before starting: Please if you are want to understand this simulation example you have firstly to read and understand all the below otherwise it will be a waste of time. When you feel it is useful for you please, pray for me, my parents and the Iraqi people.
Function description:
The
drive piston (1) is actuated in a periodic translator motion by the
crank mechanism (2). The force transmission from the drive piston to the
percussion piston (3) results from the
air cushion (4). Due to this excitation the percussion piston performs an oscillating translator motion and axial percussions on an interposed piston, which itself impacts on the tool (in the following the interposed piston and the tool are neglected).
System equations:
The rotation of the drive crank is assumed to be constant. The position of the drive piston is explicitly described by the length
s, which is dependent on the geometric parameters
r,
q as well as the angular velocity
w (omega) of the drive crank {
equation no. 1}
The percussion piston can move independently in x-direction.
A friction force (Coulomb’s friction) acts between the percussion piston and the wall of the cylinder, arranged by {
equation no. 2}
A is the cross sectional area of the cylinder,
M (mue) the dynamic friction coefficient between piston and the wall of the cylinder and
Po is the ambient pressure.
A force acts between the drive and the percussion piston due to the air cushion, which depends on the distance
h-Xs-s between the piston surfaces and in a nonlinear {
equation no. 3}
Applying the principle of linear momentum we obtain the equation of motion {
equation no. 4}
Modeling of the impact process:
When the percussion piston impinges on the tool respectively the header, a momentum appears which is approximately described by a spring-damper combination with spring constant
c and damping coefficient
d {
equation no. 5}
However, this force only acts when the percussion piston tries to penetrate into tool (Xs<0). Consider this circumstance with an appropriate logical block in the block diagram (simulation model).
Realization of the simulation:
Develop a block diagram, which can establish a basis for the input in SIMULINK. Initially generate separate block diagrams for the motion of the drive piston, the friction force, the air force as well as the momentum. Afterwards develop a block diagram of the equations of motion, which imply the forces to be combined in subsystems being dependent on
Xs(t) and
s(t).
Enter the block diagram in SIMULINK and perform simulations of different initial conditions and parameters. Pore over the influence of the rotational velocity of the crank on the function of the hammer in particular.
An important characteristic of the function of the hammer is the impulsion velocity of the percussion.
We will apply the following numerical values for the simulation:
ms = 0.6; % percussion mass [kg]
h = 0.2; % cylinder length [m]
A = 0.00151976; % cross-sectional area of the air cushion [m^2]
l0 = 0.0365; % air cushion height at ambient pressure [m]
p0 = 1e5; % ambient pressure [N/m^2]
r = 0.022; % crank radius [m]
q = 0.076; % length of conrod [m]
xs0 = 1e-4; % initial position of the percussion [m]
mue = 0.2; % friction coefficient [-]
c = 1e8; % spring constant for impact modelling [N/m]
d = 7610.8; % damping constant for impact modelling [Ns/m]
ns = 1300; % input speed [1/min] Hint: we need angular velocity
So, first we will generate Matlab (M-file) with the above numerical values and save this file to define all the parameters which we will use them later in our model (you should see all these parameters in the workspace after running your M-file) this is very important step to be ready to build our model in the next step