Clutches, Brakes, Coupling, And Flywheels

Clutches, Brakes, Coupling, and Flywheels Clutches, brakes, couplings, and flywheels are a group of elementsusually associated with rotation that have in common the functionof storing and/or transferring rotating energy In analyzing the performance of these devices we shall beinterested in: The actuating force The torque transmitted The energy loss The temperature rise

Two inertias, I1 and I2, traveling at the respective angularvelocities; ω1and ω2, one of which may be zero in the case ofbrakes, are to be brought to the same speed by engaging the clutchor brake. Slippage occurs because the two elements are running atdifferent speeds and energy is dissipated during actuation, resultingin a temperature rise.A simplified dynamic representation of a frictionclutch or brake is shown in Fig. 16-la

The varies types of devices to be studied may be classified asfollowing: Rim types with internal expanding shoes Rim types with external contracting shoes Band types Disk or axial types Cone types Miscellaneous types

A flywheel is an inertial energy-storage device. It absorbs mechanical energy by increasing its angularvelocity and delivers energy by decreasing its velocity. Figure 16-lb is a mathematical representation of aflywheel. An input torque Ti, corresponding to a coordinate θi, willcause the flywheel speed to increase. And a load or outputtorque T0, with coordinate θo, will absorb energy from theflywheel and cause it to slow down.Figure 16-lb

Static Analysis of Clutches and BrakesAnalyzing general procedure: Estimate, model, or measure thepressure distribution on the frictionsurfaces. Find a relationship between thelargest pressure and the pressure atany point. Use the conditions of staticequilibrium to find the braking force ortorque and the support reactions.The net force in the y direction:moment about C from the pressure:

sum of forces in the x-direction :sum of forces in the y-direction :sum of moment about the pin located at A:Can F be equal to or less than zero?

4.2 Internal Expanding Rim Clutches and Brakes often used in textile machinery, excavators, and machine toolswhere the clutch may be located within the driving pulley. Expanding ring clutches benefit from centrifugal effects; transmithigh torque, even at low speeds; and require both positiveengagement and ample release force. The internal-shoe rim clutch asshown in Fig. 16-3 consistsessentially of three elements: The mating frictional surface. The means of transmitting the torqueto and from the surfaces. The actuating mechanism.Fig. 16-3

To analyze an internal-shoe device, figure 16-4 shows ashoe pivoted at point A, with the actuating force acting at theother end of the shoe. Since the shoe is long, we cannotmake the assumption that thedistribution of normal forces isuniform. The mechanical arrangementpermits no pressure to be appliedat the heel, thus we will assumethe pressure at this point to bezero.Figure 16-4: internal friction shoe geometry

It is the usual practice to omit the friction material for a shortdistance away from point A. This eliminates interference, and thematerial would contribute little to the performance anyway, as willbe shown. Let us consider the pressure p acting upon an element of area ofthe frictional material located at an angle θ from the hinge pin(Figure 16-4). We designate the maximum pressure pa located at an angle θa fromfrom the hinge pin.

To find the pressure distribution on the periphery of the internal shoe,consider point BDeformation perpendicular to AB hΔɸ.From the isosceles Δ AOB, h 2 r sin(ө/2)h Δɸ 2 rΔɸsin(ө/2) rΔɸsin(ө)The deformation, and consequently the pressure, is proportional to sin θ.NB If the shoe is short, pa occurring at theend of the shoe, θ2. If the shoe is long, pa occurs at θa 90

This pressure distribution has interesting and useful characteristics: The pressure distribution issinusoidal with respect to theangle θ. If the shoe is short, as shown inFig. 16-6a, the largest pressure onthe shoe is pa occurring at the end ofthe shoe, θ2. If the shoe is long, as shown in Figure 16-6: Defining the angle θa atFig. 16-6b, the largest pressure on which the maximum pressure pa occursthe shoe is pa occurring atwhen(a)shoe exists in zone θ1 θ2 π/2θa 900(b)(b) shoe exists in zone θ1 π/2 θ2

When θ 0, Eq. (16-1) shows that thepressure is zero. The frictional material located at theheel therefore contributes very little tothe braking action and might as well beomitted. A good design would concentrate asmuch frictional material as possible inthe neighborhood of the point ofmaximum pressure. In this figure the frictional materialbegins at an angle θ1, measured from thehinge pin A, and ends at an angle θ2. Anyarrangement such as this will give a gooddistribution of the frictional material. The actuating force F has componentsFx and Fy and operates at distance c fromthe hinge pin.Figure 16-7: Forces on the shoe

normal force,The moment Mf of these frictional forces:The moment MN of normal force:The actuating force FMN Mfself-lockingthe dimension a must be such thatThe torque T:summation of the horizontaland vertical forces:MN Mf

The following assumptions are implied by the preceding analysis: The pressure at any point on the shoe is assumed to beproportional to the distance from the hinge pin, beingzero at the heel. This should be considered from the standpoint thatpressures specified by manufacturers are averages ratherthan maxima. The effect of centrifugal force has been neglected. In the case of brakes, the shoes are not rotating, and nocentrifugal force exists. In clutch design, the effect of this force must beconsidered in writing the equations of static equilibrium

The shoe is assumed to be rigid. Since thiscannot be true, some deflection will occur,depending upon the load, pressure, and stiffnessof the shoe. The resulting pressure distribution may bedifferent from that which has been assumed. The entire analysis has been based upon acoefficient of friction that does not vary withpressure. Actually, the coefficient may vary with anumber of conditions, including temperature,wear, and environment.

External Contracting Rim Clutches and Brakes The moments of the frictional and normal forcesabout the hinge pin are the same as for the internalexpanding shoes. Note: when external contracting designs are used as clutches, the effect of centrifugalforce is to decrease the normal force. Thus, as the speed increases, a larger value of the actuating force F is required.

Symmetrically Located PivotΔTo get a pressure-distribution relation, we note that lining wear is such as to retain thecylindrical shapeΔ This means the abscissa component of wear is w0 for all positions θ.If wear in the radial directionis expressed as w(θ),w(θ) w0 cos θ KPVtAs, w0/(KVt) constantp(ө) (constant) cosө pa cosөNormal forcedN pbrdө pa brcos(ө)dөThe distance a to the pivot is chosen by finding wherethe moment of the frictional forces Mf is zero.Substituting dNK a material constantP pressureV rim velocity, andt time

because of symmetrybecause of symmetryRx N andRy f NT afN

Band-Type Clutches and BrakesBecause of friction and the rotation of the drum, the actuating force P2 is less thanthe pin reaction P1Summation of force in y-direction:as sin(dө/2) dө/2Summation of force in x-direction:TorqueNormal forceas dN pdө

Machine systems can operate with intermittent motion. Starting and stoppingoperations can cycle frequently.Motion control elements permit machine systems to achieve intermittent motion.Motion Control elements: Clutches: Devices used to transmit power on an intermittent basis by connectingand/or disconnecting a driven component to and/or from the prime mover.– Motor operates efficiently at continuous speeds.– Avoids accelerating and/or de-accelerating the rotor of the motor each timea driven component of a machine needs to be cycled. Brakes: Device that absorbs the kinetic energy of a system and thus controls themotion of the system by slowing down the system and/or bringing the system torest.Functions of a clutch: Connect a rapidly turning shaft to one that is initially stationary. Cause two shafts to turn at the same speed and to do so in a manner that shockis not produced. Limit torque that is transmitted or to prevent torque from being transmitted in areverse direction.

16.5 Frictional-Contact Axial Clutches An axial clutch is one in which the mating frictional members aremoved in a direction parallel to the shaft. One of the earliest of these is the cone clutch, which is simple inconstruction and quite powerful. Advantages of the disk clutch include the more effective heat-dissipationsurfaces, the favorable pressure distribution. the large frictional area that can beinstalled in a small space, the freedom from centrifugal effects,

Let us now determine the capacity of such a clutch or brake in terms of thematerial and geometry. Figure 16-16 shows a friction disk having an outside diameter D and an insidediameter d. We are interested in obtaining the axial force F necessary to produce a certaintorque T and pressure p. Two methods of solving the problem,depending upon the construction of the clutch,are in general use. If the disks are rigid, then the greatest amountof wear will at first occur in the outer areas, sincethe work of friction is greater in those areas. After a certain amount of wear has takenplace, the pressure distribution will change soas to permit the wear to be uniform. This isthe basis of the first method of solution. Another method of construction employssprings to obtain a uniform pressure overthe area. It is this assumption of uniformpressure that is used in the second method ofsolution.Figure 16-16 a friction disk

Uniform Wear After initial wear has taken place and the disks have worndown to a point where uniform wear is established, theaxial wear can be expressed by :By definition uniform wear is constant from place to place; therefore,the total normal forceThe torque is found by integrating the product of the frictional force and the radius:substituting the value of F

Uniform Pressure When uniform pressure can be assumed over the area of the disk, the actuatingforce F is simply the product of the pressure and the area. This gives: The torque is found by integrating the product of the frictional force and the radius:substituting the value of F and noting p pa

Disk Brakes There is no fundamental difference between a disk clutch and a disk brake. The analysis of the preceding section applies to disk brakes too. We have seen that rim or drum brakes can be designed for self-energization While this feature is important in reducing the braking effort required, it also has adisadvantage. Depicted in Fig. 16-19 is the geometry of an annular-pad brake contact area.The governing axial wear equation isw f1f2KPVt The coordinate locates the line ofaction of force F that intersects the y axis.re which is the radius of an equivalentshoe of infinitesimal radial thickness.p the local contact pressure,the actuating forcethe friction torque TFigure 16–19 Geometry of contact area ofan annular-pad segment of a caliper brake.

The equivalent radius re can be found from fFre T The locating coordinate r bar of the activating force is found by taking momentsabout the x axis:Uniform Wear It is clear that for the axial wear to be the same everywhere, the product PV must be aconstant. The pressure p can be expressed in terms of the largest allowable pressurepa (which occurs at the inner radius ri) as : p p r /ra iand

Uniform PressureIn this situation, approximated by a new brake, p pa