Inertia

About: Inertia is a research topic. Over the lifetime, 12006 publications have been published within this topic receiving 164291 citations.

Hybrid machine modelling and control.

Abstract: Non-uniform motion in machines can be conceived in terms of linkage mechanisms or cams which transform the notionally uniform motion of a motor. Alternatively the non-uniform motion can be generated directly by a servo~motor under computer control. The advantage of linkage mechanisms and cams is that they are capable of higher speeds. They usually admit the means of introduction of dynamic balancing without extra parts and a high degree of energy conservation exists within the arrangement in motion. The advantage of servo~motors is that it is easier to re-program their motion to provide the versatility required of many manufacturing processes. To generate non-uniform mechanism motion, two alternative techniques are envisaged in the work presented. (i) where a servo-motor drives a linkage to produce an output. The motion transformation is determined with the geometry of the linkage. The mechanism acts as a non-uniform inertia buffer between the output and the motor. (ii) where a constant speed motor acts in combination with a servo-motor and a differential mechanism to produce the output motion of a linkage. Machines of these two kinds combine both linkage and a programmable driver. The first configuration is referred to a programmable machine, the second one is referred to as a hybrid machine. The focus of interest here is on the hybrid machine. One anticipated benefit, the second would have over the first, is that the size of the servo-motor power requirement should come down. In order to explore the idea an experimental rig involving a slider-crank mechanism is designed and built. Initially a computer model is developed for this so-called hybrid machine. The motion is implemented on an experimental rig using a sampled data control system. The torque and power relations for the system are considered. The power flow in the rig is analysed and compared with the computer model. The merits of the hybrid machine are then compared with the programmable machine. The hybrid machine is further represented with bond graphs. Lastly, the observations on the present work are presented as a guide for the development and use of hybrid machines.

Kirchhoff plate theory-based electromechanically-coupled analytical model considering inertia and stiffness effects of a surface-bonded piezoelectric patch

Abstract: As a compact and durable design concept, piezoelectric energy harvesting skin (PEH skin) has been recently proposed for self-powered electronic device applications. This study aims to develop an electromechanically-coupled analytical model of PEH skin considering the inertia and stiffness effects of a piezoelectric patch. Based on Kirchhoff plate theory, Hamilton's principle is used to derive the electromechanically-coupled differential equation of motion. Due to the geometric discontinuity of the piezoelectric patch, the Rayleigh–Ritz method is applied to calculate the natural frequency and corresponding mode shapes. The electrical circuit equation is derived from Gauss's law. Output voltage is estimated by solving the equation of motion and electrical circuit equation, simultaneously. For the purpose of evaluating the predictive capability, the results of the electromechanically-coupled analytical model are compared with those of the finite element method in a hierarchical manner. The outstanding merits of the electromechanically-coupled analytical model of PEH skin are three-fold: (1) consideration of the inertia and stiffness effects of the piezoelectric patches; (2) physical parameterization between the two-dimensional mechanical configuration and piezoelectric transduction; (3) manipulability of the twisting modes of a cantilever plate with a small aspect ratio.

Effects of structural vibrations on the film thickness in an EHL circular contact

Abstract: In elastohydrodynamic lubrication (EHL), one generally imposes force balance, i.e., the contact force resulting from the pressure in the contact is equal to the applied load. When studying the effect of structural vibrations, this force balance equation obviously does not hold and the more general equation of motion is required. In Wijnant and Venner (1996), an EHL contact model was introduced that incorporates both squeeze and entraining motion as well as the equation of motion. It was shown numerically that due to a small initial deviation or initial velocity, the rolling element starts an oscillatory motion around the equilibrium position. This motion is slightly damped because of the viscous losses in the lubricant. Moreover, it was shown that these oscillations cause film thickness modulations with a wavelength, directly related to the dimensionless frequency Ω. This paper compares results from experiments that were carried out on a ball and disk apparatus with results obtained with the EHL contact model. In this experiment, the applied load was rapidly increased by impacting a wedge between the base and the ball holder. This results in an increase of the contact area and, as a result of inertia forces of the ball, disk and supports, and oscillatory motion of the contacting bodies. Modulations in the film thickness which result from these oscillations, are clearly visible. The contact model was tailored to this experiment and a qualitatively close agreement has been found.

Brownian transport in corrugated channels with inertia.

Abstract: Transport of suspended Brownian particles dc driven along corrugated narrow channels is numerically investigated in the regime of finite damping. We show that inertial corrections cannot be neglected as long as the width of the channel bottlenecks is smaller than an appropriate particle diffusion length, which depends on the the channel corrugation and the drive intensity. With such a diffusion length being inversely proportional to the damping constant, transport through sufficiently narrow obstructions turns out to be always sensitive to the viscosity of the suspension fluid. The inertia corrections to the transport quantifiers, mobility, and diffusivity markedly differ for smoothly and sharply corrugated channels.

Numerical control unit for estimating movement parameters using a model

Abstract: A numerical control unit for controlling the position of a movable part, such as a machine table, in response to input machining information. The unit employs a servo control loop that detects the values of the position, velocity, acceleration and motor current for the movable part at predetermined times. Using such detected values and, on the basis of a representative spring mass system model, values of inertia, mass, viscous friction and sliding friction can be calculated and used for automatically optimizing the gain and offset parameters applicable to control of the machine.