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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`

.

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,

$${F}_{e}=\frac{1}{2}{i}^{2}\frac{\partial L(x)}{\partial x}$$

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 force-stroke 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,
right-click 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.

**+**Positive electrical input

**-**Negative electrical input

**C**Mechanical translational conserving port

**R**Mechanical translational conserving port

**Forces [F1 F2]**A vector of the force values at the two points on the force-stroke curve. The second measurement point must be at a stroke that is greater than that of the first measurement point. When the manufacturer does not provide a force-stroke curve, set F1 to the holding force (when X1 = 0) and F2 to the pull-in force when running the solenoid at the

**Rated voltage Vdc**and**Rated current Idc**values. The default value is`[7.5 0.75]`

`N`

.**Stroke [X1 X2]**A vector of the stroke (plunger distance from the fully closed position) values at the two points on the force-stroke curve. The second measurement point must be at a stroke that is greater than that of the first measurement point. To ensure a finite force value, the points must meet the condition

$$\frac{X2}{X1}>\sqrt{\frac{F1}{F2}}$$

The default value is

`[1 5]`

`mm`

.**Rated voltage Vdc**The voltage at which the solenoid is rated to operate. This voltage value is used to measure the

**Forces [F1 F2]**and**Stroke [X1 X2]**values. The default value is`50`

`V`

.**Rated current Idc**The current that flows when the solenoid is supplied with the

**Rated voltage Vdc**voltage. The default value is`0.05`

`A`

.

**Spring constant**Constant representing the stiffness of the spring that acts to retract the plunger when the solenoid is powered off. The force is zero when the plunger is displaced to the

**Stroke for zero spring force**parameter value. The default value is`200`

`N/m`

. Set the spring constant to zero if there is no spring.**Stroke for zero spring force**The stroke at which the spring provides no force. The default value is

`5`

`mm`

.**Damping**The term λ in the equation of motion for the plunger as a function of position that linearly damps the plunger motion. The default value is

`1`

`N/(m/s)`

. The value can be zero.**Plunger mass**The weight of the solenoid plunger. The default value is

`0.05`

`kg`

. The value can be zero.**Maximum stroke**The maximum amount by which the plunger can be displaced. You can use this parameter to model a hard endstop that limits the stroke. The default value is

`Inf`

mm, which means no stroke limit.**Contact stiffness**Stiffness of the plunger contact that models the hard stop at the minimum (

*x*= 0) and maximum (*x*=**Maximum stroke**) plunger positions. The default value is`1e+06`

`N/m`

.**Contact damping**Damping of the plunger contact that models the hard stop at the minimum (

*x*= 0) and maximum (*x*=**Maximum stroke**) plunger positions. The default value is`500`

`N/(m/s)`

.

[1] S.E. Lyshevski. *Electromechanical Systems, Electric Machines, and
Applied Mechatronics*. CRC, 1999.