Kinematics and Dynamics of a Combustion Engine

The goal of the project is to analyze the kinematics and dynamics of a combustion engine through a MATLAB code that will give valuable data in the gear crank mechanism, works, forces and momentums present in the system.

Engine Data

The table on the left presents the information related to the engine with both geometric and operational parameters like displacement, plunger stroke, admission pressure or exhaust pressure.

Cinematic Variables

First step will be analysing the different variables of the engine with respect to the crankshaft rotation angle for two different rotation regimes. The analysis will be made for three different cases:

Real crank size
Crank 10% larger
Crank 10% shorter

Piston Position

Two graphs were extracted with the two different regimes of the engine and different crank sizes. As it may be noticed from the graphs, a bigger crank, the distance between the crankshaft and piston gets larger. Even for higher rotation regime, the distance remains practically the same.

Piston Speed

The graphs below show the piston speed for the two rotation regimes at 1500 rpm and 4500 rpm. As it can be seen, a larger crank size implies a larger stroke from the piston that requires higher speeds to work at the same rpms.

Piston Acceleration

The graphs below show the piston acceleration for the two rotation regimes at 1500 rpm and 4500 rpm. The effect of the crank size variation is similar to the piston acceleration. If the piston speed is larger, the accelerations to reach that speed must be larger . In this case, the maximum and minimum acceleration coincide with the TDC and BDC of the engine.

Crank Position

The graphs below show the crank position for the two rotation regimes at 1500 rpm and 4500 rpm. Same way as piston position, the rotation regime doesn't affect the crank position.

Crank Angular Speed

The graphs below show the crank angular speed for the two rotation regimes at 1500 rpm and 4500 rpm. It can be seen that as the rotation regime increases, the angular velocity of the crank also increases.

Crank Angular Acceleration

The graphs below show the crank angular speed for the two rotation regimes at 1500 rpm and 4500 rpm.

Aprroximate and Exact Result Comparison

Piston Position

The maximum and minimum points will coincide for both rotation regimes and the error will be, as it can be seen, the same.

Piston Speed

The maximum and minimum points for the approximate solution are quite smaller than the experimental results, since the model is made based on simple formulation some errors might occur.

Piston Acceleration

Crank Position

In this case, both approximate and exact solution are the same.

Crank Speed

Again, both approximate and exact solution are the same.

Crank Acceleration

In this case, a slight difference in the exact solution can be seen for the maximum and minimum points.

Plunger Force Diagram

The cycle characteristics are going to be calculated for three different cases where admission pressure at the entrance and rotation regime will vary. The three cases:

Admission pressure 0.4 bar and 1000 rpm
Admission pressure 1 bar and 2000 rpm
Admission pressure 1 bar and 4500 rpm

Motor Torque

A study of the engine torque for the three cases presented above has been performed. The engine torque can be defined as a parameter that measures the engine's capacity to develop a specific amount of work. This is measured at the end of the crankshaft which is the part that converts alterntative movement in rotational movement.

Side Force Calculus

Logically, the relative movement of the piston and the block is not ideal and there is a side force between them. It's important to evaluate this force and minimize it as much as possible to reduce losses.

Inertia Estimation of Crankshaft-flywheel System

A flywheel is a passive element of the engine that softens the angular accelerations from high engine forces during operation.

Conclusions

It can be concluded that a deep study of the kinematics and dynamics of an engine is essential when designing an engine to know how heavy and resistent it has to be to deal with the forces and momentums present in the cycle. Rotation regimes and crank-piston sizes determine some of these parameters.

It has to be considered that sizing adjustments in a rotation engine can affect the speed and acceleration of the different parts. This can generate inertial forces that can change the performance of the engine and generate losses that might not account for smaller engines.

Page updated

Google Sites

Report abuse