Introduction to Materials

Seb_Zeppelin

24 May 2020, 17:22

Hi All,

I have been trying to find some information on which materials are used in keyboard plates, and why. I have found a lot of discussion and a lot of people sharing their experience trying different materials. I am amazed and encouraged to see the range of thinking going on, and the ideas being executed! One of the things I notice however is that there isn't much technical information on Material Science available on the forum. As a mechanical engineer, I thought I'd try and write an 'Introduction to Materials' to give those who are interested a way into learning about the maths and phyiscs of it all.

I'll start with some general basics and then going into detail about keyboards. Material science is a deep subject, but it is possible for anyone to understand the overarching concepts behind materials selection, which is the engineering process to pick the right material from the thousands that are available. One of the goals of this post is to give anyone enough knowledge to ask informed questions and do their own research by giving them the right terminology to search for.


1: Let's start off with a few definitions:
The first thing to note is that commonly used words like 'strong', 'stiff' and 'hard' have very specific (and different) meanings in materials science. These are important to understand, because a particular material may be strong but not stiff, or strong but not tough, or stiff but not strong! Carbon fibre is actually not very stiff
  • The strength of a material requires careful definition. It represents is how much force is required to permanently deform or break it. This ranges from strong to weak. There are different sub-types of strength, for example commonly used are '0.2% proof strength', which is how much force is required to plastically deform a material a very small amount, and 'Ultimate tensile strength' which is the force required to deform and break a material (called fracture or rupture).
  • The toughness of a material is how much energy is required to break it. This ranges from tough to brittle.
  • The hardness of a material is how resistant to indentation or scratching a material is. It ranges from hard to soft. It is also a relatively crude definition of strength, but is useful because we often care about how resistant a material is to cosmetic damage such as scratches.
  • The stiffness of a material is how much it moves (technically called the deflection) for a given applied force. It can be measured by the Young's Modulus of a material. This ranges from Stiff to Flexible. Stiffness is more complicated and subtly different from strength and toughness, because it also depends highly on the geometry of the component.
  • The damping capacity is a measure of quickly energy from vibrations is absorbed by the material. Picture a bell made from plastic compared to one made from bronze - the sustained ring of the bronze bell occurs because the material does not absorb the vibrations easily. The plastic bell will just give a dull 'thud' when struck, because it absorbs the energy of the impact much more quickly.
Imagine I have two metal rods; one twice the diameter of the other. It is obvious that the bigger rod will be stronger and stiffer. But by how much? Doubling the diameter means I have quadrupled the area (area is proportional to the quare of the radius, i.e. r^2. If r is multiplied by 2, r^2 increases by 2^2=4). In tension (i.e. pulling along the length of the rod) this means the strength will have also increased by a factor of 4. However, if I try to bend the two rods over my knee, the difference in stiffness will be much more dramatic. Bending stiffness for a round rod is proportional to r^4. (look up 'beam bending' and 'second moment of area' for more detail). If r doubles, r^4 goes up by 16. So my thicker rod is 16 times harder to bend! A keyboard plate is a very long rectangle in cross-section, so the relationship is different from the rod example. In a plate, stiffness varies with height^3. doubling the thickness will therefore increase the stiffness by a factor of 8. The shape has a strong effect on the stiffness; this is why structural steel beams have 'U' or 'I' shapes to maximise their stiffness for a given quantity of material.

So, what does this mean for keyboard plates? Well, thickness is by far the most powerful factor to control the deflection of the plate. Crucially however, a plate does not need to be flat. Even local thickening can dramatically increase the stiffness of a plate. Acrylic is relatively easy to join, so to resolve the classic 'I can't get my switches to snap into a thick acrylic plate' problem, consider using a thin plate and bonding ribs to the back of the plate inbetween the switches. Depending on the case, you can fit very deep (and therefore stiff) ribs.


2: Material types and categories
The second important thing to remember is that there are many, many different types of materials. 'Steel' for example is a whole category of differeny alloys, which can have significantly different properties (and costs!). One thing most steel alloys share is very similar Young's modulus (within a range of +/- 10%), while their strengths and hardnesses vary dramatically (high strength steels may have an ultimate tensile strength (UTS) up to 4 times low strength steels). For the same geometry, stiffness will therefore be very similar. Selecting the correct alloy requires careful consideration of the application. For a keyboard plate for example, stiffness and internal dampening are the important parameters. Toughness, ductility, weldeability and to some degree corrosion resistance are secondary. Steel alloys are often developed to meet other demanding requirements (for example toughness, which is a fairly irrelevant secondary parameters for us). Therefore, we need to be careful when someone says something like "This aerospace-grade steel has high strength, so is perfect to use for the plate of a keyboard". High strength is essential for aircraft landing gear where high forces are encounteded and integrity (i.e. guarantee of not breaking) is safety-critical. In a keyboard plate we aren't really concerned about strength; we don't come close to breaking a plate. Instead we care about stiffness, sound and appearance.

In most applications, metals tend to be used as alloys of several chemical elements. Apart from speciality applications, it is almost unheard of to use pure elements. So be careful when someone talks about a 'copper' plate. Which alloy do they mean? Copper alloys range continuously from relatively pure copper to brasses, bronzes (plural as there are many varieties) and exotic alloys such as beryllium copper or copper nickel. Copper alloys again tend to have somewhat similar Young's modulii, but will vary dramatically in their internam dampening - which contributes to their sonority (how well they ring after being struck, like a bell or a gong).


3) Requirements
In almost every case the user of a device doesn't care about the underlying physical properties such as stength or stiffness. In a keyboard we care about the emergent properties that arise from the physical properties, e.g. sound, keyfeel and aesthetics.

One of the things I see often in discussions around materials are very detailed questions such as 'does the roughness of the plate affect sound?', or statements such as 'the strength of a material will affect the sound', followed by a long discussion. The answer to a lot of very specific questions like this is 'Technically, yes. But in practice, only insignificantly'. Some unaware (or downright stubborn) people then absorb only the first word ('Yes') and go off to try and polish their plate to improve the sound for hours on end. Engineering is all about trying to find the easiest way to effect a desired outcome. In the case of sound, the mounting rigidity of the plate, the stiffness of the housing, presence of lube, will all have much more of an effect than the key plate surface finish.

Note that this example is a closed question - there is only 'yes' or 'no' as an answer. An important approach in engineering is to try and ask more open questions suc has 'what are all the things that could affect the sound a keyboard makes?' and 'Which of these has the biggest impact?'. These open questions are part of divergent thinking is an important way of exploring and recognising that many factors contribute. and identifying things do consider. It will then prompt questions such as 'How do I assess the noise the plate material makes versus the noise the plate mount makes?'. This allows you to logically build up understanding and converge on the best answer rather than trying to jump to an answer immediately. Very often when you see a novel idea or a clever solution, it has not been arrived at just by a sudden single jolt of inspiration, but by a lot of consideration and refinement.

Another example would be someone who enjoys cars stating: 'I want to reduce the weight of this car that I'm going to use exclusively as a weekend racer'. Some individuals will go out and spend £2000 on a carbon fiber bonnet because 'it's lighter'. This indivudial would be much better off first removing the rear seats and as much of the interior trim as practical first. This will have the same effect (reduced weight) at virtually no cost. But our individual might go and but the carbon bonnet anyway (without removing the interior) because it also looks cool. So which was your main objective to begin with? Weight reduction or aesthetics? The engineering discipline that deals with this is known as Requirements Engineering or Systems Engineering and is a whole field of it's own.

The key lesson for us is to think in advance what you want to achieve, and then focus on achieving that. Quite often we have an idea of a solution ('I want a titanium plate because it's stronger.'), but haven't really thought about the requirement. In this case, the person probably meant stiffer, not stronger. You'd only want a stronger keyplate if you are worried you're going to break it - which I hope isn't the case! So, having realised that we actually want more stiffness, we find that titanium is actually less stiff than steel so will defom more and isn't the material to use. Often your first idea comes with many requirements that you haven't realised. The lesson here is that a little thinking about requirements can dramatically shape the final solution.

Want to make a keyboard heavier? Don't try to make a tungsten switch plate, just bolt/glue in some extra weights to the back of the case! If you persist with the tungsten plate anyway, recognise that your goal wasn't to make the whole keyboard heavier, but perhaps to do it for aesthetics, or an experiment to see what happens, or even just for the sake of doing something for the first time. These are all equally valid requirements / reasons. Often, the first solution to a requirement won't turn out to be the best. Consider lots of options before deciding.


4: Sound
The sound a single oject such as a bell or a metal plate makes can be predicted and simulated fairly accurately. A 3D finite element analysis of the geometry allows the mode shapes an object will assume when excited (such as through being hit). Each shape will have an associated frequency. Multiple mode shapes will be superimposed on top of each other to give the whole sound. If the internal dampening of the material is understood, it becomes possible to predict the ring of single objects such as bells or plates.

The complexity arises when trying to extend this to assemblies. If parts are not well joined together (i.e. not in permanent contact such as a glued or bolted joint, then things become much harder to describe. Gaps result in 'rattles' where parts strike each other and are in intermittent contact. This whole situation is highly non-linear, and therefore much, much harder to model and predict. In keyboards, gaps between the keyboard plate and the housing, or the switch housing and the plate are common causes of the characteristic sound of a keyboard.

From a materials perspective, the main influences on sound are internal dampening (formally its damping capacity). Plastics and soft materials tend to readily absorb vibrational energy and dissipate it as (minute amounts) of heat, which is why they sound dull when struck; you can't get a 'ding' sound out of a plastic bucket, but you can from a metal one. Metals are therefore called sonorous, although there is significant variation in their damping capacity. Brass and especially bronze are known for their warm sound compared to other metals, this is due to their low dampening capacity. Steel also generally has a lower dampening capacity. Titanium has a higher capacity compared to most metals, and grey cast iron can have as much as 20 times the dampening capacity of other iron alloys such as steel.

Note that sound is much more subjective than things like strength and stiffness, where we can conclusively say we want greater stiffness and then design for this.


5: Conclusions
Theory is always second to experiment. No matter what someone like me predicts, if someone actually builds a keyboard with a plate made from wood, they will have the best available information on how that wooden board actually behaves. The prupose of this post is to help people realise that it is important to try to understand the underlying physics when analysing the outcome, especially when deciding what to do next. For example, someone looking to build a quiet keyboard might try out a titanium plate "because it's stiffer therefore will be more quiet". They will find that it is quieter as predicted, although this will be because of high internal dampening rather than differences in stiffness. If someone else then tried to qo quieter by using an even stiffer material, they won't get the result they expect because they have not understood the fundamental reason the first person's keyboard succeeded. So, although considered in isolation an experiment usually trumps theory, experiment and theory linked together is the most powerful combination. There is no shortage of experiments in the community, hopefully some more theory will help us design and make even better devices!


6: Further reading
In case this very long post isn't quite long enough, I can recommend the following books to get into the subject of Materials science. In no particular order:
  • Materials Selection in Mechanical Design, Michael F Ashby, Butterworth-Heineman. Provides a good discussion on how materials are chosen as part of the engineering design process.
  • Materials Science and Engineering Handbook, Shackelford & Alexander, 2001, CRC press. Provides an exhaustive reference of material propery data.

If anyone has any questions (including corrections!), or requests for other topics to be covered, please let me know and I will expand and update the post as appropriate. Any feedback is welcome including criticism or the style or pointing out mistakes. If anyone thinks this information should go elsewhere (such as the Wiki maybe?) I'd be more than happy to move it.

Thanks, and happy thocking!
Last edited by Seb_Zeppelin on 26 May 2020, 00:17, edited 3 times in total.

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mcmaxmcmc

24 May 2020, 20:55

Wow, that's really lengthy thread chock full of information. Thanks for writing this! Very useful.

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Willy4876

24 May 2020, 22:32

This is a great intro to material science. I have taken one course on this in university, but we barely went into any detail. It is good to have a plain language introduction to some of the more advanced concepts.
Seb_Zeppelin wrote:
24 May 2020, 17:22

The strength of a material requires careful definition. Very approximately is how much force is required to permanently deform or break it. This ranges from Strong to Weak. There are different sub-types of strength, for example commonly used are '0.2% proof strength', which is how much force is required to plastically deform a material a very small amount, and 'Ultimate tensile strength' which is the force required to deform and break a material (called fracture or rupture).[/list]
Could you rephrase the definition of strength? The second sentence is a little awkward. Also, a nit pick, but I think that strength should be bold here.

Also, you might consider adding internal dampening to your list of definitions. I wasn't familiar with the term and while you did define it it was kinda buried.

Overall well done!

Seb_Zeppelin

24 May 2020, 23:17

Good suggestions Willy, I have updated the original post as per your suggestions. Thanks for pointing these mistakes out!

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dogmantime

26 May 2020, 00:04

great thread, really nice to see someone who's capable articulating these concepts, the entire community could benefit from understanding them properly I'm sure

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photekq
Cherry Picker

26 May 2020, 00:26

Such a great post, thanks for taking the time to write this out. I hope a lot of people see this, because it's an essential read.

I studied mechanical engineering at university too, and I think you've effectively condensed all of my materials courses into one post :mrgreen: You even reminded me of one or two details I'd completely forgotten about.

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