Enter your keyword

Different parts of a reciprocating engine is shown in Fig. 4.4 (a)

Motion of Piston and Crank of a Reciprocating Engine 1” = C

Let us consider this figure,

Point A will have linear motion towards point C along the line AC

Point B will have circular motion with an angular velocity

Thus,

Velocity at point A, VA = 0 AO

Similarly,

Velocity at point B, VB = C0 BO

Or,

r = 0 BO. 0r/ BO

VA = 0 AO

= (r) AO/ BO

Hence,

We can easily get the velocity at point A by knowing the values of all elements.

Analytical Method to find VA

Motion of Piston and Crank of a Reciprocating Engine 2” = C

Fig. 4.4 (c) shows the graphical representation of different parts of an engine.

To find the velocity at point A, we can use different analytical methods.

Method 1:

Draw line CD ⏊ AC and line BE ⏊ AC

Now,

In AOB and BCD

⦟AOB = 900 –  = ⦟BCD

⦟OAB = 900 –  = ⦟BDC     (we know that ⦟OBA = ⦟LCB)

Hence,

AO/ BO = CD/ BC = CD/ r

And,

tan = CD/ AC

CD = AC. tan

= (AE + EC) tan

= (L cos + r cos ) tan

= L sin  + r cos tan

 

Since,

VA = (r) AO/ BO

= (r) CD/ r

=  (L sin  + r cos  tan)

 

Method 2:

Suppose the crank is at IDC (Inner Death Centre). In this condition,

A1B1 = AB = L

B1C = r

Hence,

AO/ BO = CD/ BC = CD/ r

tan = CD/ AC

we know that

CD = AC. tan

= (AE + EC) tan

= (L cos + r cos ) tan

= L sin  + r cos  tan

Thus,

VA = (r) AO/ BO

= (r) CD/ r

=  (L sin  + r cos  tan)

 

Method 3:

Considering the Fig.4.4 (d),

Motion of Piston and Crank of a Reciprocating Engine 3” = C

Let, A1A be x

It can be written as,

A1C – AC = x

(A1B1 + B1C) – (AE + EC) = x

(L + r) – (L cos + r cos ) = x

 

Differentiating the above equation with respect to time, we get-

=

= L sin+ r sin

Hence,

VA = L sin+ r sin

Since,

BE = L sin = r sin

sin = r/ L sin

 

Differentiating the above equation with respect to time, we get-

 

cos =r/ L

= r/ L cos

= rcos / Lcos

 

Now, substitute this value to get VA,

Therefore velocity at point A,

VA = L sin(rcos / Lcos ) + r sin

= r cos sincos  + r sin

=  (L sin  + r cos  tan)