It might sound like lame design textbook language, but nonetheless I find it a valuable cliché, that for a systematic design process, you first determine the basic function and requirements and start from there. In this case the function is ‘Setting a string under tension’ and the special requirement is that it should be possible to use regular double bass strings like say Thomastik Spirocore.
The requirement of the use of regular double bass strings narrows options to diverge from tradition; using strings for headless necks with ball ends at both sides that can be set under tension with for instance a small thumbwheel-like mechanism, is not an option.
If you look historically at the violin and gamba family, you see that only double basses have evolved to have geared tuner mechanisms; violins and cellos just have pegs that clamp inside the pegholes.
You can set a string under tension in many different ways, but I understand and agree that in the evolution of basses the worm drive mechanism won, because it has a property none of the other methods have; the quintessential property of a worm drive is that it transfers rotation in one direction only; you can make the cog rotate by turning the worm screw, but the other way round – turning the cog to rotate the worm screw, will not work. Perfect for tuning strings.
Wormgear (image source: Wikipedia). In engineering a common way to see a worm screw, is as ‘a cog wheel with one tooth’.
I also find the ergonomic operation of tuning with the left hand while plucking the string with the right comfortable to do. The high gear ratio – as opposed to simple 1:1 pegs on cello’s or violins – allows smooth and precise tuning. Also the wing of the tuner keys provide easier operation than for instance a micro knob like you find on tail piece fine tuners.
So after this deliberation exercise it is re-established; the worm drive is and stays my basis for the design of the tuners.
One of the main reasons to buy an electric upright bass, is transportability. What you want is a comfortable weight and size. While compact size evidently leads to lower weight, I found that simply making the instrument more compact is not enough to reach a comfortable weight. The catch is that an acoustic upright bass with its large hollow volume, actually has a very low density because the instrument is mostly air, while an electric upright bass is mostly solid.
High density parts like tuners are a logical choice to start reducing weight and so gain transportation comfort. A set of 4 tuners for an acoustic bass from conventional manufacturers – like Rubner or Sloane – weighs around 0.8-1.2kg. When the goal is to design an electric upright bass of say, 4kg, conventional tuners alone would make up at least one fifth of the total weight. So it is worth investigating this. As a design challenge I assumed that the tuners may weigh 10% of the total weight of the instrument.
Searching the internet for lightweight sets of upright bass tuners, I didn’t find something that met my desires. Of course there are already tuners that are lightweight, but these are for bass guitars. I simply want lightweight tuners that fit a classical double bass’ pegbox. (see also my article on headstock design)
The first lightweight solution I designed, was a set of brass tuners. This set was based on a conventional set where I bored out the pegs and replaced the baseplate with a self designed and produced version. The weight of the set of 4 tuners was 650 grams:
Boring out brass pegs
CNC milling brass bar
CNC milling brass bar
Sandblasting 150 grit
Brass patina process
Set of 4 tuners, total weight 650gr
From 1kg to 650grams is not bad, but it just didn’t feel right to buy a finished product, strip it, and have a large amount of waste material. Also the weight reduction turned out to be somewhat disappointing.
A worm drive with a baseplate like I had on my brass set, is relatively easy to install 'foolproof', because the baseplate ensures that the cog sits on the middle of the worm screw. But it isn’t the option with the lowest weight.
Next to weight reduction there's another reason to get rid of the baseplate. The proper or 'ideal' situation when using cogs to transfer rotation, is to fix the position at which the cogs rotate - in a bearing - to prevent the cogs from being pressed together. In that ideal configuration the forces on the teeth of the cogs are only tangential. You need the cogs to transfer rotation, when the cogs lean on eachother, they get jammed.
Since the goal is to make lightweight tuners, the baseplate should be a thin sheet of material. But a thin sheet is not suited to perform the task of a durable and dependable bearing, it will wear out over time. So the designs of these baseplates often have a thick baseplate, or - bad practice - a slotted hole, which keeps the cog centered on the worm srew, but does allow the cog to press against the worm screw.
So to recapture; the cog of the peg should not lean on the wormdrive. This is why I chose to get rid of the baseplate all together and simply hold the peg in place with bearings inside the pegholes in the wooden pegbox. The pegbox itself is already a baseplate, an extra baseplate is not necessary.
Now I have a simple and clear scheme of forces: The peg and cog sit in the pegbox. The pegbox is holding the peg, while the worm screw with the tuning key prevents the peg from unwinding. The teeth of the cog are only loaded tangentially.
Worm prevents peg from unwinding, the force on the cogs' teeth is tangential.
To prevent the tuning pegs to jam like those of a violin or cello, the friction is almost eliminated using flanged Igus bearings especially designed for static loads.
As illustrated above, the load on the worm drive is axial. The result is that the two saddles that hold the worm screw and tuning keys each have a very different load. As shown in the diagram, the saddle screws are loaded with pull, shear and momentum.
Forces on the saddle screws. Action forces in red, Reaction forces in blue.
I made a computer simulation of the stress and deformation pattern (Fusion360). This just as an indication to see what is going on, not so much to get reliably quantized results (I could have, but that would demand a lot more input data I didn’t have, like the stiffness properties of the materials involved. In the end it turned out that the minimum practical shape was already strong enough, so cutting edge engineering was not necessary).
fusion 360 deformation simulation of axial force on a schematic worm wheel between two saddles
Conventional tuners are worm drives made from metal, usually brass for the cog and steel for the worm screw. This is because brass is self lubricating, and steel is strong. This combination is a major advantage because you don’t need oil. But brass also has a very high density (= heavy), even higher than steel.
There are also strong plastics with self lubricating properties, like pom (Polyoxymethylene). Using a plastic like pom would lower the weight by factor 8 and keep the desired self lubricating properties. Pom is also regularly used for gears, but since the tuners of a bass are gears that most of the time have a static load, I expect that the teeth and worm made out of pom will probably deform (creep) over time (decades). Also UV light and dirt might make pom degrade.
Other disadvantages are that you can’t glue or mold pom easily if at all (in a small workshop setting), so then you need to take a solid bar and remove material until you have the shape you want. The production process would become expensive, probably using a cnc lathe in several procedures to make the cog plus peg out of one cylinder piece. Quality control in plastics is difficult because there may be tensions due to faster cooling of the outside (also in stock material). All-in all, I think using pom for the worm gear in a small workshop setting has too many uncertainties.
The parts that need to be metal are actually only the surfaces that are susceptible to wear and creep, which are the teeth of the cog and worm. It is possible to reduce the solid brass cog wheel to a brass toothed ring with a composite plastic filling.
Milling out a cog to a ring
Peg mold ready for filling with carbon reinforced epoxy
One-piece tuner peg with cog
Historically, pegs are conical, because this conical shape provides the wedge clamping principle as is still used in for instance violins and cellos.
Wedged tuner peg (of a cello), a 'single axis gear'
Notice the wing of the cello peg is much wider (37mm) than the diameter of the peg itself (14mm). This is actually a gear (of ratio 37/14), which means it is around 2,5 times lighter to turn at the wing than to turn at the peg. You could compare it to having two cogs of different size on the same axis (a really clever innovative expansion on this 'same axis gear' idea is the Variomatic, which was invented near where I live).
The clamping property is the main reason for having the conical shape. The other advantages are ‘lucky’, as you sometimes get when designing and things fall conveniently into place.
The first ‘lucky’ secondary advantage is that winding the string towards the thicker part of the peg makes that the string winds neatly without gaps and even tightens the previous winding somewhat. This makes winding a new string easier. This method of winding where you do not overlap the (last few) windings, will also give a nice ‘anchoring length’, meaning the tension build up in the strings end is gradual, it is spread out over a longer length.
In the ideal situation the string runs from the tuner peg to the top nut without touching anything. When the tuner pegs lie in the same plane and the top nut is placed well above this plane, there should not be a problem.
Unfortunately... in the bended classical shape of the pegbox the tuners do not lie in the same plane, and this almost ruins the effect… And here the second advantage of the conical shape comes into play, because when alternating the pegs left and right in a pegbox, the strings ‘fly’ over the thin end of the nearest peg more easily.
When designing the pegbox (and topnut /fingerboard height), the greatest concern goes to the position of the D-string tuner peg, because this one lies quite deep in the pegbox (almost below the horizon so to say) and makes the ‘fly over’ at the thicker part of the G-string peg challenging.
Keep in mind that when changing strings, you wind up the strings towards the thicker part of the peg (towards the tuning key you are turning), because this is how the pegbox and tuners are designed to get the fly-over.
Since I am already working with carbon reinforced epoxy resin, I might as well use it for the saddles also. The huge advantage of epoxy resin is that it is a liquid that solidifies when mixed with a hardener (and in this case, after that cured in an oven). This means you can mass produce parts by simply pooring the resin into molds.
Carbon reinforced epoxy is not suited to be used as a bearing material, it doesn't glide well. So I placed flanged bearings (also Igus) inside the saddles, now the key-D-shaft with the worm runs smoothly.
The saddles are a rather straight forward omega shape, a saddle is really just a bearing casing with two flanges to fit the screws (fun fact of the word omega is that it is the greek letter for the long ooo -sound, while the omicron letter is for the short o sound. So you have o Mega and o Micron).
The goal is to have a steady quality of high precision parts while keeping the production time and energy consumption at a minimum. To achieve this, I used the cnc machine to make a master dummy out of phenol formaldehyde resin. With this dummy I made a bunch of rubber molds. This concludes more or less the complete preparation for the production line of the saddles.
To make the omega saddles, I just have to (re)fill these rubber molds with carbon reinforced epoxy resin. Small workshop 'Mass Production' and easy to scale up:
Master mold out of phenol formaldehyde
Cast rubber mold of omega saddle
'Mass' production of saddles
Drilling screw holes in a saddle
I can apply the same recipe – or style even I used for the omega saddles, to the wings of the tuner keys; use molds. So I milled the key molds out of phenol formaldehyde resin. The mill path lines are just 0,2mm apart, which makes it somewhat resemble wood grain. Actually this wood grain-like appearance was not planned, but because I didn’t have a ball end mill flute, I had to resort to a straight one. I suspect most designers would feel the urge to sand the mold to a smooth finish, but I actually really like that you can see the details of ‘how it’s made’ in the finished product.
It was quite a challenge to find the right filling method, because it is a deep mold with a small opening. With some frustration, trickery and skill development I managed to control the molding process to such a degree that incapsulated air bubbles are prevented.
The only part of the tuner key that needs to be metal is the shaft, because it goes together with the worm. For the rest of the key I can use molded carbon fiber reinforced epoxy resin, which makes that color and method are consistent and production is also relatively easy to scale up.
Actually... It is not really as easy as this line of thought suggests. The torsion of the epoxy tuner key wings when winding the string, needs to be coupled with the steel D shaft. To achieve this, I bored out the D-shaft and glued in a Ø4mm carbon rod. Drilling a 4mm hole into a ¼ inch D-shaft requires perseverance to master; this paragraph of a few lines represents months of R&D time.
Boring out the D-shaft
D-shaft bored out
Key molds for mass production
Tuner key after demolding
Key mold cnc lines
Tuner key 'woodgrain' detail
The set of ultralight tuners weighs only 300grams (4x ±75gr) which is less than 10% of the total weight of the bass (3,5kg).
The gear ratio of the cog-worm gear is 1:27. This means it takes 54 half turns (27 full turns) of the tuner key to achieve one revolution of the peg where the string is wound around. When changing strings it will take around one second to reel in 1mm, 6cm per minute. This ratio provides enough precision for accurate tuning.