Electrical characteristics and generated force of solenoid
Simscape / Electrical / Electromechanical / Mechatronic Actuators
The Solenoid block represents the electrical characteristics and generated force for the solenoid in the following figure:
The return spring is optional. To remove the effects of this spring
from the model, set the Spring constant parameter to
0
.
To show the direction in which the solenoid acts, the block icon changes dynamically based on value of the Motion direction under excitation parameter.
When The Motion direction under excitation Parameter Is Set To...  Block Icon 

Port R moves away from port C


Port R moves towards port C


The equation of motion for the plunger as a function of position, x, is:
$${F}_{l}+m\ddot{x}+\lambda \dot{x}+kx={F}_{e}$$
where F_{e} is the electromagnetic force, F_{l} is the load force, λ is the viscous damping term and m is the plunger mass. The electromagnetic force is related to the solenoid current and inductance by:
$${F}_{e}=\frac{1}{2}{i}^{2}\frac{\partial L(x)}{\partial x}$$
The inductance, which is derived in [1], can be written as:
$$\frac{\partial L(x)}{\partial x}=\frac{\beta}{{\left(\alpha +\beta x\right)}^{2}}$$
where α and β are constants. Plugging the preceding equation into the equation for electromagnetic force gives the forcestroke relationship of the solenoid for a current i_{0}:
$$F=\frac{1}{2}{i}_{0}{}^{2}\frac{\beta}{{\left(\alpha +\beta x\right)}^{2}}$$
The Solenoid block solves for α and β by taking the two specified force and stroke measurements and substituting them into the preceding equation. It solves the resulting equations for α and β.
A positive current from the electrical + to  ports creates a negative force (i.e., a pulling force) from the mechanical C to R ports.
The block has an optional thermal port, hidden by default. To expose the thermal port, rightclick the block in your model, and then from the context menu select Simscape > Block choices > Show thermal port. This action displays the thermal port H on the block icon, and exposes the Temperature Dependence and Thermal Port parameters.
Use the thermal port to simulate the effects of copper resistance losses that convert electrical power to heat. For more information on using thermal ports and on the Temperature Dependence and Thermal Port parameters, see Simulating Thermal Effects in Rotational and Translational Actuators.
Use the Variables section of the block interface to set the priority and initial target values for the block variables prior to simulation. For more information, see Set Priority and Initial Target for Block Variables (Simscape).
Use the Position, X variable to set the target for the initial plunger position at the start of simulation.
The Position, X variable is the initial air gap or
stroke of the solenoid, and so should be greater than or equal to
0
.
[1] S.E. Lyshevski. Electromechanical Systems, Electric Machines, and Applied Mechatronics. CRC, 1999.