# Tattoo machine electromagnetics

• Phaedrus
In summary: The frequency at which the tattoo machine runs is determined by the combination of the coils and the capacator. The larger the capacitance, the more charge it can store and so the more time before it triggers the reversal (i.e. slow). Smaller capacitance, less charge stored, faster reversal.
Phaedrus
Hello, New to this forum, thanks for having me. I have been researching electromagnetics to better understand the workings of the tools of my trade (tattoo artist) and have come upon a number of questions and cannot seem to find the answers. I would appreciate any help to point me in the right direction. This will be my first question.
A tattoo machine is basically a dc circuit containing two magnetic coils in series with a capacitor in parallel which operate an armature on a spring contact. Think doorbell. The capacitor is basically there to suppress the spark generated by the rapid collapse of the magnetic field as it switches itself on and off. My question at this point (I will have more concerning magnetics later) is...why does changing the value of the capacitor cause the machine to run faster for smaller and slower for larger values of capatance. As I understand it the energy created by the collapse of the magnetic field (since dc will not go through a cap.) is kind of sloshed back and forth through the coils until it is reduced to zero by the resistance. Why would the speed of the armature be related to the speed at which the cap. discharges this energy back and forth. Thanks

I will confess to not being very familiar with tattoos or the "implements of torture" but I'll take a stab at it!

If I understand correctly, a tattoo needle goes a short distance into the skin and then back out again. That's controlled basically by an electromagnet. The magnetic field is one direction for the "stab", the opposite direction for the retraction. That means that the field has to reverse at regular intervals.

I suspect the capacitor is there not just to "suppress the spark" but to hold the electrical charge until it is time for the reversal in direction. The larger the capacitance, the more charge it can store and so the more time before it triggers the reversal (i.e. slow). Smaller capacitance, less charge stored, faster reversal.

Actually the reverse motion is a function of the spring tension. The spring returns the armature and contact to a closed point at which the circuit is closed and the motion starts all over again. the magnet is off when the circuit is open and that is when the field collapses producing the opposing voltage. Remember how a capacitor functions in a dc circuit. Thanks

The circiut you describe is called a Resonate Tank. It essentially alternatly stores energy in the field of the coils and between the plates of the capacator. Thus it is creating AC from the DC current. The frequency at which the tank circiut runs is determined by the combination of the coils and the capacator, change the value of either of them will change the operation frequency of your needle.
EDIT:
I went looking for the relationship between Inductance, Capacitance and frequency.

&omega;=1/([sqr]LC)

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That really helps...I spent all night researching tank circuits trying to understand. So if I use that equation and come up with a frequency value of 120 (for example) does that mean that my machine will run at optimum performance at 120 hz.
Also my equation for inductance is rather cumbersome(L=Number of turns * Permeability of soft iron core(600?)* Area of coil in square meters divided by Length of coil in meters) Does this seem accurate enough or is there something else)
thanks

Inductance is tough, I would not advise unwinding your coils to attempt to learn this number. To make it worse inductors are the worst for having a value printed on them. If you are able to measure the operating frequency (or know it for some value of capacitance) you can compute the inductance. This would be the best way to go. I am not sure how much you want to spend to study this, the best tool would be an oscilloscope, these are very expensive and require substantial training/knowledge to use. Radio Shack does sell Multimeters which can measure frequency. You seem pretty knowledgeable about circuits (ie you were able to identify caps and coils) so should be able to master it with no difficulty.

3 weeks ago I knew nothing about electromagnetism or circuits...now it seems I know even less.
I can get a pretty accurate number for turns as I know there are about 44 turns per inch with 22 gauge wire... The coils are sold as 6 wrap, 8 wrap or 10 wrap usually, so I can figure the number of turns without unwraping them. Most machines come with a 47uF 35v capacitors. I bought a good multimeter at radio shack last week (having problems getting accurate Hz readings, most of the time it jumps around a lot, not sure why, maybe the spring is bouncing at the contact on return) So the coils I have in front of me have about 336 turns per coil (there are 2 coils and one cap.) There are several things I can do to change the operating freq. I can adjust spring tension/stiffness, armature weight. The problem comes down to...If the machine is not tuned correctly it can get very hot and just not work as well. Also there seems to be some misunderstandings in the tattoo world concerning the function of the capacitor. So I am trying to figure out why diff. cap. sizes cause diff. performance and to arrive at an algorythm or value for a well tuned machine.
thanks

You also need to consider the interaction with the spring. The mechanical system also has a resonate frequency. If you get a mismatch between the electrical oscillations and the mechanical you will indeed lose efficiency. Figuring the resonate frequency of the mechanical system will be more difficult then the electrical. I'll do a bit of digging see if I can find a formula for it. It is interesting that that the fundamental equations for electrical and mechanical oscillation problems are identical. This fact is frequently used when modeling systems.

Ok. with that said, I found this.

In mechanical systems m plays the part of inductance and Capacitance corresponds to Mechanical compliance= 1/k were k is the Hook's Law spring constant so your mechanical resonate frequency is

&omega;m= [squ]k/m
k can be measured if you can remove the spring and carefully measure its extension with addition of mass.

k= Mg/x here M is that added mass, g is the acceleration due to gravity.

ok...I looked into Hooke's Law and it seems that it applies to coil type springs. What we have here is a flat spring.
http://crkail.launchbase.com/images/machinediagrm2.jpg
This diagram may shed some light on the problem. But I would think that you are still right about the mechanical resonance. Because when things are out of sync on this system it creats a nightmare.

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Hook's law is always shown with a coil spring but it holds for your spring also. It has a spring constant and the resonate frequency is determined by the equation I gave. It may be very difficult to determine your spring constant.

I'm curious: the capacitor in the drawing looks like it might be eletrolytic. Is the one on the actual tool electrolytic?

I would bet it is. Why would that be of any particular significance?

Here's my thinking: the basic vibrator circuit behind this machine is as old as the hills.
Peole have, since they were invented, been trying all kinds of ways to prevent the spark that occurs when the points come apart. Everyone has resorted to the capacitor, which while it doesn't eliminate the spark, seems to cut it down.

I've been trying to think if arranging it as a tank circuit, as Integral suggests is what is going on, would stop the spark somehow, but I can't see that it would. I must arrive at the conclusion that the capacitor is not put there to make it into a tank circuit.

For whatever its worth, the person who put this site together believes the capacitor is for controlling the spark as well:

HOW DOES A MODERN TATTOO MACHINE WORK?

I don't know how the capacitor is affecting the performance. I do know you could remove it altogether and it would work fine, except that the spark would be at its maximum.

Thomas Edison invented this basic machine in 1876 for engraving or some such thing, and about 20 years later someone modified it to make tattoos. It is also the same circuit used in the Model T spark coil to make and break the juice to the primary.

Now your hitting on what I am trying to figure out. You would think that taking the cap. off would not change the way it runs...but it does...significantly. Aside from the blue light show...the machine requires more voltage just to operate then is rather erratic. I have a machine that I have modified as to be able to clip in various capacitors or none at all. With a 47uf 35v cap. at 5 volts it runs with a duty cycle of about 60%. when you remove the cap. it will draw more in amps run very weak and the duty cycle goes to 80%.

Some thoughts I have had on the problem. When the contact is broken the magnetic field collapses and generates a significant spike of voltage. The way the cap. suppresses this spike is that instead of arcing across the contact it is builds up on one side of the cap...at some point enough has built up on one side that it wants to go to the other side. Since dc current will not travel through a cap. it takes the next best route which is back through the coils. When enough has built up on the other side the process begins again sending the energy back and forth each time creating and collapsing a magnetic field. The coils can have about 2.5 ohms of resistance from one side to the other, so within x number of passes the energy is completely dispersed. So then some time later the contact returns to its original position...the circuit is closed and the whole thing starts again. So this is where the resonance may come in...the rate at which this spike is sent back and forth at the moment the contact is broken seems to drastically effect how the machine runs.
Also keep this in mind...it is not enough that the armature simply go up and down...I use two machines for nearly every tattoo...sometimes 3-4. Some artists use as many as 5-6. Each machine has it's own characterists involving speed, power etc. depending on how it is set up.

Clearly the coils and capacitor from a tank circuit, for optimal performance the natural frequency of the electrical must match the natural frequency of the spring mechanism. I would guess that the best of all worlds would occur if you time the points to open near the zero current point of the tank circuit. This is called zero crossing and is in common use with Solid State Relays. If you can achieve this condition then there will be little or no spark when the contacts open or close. To get this with a mechanical system would be difficult, but not impossible.

Here is the schematic of the circiut as shown in the link above. http://home.comcast.net/~rossgr1/tatto.jpg This is a driven harmonic oscillator, the electrical system dirves the mechanial spring system. Do a search on that you should find lots of infomation. Maximum efficeny will come when the electrial and mechanical systems are tuned to the same frequency operation. The tank circiut should be able to drive the mechanical system for a short period with the points OPEN. If this circiut is tuned correctly the current draw from the source will be small, it is only needed to replace losses. If you are not tuned current form the source will increase and operation will be compromised.

Think of the electrical circiut as a fellow pushing his child in a swing, the mechanical system is the swing. If you push at the wrong time it requires more work and you simply stop the swing, if you push at just the right moment, it requires little effort and the swing goes further. That is the goal of the tank circiut, it needs to apply max current to the coils just as the points are opening. When the mechanism is at its maximum displacement the coil current must be near 0, thus releasing the mechanism to begin the upward travel.

When the spring mechanism (which will include everything that moves with the needle) is allowed to operate at its natural frequency (as given in a previous post) it will require little energy to sustain motion. So the goal of the electrical system is to provide gentle pushs at the right moment.

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Integral makes excellent points here, and I don't see any way to get around the fact that adding the cap to suppress the spark creates a tank circuit as well, which will have to be tuned for optimum performance, in conjunction with the tuning of the mechanical oscillations: all stuff that should have been worked out by whoever engineered this particular machine.

One thing to bear in mind, if you aren't already, is that the current created when the magnetic field collapses always goes in the same direction the original current was going. This is why I asked if the cap was electrolytic. Another is that sparks, whenever they occur, are not straightforward, unidirectional propositions: they actually oscillate at high frequencies but with a general overall direction. This makes Integral's goal of a no spark situation definitely the one to shoot for.

Engineered...are you kidding...the worst running machines on the market are the ones stamped out in factories made by engineers. The best and most sought after machines are hand made by people who understand the feel of a fine tuned machine. Once you have the geometry correct then all you have is the electronics and mechanics. But I'm willing to bet that some of the best machine makers in the world have never heard of a resonant tank or a harmonic oscillator. Like a violin maker from 100 years ago. That is what has brought me here...If you research tattoo machines and tattoo forums you will find tons of misinformation, whether it be from misunderstanding, superstition and/or just plain old ignorance. At this point it is a very misundertood area amongst even the people who use it everyday.

Also...Are you sure about the spike going in the same direction as the current that created it...I was under the impression that the whole idea was that it was in opposition to the current that created it in an effort to equalize the experienced loss. I've got it in my notes somewhere and will try to find the reference.
Thanks for the interest.
integral...with that new info on springs and driven harmonic oscillators I am finding tons of pertinant information. Thanks

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Notice in my drawing that the cap is not parallel to the points but in series with. This is a different arrangement then you see in the now out dated automotive points. This circiut is a resonate tank, it must be tuned to the Natural frequency of the mechanical spring system. If not it will not function properly.

The second link above implies that this is essentially the circiut designed by Henry Ford for the model T ingnition system, therefore the initial design was by a mechanical genious who had a lot of practical knowledge. I'll bet the original design was by indent. What has happened since then I do not know. Clearly it works.

Engineered...are you kidding...the worst running machines on the market are the ones stamped out in factories made by engineers.

It is my opinion that it is rare that the final design of most manufactued goods actually lies in the hands of an engineer. All to often Marketing and the bean counters dictate the final production. Much of the sublties of engineering can be lost with the stroke of a pen that maintains form but guts functionality.

Much of the sublties of engineering can be lost with the stroke of a pen that maintains form but guts functionality.

That's exactly the problem...I really doubt that many of the manufacturers even bothered with spending money on engineering research...it's so much easier to copy old designs...then cut corners sacrificing the functionality.

Originally posted by Phaedrus Also...Are you sure about the spike going in the same direction as the current that created it...I was under the impression that the whole idea was that it was in opposition to the current that created it in an effort to equalize the experienced loss.
I'm sure I read this because they made the point that going the same direction the current was going, was the opposite of what you'd expect given the collapsing field is the opposite of the expanding field. This was in one of the Audels series of books on electricity. They wanted to alert the student to the fact that what actually occurs isn't what you would expect. I'm sure this is what I read, those books are pretty reliable as far as I know, but I never tried to check it myself.

You say that in your drawing the cap. is "not" in parallel but in series...are you sure...wouldn't a series be on after the other. Maybe I have made some fundamental misunderstanding.

ohoh ok in series with the points ...sorryy i got it.

what actually occurs isn't what you would expect.
Ok that sound familiar...thanks

There is one other parameter that you have not mentioned that should/could have significant effect on the operation.

The time perior over which the points are closed.

If they are not closed long enough you will not get sufficent kick, if they are closed to long the source current will fight the natural frequency disrupting motion.

Just another knob for you to tweak!

I have found the governing equations for a impulse driven harmonic oscillator, am looking at them to see if a simulation can easily be created. Might be fun to play with.

I think you hit the nail on the head...It occurred to me that perhaps the single most important thing in controlling the resonance between the two systems would be the amount of time that the circuit is closed. And possibly the most difficult to control or adjust. As the mass of the armature returns to the contact point the inertia carries it for some time past its resting point. How long and how far it does this can vary depending on the mass of the armature and the spring tension of the front and rear springs. Making adjustments on these are crude to say the least...like changing the channel on your tv with a sledghammer. What if I were to use an optical switch to close the circuit for an adjustable amount of time, when it reached the point of contact. Is there such a device capable of anywhere from 60 to 250 switches per second that could define the amount of time the cicuit remains closed.

The 2 key functions of the points is to maintain a proper phase relationship between the mechanical and electrical oscillators and to feed current into replace system energy loss.

The 2 circuits could be running at precisely the same frequency but if the points close at the wrong time motion will grind to a halt. This is the feedback that is essential to oscillator operation. I believe that you should be able to use a SOLID STATE RELAY to do this.

All caps imply another google search for you! I think this could work, but am not 100% certain on how to implement it. Do a bit of research on the device see what you can learn.

The problem I am having is that we still need feedback from the mechanical circuit, perhaps this is why you mention optical. There indeed are optical thru beam sensors. which could be used to monitor the position of your armature, I am not sure if they have quick enough response times. Check websites of OMEGA, OMRON and KEYENCE for lots of sensor information.

These guys are used to selling stuff to the High Tech industries so get ready for some sticker shock!

Ok...I've been researching optics now and this is what I have found. It seems that what I am looking for is a photoelectric sensor with "one shot logic" which would give me an output of set length no matter how long the object is detected. My theory is that I should be able to tune in a resonance between the two systems by adjusting the amount of time that the coils are on. I have written letters to a couple of manufacturers where they made questions for applications available and have had no replies. It has been several days and I am wondering if I am barking up the wrong tree.
thanks

I think you are on the right track, this sort of scheme should work. Use the opto sensor to switch a SSR. This would provide a spark free circuit.

The manufacturers may be in a rut, having made the same product for decades there will be a huge resistance to anything new. It may be that many there do not understand the basic functioning of the circuit. How much engineering do you suppose they need?

The major trouble I see with your modifications is cost, you are replacing a cheap set of contacts with an 2 expensive electronic components. While this sort of mod is fun and interesting, I am not sure how it could compete commercially with the standard system.

wow

I just want to say I enjoyed this post greatly. It is good to see invention and innovation in action. Especially for an inked up grad student.
Cheers,
Norm

Back again...I think I may have solved the problem. After banging my head against many walls I found the 555 IC chip. Using that and various circuit diagrams off the internet I was able to make the circuit that controls frequency (I'm still working on the duty cycle). Now I can make a tattoo machine run without a capacitor, without a contact spark and I can control the Hz completely without spring or gap adjustments. In theory allowing me to rectify the disharmony between the spring and coil function creating the desired resonance between the two.
My problem now is that I have a 9-7 dc volt input and am only getting .8 volt output. Which is enough to make the machine run very softly but not enough for practical use. As far as electronic circuitry goes I only know what I have taught myself in the last month or two so I think I may have done something wrong in my wiring as I shouldn't get such a voltage drop from the circuit if done correctly. Any input on where I might look from here would be great. Thanks

I am going to move this over to the electrical Engineering forum. You may attract some good attention over there.

My .02\$ It sounds like you need a power amp. I'll keep an eye on this, but you are moving into areas were I am not much help.

I thought I might add two more cents.

Originally posted by Phaedrus
In theory allowing me to rectify the disharmony between the spring and coil function creating the desired resonance between the two.

If I read this correctly you still have a problem. The resulting motion of the armature will be that of a forced coupled oscillator - which will yield a complex motion that includes a beat frequency, which is determined by the difference between the two characteristic frequencies - the electrical and mechanical resonant frequencies. In order to operate properly, I think the mechanical and electrical resonant frequencies must be the same [or one an integer multiple of the other at worst]. This did not sound like your intent.

My problem now is that I have a 9-7 dc volt input and am only getting .8 volt output.

Using the 555 directly as a driver? I agree with Integral, you need more power. Unless you have mis-wired the circuit the output is probably overloaded by the low circuit impedance; they are only good for a couple of hundred milliamps. Also, you need to use something with a high back EMF rating like SSRs, or even standard bipolar transistors, or FETs, or even IGBTs. The back EMF spikes are critical and unavoidable, however they can be reduced if the driver circuit is sinusoidal...meaning no square waves coming out of the 555 timer. But the action of the armature I think insures a lot of noise. Also, you may need short rise times in the coil current in order to provide the proper kick to the armature [to get the desired mechanical action]. The proper selection of the components used is likely critical here for this reason. As rule, you want the driver – the transistor or SSR – designed to withstand at least 10X the nominal operating voltage. So if your circuit is 10 volts, you should use 100 volt transistors which are also rated well above the current requirements [maximum amps drawn] of the coils. Next, by turning the coils on or off slowly, you will burn off a lot of power in the transistors [drivers]. This may require that some heat sinks be added. Altenately, if you turn the coils on and off quickly you will start creating high back EMFs. You may need to find a balance here. EDIT: again, I am speaking of the rise time for the coil current; not the frequency of the cycle.

The tank circuit presumably made efficient use of the back EMF whereas you may be losing this benefit...if I am reading this thread correctly. Your power supply may not have enough power any longer. What are you doing with the energy stored in the magnetic field of the coils?

What do you actually hope to achieve here? I wasn’t entirely clear what motivates the change in the operating frequency.

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Wow I am talking with a couple electrical engineers to build a similar circuit for a tattoo machine, They were saying to use 2 555's and a power FET the cap would still be in the system but moved from the machine to the power supply and new circuit, to simplify the machine.
The standard tattoo machine is adjusted through changing physical mechanical attributes on the machine, along with the coils, which is not done while your tattooing, instead you have 2+ machines setup differently, I would like to be able to adjust the machine based on electrical than mechanical (so as to adjust it on the fly), we want to isolate the coils from the mechaincs of the machine so that there is no electrical running through the spring contact points, I wanted to add a dc power supplies output through the power FET, and use the voltage/current adjustment on the power supply to adjust the strength of the coils pull(soft or hard) and have the 555's control the frequency of the pulse of the DC voltage I set, I am not sure how exactly this all needs to work together, but any info you have would be great, the engineer that's trying to build this for me is taking forever so If I could get the circuit layout from someone on this board I would build it myself if its not too complex, I only have a MECP electronics background witch doesn't cover this type of thing exactly . Any help would be appreciated.

Hello

Hi, I'm new to the site. I realize that I am digging up an old thread, but I am doing research on tattoo machine mechanics and this came up in Google. It is very interesting, so here I am. I don't have a lot of technical knowledge regarding any of the systems at work here, but I do have a general idea based on what I have been reading. I am fairly intuitive and can learn almost anything. I am fascinated with these machines and want to be able to build my own. I have done a few rebuilds and have run into some issues that I need some technical assistance with. I have a few different questions, but I'll try to work them out one at a time so I don't get any more confused.
The basic function of the machine is to place tattoo ink into the dermis of a person's skin. Different people have different skin and the required needle configurations differ as well which require different amounts of force to accomplish this. The machine must generate enough force to drive the needle configuration into where it needs to be. Also different skin types require different amounts of force and different depths of needle travel. The taper of the needle tips are also a factor. For example a single, long taper needle does not require much force to go into thin skin. On the other hand it takes much more force to drive 13 short taper needles into tough skin.
The electromagnets of the machine use electricity to create "pull" on the steel armature of the machine. The needle configuration is attached to this armature so as to move with it. The distance of travel, or stroke, is determined by; the bottom gap (space between the armature and the magnet surface) and the amount of front spring compression. A rear spring attached to the base frame of the machine applies force to the front spring and is used to counteract the magnetic pull. At rest, the front spring is compressed against the electrical contact completing an electrical circuit used to power the magnets. When you step on the foot switch and apply voltage to the circuit, the magnets pull the armature toward them releasing the front spring compression until the circuit is broken as the front spring leaves the contact point. The weight of the armature, the stiffness of the rear spring, the needle configuration, and skin type are all factors in how much pull is required.
My first question is how to maximize the efficiency of the voltage used to power the magnets. Standard magnets are made by taking a 1" or 1-1/4" lengths of 5/16" or 3/8" diameter 1018 low carbon steel rod, insulating it with a thin layer, putting ends on it to form a spool and winding 24 or 26 gauge magnet wire around it, 8 - 12 layers thick. I am currently planning on making my own coils and am hoping to get some insight into how to maximize the efficiency of the voltage in the coil. What effect the diameter and length of the steel and the gauge and length of wire have on how the electricity is used to create the magnetic pull?
Any comments on this are greatly appreciated

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