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Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.

Example 2. An engine has the torque-angle curve given in Fig. 7.2. If the average speed at the flywheel is 2000 rpm and the output speed is allowed to vary by 2.5 percent, how large a flywheel is necessary if the loading torque is assumed constant The inertia of the other rotating parts, referred to the flywheel, is 0.11 lb s2 ft. The net area under the curve, using a planimeter, is 1156 lb ft. One machine cycle for the four-stroke engine consists of two crankshaft cycles. The average torque is therefore 1156/(4 ) = 92.0 lb ft. This average torque is shown as the dashed line in Fig. 7.2. The maximum and minimum velocities will occur at the points where the curve crosses this line. Each area between crossover points is measured and tabulated (see Table 7.2). The relative maxima and minima of the speed occur at the crossover points; therefore, the largest energy difference between any two crossover points will determine U. Since these two points will not necessarily be adjacent to each other, a running sum of the individual areas A + I through H is formed, starting at an arbitrary crossover point. The largest energy difference is then the maximum sum minus the minimum sum; in this case, U = 1106 ( 95) = 1201 lb ft. With = 2 (2000)/60 = 209.4 rad/s and Cs = 2(0.025) = 0.05, Eq. (7.2) gives J= 1201 0.11 = 0.438 lb s2 ft 209.42(0.05) (7.9)

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Note that if the engine were operated at a slower speed, Eq. (7.2) indicates that a larger flywheel would be necessary even if the torque-angle curve did not change.

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FIGURE 7.2 Torque-angle curve for the engine in Example 2. The dashed line indicates the average torque of 92.0 lb ft, and the shaded areas are the energy variations from the average speed. Sections A and I correspond to the values given in Table 7.2.

MemoryBugsViewController.mm ... #import "MemoryBugsViewController.h" #import "TestClass.h" #import "TestCPPClass.h" ...

Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.

7.2.3 Coefficient of Energy Variation The torque-angle relationship for an engine depends on the fuel, gas pressures, reciprocating masses, speed, and engine geometry [7.2]. The large variation that is possible between different engine designs shows that dynamic measurement or kinematic analysis is necessary to determine the torque fluctuation. It is often necessary, however, to come up with a rough estimate for preliminary design purposes or for checking the reasonableness of calculated values. For these purposes, the energy variation for an internal-combustion engine can be estimated by U = Cu KP (7.10)

where K = 33 000 lb ft rpm/hp [2 J rad/(W s)]. The coefficient of energy variation Cu can be approximated for a two-stroke engine with from 1 to 8 cylinders using the equation Cu = 7.46 (Nc + 1)3 (7.11)

Listing 11-1

and for a four-stroke engine with from 1 to 16 cylinders using the two-branched equation Cu = 0.8 0.015 |Nc 1.4|1.3 (7.12)

Finally, inside your MemoryBugsViewController class implementation, find the viewDidLoad method, and uncomment it.

Example 3. A 150-hp four-cylinder, four-stroke engine has a flywheel speed of 1000 rpm. Estimate the flywheel necessary for a 2 percent speed variation with a uniform load at an engine speed of 3000 rpm, neglecting the flywheel effect of the other rotating parts. Using Eq. (7.12), Cu = Then from Eq. (7.10), U = 0.22 33 000(150) = 363 lb ft 3000 (7.14) 0.8 0.015 = 0.22 |4 1.4|1.3 (7.13)

so that from Eq. (7.2), with = 2 (1000)/60 = 105 rad/s, J= 363 = 1.6 lb s2 ft 1052(0.02) (7.15)

7.2.4 Angular Fluctuation Certain machines, such as electric generators and magnetic digital storage systems, must maintain their angular position within a close tolerance of the constant-speed position. If the torque is known as a function of time, it can be integrated to deter-

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Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.

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