A single cylinder vertical engine show in figure has bore of 30.5cm an...
Calculation of Turning Moment on Crankshaft
Given Parameters
- Bore of engine (d) = 30.5 cm
- Length of connecting rod (l) = 80 cm
- Stroke of engine (L) = 40 cm
- Mass of reciprocating parts (m) = 135 kg
- Net pressure on piston (P) = 650 kN/mm^2
- Engine speed (N) = 250 rpm
Calculation of Piston Area
The area of the piston can be calculated using the formula:
A = (pi/4) * d^2
A = (3.14/4) * (30.5)^2
A = 730.97 cm^2
Calculation of Angular Velocity
The angular velocity can be calculated using the formula:
w = 2 * pi * N / 60
w = 2 * 3.14 * 250 / 60
w = 26.18 rad/s
Calculation of Crank Radius
The crank radius can be calculated using the formula:
r = L / 2
r = 40 / 2
r = 20 cm
Calculation of Angle of Crank
The angle of the crank can be calculated as follows:
theta = sin^-1 (l * sin(phi) / r)
where phi is the angle made by the connecting rod with the horizontal.
At quarter stroke position, phi can be calculated using the formula:
phi = cos^-1 ((L/4 - r) / l)
phi = cos^-1 ((40/4 - 20) / 80)
phi = 36.87 degrees
Substituting values in the first equation, we get:
theta = sin^-1 (80 * sin(36.87) / 20)
theta = 100.76 degrees
Calculation of Velocity of Piston
The velocity of the piston can be calculated using the formula:
v = w * r * cos(theta)
v = 26.18 * 20 * cos(100.76)
v = -10.03 cm/s (negative sign indicates downward motion)
Calculation of Acceleration of Piston
The acceleration of the piston can be calculated using the formula:
a = w^2 * r * sin(theta)
a = (26.18)^2 * 20 * sin(100.76)
a = -424.83 cm/s^2 (negative sign indicates downward acceleration)
Calculation of Force on Piston
The force on the piston can be calculated using the formula:
F = m * a
F = 135 * (-424.83)
F = -57,327.45 N (negative sign indicates downward force)
Calc