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An engine has a bore of 78mm, a stroke of 82mm, and a con- necting rod length of 168mm. The crank is turning at 7200rpm. At top dead centre, the flat top of the piston is level with the upper deck of the block. At the instant when the crank is at 90° after top dead centre, using the approximate formula for the piston displacement as shown in part (b) of this question, cal- culate; i the depth of the flat top of the piston below the upper deck of the engine block ii the velocity of the piston in the direction of the cylinder axis ii the acceleration of the piston in the direction of the cylinder axis

An engine has a bore of 78mm, a stroke of 82mm, and a con- necting rod length of 168mm. The crank is turning at 7200rpm. At top dead centre, the flat top of the piston is level with the upper deck of the block. At the instant when the crank is at 90° after top dead centre, using the approximate formula for the piston displacement as shown in part (b) of this question, cal- culate; i the depth of the flat top of the piston below the upper deck of the engine block ii the velocity of the piston in the direction of the cylinder axis ii the acceleration of the piston in the direction of the cylinder axis

Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter1: Tension, Compression, And Shear
Section: Chapter Questions
Problem 1.8.7P: A special-purpose eye boll with a shank diameter d - 0.50 in. passes through, a hole in a steel...
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please send handwritten solution for part c
6. Shown in figure 4 is a piston, connecting rod and crank, i.e., a slider- crank mechanism. BIG END BEARING MAIN BEARING Figure 4: Slider Crank Mechanism (a) For the slider crank shown in figure 4, the throw of the crank is denoted by R, the connecting rod length by L, the crank angle by 0, and the displacement of the piston below TDC by x. Derive an equation to determine the piston displacement, x, as a function of crank angle.
Transcribed Image Text:6. Shown in figure 4 is a piston, connecting rod and crank, i.e., a slider- crank mechanism. BIG END BEARING MAIN BEARING Figure 4: Slider Crank Mechanism (a) For the slider crank shown in figure 4, the throw of the crank is denoted by R, the connecting rod length by L, the crank angle by 0, and the displacement of the piston below TDC by x. Derive an equation to determine the piston displacement, x, as a function of crank angle.
Question 6 continued (b) Using the binomial expansion; (1+ p)" = 1+ np+ n(n - 1)p n(n – 1)p +... 2! and the double angle formula; 2sin (0) = 1 – cos(20) Show that the piston displacement may be represented by the approximate formula below; R2 I R(1 – cos(0)) + [1 – cos(26)] 4L (c) An engine has a bore of 78mm, a stroke of 82mm, and a con- necting rod length of 168mm. The crank is turning at 7200rpm. At top dead centre, the flat top of the piston is level with the upper deck of the block. At the instant when the crank is at 90° after top dead centre, using the approximate formula for the piston displacement as shown in part (b) of this question, cal- culate; i the depth of the flat top of the piston below the upper deck of the engine block ii the velocity of the piston in the direction of the cylinder axis ii the acceleration of the piston in the direction of the cylinder axis Question 6 continued (d) Summarise the crankshaft layouts and therefore the also de- scribe the out of balance forces and moments for the following engine types; i single cylinder four stroke engine ii four cylinder inline four stroke engine iii three cylinder inline four stroke engine
Transcribed Image Text:Question 6 continued (b) Using the binomial expansion; (1+ p)" = 1+ np+ n(n - 1)p n(n – 1)p +... 2! and the double angle formula; 2sin (0) = 1 – cos(20) Show that the piston displacement may be represented by the approximate formula below; R2 I R(1 – cos(0)) + [1 – cos(26)] 4L (c) An engine has a bore of 78mm, a stroke of 82mm, and a con- necting rod length of 168mm. The crank is turning at 7200rpm. At top dead centre, the flat top of the piston is level with the upper deck of the block. At the instant when the crank is at 90° after top dead centre, using the approximate formula for the piston displacement as shown in part (b) of this question, cal- culate; i the depth of the flat top of the piston below the upper deck of the engine block ii the velocity of the piston in the direction of the cylinder axis ii the acceleration of the piston in the direction of the cylinder axis Question 6 continued (d) Summarise the crankshaft layouts and therefore the also de- scribe the out of balance forces and moments for the following engine types; i single cylinder four stroke engine ii four cylinder inline four stroke engine iii three cylinder inline four stroke engine
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