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Two basic laws govern solenoids:
1- Faraday's Law
2- Ampere's Law

Faraday's Law:
The voltage induced in a coil is proportional to the number of turns and rate of change of flux. The induced current flows in the direction that opposes the changing flux. Flux has no source or sink (What goes in comes out)
Ampere's Law:
The magnetomotive force (mmf) around a closed loop is equal to net current enclosed by the loop. The objective of solenoid design is to transfer the maximum amount of NI (energy) from the coil to the working air gap.

Types of Solenoids:
There are two main categories of solenoids - Rotary & Linear.
Linear solenoids have applications in appliances, vending machines, door locks, coin changers, circuit breakers, pumps, medical apparatus, automotive transmissions and postal machines to name just a few.
Rotary solenoids have applications in machine tools, lasers, photo processing, media storage, medical apparatus, sorters, fire door closures, and postal machines, also just to name a few.
Solenoids are used in almost every conceivable industry in the world and are well known as an efficient, affordable and reliable actuation alternative.

Eight Essential Application Considerations when designing a solenoid into your assembly

• Stroke
  Force or Torque
  Voltage
  Current / Power
  Duty Cycle
  Temperature
  Operating Time / Speed
  Environmental
  AC / DC
  Life

Stroke – when applying solenoids, keep the stroke as short as possible to keep the size, weight and power consumption to a minimum.

Force – applies to linear products. Starting force is typically more important than ending force. A safety factor of 1.5 is suggested. For example, an application requiring 3 pounds of force should employ a solenoid that provides at least 4.5 pounds of force. Force is inversely proportional to the square of the air gap with flat face plunger designs. The air gap is the space in the magnetic circuit allowing the armature to move without interference, and the magnetic flux to circulate with minimum resistance (reluctance).
To determine your requirements for force or torque, you need to consider the following:

• The actual load you are moving
  Return spring force or torque
  Frictional loads
  Temperature rise
  Duty cycle
  Orientation of the solenoid vs. gravity (the weight of the plunger is added or subtracted depending on how the solenoid is mounted.

In linear solenoids, force can be modified by the shape of the plunger used. A conical face plunger is used for medium to long stroke applications. The effective air gap changes to become a fraction of actual stroke. Flat face plungers are used for short stroke applications. Stepped conical face plungers can provide various stroke (medium to long) dependent on the angle of the step. These are advantageous for high holding force requirements.

Torque – applies to rotary products. Starting torque is typically more important than ending torque. A safety factor of 1.5 is suggested. For example, an application requiring 3 pound of torque should employ a solenoid that provides at least 4.5 pounds of torque. Torque produced by Ledex™ Rotary Solenoids is inversely proportional to the total length of the stroke. The longer the stroke, the lower the torque output. The shorter the stroke, the higher the torque output.

Voltage – the voltage source determines the coil winding to be used in the appropriate solenoid. Common DC power supply ratings are 6,12,24,36, and 48 VDC. AC vs. DC solenoids – AC solenoids are most commonly used in household appliances. Generally AC solenoids have been specified when there was a high cost to rectify to DC. AC solenoids typically require twice the in rush power of an equivalent DC solenoid. As a result, many more DC solenoids are chosen for today's applications.

Current / Power – Force produced by a DC solenoid is proportional to the square of the number of turns (N) in the coil winding and current flow (I). This determines the ampere turns or NI. Solenoid coil requirements must match the power source.

Duty Cycle – The duty cycle of your application is the ratio of the "on-time" divided by the total time for one complete cycle (on + off). Duty cycle is usually expressed as a percentage or a fraction (50%, 100%). A more simplistic representation of duty cycle is to call < 100% duty solenoids "Intermittent" and 100% duty cycle solenoids "Continuous". All intermittent duty solenoids (< 100% duty cycle) also must have a maximum "on-time" allowed to avoid overheating that can eventually lead to a burned out coil. The "on-time" must not exceed the power dissipation limits of the coil. Proper heat sinking and/or additional cooling improves heat dissipation which allows a broader duty cycle range. Very close attention must be paid to the maximum "on-time" data provided in conjunction with the duty cycle calculation to avoid damaging your solenoids. For example, although an application with a one hour cycle time and a 3 hour off-time might calculate to a 25% duty cycle, this is not realistic in practice. A more realistic solenoid application might be an on-time of one second and an off-time of 3 seconds for the same 25% duty cycle.

Temperature – Both the ambient temperature of the solenoid environment and the self -heating of the solenoid at work must be considered. The resistance of the coil varies with temperature which affects force output. The self-heating temperature is dictated by the duty cycle. Each 1¡ increase above 20º C equates to an increase of 0.39% of rated resistance; thereby reducing force or torque output. There are various ways to compensate for temperature restrictions:

• Specify a Class C Coil
  Specify an overmolded coil
  Use a E Model Rotary solenoid vs. the S Model
  Actuate at one power level and cut back to a reduced power level for holding (pick and hold)
  Use a latching solenoid
  Use a multiple winding solenoid
  Operate intermittently, not at continuous duty
  Use a larger solenoid
  Use a heat sink
  Add a cooling fan

The limiting factor of operating temperature of a solenoid is the insulation material of the magnet wire used. Insulation classes:

• Class B- 130º C
  Class F- 155º C
  Class H- 180º C
  Class C- 220º C

A typical solenoid requires 10% of the normal current to remain energized. To accomplish this, use one of the following:

• Mechanical hold in resistor
  Capacitor discharge and hold in resistor
  Transistorized hold in circuit
  Pulse-width modulation
  Pick and Hold
  Dual voltage
  Multiple coils

Operating Time / Speed – Factors affecting time and speed include the mass of the load, available power / watts and stroke. De-energizing also plays an important role and is affected by the air gap, coil suppression, the plunger or armature return mechanism, and residual magnetism.
The air gap is the space in the magnetic circuit allowing the armature to move without interference, and the magnetic flux to flow with minimum resistance (reluctance). The smaller the air gap, the longer it takes for the magnetic field resulting from the excited coil to diminish. This causes a longer de-energizing time.

• The application of electronic protection devices to reduce spikes caused by interrupting the current in the coil is necessary to ensure protection of your switching device. Coil suppression tends to increase the de-energizing time of the solenoid.
  Since solenoids have force in one direction only, there must be some restoring force (such as gravity or a spring) to take the solenoid back to the starting or de-energized position. This positions the solenoid for the next operation.
  Air gap surfaces of a solenoid become the north pole and south pole of a magnet when energized. When the solenoid is off, a small but measurable magnetic attraction between the poles still exists called residual magnetism. Residual magnetism can be reduced by hyperannealing the solenoid parts of by increasing the size of the air gap.

Environmental – Many environmental factors must be noted when choosing a solenoid. These include temperature, sand/ dust, humidity, shock, vibration, altitude, vacuum, chemicals and paper dust.
Solenoid Life – Life is determined by / optimized by the:

• Bearing system and shaft surface finish
  Side loading and load alignment
  Preventing the pole pieces from slamming together
  Reducing impact shock upon energizing

Solenoid life expectations range from 50 thousand cycles to over 100 million cycles.

Custom Solenoids - 80% of solenoids used are custom designs. Typical modifications include termination, lead wires, plunger configurations, shaft extensions, mounting changes and linkages.

Application Hints:

To achieve extended life, try the following options:

• Drive the load from the armature end of a rotary solenoid rather than the base end
  Use vespel or oilite bearings in a low profile solenoid design
  Use dual ring bearings or a groove in the shaft to act as a lube reservoir
  Use glass-filled or carbon-filled nylon couplings

To achieve increased holding torque / force performance try the following options:

• Use indented ball races in a rotary solenoid
  Use flat pole pieces
  Use latching solenoids

To determine the temperature at which a coil has stabilized follow this sequence of steps:

• Measure the coil resistance at room temperature
  Measure the current at the stabilized temperature and determine the coil resistance using Ohm's Law
  Divide this resistance by the resistance at room temperature to obtain the resistance factor
  Using the resistance factor chart, read the temperature at which the solenoid coil has stabilized.

To compensate for temperature rise:

• Mount the solenoid on a metal surface (heat sink)
  Use a cooling fan
  Use a larger solenoid
  Operate at < 100% duty cycle
  Consider a higher insulation class
  Use a solenoid with multiple windings
  Use a pick and hold circuit such as PWM