Mechanical Drag Reduction System (DRS) - Design

Typically drag reduction systems (DRS), as used in F1 and some Formula Student vehicles, are electronic and lift towards the end of the chord of the flaps, this is done when there is a reduced requirement for down force and an increased desire to reduce drag.

The reason for these being electronically controlled are to allow certain limits on the activation of the system, such as yaw rate, steer angle, throttle demand etc. However this can be difficult to control, measure and implement so there is potentially room for a mechanical system.

The design initially has flaws as any method that mechanically, and automatically, prevents the flap from dropping also mean that there is an release and a return threshold. The return threshold velocity (in terms of a moment on the flap) is lower than the release threshold, meaning that going into a long sweeping corner then the flap may not return and thus you have reduced the down force when it is required.

Even with the known flaws with the core design principal it is still seen as a good technical exercise to explore the possibilities of another potential system rather than following the path most common.

The insert used is seen in Figure 1, this is used in place of a thinner aluminium flap insert design but has essentially the same external profile.

Figure 1 - Insert Design

In order to have a release threshold a bales catch has been used, this can be seen dissembled in Figure 2 but is just a sprung ball bearing, in a drilled hole in the plate (which could be an end plate) it is attached to, this provides the necessary resistance for a release threshold.

In principal this value is calculable and the equation that I have derived is seen below (Equation 1), it is a simple threshold calculation (F_release if the force required acting perpendicular to spring force direction, F_spring is spring preload force, r_ball is the ball bearing diameter and y_insertion is the depth below the surface that the bottom of the ball bearings sits). However as this bales catch was purchased from a popular hardware retailer the calculations have not been performed.

Figure 2 - Bales Catch exploded view

Equation 1 - Release Force Calculation

In order to allow for the return, a linear pull spring has been added. Whilst the system does not currently have secondary position in which the flap can rest but this would be an easy addition. The lack of this addition would mean that the amount of flutter (oscillation of the flap position) would be higher.

In Figure 3 two images can be seen, the first being the resting position of the flap insert and the second being an extended flap position, as would be expected once the moment on the flap was greater than the threshold. Whilst a torsional spring would be better (and more integrated), that could be designed in at a later date, there wasn't one suitable to hand.

Figure 3 - Compressed and Extended Operation

Figure 4 - Video of operation/return

In Figure 4 there is a video of the general operation of the system. It can be seen to work in principal (note also the return position is aided by the full compression of the spring), however the practice and implementation into a full size system is both impractical and counter productive as the time spent refining this system would be better spent refining an electrical system.

Hydroformed Steel Bike Frame - Design

Typically hydroformed bike frames are aluminium due to the low yield strength (relatively compared to 4130), however it is possible to hydroform steel as has been shown by Colin Furze who produced a number of things including a steel "pillow", 2 stroke exhaust, exhaust cone and a pulse jet.

All that is required to do this hydroforming, technically "low pressure twin plate hydroforming", is some BSP fittings, a modified trigger to a pressure washer (which are often rated upwards or 70bar) and 2 flat patterns of a shape you want to hydroform that have been welded around the seams.

To hydroform a bike frame I have decided to aim for the geometry as used in the 29er that I made previously. Achieving the desired geometry is simple in CAD/drawings after the hydroforming process is completed, however transforming this to a flat pattern that can be cut out of steel sheet is more complex.

As has been shown by Colin Furze there is a difficulty when transferring a flat pattern into a 3d form, this problem comes with curves, radii and bends. The way to do this is making the width of your plate half the circumference of the tube overall diameter that you require (Fig. 1 and Fig. 2). When considering bends and curves you have to consider the desired finished bend radius, when you think about it, it is the arc length of the curve that stays constant for both the inside and the outside radii, regardless of the flat pattern or blown up piece, this being how to work out your flat pattern (setting both the same, Fig 3. and Fig 4.).

Fig. 1 - Overall Diameter Desired

Fig 2. - Flat Plate Equivalent

Fig 3. - Arc Length of the Bend Around the Bottom Bracket at Desired Tube OD

Fig 4. - Arc Length of the Bend Around the Bottom Bracket on Flat Pattern

This method of making a flat pattern isn't as simple as it seems, as if it were to be a complete front triangle the bending of each of the radii would work against each other and could cause a undesirable bending or folding in the centers of the tubes.

As such it is much simpler to build it in a single "tube" that is designed to fold back on itself, this can then be welded with only a single weld afterwards. This can be seen below with the desired geometry outline along with the 2D profiles that are required to achieve this.

Unfortunately, as a result of potential issues with buckling and folding, I shall not be trying to hydroform a head tube, bottom bracket, brake mount or drop outs. I shall also by forming 3 pieces (2x chainstays [Fig. 6], 1x front triangle [Fig. 5]) and then using a post welding/brazing process to complete the frame using my previously made frame jig.

Fig 5. - Flat Pattern of the Front Triangle (Solid Lines) with the Desired Outcome (Broken Lines)

Fig 6. - Flat Pattern of the Rear Triangle (Solid Lines) with the Desired Outcome (Broken Lines)

Formula Student Torsional Stiffness FEA Validation

Every year the Loughborough Formula Student team (LUM) use 1D FEA to test the torsional stiffness of their chassis as a comparison to previous years, other teams and the effect on the handling of the car, yet very little work has been carried out as to the suitability of this method.

Along side the minimal work of comparing experimental and theoretical results there has also not been any inclusion as to the effect of any of the other attachments to the chassis, such as the engine or the carbon fibre body panels.

By doing the tests with the theory with and without the body panels the accuracy of the theory can be found as well as the effect of the body panels

Experimental work

Due to this being a university project the full use of equipment was allowed and as such the torsional stiffness was measured using a 4 poster rig, this rig has been used in the past to put a car on the 4 posts to test the suspension of a simulated road. This can be seen below along with the chassis mounted on the rig.

Fig 1. LFS09 Chassis on the 4 poster rig

Pretty quickly during experimental testing it was found that a number of issues of strength needed addressing such as the bending of bolts and the tearing of suspension tabs. After this has been solved by changing the mounting method and welding up the suspension tabs the testing could be carried out.

By inputting a displacement over a time into the posts, the forces are measured using the pressure in the hydraulic posts. The demanded displacement profile for both the left and the right hand posts can be seen below. Running this profile 3 times allowed for an average of each of the three runs at the 4 different displacement points to be averaged.

Fig 2. Displacement post demand

Theoretical Work

The FEA was set up in Nx 8.5 with 1D PBeam elements with T45/CDS tubing in the appropriate places with the fixed nodes to match that in the experimental testing along side the forces being applied at the equivalent suspension node. With the 2D elements a Tri3 PCOMPG element was used with 1 ply of CYCOM-2040 2x2 twill weave T800 as the material.

In order to get deformation of the 1D and the 2D synchronised a nodal equivalence was used. This does have the unfortunate side effect of producing an infinitely stiff bond but was deemed to be a small factor in the comparison.

A mesh sensitivity study was carried out and very little change in the displacement was seen below 100mm for the space frame only and 20mm for the combined FEA. An example of the sort of results acquired can be seen below (this animation is a early FEA set-up test, not a CFRP body panel and not the final FEA).

Fig 3. Space frame and body panel.

 

Comparison of results

Using simple trigonometry calculations the values have been corrected so that the theory and experimental results can be compared as the experimental tests are measured at the suspension tabs but the FEA values are measured at the centre of the tube elements.

After the corrections had been carried out, another calculation was carried out to find the torsional stiffness value.

	Space frame	Space frame with body panels	Stiffness Increase (%)
Experimental (Nm/deg)	797.45	1079.20	35
FEA (Nm/deg)	720.77	1054.39	48
Error (%)	9.6	2.4

It can be seen from the table above that the value with body panels is within a working experimental error however the bare space frame error is ~10%.

The low error when including the body panels is likely due to the properties of the carbon panels not being known fully due to the age of the chassis, and as such it suggests a much larger contribution in the FEA when compared the experimental results.

Whilst this doesn't show that 1D FEA is perfect, it does show that there is a significant increase regardless of theory or practice when it comes to including carbon body panels on a tubular steel space frame and these should not be omitted in future FEA testing.

The experimental results being stiffer than that of the FEA is likely due to the fact that the tubes are not joined at the nodes on a chassis, but are actually ~12.7mm off node, on some of the elements this constitutes 10% of the length of that member. This shows that if you wish to get a more accurate value for torsional stiffness then a 3D FEA analysis is required, but is not necessary for value comparison with previous years so long as there is a consistent method used.

If you would like any of the data then all you need to do is message me and I will try my best to get it to you.

Simple dropper post

For a while my dad has been looking into buying a dropper post (similar to a rock shox reverb) that means you can adjust the height of the saddle without having to stop or get off of the bike. As this is quite a specific area with a lot of engineering packaged into a small (typically no more than 34.9mm in diameter) package the prices start at £150. This price was seen to be too high for a simplistic function.

As I only had one week left, at this point, with access to a work shop I designed a simple system that works off a gas strut and four machined pieces of aluminium (two different diameters, as seen in Fig. 1) that work like a quill stem. See Fig. 2 and Fig. 3 as they show an visual explanation of the clamps.

Unfortunately these pieces have a high quality finish on the outer diameter, if this project were to be done again I would specify a knurled finish on the outside surface to provide a better grip on the tubes. However these are working well having been assembled with a grit assembly paste.

Fig. 1 - Machined pieces of aluminium

Fig. 2 - Smallest diameter

Fig. 3 - Largest diameter

The smaller diameter was to inside of the seat post (Fig. 4) and the larger diameter to go inside the seat tube (Fig. 5). There was a lot of trial and error involved in getting the distances inside the tube set up correctly.

Fig. 4 - Inside the seat post

Fig. 5  - Inside the seat tube

At either end of the gas strut used is a M6 10mm thread which meant that one of the bolts (as shown in Fig. 2 and Fig. 3) could have the head threaded to accept the smaller diameter side of the gas strut. On the larger end of the gas strut was an eyelet fitting which was domed (Fig. 6), the dome provided a means or pushing off of the clamp inside the seat tube.

Fig. 6 - Eyelet fitting on the end of the gas strut

Fig. 7 shows a video of the whole system working. This now allows the saddle to be lowered or raised without having to stop if a quick release saddle clamp is used.

Fig. 7 - Completed system

Further work needs to be done to have a bar mounted lever to operate the system so that you don't need to operate a quick release. If more time was available I would not have two toleranced faces as the wear faces (especially in the muddy UK) but as this bike is not often ridden it should be of no detrimental effect.

The 36er - Some design and calcualtions

The design for the 36er is now well under way (Initial idea, dual disc justification). The geometry is all but finalised (first draft anyway) for the entire project but it will need it to be checked and may be modified depending on the frame calculations and any wall thickness's that I wouldn't be able to obtain. Below the geometry for the bike can be found (On one midge bars would be used for this hence the really long effective top tube) and will involve quite a lot of bracing to get the frame strong enough to withstand all of the forces that are required in BS EN 13766. As you can see in order to get the chain stays (and the wheelbase) as short as possible a split in the seat tube would be required to provide clearance for the 3 foot diameter wheels. In another attempt to get the bike to handle reasonably and try to counteract the overly large wheels the trail value that has been selected (~85mm) is similar to that of a Trek Superfly in the smaller sizes, any less trail (i.e. any more fork offset) made me uncomfortable with the strength of the material selected for the fork stanchions. In Fig. 2 the trail relation to the head angle and the fork offset can be seen.

Fig. 1 36er Geometry

Fig. 2 Trail relation to head angle and fork offset

The calculations for the forks (in accordance with BS EN 14766:2005) have all been done. This includes a horizontal fore aft force of 600N followed by 1200N in a repeating cycle (1e5 cycles) in the configuration seen in Fig. 1 (this is actually a frame test but the forks can be fitted during said test), a 1500N load applied vertically through the axle (to induce bending, failure for rigids if displacement is greater than 5mm), a +/- 650N vertical loading through the axle cycled (1e5 cycles), a 22.5kg striker dropped from 360mm onto the axle (if passed same test but from 600mm), a cycled braking torque (600N at 330mm from the axle, 12000 cycles) and a 330Nm torque test about the axle.

Unfortunately for some of the tests (striker and cycled tests) I do not have enough information about the forces involved to be able to calculate it correctly. In the case of the striker a safety factor of 4 has been assumed to take up any shock loading. In the terms of the cycled test I have no information about the low cycle fatigue properties of my chosen material (T45) or high cycle fatigue properties, hence safety factors have been taken into account (various depending on the specific test).

In order to make forks there are some very specific tools to cut the face for the crown race to sit on, due to how expensive these are and the lack of a shop near me that stocks the tools I opted to design the forks around the only system that I could find that would allow a pre-made crown and steerer system which would be any dual crown fork. Fig. 3 shows the crowns that I managed to buy second hand and are made for 32mm (~1.25") stanchions.

Fig. 3 - 2010 Rockshox Boxxer dual crown steerer and crowns

From the geometry given in Fig. 1 (i.e. a 120mm head tube, 510 ATC and 67.5mm fork offset) there was very little in the way of flexibility in the geometry. For the chosen material (T45, a material primarilly used for roll cages and space frame chassis, 620MPa minimum yield) there is one supplier that I would trust (as recommended by the Formula Student team) and of all the sizes they stock I am only able to use on of them, a 10SWG (3.251mm) thickness tube. This thickness was decided upon only during the frame and fork testing based on the stress and resulted in a stress of 600MPa which although would pass a single cycle did not provide a high enough factor of safety.

In order to get around the factor of safety issue without buying new crowns from a fork that uses a larger stanchion or getting custom tubing that had a thickness of 8SWG (4.064mm) I incorporated the second moment of area of the area of the steerer as well as the crowns. To get around the issue of dissimilar materials their strength was taken to be a half of its true value which will provide a accurate enough stress profile.

Another way to get around the high stress towards the crowns (which were treated as pin supports for the purposes of calculation) a tube with an outer diameter of 1-3/8" and then bored out to slide over the top of the stanchion as a lug and then brazed on. This allows for a much higher thickness where required, for a minimum lug length of 150mm (it would not be clean cut but shaped to reduce the stress risers) then provides a maximum stress of 400MPa which is a much more acceptable factor of safety for cycled loading.

Below (Fig. 4 through 11) can be seen the results of the calculations performed for the different tests. It should be noted that the steps in stress are due to a non-constant second moment of area value throughout the length of the forks. Ideally this should be taken into account throughout (for the slope and displacement), however I have decided that regardless of the displacement that the material being used is the thickest that I can purchase so there is nothing more that I can do about it. Along side this it would take me a long while longer to perform these calculations to gain a slightly higher level of accuracy.

Fig. 4 - 22.5kg drop with 4G safety

Fig. 5 - 22.5kg with 4G safety

Fig. 6 - 1500N fork bending

Fig. 7 - 1500N fork bending

Fig. 8 - 1200N frame and fork bending

Fig. 9 - 1200N frame and fork bending

Fig. 10 - 330Nm Braking torque

Fig. 11 - 330Nm Braking torque

Unfortunately, as can be seen in Fig. 6, the displacement is greater than 5mm for the 1500N test, this would mean that (if the calculations are accurate) the forks would fail type approval. However for a project such as this it is of little concern to myself as I will make sure there is ample clearance between the down tube and the wheel (by using a cranked down tube).

In addition to the calculations I have performed some basic finite element analysis, FEA, (due to only having a student license for the software) on a basic cad model of the forks. The pin supports were created by making large thin discs attached to the stanchions and then fixing the outside face of these discs to allow rotation the most free rotation whilst preventing vertical and motion as best as possible (any torque arms were applied to not create lateral reaction forces in the thin discs). Below are some images for the torque moment (330Nm) and the e-drawings files (edrawings download here) with the deflections, stresses and factors of safety (it should also be noted that the material is similar but not identical, the yield strength in T45 is ~20% greater than that of the material chosen), in the factor of safety plots there is often a very high factor of safety around the axle, this is irrelevant due to the axle only being used during testing and not being representative of the hub assembly.

TO THE EDRAWINGS FILES

Fig. 12 - Displacement in basic fork

Fig. 13 - FOS in basic fork

Fig. 14 - Stresses in basic fork

The tests carried out, in FEA, are the 1200N frame and fork, the 1500N fork bending, 330Nm braking torque and a 660Nm braking torque. The stresses around the drop outs are not of concern as there would be radii to lower the stress concentration. Interestingly the FEA does not show a displacement of more than 5mm for the 1500N test and this discrepancy will be due to my stepped inertia values during the calculation stages (mentioned previously).

Now that I have decided upon the material, sizes, thickness's and general frame geometry I can begin to purchase components. The most important components at this stage are the wheels as they will be used to implement my dual disc system. In order to do this I am using a double fixed sealed hub with two 'dixxie' (disc fixed) adaptors for the hub instead of my previously designed hub (as it is easier to buy the components than to make my own hub costing me a lot of time) which can be seen in my previous blog post (here). After this has been designed in the wheels can be built. In order to get enough strength for these 36 inch wheels (10 inches bigger than the standard mountain bike size) the wheels will be built into a 4x pattern by the wheel builder Mike Moore (Mike's Bikes), this should provide ample strength in the wheel for the dual disc system and for general trail riding.

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The Homebred 29er is finally complete.

The frame has now been finished, fully brazed up with all the add ons silver soldered to the main frame. I am not 100% happy with the braze as the largest gap I have is roughly 0.5mm (as everything was done by hand and the tubes moved a bit whilst tacing them) but there is plenty of brass in there, so it should hold (we will see after the first test ride!). Thankfully the head tube is perpendicular to the bottom bracket within 0.1deg, also the top tube is 1.4mm off over the length of it, which is nice!

Once the frame was done I went about partially finishing off the joints to make them a bit neater, went over everything with P120 paper and then it was clear lacquered with a 2 part lacquer. This was then taken to a not so local bike shop to get the threads chased, head tube and seat post reamed and the head tube and bottom bracket faced.

I am pleased with the results and am very much looking forward to getting the whole bike built up and ridden!

All in all, it's 2.5kg, which is less than I had aimed for (3kg, at a very high estimate).

Straight 44mm Head Tube

Brake mount

BB-DT-ST-CS junction

Seat stays, seat tube cut out and bracing.

Inside of the brake mount with the bracing

Other side of the BB-ST-DT-CS join.

ST bottle bosses

Under the DT bottle bosses

Top tube - Had to flat the surface and to do that it went through and polished it nicely in patches.

The finished frame.

Homebred 29er - Progress!

So far the design has changed slightly in a few key places since the last blog post on the matter. The top tube has grown by 40mm so that I can have the option to not have my seat slammed all the way back on a layback post and then put myself in a better position on the bike. Along with that I have bought some new Columbus pre-bent 29er Zona chain stays as I was no longer confident of the shear condition that the braze would be under in the previous stay design so bought some new stays for ~£40.

Other than these design changes the jig has been set and all the measurements are correct, as can be seen in the pictures below. Everything is set central and my biggest fear the head tube not being vertical has now been sorted.

Fig 1. Head Angle.

 Fig 2. Seat Angle

 Fig 3. ~447mm Chain Stay Length

Fig 4. 55mm BB Drop.

Fig 4. Bottom of the HT

Fig 5. Centre of the HT

Fig 6. Drop Outs central and square

Fig 7. BB Central

Now that the jig is complete there is really only the tubes left to mitre. Having found a program online to produce profiles for the mitres I was able to input all the information and this then I could stick the profiles onto the tubes and file away until I got up to the line. I then finished them off by getting the tube that mates to them, wrapping it in sand paper and filing the last bit as such, resulting in very little, if any, clearance. Thus far the seat tube and chain stays have been completed, half the top tube and down tube have been done.

Fig 8. HT/DT Junction

Unfortunately the chain stays can not be done in the same way as the other tubes as they are oval at one end, thankfully  I do have the CAD for them that will allow me to get a rough mitre that can be finished off with sand paper wrapped around a 1.5" block. This can all be checked (albeit roughly) as I offer the cranks up to the jig to make sure nothing is going to clash once assembled, which would be very unfortunate. As the chain stays were nearing completion it was found to be very difficult as the tip was only 13mm and the block to be mitred to is 1.5" so although the profile is perfect, the angle that it sits at could be better (Fig. 12). This shouldn't be a problem with the amount of brass that can be put in there.

Fig. 9 CS/drop out Junction

Fig 10. Chain stay/BB Junction

Fig 11. Chain stay in place with blue tac

The next blog post will either be about the completed frame or how something has gone disastrously wrong.