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Dental drills have always been cutting edge technology when it comes to high rotational speeds. According to Wikipedia modern drills reach more than 180 000 rotations per minute (rpm), which is 3000 rotations per second! For comparison, household drills operate at around 1000 rpm. Obviously a dental drill operates much smoother than a concrete drill, but what's less obvious to me is why?

I could imagine that conservation of angular momentum make the rotational movement less sensitive to external forces. On the other hand a small misplacement of the center of mass with respect to the axis of rotation would cause severe juddering.

Another big difference is that the surface of the dental drill is much smoother than that of a concrete drill. Clearly, with a smoother surface there are many small impacts on the surface per second, while a rough surface leads to less, but more intense impacts. But a smooth drill being operated with low rpm would give rise to few small impacts, isn't that even smoother? The counter-argument to this could be that to drill a hole of a certain size you need a fixed number of impacts and the patients prefer a short treatment.

What are the physical and technical arguments that high rotational speeds have unanimously prevailed in all dentist's offices?

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    $\begingroup$ I guess you are too young to have had a dentist grinding away for half an hour with an old-style belt-driven low speed drill like this one youtube.com/watch?v=pC6KSTTytGw Otherwise, the answer is fairly obvious! $\endgroup$ – alephzero Oct 26 '20 at 21:57
  • $\begingroup$ Even harder: Dental drill by pedals imgur.com/a/Jpxllmo $\endgroup$ – HolgerFiedler Oct 27 '20 at 5:18
  • $\begingroup$ @HolgerFiedler Did Torquemada invent that? $\endgroup$ – David Hammen Oct 27 '20 at 10:46
  • $\begingroup$ @alephzero, HolgerFiedler: I luckily never had that experience. Can you describe the forces with the slow drill and how it's different at high drill speeds? Is the treatment duration the main argument to have faster drills? $\endgroup$ – A. P. Oct 27 '20 at 11:12
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    $\begingroup$ The physics demonstrated may be relevant: youtube.com/watch?v=Wn-IXgxNSiE $\endgroup$ – Sean E. Lake Mar 18 at 8:07
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I got this answer from a friend who is an orthodontic surgeon.

Without consulting Wiki (incomplete article) - I can say this off the top of my head - The rpm is closer to 400 K.

The speed is needed to give the bit/burr some rotational momentum to provide torque. There is no direct connection between the source of the energy- compressed air - and the burr. The compressed air is only at about 2.7 bar and spins a turbine in the head of the drill, which the burr is attached to. You can hold the burr with your fingers stationary from start-up - no torque like a concrete bit. Another mistake in the question is that unlike a concrete drill - most of the cutting takes place on the side of the burr from a sweeping motion, not at the tip pushing down on the rotational axis.

What I described here is the high-speed air rotor. The one that makes the high pitched whine. It has water cooling and lighting (optic fibers or piezoelectric) built into the head. It is used mostly to remove enamel with minimum discomfort. The "slow" handpiece - up to 200 K rpm has a motor with direct drive through gears to the burr. Can also have water and fiber optics. Much more torque and vibration. Does not cut enamel efficiently. The motor can be driven by compressed air or electric- more control and torque- more expensive. The handpiece can be "regular " to remove caries mostly. This is known as a Contra angle handpiece. More sophisticated ones are required to place implants and do endo/root canal treatment. On the same drive system you also fit a straight handpiece used to cut bone in surgery. Then you can also cut bone with a piezoelectric handpiece or a laser.

The one type (air rotor) that I assume the question was about - is described as an "abrasive device" - not a "drill" as I pointed out. They also come in the regular head (more torque) and small to reach inaccessible areas (less torque).

Air Turbine Handpiece

An air turbine handpiece is highly valued as a dental abrasive device that rotates at a high speed, and it is an essential device for dental treatment. Since its development, many studies have been conducted to measure and evaluate rotation performance and measure and evaluate noise. An air turbine handpiece uses compressed air as the driving force and is characterized by its small size, lightweight, and painless abrading at a high rotation speed. However, compared to an electric handpiece that uses a motor as the driving force, its torque is small and the noise level is high.

As such, improved performance and reduced noise for an air turbine, handpiece are desired. Considering that an air turbine handpiece has the equivalent rotation performance as turbine performance, it can be considered as a type of turbomachinery, and the fluid mechanics approach would be effective. In other words, it would be effective to first elucidate the internal flow of an air turbine handpiece and the relation between the performance and the noise characteristics and then control the flow. However, the main component of an air turbine handpiece, the rotor, is small and rotates at high speeds (250,000–400,000 min−1); thus, measuring the flow is not easy.

The whole subject is obviously a lot more complicated than the question posed by the OP. I think my off-the-cuff answer is adequate without going into too much technical detail.

Overview

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    $\begingroup$ Thank you for getting a professional on board. I see, a better comparison than a concrete drill would have been a milling machine. Can you explain how noise and vibrations reduce with increasing rotational speed? $\endgroup$ – A. P. Oct 27 '20 at 13:26
  • $\begingroup$ @A.P. The second-last paragraph says that the noise level is high. The last paragraph talks about the effort to achieve a lower noise level. Vibrations are decreased by more precise manufacture of the turbine and burrs. $\endgroup$ – Raffles Oct 27 '20 at 16:25
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Dental enamel is a hard material so the drill needs to exert a large force on it in order to break it. The force is proportional to both the drill radius (r) and it angular frequency ($\omega$, rpm), simply because the speed of the drill material at the interface is $v=\omega r$. So you could go for large $r$ and moderate $\omega$ as for concrete. However dental repair requires narrow holes. This drives the requirement of high angular speed $\omega$.

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  • $\begingroup$ Thanks, this is so far the answer which is addressing the reason I set the bounty the most. Could you elaborate why the force is proportional to the speed of the drill material? With the right gears also a slow movement can excert a lot of force. Do you mean the force due to the inertia of the drill during collisions? If so, could you add the fact that where the tooth breaks depends on the speed of the impact (if you agree), as indirectly pointed out by Sean E. Lake's comment. $\endgroup$ – A. P. Mar 20 at 10:39
  • $\begingroup$ If the outer surface of the drill moves slowly it exerts less force if the enamel slows it down and delivers less power. You can also think of the drilling as friction. Then the power(f.v) delivered is friction force (proportional to speed hence $\omega r$) times speed. Ultimately it is the power of the drill, the friction and width of the hole that set the rotation speed. You will want not too much friction to have a well determined hole. $\endgroup$ – my2cts Mar 21 at 15:02
  • $\begingroup$ But why is the friction force proportional to the speed? The typical model of sliding friction assumes the force to be independent of the speed. "You will want not too much friction to have a well determined hole." Doesn't that mean one should go for slower rotation? $\endgroup$ – A. P. Mar 21 at 17:29
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Teeth are brittle, which I painfully know since a school "mate" broke my incisor off during a fight (sudden floor contact). Hence, trying to grind big chunks out of it might cause more damage than intended (e.g. invisible cracks that cause caries years later). It is because bigger chunks require higher forces, no more complicated than that. Consequently one prefers smaller chunks and smaller forces, which requires finer tools and, of course, higher RPM in order to get the same cutting performance.

It is much like grinding tiles. Eagerly using the hammer drill in an attempt to get home from work early might cause the opposite: a huge pile of smashed tiles and no beer'o'clock. Using an angle grinder with high RPM and a diamond disc makes your wife happy.

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I have little experience with dental drills (although I have indeed just come from the dentist), but I have written a few milling programs on a CNC mill, so that I think: I can answer this one!

It's not entirely clear to me whether milling or grinding is generally used in dental treatment. But the considerations are similar. Let's start with milling: A milling cutter cuts chips from the workpiece (in this case, the tooth). At the very least, the cutting edge should be harder than the material being cut, otherwise it will not survive for long. In milling, there are two main parameters that affect the process: The speed of the cutting edge and the "feed" of the cutter.

  1. The speed of the cutting edge (the so-called cutting speed) can be easily calculated if you know the diameter of the cutter and its rotational speed: v = Pi * D * f. Of course, this only applies to the outer edge of the cutter. There are milling cutters that have the cutting edges at the bottom (similar to a metal drill). Then the cutting speed at the edge is like according to the formula - and it becomes smaller and smaller towards the inside. In the middle it is theoretically zero. However, one tries to avoid this situation if possible. The cutting speed is therefore the speed with which the cutting edge is moved through the material. It can be varied via the cutter diameter and the speed of rotation.
  2. The "feed" is actually about the thickness of the chips: Let's say a cutter with one cutting edge rotates 100 times per second and is moved into the material at 1 mm per second: Then each chip is 0.01 mm thick. If the cutter had 2 cutting edges, it would cut chips 0.005mm thick, because then a cutting edge would be fed through the material twice as often. The feed rate is always what you have to set for CNC milling. There it is specified in mm/min. If you want Chips with thickness d, your tool has n cutting edges and is turning with f turns per second, then the feedrate is d * n * f.

There are a few different angles at which the cutting edge of the milling cutter can be set. Nowadays, you just buy a milling-tool for a certain material, where the manufacturer has it all worked out. That is why I know almost nothing about that.

Now to the question of why dental drills turn so fast:

I am not an expert in the field of dental treatment, so as a physicist I would just like to make an educated guess: I believe that the high rotational speed is about small forces that are supposed to act on the tool, the handle and, above all, the dentist's hand.

The feed is literally in the dentist's hand. He moves the tool with his hand. I know from experience that the forces on the milling cutter can be very high if the material removal rate is too high (that is the chips are to thick). (I still remember how my milling machine rattled when I once accidentally removed too much material at once). The finer the chips you cut, the lower the forces acting on the cutting edge and therefore the whole tool.

In addition, the high rotation frequency means that vibrations from the milling are also transmitted to the handle at this frequency. (Is that ultrasound then?) I assume that the dentist is less disturbed by this when working.

When I think about it, the laws of grinding are very similar. The only difference is that the material is not cut, but rather "scratched out" with small particles.

Optimizing the milling process is always a trial and error process. You try out which cutting speed works with which feed rate for a certain material.

And of one thing I am sure: they do it because it works better!

Hope I could help.

*** Translated with www.DeepL.com/Translator (free version) ***

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