Question

can you please prioritize #4

Piston velocity Y [mm/s] vs 0 [rad] Piston acceleration ï [mm/s?] vs 0 [rad] 4) Crank AB rotates starting from rest with a constant angular acceleration of 0.25 rad/sec (= 0.25 rad/sec ) clockwise in positive direction as shown Perform computer simulations using above formulas to plot Piston displacement - Y [mm] vs Time [sec] Piston velocity Y [mm/s] vs Time [sec] Piston acceleration Y [mm/s?] vs Time [sec] Р 150 mm 5) Crank AB rotates starting from rest with a constant angular acceleration of 0.25 rad/sec (ö = 0.25 rad/sec ) clockwise in positive e direction as shown Perform computer simulations using above formulas to plot Piston displacement - Y [mm] vs 0 [rad] Piston velocity Y [mm/s) vs [rad] Piston acceleration Y [mm/s?] vs 0 [rad] Notes for all above cases. When you are simulating and plotting, use small time increments to obtain smooth plots. Show axis titles, units etc. on your figures clearly. Perform all simulations for two revolutions of the crank (4tt rad) When time = 0, 0 = 0 for all cases You can use any software such as Matlab, Excel etc. You can access to campus computers and Matlab remotely if you do not have suitable software in your computer. In all plots, Time [sec] or angular position [rad) will be on x axis. . . . A B C 50 mm

Answer 1

MatLab Code

1 - clear all close all 2 3 clc 4 5 - 6 - 1 = 150; r = 50; alpha = 0.25; Length of the Connecting rod BD, mm Length of the Crank AB, mm Angular acceleration of the crank AB, rad/s^2 7 8 9 - 10 III 1 n = 1/r; time = 0:0.01:sqrt (8*pi/alpha); omega - alpha*time; t = (1/2)*alpha* (time.^2); 11 - Time vector, s Angular velocity of crank AB at time 't', rad/s Theta at time 't', rad 12 13 14 - d = sqrt (n^2 - sin(t).^2); 15 16 17 - y = r* (cos(t) + d); Displacemment of the piston, mm 18 19 v = -r*omega.*( sin(t) + sin(2*t)./(2*d)); & Velocity, mm/s 20 21 22 a = -r* (omega.^2).* ( cos(t) + cos (2*t)./d + (sin(2*t).^2)./(4*d.-3)); $acceleration of $ piston, mm/s^2 23

24 25 26 27 28 29 $ Plot piston diplacement vs time figure plot (time, y); xlabel('Time (s)'); ylabel('Displacement (mm)'); title('Piston Displacement vs Time'); grid on 30 & label x-axis $label y-axis & title Shows the grids 31 32 33 34 35 36 - 37 000 plot piston velocity vs time figure plot(time, v); xlabel('Time (s)'); vlabel ('Velocity (mm/s)'); title('Piston Velocity vs Time'); grid on 39 40 41 - 42 43 45 - 46 47 plot piston acceleration vs time figure plot (time, a); xlabel('Time (s)'); vlabel ("Acceleration (mm/s^2)'); title('Piston Acceleration vs Time'); grid on 49 50 51

Output

Piston Displacement vs Time 200 190 180 170 160 Displacement (mm) 150 140 130 120 110 100 0 4 8 10 12 N 6 Time(s)

Piston Velocity vs Time 150 100 50 Velocity (mm/s) A -50 -100 -150 N 0 4 00 10 N 6 Time(s)

Piston Acceleration vs Time 200 100 0 -100 Acceleration (mm/s2) -200 -300 -400 -500 0 2 4 00 10 12 6 Time(s)

Equations used:

D 1 B o Referring to the figure shown, displacement of the piston as the crank rotates through an angle e from the inner dead centre, can be written as y = AD = (l cos + r cos ) Or y=r =r{cos e cos º + cose) = r(n cos $ + cos e) Where we have substituted , n r From the trigonometric relation cos o = 1 - sina o From the figure I sin = r sine or rsin sin sinº n Substituting this

sin e 2 cos = 1 - n? - sin Substituting this in the equation for displacement, y 1 y = 1 In2 - sin2 0 + cos Or y = =r [cos e + Vn? - sin2 ---(1) Velocity of the piston can be obtained by differentiating above equation with respect to time. dy dy de dy v = y = - dt Substituting for y j = r (cos e + Vn2 – sin? )] (0) Or -2 sin cos e y =re (- - sin + zorgin com or v=y=-ré (sin e sin 20 10+ 2n2 - since (2) Differentiating the above equation with respect to time, we get the acceleration of the piston dý dy do a = y = de dt

Substituting the expression for y del-ro (si sin 20 -ré (sin @ + 2 Vn2 - sin2 ) 0 Or 2 cos 20 sin 20 (-sin 20)] = -rh2 cose + 2Vn2 - sin0 4(n2 – sin2 )3/2 cos 20 sin? 20 a = y = -ró2 cose + Vn? - sin? @ 4(n2 - sin? 0)2) (3) 3 Since, a is the constant acceleration of the crank AB and crank starts from rest (i.e. w(0= 0), at any instant t w(t) = . = at (4) 8(t) = zar (5) One can convert the equations (1) → (3) to functions of time by substituting the above equations. Time taken to complete, 2 revolutions (6 = 4ft) can be calculated from equation (5) as follows 2 x 47 |81 t = S a a