Mechanical Power

3 Key excerpts on "Mechanical Power"

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  eBook - ePub

  Basic Mechanics with Engineering Applications

  • J Jones, J Burdess, J Fawcett(Authors)
  • 2012(Publication Date)
  • Routledge

    (Publisher)

  power of the system which is applying the force. For example, the power of an engine is the rate at which the engine can do work on another system.

  The units of power are Js−1 , Nms−1 or in fundamental units, kgm2 s−3 . Power is often quoted in Watts (W) so that 1W = 1 Js−1 = 1 Nms−1 = 1 kgm2 s−3 .

  Using eqn (5.21) power may also be expressed as

  The term δr/δt is the magnitude of the velocity vector ν of the point of application of the force.

  in which θ can be interpreted as the angle between the force vector F and the velocity vector ν of the point of application of the force, as shown in Fig. 5.16 .

  FIG . 5.16

  When F and ν are given in terms of their components Fx , Fy and νx , νy eqn (5.3) shows that the power P can also be written in the form

  Similarly if the point of application of the force moves with ν = ds/dt along a curve C as shown in Fig. 5.17 then eqn (5.8) gives the power P as

  FIG . 5.17

  The power is therefore determined by the tangential component of the force Ft , and the velocity ν of the point of application of the force along its curve.

  From example 5.2 the work δW done by a moment, or torque, M can be written as

  The rate at which work is done by the moment is therefore

  For example, in a case where the moment M is applied to the end of a shaft, will be the angular velocity of the shaft.

  Example 5.4   Figure 5.18(a) shows the torque characteristic of a motor in which the torque M varies with its rotational speed ω such that

  Let us find how the power output of the motor varies with speed. From eqn (5.27)

  FIG . 5.18

  The speed at which maximum power is developed can be obtained by differentiating eqn (ii) with respect to ω and equating the result to zero, i.e.

  Thus, at maximum power,

  The graph of P against ω is as shown in Fig. 5.18(b) .

  When a motor with such a torque characteristic is used to drive a steady load, the size of the motor can be minimised by ensuring that the motor runs at a speed of ω0 /2 i.e. at its maximum power condition. If the required steady angular velocity ωL of the load is different from ω0 /2 it would be desirable to connect the motor and load together via a gearbox with speed ratio ω0 /2:ωL

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  eBook - ePub

  Higher Engineering Science

  • William Bolton(Author)
  • 2012(Publication Date)
  • Routledge

    (Publisher)

  5 Energy transfer

  5.1 Introduction

  This chapter is concerned with the energy transfers that can occur with mechanical systems. Energy can be transferred from one form to another by work being done or by heat transfer. Here we restrict the discussion to transfers involving work. There are many forms that energy can take and in this chapter potential energy, linear and angular kinetic energy and strain energy are discussed and the principles applied to the solution of mechanical system problems.

  5.1.1 Conservation of energy

  There is a basic principle that is used in all discussions of energy and that is that energy is never lost, it is only transformed from one form to another or transferred from one object to another. This is the principle of the conservation of energy. In any process we never increase the total amount of energy, all we do is transform it from one form to another.

  The principle of the conservation of energy is that energy is never created or lost but only converted from one form to another. In all such conversions, the total amount of energy remains constant.

  5.2 Work

  Work is said to be done when the energy transfer takes place as a result of a force pushing something through a distance (Figure 5.1 ), the amount of energy transferred W being the product of the force F and the displacement s of the point of application of the force in the direction of the force.

  Figure 5.1 Work

  Work done by a constant force W = Fs

  [1]

  With force in newtons and distance in metres, the unit of work is the joule (J) with 1 J being 1 N m.

  Consider the work done by a force F when the resulting displacement s is at some angle 0 to the force (Figure 5.2 ). We can look at this in two equivalent ways. We can consider the displacement in the direction of the force F is s cos θ and so the work done is:

  work done = F × s cos θ

  [2]

  Figure 5.2 An oblique force

  Alternatively, we can consider the force component acting in the direction of the displacement. The force can be resolved into two components, namely F cos θ in the direction of the displacement and F sin θ at right angles to it. There is no displacement in the direction of the F sin θ component and so it does no work. Hence the work done by the oblique force is solely due to the F cos θ

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  eBook - ePub

  Introduction to Energy Technologies for Efficient Power Generation

  • Alexander V. Dimitrov(Author)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  2

  Conversion of Thermal Energy into Mechanical Work (Thermal Engines)

  Energy-related (power) technologies may be treated as a combination of engineering-technical methods of energy and work conversion employed to facilitate human life. They are divided into two main groups. The first group comprises technologies of heat conversion into another type of energy (mechanical, electrical, electromagnetic, etc.) while the second one comprises technologies of heat transfer, accumulation, and regeneration. Each thermal technology discussed herein will be illustrated by specific physical schemes and devices. We shall consider them in the following order:

  •Technologies of mechanical work performance (so called thermomechanical technologies) •Technologies of generation of electrical energy (thermoelectric technologies) •Technologies of heat transformation (regeneration and recuperation) •Technologies of heat transfer and collection (transfer and accumulation) •Technologies creating comfortable environment (air conditioning and ventilation)

  Thus, we will treat a certain technology as an object of study of respective scientific-applied research fields, on one hand, and we will follow the teaching programs on “Power engineering,” “Transport management” and “General mechanical engineering,” on the other hand.

  2.1 Evolution of Engine Technologies

  As is known from physics, energy conversion follows a natural course, that is, energy of motion of macro- and microbodies (popular as mechanical energy) is converted into heat by mechanisms that are studied by tribology (including dry, semi-dry, viscous, or turbulent friction). No opposite transformation is observed in nature. Heat conversion into energy needed for the operation of machines and mechanisms was an impossible task for primitive people as well as for those living in slave-holding* and feudal†

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