Engine kinematics

Question 1

Which two kinds of motion can be distinguished considering the engines’ crank drive? Name the crank drives’ components and their associated motion

Answer 1

rotary motion: crankshaft, crankpin, connectionrod bearing

oscillating motion: Piston, piston pin, piston rings…

Question 2

Briefly explain the motion of the con-rod. State why this is an exception.

Answer 2

connecting rod: both rotary and oscillating movement, it is connected to piston and to the crank

Question 3

Briefly show why the kinematics of the slider crank result in pure cosine correlations regarding displacement, velocity, acceleration and force.

Answer 3

con-rod does not pivot -> no beta angle-> pure cosine

𝑥=𝑓(𝛼) 𝑑𝛼/𝑑𝑡=𝜔⇒𝑑𝛼=𝜔⋅𝑑𝑡
The displacement, velocity, acceleration can then be calculated as follows:
𝑥=𝑙+rcos(𝛼)
𝑥´=𝑑𝑥/𝑑𝑡=−𝑟𝜔sin𝜔𝑡
𝑥´´=−𝑟𝜔²cos𝜔𝑡
𝐹𝑜𝑠𝑐=−𝑚𝑂𝑆𝑍⋅𝑥´´=𝑚𝑂𝑆𝑍⋅𝑟𝜔²cos(𝜔𝑡)
𝐹𝑜𝑠𝑐=𝐹0cos(𝜔𝑡)
Very simple correlations!Simple balancing! Newtons2ndlaw of motion!

Question 4

State the reason for more complex formulae when considering the (conventional) crank drive.

Answer 4

pivoting motion of the con-rod

piston displacement as function of the crank angle alpha

Question 5

What is the main problem when deriving the pistons’ displacement from its kinematics? Why must binominal expansion series be used?

Answer 5

Function depends on alpha and beta
the binominal expansion series is used to eliminate beta
+?

Question 6

Name a method to consider the con-rods’ rotatory and oscillating masses

Answer 6

-simplification as point masses
𝑚𝑜𝑠𝑐=1/3𝑚𝑐𝑟+mp
𝑚𝑟𝑜𝑡=2/3𝑚𝑐𝑟+mcs
-more precise: center of gravity and moment of inertia

Question 7

Explain two methods to express the oscillating forces

Answer 7

• two rotating vectors
• one complex rotating vector
  (Bildchen merken F27 engine kinematics)

Question 8

Explain how mass forces can be balanced in general

Answer 8

mass forces balanced by counter weight added to crankshaft

Question 9

Which disadvantages of the balancing can be identified?

Answer 9

• engine weight
• more parts
• more friction losses

Question 10

Briefly explain the influence of mass forces of 2,3,4,… cylinder engines.

Answer 10

depending on the number of pistons the mass forces may be balanced internally, by the counter moving pistons
3 cylinders-> balanced
4 cylinders -> 1st Order balanced internally -> 2nd Order not balanced internally

Question 11

Show how the gas force resulting from the combustion process correlates to the radial and tangential forces acting on the crankshaft

Answer 11

stroke force: 𝐹s=𝐹G/𝑐𝑜𝑠𝛽
radial force: 𝐹r=𝐹s⋅cos(𝛼+𝛽)
tangential force: 𝐹t=𝐹s⋅sin(𝛼+𝛽)
F33