Question

An internal combustion engine slider-crank mechanism is shown in the figure. Crank AB rotates in selected clockwise positive direction as shown. Piston position is Y=AD.

 

 is angular position of the crank,   is angular velocity of the crank,  is angular acceleration of the crank.

 

A-Analytical formulations part:

 

1)     With the given parameters find analytical expressions for :

a)      Piston position, Y [mm]

b)   Piston velocity,   [mm/s]

c)   Piston acceleration  [mm/s²].

(Show all the details of the derivations including your figure with given coordinate directions etc.)

 

B-Computer Simulations part:

 

2)   Crank AB rotates with a constant angular velocity of 5 rad/s clockwise in positive direction as shown. Perform computer simulations using above formulas to plot

Piston displacement – Y [mm] vs Time [sec]

Piston velocity   [mm/s] vs Time [sec]

Piston acceleration  [mm/s²] vs Time [sec]

 

3)   Crank AB rotates with a constant angular velocity of 5 rad/s clockwise in positive direction as shown. Perform computer simulations using above formulas to plot

Piston displacement – Y [mm]  vs  [rad]

Piston velocity   [mm/s] vs  [rad]

Piston acceleration  [mm/s²] vs  [rad]

 

4)    Crank AB rotates starting from rest with a constant angular acceleration of 0.25  (  ) clockwise in positive direction as shown Perform computer simulations using above formulas to plot

Piston displacement – Y [mm]  vs Time [sec]

Piston velocity   [mm/s] vs Time [sec]

Piston acceleration  [mm/s²] vs Time [sec]

 

5)    Crank AB rotates starting from rest with a constant angular acceleration of 0.25  (  ) clockwise in positive direction as shown Perform computer simulations using above formulas to plot

Piston displacement – Y [mm]  vs  [rad]

Piston velocity   [mm/s] vs  [rad]

Piston acceleration  [mm/s²] vs  [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 (4π rad)

·    When time = 0 ,   for all cases

·        You can use any software such as Matlab, Excel etc.

·    In all plots, Time [sec] or angular position  [rad] will be on x axis.