Usually you only get to see the finished product, the tip of the iceberg that is pushed out of the safe development-stage and then exposed to the real world.
For those who want to take a peek under the shiny surface, I plan to write a series of articles to illustrate the deliberation processes during the design stage. In this post I discuss the tuners of my upright bass.
One of the main reasons to buy an electric upright bass, is transportability. While compact size evidently leads to lower weight, I found that simply making it smaller is not enough to reach a comfortable weight for easy shoulderbag-ish transport in for instance a subway or at an airport.
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.
Of course there are already tuners that are lightweight, these are for bass guitars. However, – and I fully realize this is a nonlogical overruling ‘however’- I like the classical headstock with scroll too much to compromize on this headstock shape. I simply want lightweight tuners that fit a double bass’ pegbox type.
Searching the internet for lightweight sets of upright bass tuners, I didn’t find something that meets my desires. So I started experimenting…
Brass Tuner Experiment:
The first lightweight solution I designed, was a set of brass tuners (see below). 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:
Not bad, but it just didn’t feel right to buy a finished product, strip it, and have this large amount of waste material from it.
Second to the waste, there was the relatively large amount of work. If you are an employee working for a company, you need to make yourself unmissable so you won’t get redundant. For me – working alone – the aim is to make myself as missable as possible; the production process may take time, but preferably not my time.
Sadly, making the brass baseplate was very time consuming; the brass blank bar went through the procedures of predrilling; 3 different clamping positions and cnc programs per baseplate; a saw line; post drilling; countersink… Here each new clamping procedure really eats away time while also the chance of error increased. This led to even more waste (and loss of job satisfaction).
Last but not least, the loud sneering noise of brass milling made the workshop sound like a catfight in a busy abattoir; inspirational enough to perform a genuine kill your darlings, and loop the timeline back to the quiet, erased drawing board.
Diverge and deliberate
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. In this case ‘Setting a string under tension’ and start from there.
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. 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. BTW, in engineering the 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 blades 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.
Stripping the Tuner Baseplate
A worm drive with a baseplate like I had on my brass set, is relatively easy to install, because the position of the cog relative to the worm screw is fixed. But it isn’t the option with the lowest weight.
Also, the design with a baseplate takes a lot of forces which are – as engineers tend to say – undetermined; like a table with 4 legs instead of 3, it is one too many. This makes it unpredictable what the actual load of a particular leg is. In other words, an even load for every leg is statistically not the most probable distribution of load.
What you want, is a simple and clear scheme of forces. In the design I prefer, the peg+cog sit in the pegbox. The pegbox is holding the peg, while the worm screw with the tuning key prevents the peg from unwinding.
When the peg rests on a baseplate, it is unclear which partion of the load is held by the wooden pegbox via the pegholes and which part of the load is held by the screws with which the baseplate is attached to the pegbox. It may even vary over time if the wood of the pegbox holes wears out and the load then takes the path of the baseplate. Then the forces at play change a lot, also in direction. This is why I chose to hold the peg in place with bearings inside the pegholes in the wooden pegbox. A baseplate is not necessary.
To prevent the tuning pegs to jam like those of a violin or cello, the friction is almost eliminated using an Igus bearing especially designed for static load at the cog-side, and a brass ring with a tiny axial bearing at the opposing side of the pegbox. This makes the pegbox is holding the peg; the peg is an axle.
As a consequence, the load on the saddles via the worm screw is mostly axial and actually one of the two saddles is taking almost all the load (there is a small momentum also, which makes the non-compressed saddle pull away from the pegbox).
So the two saddles that hold the worm screw and tuning pegs have a very different load. In a computer simulation (Fusion360) I tried to map the stress and deformation patterns. 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 bending stiffness of the worm screw. In the end it turned out that the minimum practical shape was already strong enough, so cutting edge engineering was not necessary).
How About High Grade Plastics?
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). Fundamental design question; is metal necessary?
Choosing 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.
You can’t glue or mold pom easily if at all, so then you need to take a solid 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. The most economical basic shape out of which you can produce the cog +peg on a lathe would be an extruded plastic cylinder, where the production process may cause rest tensions due to faster cooling of the outside. All-in all, I think using pom for the worm gear is a dead end.
Let’s zoom in on the boundary conditions. The parts that need to be metal are actually only the surfaces that are susceptible to wear and creep. It is possible to reduce the solid brass cog wheel to a brass toothed ring with a composite plastic filling. But a ring is not practical; how do you make this ring while keeping it precisely round, how do you transfer the torsion forces from ring to the core that has the peg attached to it? How can you center the ring in further processes? Production is probably safer and stronger, more reliable and easier (=cheaper & better) when when you hollow out a solid cog wheel. To exactly match the centers, you can use the same clamping for the center(ing) hole and the toothed ring.
So, I found a supplier that makes very precise worm drive sets. The hollowed out cogs are excellent for glueing on a carbon fiber reinforced peg, so then cog and peg become one solid body.
The worm screw has a steel axle, a D shaft actually, I want this axle to sit in two omega shaped saddles. Since I am already working with carbon reinforced epoxy resin, this might seem an obvious choice. The huge advantage of epoxy resin is that it is a liquid. This means you can mass produce parts by simply pooring the resin into molds. So, no problem then when using epoxy instead of pom?
Well, contrary to pom, fiber reinforced epoxy is not a low friction material, which would mean the D-shaft of the worm screw would not run smoothly and therefore would wear out fast. So just like with the worm gear, only the contact surfaces need to be wear resistant and low friction.
I found low friction bearing inlays that could withstand long term (axial!) loads without deforming, made from sintered bronze. I can position the sintered bronze shaft bearings in the epoxy mold before pooring in the resin. And because sintered bronze – which is actually a porous kind of bronze – is impregnated with oil, it does not adhere to the epoxy. This makes it easier to recycle the materials.
Making the Tuner Saddles
The saddles are a rather straight forward omega shape. The aim is to have 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. Mass production and easy to scale up:
The Tuner Key Shaft
The only part of the tuner key that needs to be metal is the shaft, because of the sintered bronze bearing in the saddle. 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.
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.
Carbon Epoxy Tuner Keys
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 out 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 appearance was not planned, but because I didn’t have a short mill flute, I had to resort to a longer one. The longer mill flute has a bit of jitter at the tip which made path somewhat irregular, wich makes it look more ‘biological’ wood grain (I think most designers 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.
Tuner Cog Wheel and Peg
The hollowed out cog wheel will form a one-piece part together with the peg. Again, same idea; fill a mold with the cog and carbon reinforced epoxy resin and let it cure.
The set of ultralight tuners weighs only 360grams (4x ±90gr).
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. The (average) diameter of the (tapered) peg is 14mm, add to that 1x the thickness of the string say 2mm, then per full revolution of the peg, you reel in ( (14+2)*pi)/27 = 1.9mm. So when changing strings it will take around one second to reel in 1mm, 6cm per minute. This ratio provides enough precision for accurate tuning.