A solenoid is a basic, rugged device. Its component parts consist of a coil (to carry current and generate ampere turns), an iron shell or case (to provide a magnetic circuit), and a movable plunger or pole (to act as the working element). A major objective in the design of a solenoid is to provide an iron path capable of transmitting maximum magnetic flux density with a minimum energy input. Another objective is to get the best relationship between the variable ampere turns and the working flux density in the air gap. When applying a solenoid, it is extremely important to consider the effects of heat, since for a constant voltage application, an increase in coil temperature reduces the work output. Ambient temperature range, voltage fluctuation, return springs and temperature rise all affect the net output torque/force. For preliminary calculations, we recommend that a 1.5 safety factor be applied to the variables.
Magnetic Flux in Solenoids
Magnetic flux lines are transmitted through the iron shell and the air gap between the shell and the plunger (for linear solenoids) or the armature (for rotary solenoids). An iron path is much more efficient than air, but the air gap is needed to permit movement of the plunger or armature. The force or torque of a given solenoid is inversely proportional to the square of the distance between the pole faces. The lowest force or torque is generated when the distance is widest/longest; the strongest when the distance is smallest.
Saturation
Saturation of the iron path in a solenoid can be considered in two ways. In the true sense it is point (a) at which the iron ceases to carry any increase in flux. In broader terms, saturation is usually considered as point (b), where the iron begins to saturate.
As the pole pieces are moved together or when input power is increased, the flux density of the magnetic circuit increases until the iron saturates near point (b). Beyond this point any further increase in power only serves to add heat without an appreciable increase in force or torque. By changing the iron path area, the pole shape, or the magnetic circuit material, output torque/force can be increased.
Ampere Turns
The number of copper wire turns, the magnitude of the current, and permeance of the magnetic circuit determine the absolute value of magnetic flux within the solenoid. The permissible temperature rise limits the magnitude of the power input. When using a constant voltage, heat makes the coil less efficient because it reduces the ampere turns and, hence, the flux density and the torque/force output.
Heat in Solenoids
Heat can be dissipated by controlling the air flow, by mounting the solenoid on a surface large enough to dissipate the energy (heat sink), or by resorting to some other cooling method. When space permits, a simple solution is to use a larger solenoid. Heat in a solenoid is a function of power and the time during which power is applied. For continuous duty, hold-in resistor circuits are commonly used to provide higher starting torques/ forces than are obtainable at continuous duty rating. Our stock model standard solenoids are designed to operate in ambient temperatures of -55°C to 80°C. A solenoid operating at the predetermined conditions established in the coil data charts, with the specified heat sink, will have a coil temperature rise of about 80°C (above ambient temperature). Our standard solenoids will withstand 120°C without thermal damage. A special high temperature coil with a 175°C temperature limit, for operation in up to 95°C ambient, is available for rotary and low profile solenoids.
Duty Cycle in Solenoids
Duty cycle is determined by ON time/(ON + OFF) time. For example, if a solenoid is energized one second out of four seconds, the duty cycle is 1/(1 + 3) = 1/4 or 25%. Duty cycle is the time factor which determines the permissible watts input and the subsequent amount of torque/force and heat. If, for example, a 10-watt input power causes a heat rise of 20°C in 10 seconds, approximately the same temperature rise will result if a power of 100 watts is applied for one second. In terms of duty cycle, a solenoid designed for continuous duty can dissipate ten times the input power at 10% duty.
Maximum ON Time for Solenoids
Solenoids have a maximum ON time for a given duty cycle, wattage and power input. For example, if a solenoid is energized for one second out of four (25% duty cycle), its ON time is one second, which will cause no damage. On the other hand, if the solenoid is energized for 10 minutes out of every 40 minutes at the 25% duty cycle wattage, the duty cycle is still 25%, but its ON time is now 600 seconds. A single pulse of this duration would burn out the solenoid. Ledex and Dormeyer DC solenoids are specified with two criteria for maximum ON time: when pulsed repeatedly at the stated watts and duty cycle, and; for a single pulse at the stated watts (with the coil at 20°C ambient temperature).
Operating Speed in Solenoids
The energizing time for a solenoid to complete a given stroke is measured from the beginning of the initial pulse to the seated or energized position. For a given solenoid, this time is dependent upon the load, duty cycle, input power, stroke and temperature range. When a DC voltage is impressed across the solenoid coil, the current will rise to point (a) as shown on the graph below.
This time delay, which occurs prior to the plunger motion, is a function of the inductance and resistance of the coil, and the flux required to move the Time — Milliseconds Current Steady State Current
The length of the OFF time or interval between pulses is established by the duty cycle and the input power. If a pulse train is applied for an indefinite period, the interval between pulses should be sufficient to maintain the duty cycle for the input power and wire size tabulated in the coil data tables. Response to a faster pulse rate for intermittent operation is then limited by the temperature rating of the coil and the return speed of the plunger. The return speed can be established by reducing the OFF period until the solenoid energizing trace becomes erratic. When designing for high speed pulse trains, it is important to consider the type of coil suppression used, and the location of the control circuit. A diode across the coil may provide satisfactory coil suppression, but it causes a slower collapse of the magnetic field, lengthening the OFF interval required. Ledex high speed coil suppressors use a diode/ capacitor/zener diode principle to decrease the drop-out time as well as effectively suppress transients. Placing the control switch to the solenoid on the AC side of a rectifier will have an effect similar to that of using a diode across the coil. If deenergizing speed is critical, the control switch should be located on the DC side of the rectifier and a high speed coil suppressor should be used to provide adequate suppression while allowing fast plunger return speed.
Continuous Duty for Solenoids
For continuous duty applications, or where there is a chance that an operator might close the control switch for a long period, the project engineer has several choices. He can specify a solenoid large enough to provide the torque/force needed on a continuous basis or, if the application permits a higher coil temperature rise, he can specify a smaller solenoid with a high temperature coil to obtain continuous duty operation at a higher power level. He can also use a smaller solenoid and take advantage of the higher torque/force obtainable with an intermittent duty cycle input power. This can be accomplished by using a hold-in circuit to reduce current to a point where torque/force is sufficient to maintain the solenoid in the energized position.
Hold-in” Resistor Value Estimates
Mechanical Hold-In Resistor Circuit - Solenoids
One of the more common methods to reduce coil current is a normally closed (NC) switch in parallel with a hold-in resistor. When push button (PB) closes the circuit, full voltage is impressed across the solenoid coil, bypassing the resistor through the NC switch. As the solenoid approaches the end of its stroke, a mechanical connection opens the NC contacts, inserting the resistor in series with the coil. This reduces the solenoid voltage to a point where the power input is high enough to allow the solenoid to hold in, and yet stay within its normal heat dissipating range.
Capacitor Hold-In Resistor Circuit - Solenoids
In some cases, a switchless hold-in circuit may be used on 115 VAC applications. This consists of a capacitor which charges to a peak of approximately 150 volts. A resistor in the line ahead of the rectifier controls the hold-in current after the discharged capacitor has supplied the initial high stored energy.
Transistorized Hold-In Circuit - Solenoids
As shown in the transistorized circuit on page H2, when the NO switch is closed, current flows through the base-collector while the capacitor is charging to input voltage. As the base-collector current flows, the emitter-collector circuit allows full power to be impressed across the solenoid coil. The transistor is switched off when the capacitor reaches full charge. Current flow is then through the hold-in resistor and solenoid coil at continuous duty power or less. When using this circuit, it is important that the transistor be on long enough to allow the solenoid to move the load through the complete stroke. The graph on page H2 is a convenient guide to estimate hold-in resistor values. Because the actual value can vary according to the size of the load to be held, it should be used only as a starting point. Keep in mind that more hold-in current (lower resistance) is needed as the hold-in load increases. To use the graph, locate the coil resistance on the horizontal scale, then read the approximate hold-in resistor value on the vertical scale.
Temperature and Force/ Torque Resistance - Solenoids
The force/torque curves and coil data in this catalog are based on the coil being at an ambient temperature of 20°C, and the use of a heat sink comparable to that called out in the notes below each table.
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When a solenoid
is energized,the coil temperature rises. Since resistance varies with temperature, an increase in temperature produces a proportional increase in resistance. Increased resistance reduces the current flow when constant voltage is applied, and decreases the effective ampere turns and torque/ force output. For each degree above or below 20°C, the resistance of the coil’s copper wire changes by 0.393 percent per degree. A coil temperature rise of 80°C, for example, will increase the coil resistance by a factor of 0.314, which is equal to 80°C x 0.00393/°C.
Rearrangement of the formula produces a ratio between R20°C and Rt2 as follows:
Calculation of resistance at any other temperature (t2) can be made using the following formula:
The Resistance Factor of copper wire at temperatures from -60°C (-76°F) to 260°C (500°F) is graphed below.
Once the actual coil temperature (ambient plus rise) is determined, the resistance factor can be determined as follows:
A size 3E, 31 awg coil has a resistance of 31.8 ohms at 20°C. After operating for a prolonged period at 10% duty, the approximate coil rise is 80°C. Added to 20°C, the coil temperature is 100°C. The Resistance Factor graph indicates a 1.3 factor (point where 100°C and diagonal intersect). At 100°C, the resistance of the 31.8 ohm coil is increased by this factor. With a constant voltage applied, the power decrease is proportional to the resistance increase (P =E2/R). The 10% duty power of a size 3 solenoid is 90 watts (at 20°C). The decrease in power at the elevated temperature is calculated by:
By interpolating between the 25% and 10% duty cycle curves, the reduction in force due to the 80°C rise can be estimated for a given stroke.
How to Simulate a Coil Wire Size
If you have a stock model Ledex or Dormeyer solenoid, you can simulate performance with a different wire gage by changing the input voltage. A rule of thumb is that, as each wire size changes from one gage to the next, the voltage increases or decreases by the cube root of 2, or a factor of 1.26.
Coil data charts in this catalog are tabulated with voltage values which provide essentially constant ampere turns for each wire size at given duty cycles. A stock model solenoid with a given coil awg can be used to simulate other wire gages under different voltage conditions as follows:
Assume you have a 12-volt power supply and you want to experiment with a size 3 low profile solenoid at continuous duty. In the size 3 coil chart, the closest continuous duty coil is 30 awg (13 volts). You can simulate the exact conditions you would have with a 30 awg coil and a 12 volt input by using a stock model with (1) a 28 awg coil, or (2) a 33 awg coil.
(1) The size 3, 28 awg coil is rated at 8.4 volts, continuous duty. The desired 30 awg coil is 2 gages higher.
7.5 = voltage to simulate 30 awg coil at 12 volts when using stock model size 3 with 28 awg coil.
(2) The 33 awg is rated at 26 volts, continuous duty. The desired 30 awg is three gages lower.
12 volts x 1.263 = 24
24 = voltage to simulate 30 awg coil at 12 volts when using stock model size 3 with 33 awg coil.
Input Power and Ohm’s Law for Direct Current
To understand the relationships of power, current, voltage and resistance, use the chart below.
Estimating Temperature Rise in Solenoids
Two constants are specific to a system or device to determine temperature rise: thermal resistance and thermal time constant. Knowing that Ledex solenoids, with their associated heat sinks, are designed for an 80°C rise over ambient, thermal resistance may be calculated by dividing the continuous duty wattage into 80 and adjusting for temperature. For example, a size 5 solenoid has a continuous duty wattage of 21 watts. Adjusting for a 80°C rise by the resistance factor of 1.314 gives
The thermal time constant can be estimated by looking at the maximum allowable single pulse. Before the thermal resistance can be solved for, it must be remembered that the resistance changes due to temperature. The resistance factor is
1 + (80 * 0.00393) = 1.314
This changes the power at high temperature. To find the thermal resistance, simply divide the temperature rise by the actual power.
Where P = the continuous duty power in watts @ 20°C. For example, a size 5 solenoid again has a continuous duty rating of 21 watts. Hence, the thermal resistance is 5.00°C/watt. To find the thermal time constant, an analogy to a charging capacitor must be made. The heating equation can be related to the charging time such that:
Because the time constant is dependent on duty cycle, due to the time required for heat to transfer from the inside to the outside, it has been found that the power ratio of input to continuous raised to the 0.6 power makes a reasonable estimate. Hence, the equation is best used in the following form:
where:
D = ratio of input power to
continuous duty power.
Solving for t,
where pulse = the maximum single ON pulse in seconds for a particular duty cycle. Using the same size 5 solenoid which has a 50% duty cycle power of 42 watts and a maximum single pulse of 160 seconds yields a thermal time constant of 350 seconds. For repetitive cycles, the general cooling curve determines the initial starting temperature for the next power cycle. This equation is:
where Tc = temperature (°C) at end of OFF cycle. After this temperature is determined, the power and resistance must be recalculated for an accurate starting power. Also, the time must be calculated which, if starting at ambient, would have given that heat rise. The equation is:
A size 5 solenoid is rated for having a maximum ON time of 100 seconds for a 50% duty cycle, which means that the OFF time must be a minimum of 100 seconds also. Using the preceding values shows the temperature to vary as follows:
As can be seen here, the maximum is slightly exceeding the rated value of 105° C. This value is fine for a starting point, but may not be representative of the actual usage of the solenoid. For this case, the thermal resistance and thermal time constants of the actual system may be determined experimentally. An easy way is to put a known wattage on the system and plot resistance vs. time. By knowing the total temperature rise, the thermal resistance is calculated by temperature rise divided by known input wattage. The thermal time constant is determined by finding the time to reach 67% of the total rise. Once these values are determined, the maximum temperature can be estimated for any ambient, power and duty cycle.
Environmental Considerations for Solenoids
Factors which impact the operation and performance of solenoids include:
- Temperature
- Sand and dust
- Humidity
- Shock and vibration
- Altitude, vacuum and pressure
- Specific application considerations such as paper dust and exposure to certain chemicals
Please consult an application engineer, if any of these factors are prominent in your planned solenoid design.
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