Design of Machinery: An Introduction to the Synthesis and Analysis of Mechanisms and Machines

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Unformatted text preview: Chapter MULTICYLINDER ENGINES TOPICIPROBLEM MATRIX SECT TOPIC PROBLEMS 14.5 Shaking Moment in Inline Engines 148. 14—9 14.6 Even Firing 14—1. 14—2, 14-3, 14-4, 14—5. 14-6, 14-7, 14-19, 14-20 14.7 Vee Engine Configurations 1440, 14-11, 14-12. 14-21, 14-22 14.8 Opposed Engine Configurations 14—13, 14-14 14.9 Balancing Muiticylinder Engines 14-15, 14-16, 1447, 14-18 DESIGN OF MACHINERY SOLUTION MANUAL 14—1-1 fig PROBLEM 14-1 Statement: Draw a crank phase diagram for a three-cylinder inline engine with a 0, 120, 240-deg crankshaft and determine all possible firing orders for a. Four-stroke cycle. b. Two-stroke cycle. Select the best arrangement to give even firing for each stroke cycle. Solution: See Mathcad file P1401. . Even firing is possible with both two and four stroke designs. A l, 2, 3 firing order is required for the two-stroke and a l, 3, 2 firing order for the four-stroke. Phase rr TDC «r mo ‘ a. Four—stroke cycle "'9'" CV" /' Li ~ / 1 Exhaust ” empress a 1 l? W a» Power lntakfegi «r i mc A i E is 120 2 measth Congress “)7 > Intake 1 i Power //F‘ i //_ TDC I / I r If If ,, ,4_g / - r Corrpress [I Exhaustl f 240 3 ~ * ' i t > Jr” 2 flake I o 180 380 540 720 CrankAngle # TDC ’ TDC Phase l f/ , ‘ / ‘ ‘ b. Two—stroke cycle We cyl' / 1 7 ‘/ ’ 1 a 1 i 5 , - Poweri i ‘ Power fi 71x: § k mc / l I/ 7 // i i __ fl 1 _ V l , r i -12 2 . ~ ‘ > ° i PM u I 0 180 360 540 720 Crank Angle DESIGN OF MACHINERY SOLUTION MANUAL 14-2-1 £3 PROBLEM 14-2 Statement: Draw a crank phase diagram for an inline four-cylinder inline engine with a 0, 90, 270, ISO-deg crankshaft and determine all possible firing orders for a. Four-stroke cycle. b. Two-stroke cycle. Select the best arrangement to give even firing for each stoke cycle. Solution: See Mathcad file P1402. l. The two-stoke has even firing but even firing is not possible with this four stroke design. The best firing order is l, 2, 4, 3 for the two-stroke and l, 4, 3, 2 for the four-stroke. Phase [— TDC r’r TDC Angle / l l / l . a. Four-strokec cle - , ‘___ v 4 l y W Erhaust ’/ Compress A D 1 ‘ Power Intake 3 r E7130 3 r 3113c i é _ a i 1 42ml,“ 5, I Commas 1’ 3.; -90 2 1 . > Intake 1 1 Power ‘ “F6 2 I l r'" //’ TDC ‘ f/ 3 f/ 270 3 Compress / 3 Exhaust K F _ -take 3 Power I i In- : ‘—'J : 5 (/fi TDC l // TDC E / r/ Compress Exhaust ” -180 4 i > Power Intake ‘ o 130 360 540 720 Crank Angle Phase b. Two-stroke cycle “9‘9 o + -270 i 3 ,, -180 4 I E A DESIGN OF MACHINERY SOLUTION MANUAL 14-3-1 fig PROBLEM 14-3 Statement: Draw a crank phase diagram for a 45-deg vee, four-cylinder engine with a 0, 90, 270, l80-deg crankshaft and determine all possible firing orders for a Four-stroke cycle. b. Two—stroke cycle. Select the best arrangement to give even firing for each stroke cycle. Solution: See Mathcad file P1403. 1. Neither stroke has even firing with this design. The best firing order is l, 2, 4, 3 for the two-stroke and l, 4, 3, 2 for the four-stroke. r TDC r TDC Phase cyl / L l/ 1 ; a. Four-stroke cycle Mg“? ' ‘_____ / l l o 1 / W“ i/ W - Power : Intake 3 F TDC r imc 3 a ,/ 1 § 90 2 / Comess V ‘ E __ ' Intake ‘ LPouer 1» E ‘ TDC TDC i /i/_ I / ‘ >A l/r 270 3 [Countess i 3 Exhaust ,4 fled ; fl #5 : h TDC . r TDC 5 / i 5 y/ E (Impress 1 am: ’ 3 48° 4 k : Power I i Intake 2 ’ — E —~——~J‘ 3 ' 1&0 360 5410 720 Crank Angle f“ TDC /* TDC Phase cyl / l 2 / 1 1 b. Two-stroke cycle N‘g’e ' ‘—' /’ in; a 1 J - ,iki PM” Emc E r anc f 2 a a // i A ' ‘ f me E TDC /3 i / /3 .270 3 3 — 3 //" 1pc ‘ If m ; J/ /" ‘ ’I L = I 7.. .150 4 g 3 1 o 130 360 540 7:0 Crank Angle DESIGN OF MACHINERY SOLUTION MANUAL 14-4-1 fig PROBLEM 144 Statement: Draw a crank phase diagram for a 45-deg vee, two-cylinder engine with a 0, 90-deg crankshaft and determine all possible firing orders for a. Four-stroke cycle. b. Two-stroke cycle. Select the best arrangement to give even firing for each stroke cycle. Solution: See Mathcad file P1404. 1. Neither stroke has even firing with this design. The only possible firing order is 1, 2 for either stroke-cycle. Phase I”! mc / me I- ’i 3 fl ‘ 1 a. Four-stroke cycle “9'9 Cy / 1/ ' o 1 I - Pawer Intake 3 — ' l r 7136 : r TDC / /1 Ex / ‘ ’A—y/ i —‘ —9o 2 2,“ W” ‘ ‘ .4. "7M5 5 L, o 180 360 540 7é0 CrankAngle Cl ff mo ‘ (If we ‘ ‘ b. Two-stroke cycle We 3" 1/ ‘ I! o 1 l i i i - 3e mo ‘ r TDC // / i W, / , ,4,i7, DESIGN OF MACHINERY SOLUTION MANUAL 14-5-1 5 PROBLEM 14-5 Statement: Draw a crank phase diagram for a 90-deg vee, two-cylinder engine with a 0, ISO-deg crankshaft and determine all possible firing orders for a. Four-stroke cycle, b. Two-stroke cycle. Select the best arrangement to give even firing for each stroke cycle. Solution: See Mathcad file P1405.. Neither stroke has even firing with this design. The only possible firing order is 1, 2 for either stroke-cycle. a. F our-stroke cycle b. Two-stroke cycle 0 180 360 540 720 Crank Angle DESIGN OF MACHINERY SOLUTION MANUAL 14—6-1 fl PROBLEM 1445 Statement: Draw a crank phase diagram for a ISO-deg opposed, two-cylinder engine with a 0, ISO-deg crankshafi and determine all possible firing orders for a. Four-stroke cycle. b. Two-stroke cycle. Select the best arrangement to give even firing for each stroke cycle. Solution: See Mathcad file P1406. 1. Both stroke-cycles are even firing but the two—stroke looks like a four-stroke in its firing pattern since the second set of firing pulses is on top of the first set. The only possible firing order is 1, 2 for either stroke-cycle. r 700 (r me We Cyl. / i / i a. Four-stroke cycle 0 1 1 Exhaust ’ Empress _ PM” ,flfi‘ii § i 7 rec ‘ r TDC ~180 2 Ex 1 '- Intake Power 0 180 720 CrankAngle (r 7130 f we Angle Cyl. / W W; // b. Two-stroke cycle I“ f o 1 Power Power 3 F TDC r TDC i / 1 4’ v .. 18° 2 Power Power DESIGN OF MACHINERY ,6 PROBLEM 14:! Statement: Solution: 1 . crankshaft and determine all possible firing orders for a. Four-stroke cycle. b. Two-stroke cycle. Select the best arrangement to give even firing for each stroke cycle. See Mathcad file P1407. SOLUTION MANUAL 14-7-1 Draw a crank phase diagram for a ISO—deg opposed, four-cylinder engine with a 0, 180, 180, 0-deg Both stroke-cycles are even firing but the two-stroke looks like a four-stroke in its firing pattern since the second set of firing pulses is on top of the first set. The best firing order is l, 2, 4, 3 for the two-stroke-cycle and 1, 2, 3, 4 for the four-stoke. a. Four-stroke cycle b. Two-stroke cycle -180 480 Cyl. DESIGN OF MACHINERY SOLUTION MANUAL 14—8-1 g PROBLEM 14-8 Statement: Calculate the shaking force, torque and moment balance conditions through the second harmonic for an inline three-cylinder engine with a 0, 120, 240 deg crankshaft. Assumptions: Use File F 14-12.eng for the cylinder data required on the cylinder input screen. Solution: See program ENGINE files Pl4082.eng, Pl4084.eng, and Mathcad file Pl408.mcd. 1. Open file Pl4082.eng in program ENGINE for the two-stroke cycle or file Pl4084.eng for the four-stroke cycle. The problem setup data is input fiom the disk file. Click the Calculate button and then the Dane button, which will return you to the Home screen. Click the Balance button, accept the values shown and click Calculate and then Done, which will return you to the Home screen. Click the Assemble button, accept the values shown and click Calculate and then Done, which will return you to the Home screen. View the calculated results by clicking on the Charts drop-down menu, item the main option bar, or use the Plot or Print buttons on the Home screen. DESIGN OF MACHINERY SOLUTION MANUAL 14-9-1 fig PROBLEM 14-9 Statement: Calculate the shaking force, torque and moment balance conditions through the second harmonic for an inline four-cylinder engine with a 0, 90, 270, 180 deg crankshaft. Assumptions: Use File F l4-12.eng for the cylinder data required on the cylinder input screen. Solution: See program ENGINE files P14092.eng, Pl4094.eng, and Mathcad file P]409.mcd. 1. Open file P14092.eng in program ENGINE for the two-stroke cycle or file P14094.eng for the four-stroke cycle. The problem setup data is input from the disk file. Click the Calculate button and then the Dane button, which will return you to the Home screen. Click the Balance button, accept the values shown and click Calculate and then Done, which will return you to the Home screen. Click the Assemble button, accept the values shown and click Calculate and then Done, which will retum you to the Home screen. View the calculated results by clicking on the Charts drop-down menu, from the main option bar, or use the Plot or Print buttons on the Home screen. DESIGN OF MACHINERY SOLUTION MANUAL 14-10-1 ,6 PROBLEM 14-10 Statement: Calculate the shaking force, torque and moment balance conditions through the second harmonic for an 45-deg vee, four-cylinder engine with a 0, 90, 270, 180 deg crankshaft. Assumptions: Use File F14-12.eng for the cylinder data required on the cylinder input screen. Solution: See program ENGINE files P14] 02.eng, P14104.eng, and Mathcad file P1410.mcd. 1. Open file P14102.eng in program ENGINE for the two-stroke cycle or file Pl4104.eng for the four-stroke cycle. The problem setup data is input from the disk file. Click the Calculate button and then the Dane button, which will return you to the Home screen. Click the Balance button, accept the values shown and click Calculate and then Done, which will return you to the Home screen. Click the Assemble button, accept the values shown and click Calculate and then Done, which will return you to the Home screen. View the calculated results by clicking on the Charts drop-down menu, fiom the main option bar, or use the Plot or Print buttons on the Home screen. DESIGN OF MACHINERY SOLUTION MANUAL 14-11-1 fl PROBLEM 14—11 Statement: Calculate the shaking force, torque and moment balance conditions through the second harmonic for an 45-deg vee, two-cylinder engine with a 0, 90 deg crankshaft. Assumptions: Use File F 14-12.eng for the cylinder data required on the cylinder input screen. Solution: 1. See program ENGINE files P14112.eng, P14114.eng, and Mathcad file P14] l.mcd. Open file P141 12.eng in program ENGINE for the two—stroke cycle or file P141 l4.eng for the four-stroke cycle. The problem setup data is input from the disk file. Click the Calculate button and then the Dane button, which will return youto the Home screen. Click the Balance button, accept the values shown and click Calculate and then Done, which will return you to the Home screen. Click the Assemble button, accept the values shown and click Calculate and then Done, which will return you to the Home screen. View the calculated results by clicking on the Charts drop-down menu, from the main option bar, or use the Plot or Print buttons on the Home screen. DESIGN OF MACHINERY SOLUTION MANUAL 14—12-1 5 PROBLEM 14-12 Statement: Calculate the shaking force, torque and moment balance conditions through the second harmonic for an 90-deg vee, two-cylinder engine with a 0, 180 deg crankshaft. Assumptions: Use File F 14-12.eng for the cylinder data required on the cylinder input screen. Solution: See program ENGINE files P14 122.eng, P14124.eng, and Mathcad file P1412.mcd. 1. Open file Pl4122.eng in program ENGINE for the two-stroke cycle or file Pl4124.eng for the four-stroke cycle. The problem setup data is input from the disk file. Click the Calculate button and then the Dane button, which will return you to the Home screen. Click the Balance button, accept the values shown and click Calculate and then Done, which will return you to the Home screen. Click the Assemble button, accept the values shown and click Calculate and then Done, which will return you to the Home screen. View the calculated results by clicking on the Charts drop-down menu, fiom the main option bar, or use the Plot or Print buttons on the Home screen . DESIGN OF MACHINERY SOLUTION MANUAL 14-13-1 fig PROBLEM 14-13 Statement: Calculate the shaking force, torque and moment balance conditions through the second harmonic for an ISO-deg opposed, two-cylinder engine with a 0, 180 deg crankshafi. Assumptions: Use File F14-l2.eng for the cylinder data required on the cylinder input screen. Solution: See program ENGINE files P14132.eng, Pl4l34.eng, and Mathcad file Pl413.mcd. 1. Open file P14132.eng in program ENGINE for the two-stroke cycle or file P14 1 34.eng for the four-stroke cycle. The problem setup data is input from the disk file. Click the Calculate button and then the Dane button, which will return you to the Home screen. Click the Balance button, accept the values shown and click Calculate and then Done, which will return you to the Home screen. Click the Assemble button, accept the values shown and click Calculate and then Done, which will return you to the Home screen. View the calculated results by clicking on the Charts drop-down menu, from the main option bar, or use the Plot or Print buttons on the Home screen. IDESIGN OF MACHINERY SOLUTION MANUAL 14—14-1 ,6 PROBLEM 14-14 Statement: Calculate the shaking force, torque and moment balance conditions through the second harmonic for an l80-deg opposed, four-cylinder engine with a 0, 180, 180, 0 deg crankshaft. Assumptions: Use File F 14-12.eng for the cylinder data required on the cylinder input screen. Solution: See program ENGINE files Pl4l42.eng, P14144.eng, and Mathcad file P1414.mcd. l . Open file P14142.eng in program ENGINE for the two-stroke cycle or file P14144.eng for the four-stroke cycle. The problem setup data is input fiom the disk file. Click the Calculate button and then the Done button, which will returayou to the Home screen. Click the Balance button, accept the values shown and click Calculate and then Done, which will return you to the Home screen. Click the Assemble button, accept the values shown and click Calculate and then Done, which will return you to the Home screen. View the calculated results by clicking on the Charts drop-down menu, fiom the main option bar, or use the Plot or Print buttons on the Home screen. DESIGN OF MACHINERY SOLUTION MANUAL 14-15-1 £5 PROBLEM 14-15 Statement: Derive expressions, in general terms, for the magnitude and angular location with respect to the first crank throw, of the mass-radius products needed on the crankshaft to balance the shaking moment in a 90-deg vee-eight engine with a 0, 90, 270, ISO-deg crankshafi. Solution: No solution is provided to this algebraic exercise. DESIGN OF MACHINERY SOLUTION MANUAL 14-16-1 £3 PROBLEM 14-16 Statement: Derive expressions, in general terms, for the magnitude and angular location with respect to the first crank throw, of the mass-radius products needed on the crankshafi to balance the shaking moment in a 90-deg vee-six engine with a 0, 240, lZO-deg crankshafi. Solution: No solution is provided to this algebraic exercise. DESIGN OF MACHINERY SOLUTION MANUAL 14-17-1 g PROBLEM 14-17 Statement: Derive expressions, in general terms, for the magnitude and angular location with respect to the first crank throw, of the mass-radius products needed on the crankshaft to balance the shaking moment in a 90-deg vee-four engine with a 0, l80-deg crankshaft. Solution: No solution is provided to this algebraic exercise. DESIGN OF MACHINERY SOLUTION MANUAL 14-18-1 fig PROBLEM 14-13 Statement: Design a pair of Nakamura balance shafts to cancel the shaking force and reduce oscillations in the engine shown in Figure 14-18 (p. 662). Units: blob := lbf-secZ-in_ 1 Given: From Figure 14-18 and file Fl4-18.eng: Stroke: S := 3.537-in L/R ratio: LoverR := 3.50 Effective wrist pin mass: m B := 0.0116-blob Solution: See Figure 14-18, program ENGINE file F 14-] 8.eng, and Mathcad file P1418. 1. Calculate the crank radius and conrod length. Crank radius: r := 0.5-8 r = 1.769 in Conrod length: I := LoverR-r l = 6.190 in 2. Use equation 14.18 to calculate the mr product needed for the balance shafts. mrbal := -2r—[-mB-r mrbaz = 2.931 x 10— 3 blob-in WW I: mrbal'g wrbaz = 1.131 [bf-in 3. The specific location of the two balance shafts will depend on the specific geometry of the engine being balanced. The y-dimensions must be symmetric with respect to the engine longitudinal center plane (yz = -y1), and the vertical dimensions should be such that x, - x2 = 0.7 I . DESIGN OF MACHINERY SOLUTION MANUAL 14-19-1 ,6 PROBLEM 14-19 Statement: Using program ENGINE, data in Table [’14-] and the crank phase diagram from Problem 14-1, determine the maximum force magnitudes on main pin, crank pin, wrist pin, and piston for a 2-stroke engine with even firing. Over balance the crank, if necessary, to bring the balanced shaking force down to at least half of the unbalanced value. Solution: See program ENGINE file P]4l9.eng and Mathcad file P1419.mcd. . Open file P14] 9.eng in program ENGINE. The problem setup data is input from the disk file. Click the Calculate button and then the Dane button, which will return you to the Home screen. Click the Balance button, accept the values shown and click Calculate and then Done, which will return you to the Home screen. Click the Assemble button, accept the values shown and click Calculate and then Done, which will return you to the Home screen. Click the Flywheel button, accept the values shown and click Calculate and then Done, which will return you to the Home screen. View the calculated results by clicking on the Charts drop—down menu, from the main option bar, or use the Plot or Print buttons on the Home screen. DESIGN OF MACHINERY SOLUTION MANUAL 14-20-1 g PROBLEM 14-20 Statement: Using program ENGINE, data in Table Pl 4-1 and the crank phase diagram from Problem 14-2, determine the maximum force magnitudes on main pin, crank pin, wrist pin, and piston for a 4-stroke engine with even firing. Over balance the crank, if necessary, to bring the balanced shaking force down to at least half of the unbalanced value. Solution: See program ENGINE file Pl420.eng and Mathcad file Pl420.mcd. . Open file Pl 420.eng in program ENGINE. The problem setup data is input from the disk file. Click the Calculate button and then the Dane button, which will return you to the Home screen. Click the Balance button, accept the values shown and click Calculate and then Done, which will return you to the Home screen. Click the Assemble button, accept the values shown and click Calculate and then Done, which will return you to the Home screen. Click the Flywheel button, accept the values shown and click Calculate and then Done, which will return you to the Home screen. View the calculated results by clicking on the Charts drop-down menu, fi'om the main option bar, or use the Flat or Print buttons on the Home screen. DESIGN OF MACHINERY SOLUTION MANUAL 14-21-1 fl PROBLEM 14.21 Statement: Using program ENGINE, data in Table Pl4-l and the crank phase diagram from Problem 14-3, determine the maximum force magnitudes on main pin, crank pin, wrist pin, and piston for a 4-stroke engine with even firing. Over balance the crank, if necessary, to bring the balanced shaking force down to at least half of the unbalanced value. Solution: See program ENGINE file P1421 .eng and Mathcad file P142] .mcd. 1. Open file P142 1 .eng in program ENGINE. The problem setup data is input fi'om the disk file. Click the Calculate button and then the Dane button, which will return you to the Home screen. Click the Balance button, accept the values shown and click Calculate and then Done, which will return you to the Home screen. Click the Assemble button, accept the values shown and click Calculate and then Done, which will return you to the Home screen. Click the Flywheel button, accept the values shown and click Calculate and then Done. which will return you to the Home screen. View the calculated results by clicking on the Charts drop-down menu, from the main option bar, or use the Plot or Print buttons on the Home screen. DESIGN OF MACHINERY SOLUTION MANUAL 14—22—1 g PROBLEM 14-22 Statement: Using program ENGINE, data in Table [’14-] and the crank phase diagram from Problem 14-4, determine the maximum force magnitudes on main pin, crank pin, wrist pin, and piston for a 2-sn'oke engine with even firing. Over balance the crank, if necessary, to bring the balanced shaking force down to at least half of the unbalanced value. Solution: See program ENGINE file Pl422.eng and Mathcad file Pl 422.mcd. 1. Open file Pl422.eng in program ENGINE. The problem setup data is input from the disk file. Click the Calculate button and then the Done button, which will return you to the Home screen. Click the Balance button, accept the values shown and click Calculate and then Done, which will return you to the Home screen. Click the Assemble button, accept the values shown and click Calculate and then Done, which will return you to the Home screen. Click the Flywheel button, accept the values shown and click Calculate and then Done, which will retum you to the Home screen. View the calculated results by clicking on the Charts drop-down menu, from the main option bar, or use the Plot or Print buttons on the Home screen. ...
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ch14_solman - Chapter MULTICYLINDER ENGINES TOPICIPROBLEM...

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