Second Order Design

The second design iteration seeks to optimise parameters from the first iteration within the constraints already established, to arrive at the final working design for the engine.

Piston and Con-Rod Design

The requirements of the piston are that it:

• Is as light as possible

• Perfectly seals the gas

• Has minimal mechanical friction

• Is low cost

In order to satisfy these requirements it was decided to use a lightweight all aluminium piston, constructed in separate pieces and bolted together. The piston design should be ‘oversquare’, meaning that it is longer than it is wide, as this gives it greater stability meaning a better seal. The seals are silicone rubber O-rings, lubricated with silicone grease. Silicone is strong and temperature stable, and silicone grease will not vaporise at higher temperatures. Vaporisation of light mineral oils and the like can be a problem in Stirling engines as clogging of the regenerator elements and heat exchangers can occur. The piston is designed with 3 O-rings, the front two being for sealing the gas pressure and the back one is for stabilising the piston in the cylinder. There is provision to remove the second front O — ring if friction proves too great with the two. The back O-ring groove is machined down slightly more than the front ones so the O-ring is a looser fit. This is to help reduce friction, and as the back O-ring does not seal against any pressure it will not affect operation.

Second Order Design

Figure 54: Solidworks™ drawing of piston (left) and assembled piston and con-rod (right)

Figure 54 shows the piston design. The top and bottom discs are machined from solid billet and the sides that the discs are bolted to are made from 10 mm aluminium plate. The piston could have been machined out of a solid billet of aluminium however this would have come at a significant cost.

The requirements of the con-rod are that it:

• Is as light as possible

• Is rigid enough that it won’t flex under load

• Is adjustable in length

• Has bearings at the ends

In order for the length of the con-rod to be adjustable (to enable the stroke to be adjusted) the arrangement shown in Figure 55 was used.

Second Order Design

There is a left hand thread at one end and a right hand thread at the other, such that when the ball joint at the ends are held in place (i. e. when they are attached to the piston and crankshaft) the length of the con-rod can be adjusted by turning the middle bar, which has two flat sides to allow the use of a spanner. There are locking nuts (not pictured) that lock both ball joint and middle bar in place against the lengths of threaded rod.

It was decided to use ball joint rod ends as these have built in bearings and allow for imperfect alignment as they are able to twist. They are also available cheaply off the shelf components with both left and right hand female threads readily available.


The crankshaft is what transmits the power from the piston into rotational motion to the generator. Its requirements are that it must be:

• Very rigid, any flexing will lose power and eventually lead to failure of components

• Perfectly balanced to reduce vibration

• Able to facilitate crank length adjustment

The crank design is pictured in Figure 56, Figure 57 and Figure 58. It uses two flat aluminium plates with slots milled in them in which the crank pin is bolted between. The crank pin attaches to the con-rod, and is able to be moved within the slots to allow stroke adjustment. The length of the slots is 100 mm, meaning the stroke can be adjusted between 50 and 150 mm. The other ends of the flat plates also have slots milled in them which allow the fitment and adjustment of counterbalancing weights. The shaft itself is attached to the plates by means of four triangular braces that are bolted securely to both the shaft and the plates.

Second Order Design

Second Order Design

Figure 57: Exploded view of crankshaft assembly

The gear at the end of the shaft is for driving the generator. The smaller gear mounted to the generator means it is driven faster than the crankshaft, allowing the rated speed of the generator (480 rpm) to match up with the rated speed of the crankshaft (120 rpm).

The crankshaft is attached by four bearings to ensure that it is rigid. There is a bearing at each end (thrust bearing at the non-geared end where the shaft sits facing downward) and two stabiliser bearings (pictured bottom right in Figure 58) near the middle. The flywheel (bottom right in Figure 58) is also mounted to the crankshaft between the thrust bearing and one of the stabiliser bearings.

Second Order Design

Figure 58: (From top left) Crankshaft, attachment of cranks to shaft, stabiliser bearings and flywheel

The force exerted by the piston on the crankshaft is easily calculated. If power output is 500 Watts at 2 Hz, then torque generated is as follows:

P = rxw (51)

Where P is power, t is torque and rn in rotational speed in rad/s. To obtain rn in rad/s from Hz simply multiply by 2n. This gives torque of 500/4n = 40 Nm. To obtain the force from this:

F=l (52)


Where r is the crank radius. Worst case scenario for force is when r is at its minimum, which is at the smallest stroke of 50 mm. Using this figure, a force of 800 N is exerted on the centre of the crank. The high tensile bolt used as the crank pin is sheathed by a steel sleeve 15 mm outside diameter, and this combination will easily take this load without bending or breaking.

Heat Exchangers

The construction of the heat exchangers needs to be considered. In order to reduce both costs and weight, the fins should be made of aluminium. The pipes will be copper as this is the most readily available material in this form. This leaves the problem of how to join the fins to the copper tube — these joints need to be highly thermally conductive to enable heat to flow effectively from the pipe to the fins. Welding or soldering the fins is out of the question as the large surface area of the fins would conduct the heat away too fast, and heating the aluminium would cause it warp out of shape. This leaves mechanical attachment as the only option.

The following solution was chosen as pictured in Figure 59 and Figure 60, where the fins are stacked up over the copper tubes with aluminium spacer washers, and then the whole stack of fins and washers is clamped down with nuts at one end on lengths of threaded brass tube. The washers are a very tight fit over the copper tube and provide the necessary thermal contact. To enable them to be fitted on the copper tubes they are to be heated (in an oven or similar) to expand them before sliding them on. Thermal grease compound will also be used on all washers to improve the thermal contact in all contact areas.

Copper elbow connectors are used to make the right angle joins at the ends, and the brass tube (which is brazed onto the copper tube) also forms the entry and exit points to and from the water source. These pipes must pass out of the engine and therefore across a pressure boundary, so they must form a robust airtight seal. Because the tube is threaded, bolts can be used to tighten against washers and o-rings which seal against the base plate of the displacer chamber through which the pipes pass. Silicone sealant will also be used to space­fill around the threaded tube. This arrangement is illustrated in Figure 61.

Second Order Design

Figure 59: Heat exchanger assembly (with only two fins shown for clarity)

Second Order Design

Figure 60: Heat exchanger assembly close-up


подпись: washer

Threaded brass tube

подпись: threaded brass tube

Figure 61: Section view of pipes passing through bottom of engine housing

подпись: figure 61: section view of pipes passing through bottom of engine housing Second Order Design


подпись: o-ringEngine housing

The displacer’s purpose is to simply shuffle air between the heat exchangers and through the regenerator when it is moved. It must have seals that force the gas to move through the exchangers and regenerator rather than around the edges of the displacer. It must also be as lightweight as possible. The design of the displacer is shown in Figure 62 and Figure 64.

A framework is made up of aluminium sheet which forms the outer faces of the displacer and the central rib along which the seal is run. Having the outer faces of the displacer made of aluminium adds an extra heat exchanger effect, due to the aluminium heating up (or cooling down) as it comes in close proximity to the heater (or cooler). This heat can then be imparted on the gas as the displacer moves back and gas fills the space adjacent to the aluminium. The outer and central pieces of framework are welded and riveted to a curved central piece, which bolts onto the PVC pipe in the centre.

The purpose of the PVC pipe is to provide a rigid base for the displacer to attach to, as well as a solid flat surface at the top and bottom in which seals are located that seal around the bearings. There are two aluminium rings which attach to both the PVC pipe and the central aluminium shaft. The shaft is attached to a gear which is driven by the stepper motors.

Second Order Design

The bulk of the displacer itself is made of HP35 expanded polyurethane foam. This foam has a density of approximately 30-40 kg/m3(depending on how it is mixed), so with its volume of 0.13 m3 it will have a weight of roughly 4-5 kg.

Second Order Design

Figure 63: Displacer framework in the construction stage

In addition to the seals that run around the central rib and top and bottom of the PVC pipe, there is one more seal that runs down the back of the PVC pipe which seals against the inner surfaces of the heat exchangers and regenerator, which will be lined with a piece of polypropylene plastic.

Second Order Design

Figure 64: Displacer assembly

The bearing at the bottom of the displacer shaft is a thrust bearing, as it has significant downwards force component on it. The bearing at the top of the shaft is a regular bearing

The sizes of the tubes that will house the engine have already been decided upon in Section 3.1.4, however there are still several other considerations to be made with respect to the engine housing.

The estimated weight of the entire built engine is roughly 800 kg. It would be useful to be able to move the engine around during construction and testing, so a wheeled base was designed and constructed for the engine to sit on. It uses 6 castor wheels rated to carry 250 kg each, two of which are braked for safety. The wheels will be mounted on a box section frame that is welded to the base of the engine. The wheeled base in pictured in Figure 67.

Joining together of the tubes is achieved by means of steel flanges, welded to the tubes. The flanges are laser cut from 12 mm mild steel plate for the larger tube and 10 mm mild steel for the smaller tube. Since the bottom plates of the engine need not be removed once in place they are simply discs welded on, which reduces costs significantly over using flanges. The design of the flanges is shown in the photographs in Figure 66.

Second Order Design

Figure 65: External design of the engine housing and flanges

Second Order Design

Figure 66: External housing during construction, showing flange design

Second Order Design

Figure 67: Design and construction of wheeled base

The inside of the displacer shell (sides, top and bottom) will be lined with a sheet of 3 mm thick polypropylene plastic. The reason for this is to provide a smooth low-friction surface for the sliding seals to work against, and also to counteract heat losses through conduction of the metal outer shell.

Due to the fact that the entire outer casing of the engine will be a pressure vessel, safety is of course a major concern.

Tube Wall Thickness

The minimum wall thickness of the tube can be calculated using the method outlined in UG-27 of the 2004 ASME Pressure Vessel Code Section VIII Division 1. It states that the ‘minimum thickness of cylindrical shells shall be the greater thickness as given by [two formulas]’. The two formulas stated are:


подпись: (53)

T =

подпись: t =P. R

S. E-0.6P



подпись: (54)


подпись: t=P. R

2S. E + 0.4P

Where t is the minimum thickness of the shell, P is the internal design pressure, R is the inside radius of the shell, S is the maximum allowable stress value and E is the joint efficiency.

The value of S is obtained from the same ASME code, Section II part D, Table 1A, Line no.

16. For the material type (Spec no. SA-53 welded carbon steel pipe) at a temperature of 100°C, the maximum allowable stress value from the table is 80.7 MPa.

The value of joint efficiency E is determined by the quality and strength of the weld in the pipe seam. The value is unavailable for this specific pipe, though looking at other similar materials a value of 0.85 is a good estimate.

Using these values and calculating for the larger pipe, the greater thickness is obtained from Equation 53 and is 6 mm. This is exceeded by the wall thickness of the pipe chosen (7.9 mm) hence the pipe is safe at the design pressure.

By inspection it is clear that the smaller tube will be safe, as its radius is around half that of the larger tube.

Pressure on End Caps

The end caps must sustain the pressure of the engine without deforming or rupturing. The force on the end caps can be calculated easily. Engine pressure of 1 MPa is equivalent to a force of 1 N/mm2. By computing the area of the end caps the total force can be found.

Large end cap:

793 mm diameter, area A = nr[2] = n x 396.5[3] = 493,897 mm[4] Therefore force on the large end cap is 494 kN.

This end cap is made from 12 mm mild steel plate and will be bolted onto a mounting flange with sixteen 1” UNC high tensile bolts, rated to 32.46 tonf each bolt. Each end cap will be beam-reinforced with an 8-pointed star constructed from 10 mm thick, 80 mm high mild steel plate to stop end-plate deformation under pressure. Additionally, each flange will be reinforced with eight 10 mm thick mild steel braces to stop any flange deformation or peel.

Small end cap:

438mm diameter, area A = nr[5] = n x 2192 = 150,674 mm2 Therefore force on the small end cap is 151 kN.

This end cap is made from 10 mm mild steel plate and will be bolted onto a mounting flange with sixteen %” UNC high tensile bolts, rated to 17.90 tonf each bolt. Again, each flange will be reinforced as described above.

Hoop Stress

The hoop stress, oq, on the steel tubes is defined as the stress caused by internal pressure forcing outwards circumferentially on the tube. It can be calculated by the following formula:


подпись: (55)

O-0 =

подпись: o-0 =P. d 2t

" L’lAJ

Which for the larger displacer tube, having an inside diameter d of 793 mm and a wall thickness wt of 10 mm, is calculated as:

1 x 106 x 0.793

=—— o—^——— = 40 MPa

2 x 0.01

And for the smaller tube, having an inside diameter of 438 mm and a wall thickness of 9.5 mm:

P. d 4t

= 20 MPa

подпись: = 20 mpa4 x 0.01

And for the smaller crankcase tube is


12 MPa

подпись: 12 mpaX 106 x 0.438

4 x 0.0095

Stress Limits

The material test certificate for the larger pipe (API 5L Grade B Spiral Pipe) state the following tested values for tensile and yield strength:

• Tested Tensile strength = 456 N/mmA2 (456 MPa)

• Tested Yield point = 329 N/mmA2 (329 MPa)

Hence the values for hoop and axial stress fall well within these limits.

Stepper Motors

There are two stepper motors used to drive the displacer through a 2:1 gear reduction (see Section 4.1.2). The arrangement of the gears and motors is shown in Figure 68. The mounts for the motors have slotted bolt holes so that the motors can be precisely positioned relative to the larger central gear, which is attached directly to the displacer shaft. The whole assembly is mounted inside the motor housing chamber with the two mounting tabs welded to the inside of the housing.

Second Order Design

The generator, pictured in Figure 69, is mounted in the engine in a similar fashion to the stepper motors; bolted to a flat plate which is bolted to welded brackets on the inside of its housing. It too has slotted mounting bolts to allow perfect mating of the gears. The generator is a permanent magnet rotor, wound stator 3-phase generator with a rated power of 1 kW at 480 RPM. It is geared up (using the gears shown on the left in Figure 70 with the big gear on the crankshaft and the smaller gear on the generator) at a 6:1 ratio off the crankshaft to enable it to make its rated power from as little as 80 RPM from the engine.

Second Order Design

Figure 69: Generator assembled (left) and disassembled (middle and right) showing permanent magnet rotor

Second Order Design

Figure 70: (Left) Gears used to increase speed to generator; (Right) mounting plates for generator and motors

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