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1.13 Gears and gearing
Gears and gearing (Figure 7) are a feature of practically all machinery and are by no means confined to food mixers. The function of gearing is to transmit rotary motion and power from one place (for example, a motor) to another (in the case of the food mixer, the tools doing the mixing), usually with changes in speed, direction or both. You’ll find gears and gearing in all types of powered transport (including bicycles), in factory machinery and in many household items, from electrical drills to cameras. The gears can either be driven directly from wheel to wheel (by friction or interlocking teeth) or remotely (by belt or chain).
Figure 7: A selection of gears: top left wooden gears from a windmill; bottom left steel gears from heavy machinery; top right gears manufactured using ‘micromachining’ on a microscopic scale; bottom right a theoretical gear built up at an atomic level
So why do we need gears and gearing?
If you’ve ever ridden a bike, you’ll know that it’s easier to cycle uphill in a low gear – less effort is needed to turn the pedals. The penalty is that you appear to go more slowly – you need more turns of the pedal crank to cover a particular distance. The situation is reversed when going downhill, so you change to a higher gear. There is a pedalling speed at which your legs can operate most efficiently and comfortably, and the purpose of the gears is to allow your legs to work at that optimum speed.
The same principle applies to an electric motor or car engine. You can’t do a hill start in a car in fourth gear, and travelling along a motorway at 70 mph in first gear is unfriendly to the engine!
Let’s look at the working of gears in a bit more detail. Figure 8 shows two wheels with their rims in contact. Friction ensures that turning one will cause the other to rotate – they’ll act as a pair of gearwheels. If there is no slipping between the two as they move, then, at their contact point, the velocity (v 1) of the rim of gear 1 must equal the velocity (v 2) of the rim of gear 2, i.e.
But the two wheels have different diameters. If the velocity of their rims is the same, they must be rotating at different rates. The smaller wheel will complete more than one revolution as the larger wheel turns one revolution, simply because its circumference is smaller.
Rate of rotation is usually expressed either as the number of revolutions in a given time (e.g. revolutions per minute, or rpm) or in terms of a quantity called the angular velocity. Angular velocity is the number of degrees turned in a given time, like ‘ordinary’ velocity is the amount of distance covered in a given time. Angular velocity is conventionally symbolised by the Greek letter ω (‘omega’), and its units are degrees per second (as long as the angles are expressed in degrees).
Figure 8: Two wheels in contact
The circumference of a circle with radius r is equal to 2. A wheel with a larger radius will clearly have a larger circumference. If it is being driven from another wheel, then the larger the wheel being driven, the slower it will turn.
In order to work out the angular velocity, we need to work out how many degrees are turned through in a given time. This is all very well, but it would mean that we would always have numbers that are difficult to manipulate cropping up in calculations of angular velocity. So we use another system, which is to describe a circle as sweeping out a number of radians.
You can think of a radian as being just like a degree, but rather than there being 360 of them in a circle, there are 2π of them. This may sound complicated, but it has the huge advantage that it makes the maths easier!
Because the circumference is 2πr, and the wheel turns 2π radians in the same time that the circumference is ‘moved’ this distance, the angular velocity in radians is simply:
For our two wheels with radii r 1 and r 2, we have that
Since at the point of contact v 1 = v 2, combining these two expressions gives
The fraction r 1/r 2 defines the gear ratio of this particular system. A similar thing applies to gears with teeth, where the teeth interlock to turn the wheels, the ratio being N 1/N 2 where N is the number of teeth on each wheel. The lower the gear, the lower the value of the gear ratio. Notice also that directly-driven gearwheels like those in Figure 8 rotate in opposite directions to one another.
Gear ratios are the same for indirectly-driven gearwheels (Figure 9), whether by belt (r 1/r 2), or by chain (N 1/N 2). However, as you can see, both gears rotate in the same direction here.
Figure 9: Indirect gearing
Not all manufacturing processes can be used sensibly to make gearwheels, so occasionally we’ll look at the manufacturing aspects of some of the other parts which go into making the complete food mixer.
Figure 10: An exploded view of the train of gears in the food mixer
Figure 10 shows an exploded view of the gear train from the food mixer in Figure 6. You can see that this is a fairly complex assembly of intermeshing parts. The complexity arises because not only does the mixing tool spin on its own axis but the axis itself also moves around a circular ‘orbit’ in the bowl of the mixer. In addition, this particular gear train ‘gears down’ the motion from motor to tool by a factor of 20. But don’t worry about the details of Figure 10. We’re going to concentrate on the simplest gearwheel in this assembly, which is known as the planet gear. A photograph of this and its associated static ring gear is shown in Figure 11.
Figure 11: The ring and planet gears
1.14 Getting into shape: some basics
If you think about it, the number of different things you can do to a raw material to get it into a desired shape is pretty limited.
You could melt or liquefy the raw material and pour it into a mould that replicates the shape you want – as if making ice-cubes.
You could squeeze, squash, hammer or stretch the material into its required shape – similar to modelling with clay or Plasticene, or rolling-out a piece of dough.
You could start with a lump of raw material and cut it to shape, in the same way Michelangelo transformed a block of marble into the statue of David.
Finally, you could assemble your shape by taking different pieces and joining them together using any number of joining methods: screwing, nailing, gluing, welding or stitching for example – innumerable products are made in this way, ranging from clothing to cars and from computers to aircraft.
So, starting with a given mass of raw material, whether it is a pile of granules of plastic, an ingot of steel, a lump of clay, a block of stone or whatever, the basic process routes for manipulating it into a specified shape are essentially limited to:
However, it’s not quite as simple as that. To start with, the wide range of engineering materials means that there are many, many variations on each of these process routes. So far we have principally considered materials just to be ‘stuff’ that has a series of properties. We have seen that these properties vary from material to material but we have not really started to think about why they vary. We are not going to go into the material science behind this in any real depth in this course but what is important to realise is that materials, and hence products, exist on a whole series of size scales. We are all familiar with the sizes of tangible products ranging from a teacup all the way up to a suspension bridge or the Millennium Dome! We can call this scale macro structure. You should also be familiar with the concept that the properties of materials are controlled by the type and arrangement of their individual atoms and molecules, usually called atomic structure. Much of materials science and engineering is concerned with a size scale in between, too small to be seen with naked eye, but much larger than individual atoms and molecules. This middle ground is termed microstructure.
The properties of solid materials can be profoundly influenced by their microstructure and because the microstructure is often changed by processing, the properties of materials, and hence products, are dependent on how they are processed. Examples of these different size scales are given in Scales of material structured.
Even where a particular type of material and process combination is feasible, it could just be hopelessly uneconomic to contemplate it as a manufacturing option. Finally, the shape of the product is also important. Some manufacturing methods are better suited to particular shapes than others. Indeed, the shape of a product is a good attribute to begin with when deciding which processes are feasible. So one of the first things we must do is think about how we describe shape. One approach to this problem is given in Classifying shapes.
1.15 Scales of material structure
Exactly what influences the properties of a component can depend on many things: We’ve already mentioned the importance of materials properties and the component geometry, for example.
The component geometry is an example of structure on a macroscopic scale. Look at Figure 12(a), which shows the second Severn Crossing. The bridge has the structure it does because it was built to achieve the task of providing a path for vehicles across the estuary, at an acceptable cost and with complete safety during construction and during use. The central portion is an example of a cable-stay bridge, where the deck of the bridge is hung from the supporting cables. This structure was chosen, presumably, as being the best solution.
Figure 12(a): The second Severn Crossing
If we look at the structure of a support cable for such a bridge (Figure 12(b)), we see that it is not a solid bar of material, but is ‘woven’ from many thinner strands of wire. This structure (still a macrostructure) is chosen for several reasons, including safety, as with a reasonable safety factor, it shouldn’t matter if a flaw causes the failure of one wire strand, as there are multiple paths for the load that the cable is supporting. In addition there are some beneficial properties that cable structures have compared to large single strands, such as flexibility.
Figure 12(b): A steel cable
The structure story doesn’t stop with the material for one strand, though. I’ve already indicated that steel is a mixture of iron with carbon, and how the carbon affects the structure of the iron on a microscopic scale depends on the amount of carbon in the iron, and the heat treatment that the iron has had. Figure 12(c) shows the micro structure of a typical steel (so-called because we are looking at the steel on a microscopic scale). This shows that as we look in closer detail, we begin to see that what we thought was quite a smooth, plain metal surface has a lot of underlying structure to it. Once we’ve zoomed in so that we can see features as small as 10 micrometres, it becomes clear that the metal is composed of small individual ‘grains’. This structure in turn determines the mechanical properties, like strength and toughness, of the steel. We can change the structure of the iron: through alloying and heat treatment the grain size and structure can be altered, so tailoring the properties of the material that we make.
Figure 12(c): Optical micrograph of steel
Figure 12(d) zooms in still further, showing us more of the structure within the grains themselves. Influencing things at this level is more complicated, but it can be done, and again can help to tailor the material properties.
Figure 12(d): Transmission electron microscope (TEM) micrograph of steel
Finally, we can zoom down to the level of the atomic structure (Figure 12(e)). In this case, we’re looking at carbon, one of the elements in steel. The bonding between the atoms, and the structure they take up, critically influences the material properties, but there’s nothing we can do to change it! Some materials are more useful than others because they have the right sort of atomic bonding and atomic structure, and a microstructure that we can do useful things with. In Figure 12(e), you can see that each carbon atom is surrounded by six others in an hexagonal pattern. This is simply the way that carbon atoms arrange themselves in this instance (carbon is versatile in that it can adopt several atomic arrangements).
Figure 12(e): Scanning tunnelling microscope image of carbon atoms
We will refer to microstructure frequently in this section. It is a key factor in determining mechanical properties, and it can be greatly affected by the choice of manufacturing process for a material.
1.16 Classifying shapes
If the profile of an artefact does not change along its length – like a pipe, electrical cable or aluminium cooking foil – then it can be classified as having a simple (continuous) 2D (shorthand for two dimensional) shape. Many 2D products are used as the raw material for processes which make them into three-dimensional shapes. PVC window frames for example (Figure 13) are made from continuous extrudate (the product of the process of polymer extrusion) which is cut into suitable lengths and then joined together by fusion welding.
Figure 13: Extruded uPVC window frame
Most artefacts have profiles that vary in all three axes. Many processes are suitable for the production of 3D shapes, so we need some further breakdown of this high-level classification. We will split 3D shapes into sheet and bulk shapes.
Sheet products have an almost constant section thickness, which is small compared with their other dimensions, but without any major cavities. Therefore washing-up bowls and car-body panels (before assembly) are examples of sheet products (Figure 14).
Figure 14(a): Plastic washing up bowl
Figure.14(b): Car body panel
The majority of cast products fall into the category of bulk shapes, and have complex forms, often with little symmetry. If they have no significant cavities in them we will call them solid (Figure 15) but if they do have cavities, they will be classed as hollow. The cavities in hollow objects can be quite simple but they can also be more complex, involving re-entrant angles (re-entrant angle: a shape in the mould which would prevent the product from being removed from the mould after solidification), as is the case with the carburettor body in Figure 16.
Figure 15: Plastic saucepan handle and its mould
Figure 16: Zinc alloy carburettor body showing complex internal cavities
One way to present such a classification is by using a hierarchical tree diagram. Figure 17 shows such a diagram for our shape classification. A similar presentation is often used to show family trees. You can see that as you progress down the tree, the shape definition becomes more and more precise. One problem generated by this classification of shape is what to do about containers and similar objects. Depending on how you view the exercise, they could be either sheet, since they tend to have uniform section thicknesses, or hollow since they often have cavities which are entirely enclosed within the artefact. We have chosen to classify them as hollow shapes.
Figure 17: A hierarchical shape classification tree
Consider the following list of components and artefacts and classify each according to the shape classification given in Classifying shapes.
We’ll now start to look at the different classes of manufacturing processes, and their advantages and disadvantages.
Casting is one of the easiest classes of process to understand. Casting is simply a process where a mould is filled with a fluid, which then solidifies in the shape of the mould cavity. Provided the liquid is capable of undergoing a liquid-to-solid transition, by freezing or chemical reaction for instance, then casting can be used. Making ice cubes and jellies are useful analogies here. The production of the mould is one of the most important stages in making a casting. The casting, when solidified, must be of the right shape for the final product. In making the mould, often a ‘pattern’ made in the shape of the final component is used. This might be a wooden mock-up, for example.
Complex 3D shapes can be made using casting processes. Casting can be used to make a vast array of products, from gas-turbine blades to cheap plastic toys. Cast parts can range in size from fractions of centimetres and grams (such as the individual teeth on a zipper), to over 10 metres in length and many tonnes (such as the propellers of ocean liners). Using one of the available casting processes almost anything can be manufactured. It is a matter of optimising materials to be cast, the mould material and the pouring method (see Properties for processing – casting).
Generally, during casting, the fluid flows into the mould under gravity, but sometimes the fluid may need some extra force to push it into the cavity.
Casting is not restricted to metals (or jellies). Glass and plastics can also be cast using a variety of processes, each being dependent on the raw starting material, and the manner by which it can be made to flow when it is in its liquid state. Casting processes can be classified into three types depending on the nature of the mould used.
2.2 Properties for processing – casting
The casting (or pouring) group of processes is one of the most convenient for making three-dimensional shapes, especially if repeated copies are required. However, you do have to be able to get your material into liquid form, and it has then to be ‘runny’ enough to be poured.
What do these conditions require?
To get a liquid, you have to either melt the material; or dissolve it in a solvent which is subsequently evaporated off (the ‘solution route’); or pour liquid precursors into a mould where they react chemically to form a solid (the ‘reaction route’).
Some materials (e.g. thermosetting plastics) decompose rather than melt on heating. Others react with oxygen when heated, so need to be melted in inert atmospheres (which may prove expensive). Yet others have such high melting points (see the database) that the energy costs of heating them is only justified in special cases.
The solution route needs a suitable solvent, which you then have to be able to evaporate safely (many coatings such as paints are applied this way), but you can have shrinkage problems as the solvent is removed. The reaction route is used for both thermosets and thermoplastics and for concrete, but chemical reactions can produce considerable quantities of heat, so you must allow for this in the design of the process.
Once you have the liquid, can you pour it?
The physical property that determines the ‘runniness’ of liquid is called viscosity. This varies with temperature and is not all that useful for describing how well a mould will be filled if the temperature of the liquid is falling as it runs into the cold mould. In the casting of metals a more useful property is fluidity, which takes into account not only the viscosity changes but also the effects of cooling rate, surface tension of oxide films and the temperature range over which the alloy filling the mould actually freezes. Eutectic alloys have a high fluidity as they melt at a single temperature. Many of the alloys used for casting products are based on eutectic alloys.
Water and most liquids at room temperature have low viscosities, so can be poured easily, as can thermoset precursors. Molten thermoplastics, freshly-mixed concrete and clays have much higher viscosities. Although concrete can be poured, the others generally need to be pushed into their moulds, which is why injection-moulding machines for plastics are much ‘beefier’ than their pressure die-casting machine counterparts for metals.
2.3 Types of casting
This type of casting uses a model, or pattern, of the final product to make an impression which forms the mould cavity. Each mould is destroyed after use but the same pattern is used over and over again. Sand casting is a typical example of a permanent pattern process, where a pattern is placed into a special casting sand to form the right shape of cavity. Permanent pattern processes are usually cheaper than other methods, especially for small quantity production or ‘one-offs’, and are suitable for a wide range of sizes of product.
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