Wire & Transformer Selection

 

I recommend you read through the Understanding Transformers page so you understand transformers better if you are not familiar with them. The Power Supply Design page explains how to build a complete power supply for a hot wire foam cutter or other heating application after you have selected the wire and transformer.

 

This page combines information on how to choose both the nichrome wire and the transformer for the power supply because the two go together--one depends on the other.

 

Wire Measurement

 

Wire is measured in gauge.  There are several different gauge standards so it is common to use the decimal measurement instead of gauge now.  Nichrome wire and other non-ferrous metals use the AWG gauge standard, American Wire Gauge, and this is the standard I use on my Web site but I also list the decimal inches. The AWG is the same as B&S standard, Brown and Sharp. This standard is also used for copper and aluminum wire so is the same gauge as is used for electrical wiring in your home.

 

Ferrous wire like iron and stainless steel wire most commonly use the W&M, Washburn & Moen, wire gauge.

 

A comparison chart of wire sizes in the various gauge standards and more information on wire gauges and their origin can be found here: http://www.sizes.com/materls/wire.htm.  Another useful comparison chart tabulated by decimal equivalent rather than gauge size as above can be found here: http://www.dave-cushman.net/elect/wiregauge.html.

 

As the gauge number gets larger, the wire size gets smaller.  AWG 40 gauge is hair fine while AWG 14 gauge is nearly as large as a household wire clothes hanger.

 

What wire size should I use?

 

You can use any wire size you want to.  Foam can be and is cut with wire sizes from 40 gauge (.003" dia.) all the way up to 11 gauge (.091" dia.).  The most common size is 26 gauge.  A short piece of 40 gauge wire has been used with a 9 volt battery to cut very thin (.020") and narrow strips of foam for air surfing walk-along gliders.  Two D cell batteries can power a 4" piece of 32 gauge nichrome wire in a small hobby hand held foam cutter. 

 

A 12 volt power supply will power up to 24" of 26 gauge wire.  This would include nearly all table top foam cutters which is the most common type of foam cutter, and would include small bow cutters.  This is why 26 gauge is the most common. 24 gauge to 30 gauge has also been used for table top models.

 

16 gauge to 11 gauge is used for foam cutters to cut shapes such as molding because they are stiff enough to hold a shape rather than being straight.  A 12" piece of 14 gauge nichrome wire requires only 1.9 volts but almost 12 amps.  Larger diameter wires are also used for very long cutters such as 8 or 10 feet.

 

The Tension Factor

 

All metals expand with heat so the nichrome wire at cutting temperature also expands and gets longer.  Because of this, some method of keeping tension on the wire is needed in hot wire foam cutters.  This is usually accomplished either with a springy frame that the wire is stretched between or a spring is used.  It is also conceivable that a weight could be used with the wire over a pulley.  Tension on the wire also helps keep it taunt so when a little pressure is applied when cutting foam, the wire stays fairly straight which is necessary for a good quality and uniform cut.

 

Because of the need for tension, the smaller the wire is, the less tension can be applied without breaking or permanently stretching the wire.  Using 40 gauge wire means very little tension is possible and it will be harder to keep the wire taunt when cutting.  The longer the wire is, the more pressure needs to be applied to the wire to keep it straight and taunt.  This is why as a general rule, the longer the wire, the thicker it needs to be. There is no length vs. gauge size standard since theoretically any size can be used at any length with the proper voltage applied and current capacity of the power supply.

 

Gauge/Current/Temperature Relationship

 

The temperature of a straight wire in room temperature calm air can be calculated.  A given temperature will result in a specific current flowing through a specific diameter wire.  It doesn't matter how long the wire is, a given current flowing through the wire will result in the same temperature.  For example, a 26 gauge wire with 2.1 amps flowing through it will result in 600 degrees F whether it is 2" long or 200" long. 

 

The bigger the diameter, the more current is required to heat it to the same temperature. For example, only 0.31 amps will result in 600F in 40 gauge wire, but 11.6 amps is required for 14 gage wire.  In addition, the larger the diameter wire, the longer it will take to reach the equilibrium temperature.

 

Equilibrium Temperature.

 

The reason a strait wire reaches a given temperature and stays there in calm room temperature air is that the current continues to produce more heat as long as the current flows.  At the same time, heat is being transferred away from the wire to the surrounding air.  The hotter the wire is, the faster the heat is transferred away.  The wire reaches its equilibrium temperature when the heat generated is equal to the heat transferred away.

 

If you coil the wire, in a tight coil like in heaters, transfer of heat away from the wire is reduced because there is more wire in a given volume of air and so the wire will get hotter.

 

In the same way, a wire in contact with any other material will change the rate of heat transfer away from the wire.  If the material it is in contact with is a good conductor of heat such as copper, the equilibrium temperature will be lower because heat is transferred away faster.  If the material it is in contact with is a poor conductor of heat (an insulator) the equilibrium temperature will be higher because less heat is transferred away.  These situations result in complicated heat transfer equations that are not easily solved.  In this case, experimentation is required to find the right wire and voltage to create the desired temperature.

 

Current Created From Applied Voltage

 

As mentioned above, it doesn't matter what the length of wire is, a certain current flowing through a given wire diameter will result in a given temperature in free air.  So how is that current created?  A voltage applied across the two ends of the wire create that current.  The longer the wire, the more voltage is required to create the same current.  This is due to the difference in the total resistance of the wire in different lengths.

 

Ohms Law

 

Ohms law is required to figure out the current and voltage relationship.  Ohms law states:

 

V = IR

 

V is voltage in volts (traditional E is used for voltage and stands for electromotive force instead of V), I is current in amps, and R is resistance in ohms.  You can rearrange the formula to find the current:

 

I = V/R

 

From this you can see that is the resistance goes up, so does the required voltage to get the same current.  The resistance of nichrome wire is specified in ohms per foot.  The longer the wire, the more ohms resistance it has so the longer the wire, the more voltage is required to push the current through the resistance of the wire.

 

What Transformer Do I Need?

 

Power is calculated by the formula:

 

W = I²R    or   W = VI

 

A transformer is usually rated in watts or volt amps.  For small transformers, they are essentially the same and interchangeable.  You need to know the power required for your heated wire so you know what size transformer will be required.  To calculate that, you first decide what gauge wire you will use and find the ohms per foot resistance of that wire.  For example, 26 gauge wire has a resistance of 2.67 ohms per foot.  If you are using the wire to cut foam with, the normal temperature desired is 600F.  To allow some flexibility in temperature, figure 800F (you can always turn it down if you have a variable voltage supply).  You also need to know the length of the wire.  Lets say you will use 2 feet.  Now you can calculate the resistance, voltage, and power requirements.

 

I = 2.6 amps (from the temperature table)

r = 2.67 ohms

R = rL = 2.67 X 2 = 5.34 ohms

V = IR = 2.6 X 5.34 = 13.9 volts

P = VI = 13.9 X 2.6 = 36.1 watts

 

I = current in amps

r = resistance per foot of the wire in ohms

R = total resistance of wire

L = length of wire in feet

P = power in watts

 

So you need a transformer that can put out at least 2.6 amps rated at 36 watts or more with an output voltage of 13.9 volts or more.  The closest you can find with that voltage or higher is 24 volts. You can use a dimmer switch to turn the voltage down (see the power supply design page).  You need 2.6 amps so you have to multiply the required amps times the output voltage to get the power in watts, 2.6 X 24 = 62.4 watts or volt-amps.  The closest you can find to 62.4 watts or more is a 24 volt output, 100 watt transformer. 

 

You decide that is too big and you want to use a 50 watt transformer.  What can you do?  Turn the voltage down?  No, that will reduce the temperature.  Make the wire shorter? Maybe.  Remember that the current required is the same regardless of the wire length and a given transformer is limited to a certain amount of current flowing through its windings regardless of the voltage.  The capacity of the transformer is limited by its ability to transfer heat.  The heat is measured in Watts and is determined by the current and resistance so if neither change, the watts remains the same.  If you turn down the primary voltage to the transformer, the output voltage also goes down but the resistance of the windings does not change so the maximum current doesn't change either.  Making the wire shorter doesn't change the current requirement but does change the voltage requirement.

 

As it turns out, the voltage requirement for 18" of nichrome wire at 800F is 10.4 volts so instead of a 24 volt output transformer, a 12 volt output, 50 Watt transformer can be used.  The current capability is 50 / 12 = 4.1 amps, well above the 2.6 amps required.  The 12 volt 50 watt transformer has a heavier winding than the 24 volt output so it can handle twice the current but the whole transformer is much smaller than the 100 watt transformer.

 

Transformers - Gauge And Max Lengths

 

Below are graphs of five transformers I will have available for sale in just a few weeks.  The graphs show the maximum length that each transformer can power figuring 800F so there is a 200F extra capacity.  All but one are dual voltages outputs so the lower voltage handles higher current and so extends the range to larger diameter wires because the current capability is doubled when the voltage is halved.  The graphs are all plotted on the same scales so you can get a better feel for the range of gauges and lengths each transformer can power. Click on the graph for a larger image.