but differs markedly from the distribution observed during the moist-baroclinic phase. The major dissimilarity between the development of the model cyclones and leeside dry-baroclinic cyclogenesis is the existence of a much stronger eddy component of horizontal angular momentum transport in the model cyclones. A strong eddy transport is required for the cyclones to simultaneously deepen and spin-up over the flat terrain in the linear model, while such a transfer is not necessary for development over sloped topography.

Curvature Bias in the Florida Current off Miami

Abstract The evidences for and the mechanism of a negative curvature bias in the Florida Current off Miami are presented. The evidences consist of a re-examination of the data and tests by Schmitz (1969) and Stubbs (1971). Three different approaches are used in re-examining the first work, and all three clearly give a negative curvature bias. In revealing consistent evidence for a supergeostrophic flow, the second work supports the same bias. Thus bush works indicate a persistent tendency for fast, inertial flows to meander even when within a channel. Apparently tiggered by and hence tied to the channel constriction off Miami, the curvature mechanism involves a divergence with magnitude an order larger than the geostrophic divergence, and correspondingly large inertial torques in both the cross- and downstream directions.

A search for Chandler and nearly diurnal free wobbles using Liouville equations

Summary. The basic equations describing the dynamical effects of the Earth's fluid core (Liouville, Navier-Stokes and elasticity equations) are derived for an ellipsoidal earth model without axial symmetry but with an homogeneous and deformable fluid core and elastic mantle. We develop the balance of moment of momentum up to the second order and use Love numbers to describe the inertia tensor's variations. The inertial torque takes into account the ellipticity and the volume change of the liquid core. On the core—mantle boundary we locate dissipative, magnetic and viscous torques. In this way we obtain quite a complete formulation for the Liouville equations. These equations are restricted in order to obtain the usual Chandler and nearly diurnal eigenfrequencies. Then we propose a method for calculating the perturbations of these eigenfrequencies when considering additional terms in the Liouville equations.

A biomechanical model for actively controlled snow ski bindings.

Active control of snow ski bindings is a new design concept which potentially offers improved protection from lower extremity injury. Implementation of this concept entails measuring physical variables and calculating loading and/or deformation in injury prone musculoskeletal components. The subject of this paper is definition of a biomechanical model for calculating tibia torsion based on measurements of torsion loading between the boot and ski. Previous control schemes have used leg displacement only to indicate tibia torsion. The contributions of both inertial and velocity-dependent torques to tibia loading are explored and it is shown that both these moments must be included in addition to displacement-dependent moments. A new analog controller design which includes inertia, damping, and stiffness terms in the tibia load calculation is also presented.

Elastodynamics of Planar Mechanisms Using Planar Actual Finite Line Elements, Lumped Mass Systems, Matrix-Exponential Method, and the Method of “Critical-Geometry-Kineto-Elasto-Statics” (CGKES)

The article presents a general method for the elastodynamic analysis of planar mechanisms. It uses planar actual finite line elements (regular and irregular elements given in a companion article) and lumped mass systems to formulate the equations of motion of a mechanism. Damping coefficient matrix can incorporate time dependent viscous or coulomb damping coefficients in addition to the coefficients of velocity dependent internal damping. The forcing vector can incorporate any externally applied time dependent force or torque, inertial forces and inertial torques, any nonlinear viscous or Coulomb damping forces and torques. The matrix exponential method is introduced for the numerical solution of the equations of motion. Matrix displacement method of determining dynamic stresses using the generalized coordinate displacements is given. Elastodynamic analysis of a plane four-bar mechanism is performed for several cycles of kinematic motion, and the dynamic stresses are compared with those obtained by experiments. The method of “Critical-Geometry-Kineto-Elasto-Statics” (CGKES) is proposed for the computation of dynamic stress magnitudes making use of the critical geometry of the mechanism. It requires the analysis of a mechanism at the critical geometry position of the mechanism which is defined by the lowest fundamental frequency of the mechanism. The results predicted by the method of CGKES compares within two percent with the experimental results.

A study of an electrically driven inertial torque converter

A study of an electrically driven inertial torque converter

The Absolute Angular Momentum of Storms: Quasi–Lagrangian Diagnostics 2

The concept of absolute angular momentum and its time rate of change is developed for a translating vortex. Storm absolute angular momentum is defined to be the moment of the velocity about an origin translating with the center of the vortex. With this development in generalized coordinates, sources by transport and by internal torques are isolated. An integration over a storm volume reveals that for hydrostatic atmospheres, pressure, viscous, gravitational and inertial torques sum to boundary integrals. After the vector relations are established for storm absolute angular momentum, the component along the storm axis of rotation through the vortex is determined. By a systematic analysis, the physical basis for a geostrophic torque in an asymmetric baroclinic vortex is established. The role of the geostrophic torque is to transfer angular momentum vertically in isentropic coordinates. Angular momentum is extracted from an isentropic layer with an inward geostrophic mode of mass transport and given to a layer with an outward geostrophic mode. The vertical transfer across the isentropic layer occurs through pressure stresses. Two examples for the Midwest cyclone of 23 April 1968 are presented. Finally, the modes of mean and eddy transport of earth and relative angular momentum as well as sources for the azimuthally averaged storm absolute angular momentum are studied in isobaric, cartesian, and isentropic coordinates.

Computing Gearbox Torque and Motor Loading For Beam Pumping Units With Consideration of Inertia Effects

A method that considers inertia effects is presented for computing gearbox and motor loading on beam units. Previous methods neglected the inertia torques, which can be important when ultrahigh-slip prime movers are used. The method has practical application in determining the type of prime mover/beam unit combination to be used. Introduction During the past few years, ultrahigh-slip electric motors have been introduced for powering beam pumping units. These prime movers employ inertia effects to diminish equipment loading, particularly on the gearbox and the motor itself. The torque factor method accepted in the API standards does not consider inertia effects and so should not be expected to give correct answers when ultrahigh-slip prime movers are used. To provide a suitable computation prime movers are used. To provide a suitable computation method, two additional terms have been added to the API technique - rotary and articulating inertia torques. To account for inertias, it is necessary to measure instantaneous motor speed, an item previously not required in conventional dynamometer analysis. Once motor speed variations are known, it is possible to account for torsional work and kinetic energy interchanges as the rotary components accelerate and decelerate. Also, the torsional effects related to accelerations of the articulating components, primarily the beam assembly, can be computed. Two methods have been used to evaluate the various moments of inertia required in the analysis. The method most frequently used has been the direct calculation method, based on the engineering drawings of the unit components. The other method infers the moments of inertia by the manner in which the unit coasts to a stop after the motor switch is turned off. Review of Torque Computation Methods Two frequently used methods for inferring gearbox torque from a surface dynamometer card are the API torque factor method and an unnamed technique that is based on surface load range and unit stroke. The API torque factor method is based on the following equation. T = F (Q − Q) − M sin(0j +).........(1) The net torque is the difference between the rod load torque and the counterbalance torque. Rod load torque, Fj(Q RL -Q SU), is the product of the torque factor and the polished rod load corrected for structural unbalance of the polished rod load corrected for structural unbalance of the unit. The counterbalance torque, M sin (0 j + beta), opposes the rod load torque with a sinusoidally varying effect with amplitude M. Pumping-unit manufacturers usually publish a set of torque factors vs crank angle. To assist in relating crank angle to stroke position on the measured dynamometer card, corresponding stroke positions in nondimensional form are also published. Position zero refers to the bottom of the unit's stroke and position unity (1.0) denotes the top of the stroke. A sample set of torque factors and positions for a 120-in. unit equipped with a 456,000-in.-lb gearbox is shown in Table 1. A dynamometer card for an example well is shown in Fig. 1. To illustrate the torque factor method, the net torque at a crank angle of 60 degrees is determined as follows. According to Table 1, the crank angle of 60 degrees produces a nondimensional, polished rod position of 0.304 on the upstroke and a torque factor of 61.08 in. The polished rod load at this position is 15,036 lb. JPT P. 1153

The Coupling of the Core to the Precession of the Earth

The core follows the precession of the mantle by virtue of coupling to it. A simple model is presented which allows quantitative consideration of a superposition of both inertial and dissipative (electromagnetic) coupling torques. With the preferred value of the dissipative coupling coefficient, the dissipative mechanism accounts for only 2 or 3 per cent of the precessional coupling torque, but the dissipation amounts to about 3 times 10 Watts, which may suffice for a geomagnetic dynamo driven by precession. The dissipation itself is only weakly dependent upon the coupling coefficient and no assumption can lead to dissipation exceeding 10 W. This is much smaller than the loss of rotational energy by tidal friction; also it is hardly a significant contribution to the total core‐tomantle heat flux if we suppose that an adiabatic temperature gradient is maintained in the core, thus supporting the contention that the core contains potassium with a radioactive heat generation of order 10 W. Motion of the core is found to contribute to the semi‐annual terms of precession and nutation.

Balancing of Machines

A general method is presented for the complete balancing of a harmonic unbalance of any machine, including inertia forces, moments of the inertia forces, and inertia torques, utilizing six weights on three shafts in the machine parallel to the coordinate axes and rotating at the speed of the harmonic. For those cases where a full set of three shafts is not available, a method for optimizing unbalance is also presented, and illustrated by an example. In such cases the criterion for “best balance” must be carefully selected. This should be done to minimize some response to the unbalance.