In Fig P 32 Crank 2 is to Rotate Continuously

Bell-Crank

The conventional bell crank systems previously used by NREL to perform dual-axis testing are likely to be expensive due to the lateral space requirements (push rod length) and system mass required to sufficiently mitigate the flap/edge coupling and induced pitch moment.

From: Renewable and Sustainable Energy Reviews , 2012

'How to make a business out of Stirling engines today'

Allan J. Organ , in The Air Engine, 2007

16.5 Drive mechanism/kinematics

A proven mechanism for the single cylinder coaxial configuration is the bell-crank drive of Philips' MP1002CA air engine, shown in Fig. 16.3(a) to the conventions of mechanism synthesis (Johnson 1971), and denoted mechanism a. The work piston is subject to the effects of connecting-rod angularity. The displacer, on the other hand, is driven by near-straight-line motion.

16.3. 'Equivalent' linkages for (a) the drive mechanism of the MP1002CA and (b) the bell-crank/lever combination proposed for the VDF-750(aS).

An alternative is the linkage previously specified for an experimental hair drier engine (Organ 2001). This is shown in 'equivalent linkage' form at Fig. 16.3(b), and described in some detail in Appendices I and II. Here it becomes mechanism b. Near-straight line inputs to both piston and displacer minimize side loads on both. The feature is of greater consequence in the context of dry-running seals – as in the engine now proposed – than in the oil-lubricated MP1002CA.

No designer willingly takes an arbitrary decision. Invoking the formal study of linkages helps to make such a course unnecessary: Figs 16.3(a) and (b) are the 'equivalent linkage' forms. Both have eight links (L = 8) and ten joints (J = 10). Grübler's equation (Johnson 1971) gives number of degrees of freedom F:

16.3 $F=3\left(L-1\right)-2\mathrm{J}$

The arithmetic confirms the expectation of a single degree of freedom in both cases: F = 3(8 – 1) – 2 × 10 = 1, but suggests at first sight that there is nothing to choose between the two. Conversely, mechanism b has two ternary links vs the single ternary of mechanism a. The feature calls for a greater number of numerical dimensions for a complete geometric specification. The larger number translates into increased scope for tailoring the variations of volume with crank angle.

Mechanism a (that of the MP1002CA) does not as it stands encourage interchange of the points of attachment of piston and displacer. In other words, driving the piston via the bell crank and the displacer directly from the connecting rod promises to exceed the capacity of the latter for coping with side loads. Mechanism b does not suffer this limitation, so the piston could drive either joint S or joint T, and either joint T or S could drive the displacer. The feature amounts to further flexibility (if needed) in tailoring the volume variations. Moreover, mechanism b can sit below the cylinder unit, as in Fig. 16.3(b), or above, in which case the respective vertical excursions y _S and y _T are both reversed in algebraic sign, and the corresponding variations of volume with crank angle ϕ changed, affording yet further kinematic flexibility.

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Suspension Kinematics

James Balkwill , in Performance Vehicle Dynamics, 2018

7.2.11.1 Bell Cranks

Fig. 7.24 shows part of a suspension. The wheel moves an amount Δ _X1 as a result the bell crank rotates an amount Δ _θ1. This in turn means the spring is compressed by amount Δ _Y1. If the wheel now rises sufficiently that the bell crank is in position 2 and we again input a small displacement Δ _X2 of very similar in magnitude to Δ _X1 we see that the consequent compression in the spring is now only Δ _Y2, which is much less than Δ _Y1. Thus, the suspension has a falling rate. If the position of the spring and wheel are reversed, then it becomes a rising rate, and it is possible to achieve pretty much any desired function.

Fig. 7.24. Bell crank and variable installation ratio.

A graph of the installation ratio through the suspensions working displacement range can easily be determined by use of CAD or a kinematics package.

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Suspension

Heinz Heisler MSc., BSc., F.I.M.I., M.S.O.E., M.I.R.T.E., M.C.I.T., M.I.L.T. , in Advanced Vehicle Technology (Second Edition), 2002

10.13.3 Non-reactive bell crank lever and rod tandem axle bogie suspension ( Fig. 10.93(a and b) )

To overcome the unequal load distribution which occurs with the reactive balance beam suspension when either driving or braking, a non-reactive bell crank lever and rod linkage has been developed which automatically feeds similar directional reaction forces to both axle rear spring end supports (Fig. 10.93(a and b)).

Fig. 10.93(a and b). Non-reaction bell crank lever and rod

Both axle spring end reactions are made to balance each other by a pair of bell crank levers mounted back to back on the side of the chassis via pivot pins. Each axle rear spring end is attached by a shackle plate to the horizontal bell crank lever ends while the vertical bell crank lever ends are interconnected by a horizontally positioned rod.

When the vehicle is being driven (Fig. 10.93(a)) both axle casings react by trying to rotate in the opposite direction to that of the wheels so that the axle springs at their rear ends are pulled downward. The immediate response is that both bell crank levers will tend to twist in the opposite direction to each other, but this is resisted by the connecting rod which is put into compression. Thus the rear end of each axle spring remains at the same height relative to the chassis and both axles will equally share the vehicle's laden weight.

Applying the brakes (Fig. 10.93(b)) causes the axle casings to rotate in the same direction as the wheels so that both axle springs at their rear ends will tend to lift. Both rear spring ends are attached to the horizontal ends of the bell crank levers. Therefore they will attempt to rotate in the opposite direction to each other, but any actual movement is prevented by the interconnected rod which will be subjected to a tensile force. Therefore equal braking torques are applied to each axle and equal turning moments are imposed on each bell crank lever which neutralizes any brake reaction in the suspension linkage. Since there is no interference with the suspension height adjustment during braking, the load distribution will be equalized between axles, which will greatly improve brake performance.

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Manual gearboxes and overdrives

Heinz Heisler MSc., BSc., F.I.M.I., M.S.O.E., M.I.R.T.E., M.C.I.T., M.I.L.T. , in Advanced Vehicle Technology (Second Edition), 2002

3.4.1 Remote controlled double rod and bell cranked lever gear shift mechanism, suitable for both four and five speed transverse mounted gearbox (Talbot) (Fig. 3.10)

Twisting the remote control tube transfers movement to the first selector link rod. This motion is then redirected at right angles to the transverse gate selector/engagement shaft via the selector relay lever (bell crank) to position the required gear gate (Fig. 3.10). A forward or backward movement of the remote control tube now conveys motion via the first engagement relay lever (bell crank), engagement link rod and second relay lever to rotate the transverse gate selector/engagement shaft. Consequently, this shifts the transverse selector/engagement shaft so that it pushes the synchronizing sliding sleeve into engagement with the selected gear dog teeth.

Fig. 3.10. Remote controlled double rod and bell crank lever gearshift mechanism suitable for both four and five speed transversely mounted gearbox

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The strange case of the self-regulating air engine*

Allan J. Organ , in The Air Engine, 2007

8.3 Constructional details

Figure 8.2 is part-schematic to emphasize the detail of the crank linkage. The patent application reproduced as Appendix I describes its characteristics as a planar mechanism. Foremost among these is considerable kinematic flexibility. Achievable compression ratio appears higher than that afforded by separate cranks, or by a conventional bell-crank mechanism. There are the additional benefits of near straight-line actuation of both piston and displacer, and the accompanying reaction of the majority of side-thrust by rolling-element bearings. Appendix II is the algebra of the kinematics, which may be of use to those interested in coding the volume variations as input to computer simulation.

8.2. Crank and drive linkage. The small diameter of the crank web limits scope for dynamic balance, but size considerations prevailed for consistency with the aim of minimizing crank case volume. Outline specification in Table 8.1.

The piston drives twin connecting rods. These pivot on twin opposed gudgeon pins, each integral with, and cantilevered out from, plane arms secured by button-head socket screws against flats recessed into the sides of the piston skirt. Both ends of the connecting rod carry phosphor bronze bushes. Piston drive is via twin L-shaped bell cranks, while the displacer drive is from the single straight arm. The crank pin drives the twin bell-cranks through a drawn-cup needle roller race. The bell-cranks are pivoted to the drive arm linkage at a deep groove ball race. The beam link pivots on a deep groove ball race at a post located in a crank-case side plate.

The crank-case is of parallel, ruled shape inside and out, allowing manufacture by numerically controlled wire erosion. The internal shape is sculpted around the extremes of travel of the mechanism. With a view to keeping under-the-piston volume to a minimum, the internal cut-out is reused by dividing it into two identical halves and bolting one half to each side closure plate as boss-cum-spigot. Each boss is machined back so that, when the side plates are in position, a small lateral clearance remains either side of the mechanism.

The piston is fitted with a one-way flap valve of small flow capacity; the crank-case with a light-weight plastic disc valve. In conjunction, the two one-way valves ensure that minimum cycle pressure and peak crank case pressure coincide. The elevated mean cycle pressure calls for a rotary seal on the crankshaft. Peak pressure differential is not large, and the installed lip seal of a standard 2RS rolling-element bearing has served so far.

Displacer and expansion cylinder cap are fabricated from 0.5 mm thick drawn stainless steel tubing to AISI 316L specification. End plates are electron-beam welded into position. The annular gap around the displacer which serves as the regenerator began as a nominal 0.6 mm. The ideal value is that affording the optimum balance between the benefits of thermal regeneration and the penalties of dead space and flow resistance. Incrementally machining small amounts from the outside diameter of the displacer has already confirmed the sensitivity of brake output to gap size.

The ringless piston is of aluminium alloy HE15-TF. In the early, water-cooled arrangement shown in Fig. 8.3 it runs in a honed, cast-iron liner. The displacer rod is guided within a cylindrical boss integral with the piston crown. The displacer rod is attached at a spigoted flange to the base of the stainless steel displacer. The opposite end of the displacer rod attaches to the drive arm link via a clevis which accommodates the departure from straight-line motion. The angular excursion can be reduced ad lib by increasing the centres of the clevis.

8.3. Engine as originally assembled with water jacket as compression-end cooling provision.

The thicker of the crank-case side plates carries the main bearing housing with radial location by a cylindrical spigot. The housing is of aluminium alloy HE15-TF, and has two deep-groove ball races supporting the fabricated, cantilever crankshaft. The latter is of BS En-16 steel (range T) with case-hardened crank pin press-fitted with an interference. The outer ball race (only) is of 2RS (two rubbing-seal) type and acts as pressure seal.

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Forces and Equilibrium

K.M. SMITH C.ENG., M.I.E.E. , P. HOLROYD C.ENG., M.I.MECH.E., A.M.I.STRUCT.E. , in Engineering Principles for Electrical Technicians, 1968

Problems

1.1.

Find the reactions to the beams shown loaded in Fig. 1.42 and supported at A and B.

FIG. 1.42. ((a) R_A = 7·5 lbf, R_B = 10·5 lbf; (b) R_A = 6.3 kgf, R_B = 11·7 kgf; (c) R_A = 2·25 tonf, R_B = 4·75 tonf; (d) R_A = 66 lbf, R_B = 24 lbf; (e) R_A = 7·5 lbf, R_B = 13·5 lbf; (f) R_A = 25 lbf, R_B = 15 lbf.)

1.2.

A load of 2 tonf is being lifted by a crane using sling chains as shown in Fig. 1.43. Find the load in each leg of the sling chain for values of θ of 30°, 60° 90° and 120°. What conclusion can you draw from your answers?

FIG. 1.43.

(1·104 tonf, 1·154 tonf, 1·415 tonf, 2 tonf.)

1.3.

Two horizontal wires at right angles to each other are attached to the top of a pole. The pull in one wire is 240 lbf and in the other 280 lbf. What is the resultant pull on the pole and what would be the best angular position for a stay wire to be fixed?

(370 lbf; 130° from the 240 lbf in the opposite direction to the 90° angle.)

1.4.

Find the horizontal and vertical components of a force of 250 lbf acting in a direction 30° upwards from the horizontal.

(Horizontal component 217 lbf, vertical component 125 lbf.)

1.5.

Find the magnitude and direction of the equilibrant of the two forces shown in Fig. 1.44. What alteration must be made to this equilibrant in order that it may become the resultant of the two forces?

FIG. 1.44.

(36 lbf 145° from the 15 lbf in the opposite direction to the 60° angle. Change the sense.)

1.6.

Figure 1.45 shows the plan of a pole supporting two conductors each having a tension of 1000 lbf. Find the tension in the two horizontal stay wires S and T.

FIG. 1.45.

(S = 405 lbf, T = 550 lbf.)

1.7.

Four parallel forces act vertically downwards and are at equal distances of 3 in. apart. If the magnitude of the forces are 2, 4, 5 and 8 lbf respectively calculate the magnitude and position of the resultant force.

(19 lbf acting in the same line as the 5 lbf.)

1.8.

Figure 1.46 shows a bell-crank lever pivoted at O. Forces of 10 lbf and 15 lbf are applied on the vertical portion. Find the position of the footstep to enable the lever to be operated by a force of 20 lbf.

FIG. 1.46.

1.9.

Find the effort required to operate the lever shown loaded in Fig. 1.47. (15 lbf.)

FIG. 1.47.

1.10.

A "weightless" beam 15 ft long is simply supported at each end and is loaded as follows:

(a)

a load of 3 tonf acting vertically downwards at a point 6 ft from the left-hand end;

(b)

a load of 8 tonf acting vertically downwards at a point 6 ft from the right-hand end.

Draw the beam showing how it is loaded and find the upward force at each support. (U.E.I.)

(Right-hand support 6 tonf. Left-hand support 5 tonf.)

Answers are not given to the following questions:

1.11.

State clearly how a straight line may be used to represent the various features of a force. What force acting at right angles to one of 8 lbf will give a resultant of 12 lbf? State clearly the direction of the resultant force with reference to that of the 8 lbf.

1.12.

Explain what is meant by a Polygon of Forces.

Four forces are in equilibrium and act at a common point O. The forces are:

(ii)

Force A: 10 lbf acting horizontally left to right;

(ii)

Force B: 15 lbf acting at 60° anticlockwise to A;

(iii)

Force C: 15 lbf acting at 60° clockwise to A;

(v)

Force X: to maintain equilibrium.

Draw the force diagram to a scale of 1 inch to 5 lbf and hence find the magnitude of force X and its direction with respect to force A. (U.E.I)

1.13.

A load of 2000 lbf is suspended by two chains which are both fastened to the same point on the load. One chain makes an angle of 30° to the horizontal, and the other an angle of 45° to the horizontal. Find the force in each chain. Force scale 1 in. to 400 lbf. (U.L.C.I)

1.14.

A simple wall crane is shown in Fig. 1.48. Find the forces in the jib and tie when lifting a load of 500 lbf.

FIG. 1.48.

1.15.

A beam AB, 10 ft long, is simply supported at each end. A force of 30 lbf acts vertically downwards at a point 4 ft from A, a force of 20 lbf acts vertically downwards midway along the beam, and a force of 8 lbf acts vertically downwards at a point 2 ft from B.

Draw a sketch of the beam showing how it is loaded, and calculate the upward reaction forces A and B. (U.L.C.I.)

1.16.

State the Principle of Moments.

A bell-crank lever consists of a long arm, 8 $\frac{1}{2}$ in. long, and a short arm 4 in. long, at right angles to each other. Calculate the force to be applied at right angles to the end of the long arm to overcome a resistance of 40 lbf acting at 30° to the vertical of the short arm. Make a drawing of the arrangement.

(U.E.I.)

1.17.

Draw to scale the skeleton diagram of the bell-crank lever shown in Fig. 1.49 and measure any distance you require to find the effort required to operate the lever.

FIG. 1.49.

1.18.

A load of 50 lbf is supported by two cords, one of which makes an angle of 60° with the vertical. What must be the direction of the second cord so that the tension may be the least possible? Find the tension in the two cords in this case.

1.19.

A beam AB of uniform cross-section is 20 ft long and weighs 500 lbf. A load of 1000 lbf acts downwards 5 ft from A and a load of 750 lbf acts downwards 12 ft from A. Find the supporting forces at A and B assuming that for the purpose of taking moments the weight of the beam acts midway between the supports.

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A Programme to Integrate Horizontal Axis Wind Turbines into the Orkney Distribution System

D. Lindley , W.G. Stevenson , in Energy for Rural and Island Communities: Proceedings of the Second International Conference, Held at Inverness, Scotland, 1–4 September 1981, 1982

COMPONENT DESCRIPTIONS

Both machines are to have a synchronous generator and variable pitch rotor blade tips. The main features of the 20 m machine have been given in detail by Armstrong, Ketley and Cooper (6), and are outlined in brief below. Those for the 60 m machine are subject to revision as the design contract proceeds and cannot be specified in detail at this stage.

Rotor

The two bladed rotor is located upwind of the tower. The outer 20% of each blade can be feathered through 90° to provide power trimming and aerodynamic braking of the rotor. The structural element of each blade is a fabricated steel spar. This is enclosed in a GRP shell of aerofoil section with appropriate twist and taper, the space between the spar and shell being filled with foam. The tips are continuously moved via a bell crank and linkage system by a hydraulic actuator located in the nacelle.

Transmission

The rotor shaft is carried by two roller bearings mounted in a fabricated steel housing. The shaft carries at its aft end a two stage in-line gearbox. This is allowed to rotate against the action of springs and dampers. The mechanical compliance introduced in this way allows torque spikes from the rotor, caused by gusts, to be attenuated before reaching the generator and hence the grid.

The swinging gearbox removes the high frequency torque spikes whilst the low frequency surges are removed in combination with the movement of the blade tips which spill power. The power quality is thus maintained within limits acceptable to the grid system. A more detailed description of how this is accomplished has been given by Garrad (7).

The high speed gearbox output is connected to the generator by a one-way coupling. This allows the rotor to freewheel below synchronous speed, and prevents power being drawn from the grid during wind lulls. It also is helpful in the synchronisation procedure.

A disc brake is installed on the low speed shaft, and is capable of stopping the rotor from an overspeed condition in high winds with the tips unfeathered.

Nacelle

The power train components are mounted on a stiff steel frame which is in turn mounted on the tower by a standard crane slewing ring. The yaw drive is provided by a highly geared electric motor driving a pinion meshing with the outer gear of the slewing ring. A yaw brake is permanently applied to prevent dynamic instabilities and backlash in the gear teeth.

Tower

This is formed from a cylindrical steel tube mounted below the level of the rotor disc on a conical concrete frustum. An internal ladder leads to an external platform below the level of the nacelle; a ladder from this platform provides access to the interior of the nacelle.

Mode of Operation

The overall system is shown schematically in Figure 3.

Fig.3. ORKNEY 20m WTG INSTALLATION

There are two modes of operation:

(a)

Direct connected mode, in which the generator once having been driven to synchronous speed by the rotor is synchronised with the grid and delivers power as the rotor turns at a constant 88 rpm, and yields a wind speed versus power characteristic of a form shown in Figure 4.

Fig.4. 20m WTG POWER CHARACTERISTIC

(b)

Power conditioned mode (PCM) in which the rotor is allowed to vary in speed between 44 and 88 rpm, so as to follow the characteristic shown in Figure 5.

Fig.5. 20m WTG SPEED CHARACTERISTICS

Greater detail of the mode of operation and control systems have been given by Armstrong, Ketley and Cooper (6).

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Aircraft

MJ Cronin FRASS, FIEE, AIAA, IEEE (US) , in Electrical Engineer's Reference Book (Sixteenth Edition), 2003

47.5 Flight-control systems

Historically, the flight-control surfaces in early aircraft were operated directly by mechanical control cables (or torque tubes) running between the control stick and the surfaces. Such mechanical controls were in fact still used on modern aircraft such as the Lockheed L-1011. These systems though reliable are mechanically complex, as they involve many bell cranks, walking beams and differential levers, etc. The complexity of the design, the close manufacturing tolerances and the necessary adjustments (to minimise backlash problems, etc.) characterise this as a high maintenance support flight-control system. Given the prospective obsolescence of such mechanical systems, the aerospace industry moved to the adoption of electric/electronic flight-control systems based on the use of fly-by-wire (f.b.w.) and power-by-wire (p.b.w.) systems.

In a f.b.w. system, triple or quadruple redundant computers transmit a serial digital bit stream to the power electronics of the remote f.c.s. actuators, which operate the control surfaces. A block diagram of a typical f.b.w./p.b.w. system is shown in Figure 47.4 : the actuators can be duplex hydraulic jacks, electric or electrohydraulic. A view of a typical rotary electric actuator shown in Figure 47.5 is used for spoilers.

Figure 47.4. Digital fly-by-wire/power-by-wire system

Figure 47.5. Typical rotary electromechanical actuator. (Courtesy of Sundstrand Aviation)

Early f.b.w. systems used analogue data transmission and they go back to the early applications in the Mercury Space Vehicle (1960) and the XV-4B experimental aeroplane (in the mid-1960s): the US Air Force F-8 (1974) was the first aeroplane to adopt a digital flight control system (d.f.c.s.) (see Figure 47.6 ).

Figure 47.6. Genealogy of fly-by-wire systems

As discussed in Section 47.3, modern d.f.c.s.s brought to commercial and military aeroplanes benefits that were not possible with mechanical control systems. In addition to the ability to fly unstable aircraft, i.a.c.s provided better 'ride quality', eliminated (or damped) incipient wing-flutter conditions and allowed the aeroplane to fly through strong gust conditions without structural damage ( Figure 47.7 ). Computerised flight control (with different flight options) also became possible and autoland systems were implemented that could meet the FAA's (Federal Aviation Association) category IIIb/IIIc class conditions for landings in low-visibility conditions.

Figure 47.7. Benefits of integrated active controls

In the military aeroplane, manoeuvre load control (m.l.c.) is a feature that can be added to the d.f.c.s. and this enables the pilot to pull high g forces, during tight combat manoeuvres, without exceeding the vehicle's structural load limits. The d.f.c.s. also provides superior flight-management features in high-performance aircraft, which use interactive engine/f.c.s. controls. In these aircraft, the engine's two-dimensional thrust-vectoring system complements the flight-surface controls. The engine's sophisticated management system is typically effected via a computerised full authority digital electronic control system. These technologies are key to the complex control and flight management of aircraft such as the Harrier, AV-8A and other sophisticated aircraft.

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Vibration of pressure vessel shells in water

Carl T.F. Ross , in Pressure Vessels (Second Edition), 2011

6.3.1 Vibration of domes under external water pressure

It was not possible to vibrate all the small SUP domes under external water pressure because of the limits of the experimental apparatus available. This apparatus was similar to that used in Section 5.3.1 except for the tank, which is shown in Figs 6.13 and 6.14.

6.13. Method of exciting oblate domes under pressure.

6.14. Method of exciting the small prolate domes under pressure.

To excite the prolate domes, a bell crank mechanism was adopted, where the pivot position was changed, depending on whether an even or odd number of lobes was required, as shown in Fig. 6.14. The oblate domes were excited by applying an up-and-down motion to the noses of these vessels via a rubber strap and an electromagnetic shaker, as shown in Fig. 6.13.

Typical meshes are shown in Figs 6.15–6.20, where, because the tank was closed, and it was necessary to invert [H], P was assumed to be zero at the positions shown. These positions were at the top of the fluid, and also where the shell displacements were zero. Otherwise the tank boundary was assumed to be a natural one (i.e. ∂p/∂n  =   0, where n was a line normal to the tank boundary).

6.15. Mesh for dome/fluid (small closed tank). AR   =   1.

6.16. Mesh for dome/fluid (small closed tank). AR   =   0.44.

6.17. Mesh for dome/fluid (small closed tank). AR   =   4.

6.18. Mesh for dome/fluid (small closed tank). AR   =   3.5.

6.19. Mesh for dome/fluid (small closed tank). AR   =   3.

6.20. Mesh for dome/fluid (small closed tank). AR   =   2.5.

Comparison is made in Figs 6.21–6.27 between experimental and theoretical frequencies for different values of pressure ratio, where P  =   applied pressure; and P _cr  =   experimentally obtained static buckling pressure (Table 3.11).

6.21. Pressure effects on resonant frequencies of small hemi-ellipsoidal dome of aspect ratio 0.25.

6.22. Pressure effects on resonant frequencies of small hemi-ellipsoidal dome of aspect ratio 0.44.

6.23. Pressure effects on resonant frequencies of small hemi-ellipsoidal dome of aspect ratio 0.7.

6.24. Pressure effects on resonant frequencies of small hemi-ellipsoidal dome of aspect ratio 2.5.

6.25. Pressure effects on resonant frequencies of small hemi-ellipsoidal dome of aspect ratio 3.0.

6.26. Pressure effects on resonant frequencies of small hemi-ellipsoidal dome of aspect ratio 3.5.

6.27. Pressure effects on resonant frequencies of small hemi-ellipsoidal dome of aspect ratio 4.0.

From Figs 6.21–6.23 it can be seen that, for the oblate domes, as the pressure ratio is increased, the resonant frequencies tend to decrease, especially for the dome of aspect ratio 0.25, although this effect does not appear to be particularly significant for these vessels. The same argument does not, however, apply to the prolate domes, as can be seen from Figs 6.24–6.27, where an increase in the pressure ratio considerably decreases the resonant frequencies, and also causes the fundamental circumferential eigenmodes of vibration to become of similar form to the static buckling circumferential eigenmodes (Table 3.11). The fundamental resonant frequency of vibration at n  =   1 (i.e. for the cantilever mode) did not appear to have been affected by increasing the pressure ratio.

The experimental results for the oblate domes were not as good as those for the prolate domes, but this may be because of the experimental setup, where there was a possibility of dynamic pressure being produced by the up-and-down motion of the shell. That is, because of the up-and-down motion of the shell, there may have been dynamic suction when the shell moved upwards, and excess pressure when the shell moved downwards. This effect was less likely to occur for the prolate domes as their eigenmodes were of a sinusoidal nature, so that if part of the flank of a dome moved outwards another part of its flank moved inwards by a similar amount, and at the same time.

Unfortunately, it was not possible to excite the hemispherical dome experimentally when it was in the tank, because of the limitations of the apparatus that was available. However, a theoretical investigation of the hemispherical dome is shown in Fig. 6.28, from which it can be seen that when the pressure ratio was zero, a maximum value of resonant frequency appeared to occur when n approached infinity, but when p  =   0.95P _cr a saddle point was found at n  =   3, and a minimum value of resonant frequency was found at n  =   10 (i.e. the static buckling eigenmode was approached).

6.28. Vibration of small hemispherical dome under pressure theory, AR   =   1.0.

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Polymer nanocomposite components

S. Yousef , in Lightweight Composite Structures in Transport, 2016

16.2.3.1 Nonmetallic gear test rigs

The basic difference between test rigs is the loading mechanism as illustrated in the following. The Mk I test rig is considered the first polymer gear test rig, designed by Moa [45] and housed at the University of Birmingham, to measure endurance life and wear performance of polymer gear surfaces (mm/cycle) by applying additional friction on unreinforced and reinforced polymer gear materials, as shown in Fig. 16.23. During the test, external torque generated by a dead weight hanging on a load arm (lever) is applied to test gears and can be calculated by T  = WL/2, where W is the weight and L is the arm length.

Figure 16.23. A schematic of the Mk I test rig.

A.R. Breeds, S.N. Kukurek, K. Mao, D. Waltonb, C.J. Hooke, Wear behaviour of acetal gear pairs, Wear 166 (1993) 85–91 and N.A. Wright, S.N. Kukurek, Wear testing and measurement techniques for polymer composite gears, Wear 251 (2001) 1567–1578.

White (1999) built the Mk II to address some of the frailties of the Mk I and to make it more flexible as shown in Fig. 16.24. The applied external torque on the test gears results from an axial force generated by a dead weight hanging from a load arm mechanism that consists of a bell crank load arm, a piston, a cap, and a housing assembly. The open-loop test rig at the Océ research facility in Venlo, The Netherlands, was built to measure the traditional behavior of polymer gears as shown in Fig. 16.25, in addition to measuring advanced characteristics such as transmission errors, gear efficiencies, vibration, acoustics, and temperature continuously. The applied external torque on test gears is controlled by an advanced DSP type system, which can be set at various speeds and loads by means of optical encoders and a torque feedback loop. Fig. 16.26 shows the gear test apparatus developed by Kurokawa et al. [24] to measure the wear performance of plastic gears. The load acting on the gear results from power absorption by means of a powder clutch/brake.

Figure 16.24. A schematic arrangement of the Mk II test rig.

N.A. Wright, S.N. Kukurek, Wear testing and measurement techniques for polymer composite gears, Wear 251 (2001) 1567–1578.

Figure 16.25. A schematic arrangement of the Océ test rig.

K.D. Dearn, An Investigation into Tribological and Performance Related Aspects of Polymeric Gearing (Ph.D. thesis), The University of Birmingham, 2008.

Figure 16.26. The gear test apparatus.

M. Kurokawa, Y. Uchiyama, T. Iwai, S. Nagai. Performance of plastic gear made of carbon fiber reinforced polyamide 12, Wear 254 (2003) 468–473.

Senthilvelan et al. [25] developed a power absorption type gear test rig used for evaluating gear performance (noise and thermal performance). In this rig, the applied external torque on the test gears is established by a rheostat connected to the generator as shown in Fig. 16.27. Kim [26] at the Tribology Research Center, Korea Institute of Science and Technology, built and designed a test rig (power-circulating type) to inspect the characteristics of both wear and durability of polymer spur gears and to investigate power-transmission polymer spur gears, as shown in Fig. 16.28.

Figure 16.27. Schematic of power absorption type gear test rig.

S. Senthilvelan, R. Gnanamoorthy, Damping characteristics of unreinforced, glass and carbon fiber reinforced nylon 6/6 spur gears, Polymer Testing 25 (2006) 56–62.

The Forschungsstelle fur Zahnräder und Getriebebau (FZG) test machine is commonly used for gear tests, so several researchers depend on it to investigate wear, friction, and thermal behavior. The FZG design overall is close to that of the Mk I, but the loading mechanism in this test is generated by a loading coupling as shown in Fig. 16.29. Letzelter et al. [30] developed a new test bench to study the thermal behavior of polymer gears, as shown in Fig. 16.30. The surface temperature of gears is measured using a high-performance infrared camera to provide the temperature distribution. The load acting on the gear results from a resistive brake.

Figure 16.28. Schematic view of the gear test rig.

C. Hyun Kim, Durability improvement method for plastic spur gears, Tribol. Int. 39 (2006) 1454–1461.

Figure 16.29. Schematic view of the FZG (Forschungsstelle für Zahnäder und Getriebebau) gear test rig.

H. Imrek, Performance improvement method for Nylon 6 spur gears, Tribol. Int. 42 (2009) 503–510; H. Duzcukoglu, Study on development of polyamide gears for improvement of load-carrying capacity, Tribol. Int. 42 (2009) 1146–1153 and H. Duzcukoglu, PA 66 spur gear durability improvement with tooth width modification, Mater. Design 30 (2009) 1060–1067.

Figure 16.30. Diagram of the test bench. (1) Motor, (2) belt, (3) rotating shaft of pinion, (4) gears, (5) rotating shaft of gear, (6) bearings, (7) torquemeter, (8) brake, (9) infrared camera, (10) optical encoders.

E. Letzelter, M. Guingand, J.-P. de Vaujany, P. Schlosser, A new experimental approach for measuring thermal behavior in the case of nylon 6/6 cylindrical gears, Polymer Testing 29 (2010) 1041–1051.

Kirupasankar et al. [31] developed a test rig to study the performance of polymeric gears (transmission efficiency), as shown in Fig. 16.31, in which transmission efficiency   =   driven gear torque/driver gear torque. The loading application is similar to that of the loading mechanism of the power absorption gear test rig.

Figure 16.31. Schematic diagram of the polymer spur gear performance test rig.

S. Kirupasankar, C. Gurunathan, R. Gnanamoorthy, Transmission efficiency of polyamide nanocomposite spur gears, Mater. Design 39 (2012) 338–343.

Kodeeswaran [32] and Mohan [33] designed and built a new bending fatigue test rig design to evaluate the bending fatigue performance of nonmetallic gears. Mohan (2013) also evaluated some characteristics of dissimilar polymer gears, as shown in Fig. 16.32. The applied external torque on test gears is produced by a servo-hydraulic testing machine to give a linear motion; this motion is converted into rotary motion using a steel driver gear.

Figure 16.32. (a) Configuration of test rig. (b) Polymer gear fixation unit. (c) Mechanism layout of test rig.

M. Kodeeswaran, R. Suresh and S. Senthilvelan, Test rig design for bending fatigue performance evaluation of polymer based composite gears, in: iNaCoMM2013, 2013 and N. Anand Mohan, S. Senthilvelan, Preliminary bending fatigue performance evaluation of asymmetric composite gears, Mech. Mach. Theory 78 (2014) 92–104.

Finally, Table 16.1 shows the experimental conditions of most published polymer gear tests, including the polymer gear materials, the type of test rig used to carry out the test, and the main results.

Table 16.1. Nonmetallic gear materials, characteristics, test parameters and conditions, and results parameters according to Refs.[21,22,24–28,30,33–38]

Refs	Gear material	Test rig	Characteristics	Test conditions	Results
[21]	Acetal and nylon	Mk I test rig	Wear (mm)	Torque 7 Nm, speed 1000   rpm, No. of cycles 16   ×   104	Mk I test rig was designed and built to measure the wear rate of polymer gears.
[22]	PA 66, short glass fibers/PA, and long glass fibers/PA	Mk II test rig	Wear (weight loss)	With and without lubricant, torque 10 Nm, speed 1000   rpm, No. of cycles 5   ×   106	The results showed that there is considerable variation between wear rate measured by pin-on-disc and by gear test.
[24]	PA 6, 12, 66/carbon fiber	Gear test apparatus	Wear	Lithium type grease, torque 9.8, 19.6, 29.4 Nm, speed 100–500   rpm, No. of cycles 10   ×   106	The results show that PA 12/carbon fiber gear had an excellent wear resistance compared with other materials.
[34]	Nylon 66, glass and carbon-reinforced nylon 66	Power absorption type gear test rig	Damage mechanism and thermal resistance	Torque 1.5, 3   Nm, speed 1000   rpm, No. of cycles 5 million	Thermal resistance for nylon was improved by adding carbon fiber. Additionally, the composition and applied torque influence the failure mode.
[25]	Nylon, short glass/nylon, and carbon fiber/nylon 66	Power absorption type gear test rig	Noise and heat generation	Torque 0.5, 1.2, 1.8   Nm, speed 1000   rpm, No. of cycles 5 million	Nylon provides a lower noise compared to reinforced gears. Fiber/nylon provides a lower heat generation during service.
[26]	Nylon and acetal	Kim test rig	Wear vs rising temperature	Torque 9.8, 19.6, 29.4   Nm, speed 1273   rpm, No. of cycles 10   ×   106	A decrease in tooth surface temperature maintains the mechanical properties for longer time and reduces wear on nylon gears.
[35]	Nylon   +   glass fiber and acetal   +   PTFE	Mk I test rig	Wear rate and surface temperature	Torque 5–35   Nm, speed 1000   rpm, No. of cycles 1.2   ×   106	A new method for polymer composite gear design agreement with experimental test results.
[27]	Nylon 6	FZG	Load sharing, F/b	Torque 4.41, 6.62, 8.82   Nm, speed 1000   rpm, No. of cycles 107	The modification for tooth width resulted in lower tooth temperatures and increase in gear performance.
[28]	PA 6 + oil	FZG	Generated heat	Torque 6.12, 10.32, 16.53, 23.3 Nm, speed 1750   rpm, No. of cycles 4.2 × 105	The tooth surface temperature decreased after cooling holes were drilled on the tooth body; furthermore, the wear resistance was improved.
[36]	Acetal and nylon	Mk I test rig	Friction and wear	Torque 7 to 16.1 Nm, speed 1000   rpm, No. of cycles 1.2   ×   107	In dissimilar gears; the optimum performance occurred when acetal was used as the driver against nylon.
[30]	Nylon 66	New test bench	Temperature distribution	Torque 5, 10 Nm, speed 300, 600   rpm, time 600   min	The meshing temperature distribution was homogeneous.
[37]	Acetal	Mk I test rig	Effect of heat on wear	Torque 7 to 16.1 Nm, speed 1000   rpm, No. of cycles 2   ×   105	Acetal gear performance was entirely dependent on surface temperature.
[38]	PA, PEEK, and coated by PTFE, Molybdenum disulphide (MoS2), etc.	Mk I test rig	Friction and wear	Torque 7   Nm, speed 1500   rpm, No. of cycles 2   ×   106	The coating layer worked to protect polymer gears and provided the greatest reduction in frictional forces particularly for PTFE coating. Also failure mechanisms were focused in the coating layer.
[33]	Polypropylene and glass fiber/polypropylene	Bending fatigue test rig	Bending fatigue performance	Torque 1–20   Nm, speed 60, 90, 120   rpm, angular motion 1.7, 2.5, 3.4, 4.2, 5 degrees, deflection mode 1, 1.5, 2   Hz	The bending load carrying capacity of both symmetric and asymmetric gears was improved by adding carbon fibers.

PA, polyamide; PTFE, polytetrafluoroethylene; PEEK, polyether ether ketone; FZG, Forschungsstelle fur Zahnräder und Getriebebau.

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