WHEEL CENTERS & MOUNTING Andrei Lozzi 2013 REFERENCES

1. WHEEL CENTERS & MOUNTING Andrei Lozzi 2013 REFERENCES Wheel centres Ally Ribalko, UG thesis 2010 Adam Bolton, Carbon Fibre wheels, UG thesis, 2010 John Masi, Aluminium sheet wheels, UG thesis 2013

2. An incomplete critique of FSAE wheels and their shaft coupling Andrei Lozzi 2012 For the tyres used since 08 the transverse coefficient of friction µ1is up to about 2.0 while the tangential µ2is about 1.5 Hence a wheel generates a maximum moment about the Xaxis that is about 30% larger than the maximum about the Zaxis. Deflection about the X should be limited to about 0.5°, in order that the wheel's camber angle be not adversely increased while cornering. Dealing with the moment about the Xaxis is most important. These maximum moments do not coexist. If one is at its maximum the other will be a zero, if one increases the other decreases. The friction available is approximated by a point tracking around the ‘friction ellipse’. Y X O µ2 N r Z µ1 N N

3. Assuming a 300 kg car cornering at 2 g and braking at 1.5 g (not at the same time): The braking torque about the Z axis would be about 500 Nm, shared equally by all spokes. A good cross-section for the resulting bending moment of the spokes would be the H section 1). The weight of the car on two wheels, ie 600 N per wheel, is shared also between spokes. Some spokes in compression, others in tension and bending. Compression is usually most testing and for that hollow sections are best – 2 & 4) The bending moment while cornering, about the X axis, is in the order of 640 Nm. This is largely resisted by the bending stiffness of the upper and lower spokes. A good section for the spokes would be the I beam and box sections 1 & 2), to a lesser extent the tube, but tubes cannot be tapered easily. Cross-section of spokes Y 1) 2) X Z 3) 4) A A 5) 6) BUT, unfortunately what is most commonly seen are wheel centers machined from 10 – 12 mm plate 6), or NCd from Al alloy billet 25 – 50 mm thick making perpendicular flat ribs 5), and lastly spokes that are of a channel sections 3). The section 5) being the better one, but not nearly as effective as sections 1 & 2 or 4).

4. µN Some design oversights – not errors Wheel CL Tyre & rim a) N At left Fig a) represents half a wheel, from its CL to the tyre. N is the normal force onto the tyre, µN is the frictional force transmitting a bending moment through the wheel ribs to the wheel spindle. b) Shows that this moment increases linearly from the contact patch to the spindle CL. c) Shows that a rib of rectangular cross section, to have uniform stress along all of its upper and lower edges, should be of a parabolic height. d) Indicates how these ribs are actually shaped, hence they have relatively high stress at their outer edges. e) A wheel made from sheet material should vary in depth to a point approaching the contact patch. F) In fact we made the same oversight as has been done in d). There are conceptual difficulties imagining an effective connection between e) and the two wheel rim halves Moment b) c) Wheel rib profiles d) e) Sheet wheel profiles f)

5. A spoked wheel by Woolongong 09 The spokes become quite thin at the rim Note the nut at its center, uses pins to transmit torque to it. The locking wire is amazing A German wheel showing just how this thin the drive tube and nut can be made, Provided one can make the CF wheel first

6. In 05 the Hertfordshire team brought this wheel out. Note that the center is made from about 3 mm sheet. It is not clear how the center is attached to the rims. Other UK teams have had wheel like these, we should investigate the details before we try again

7. While we thought we had invented the sheet wheel, lo and behold the Moon buggy had used them before us

8. Nose wheel from a Hercules transport plane. Seen outside the far end of the PC lab S345. The sides of this wheel are from forged pieces, which are then machined to final dimensions. The hub seems part of the sides. Note the fine thread on the steel shaft. Holes are drilled through the shaft only in area of low stress. These sort of wheels are appropriate where one does not have to make room for brakes. Lotus F1 had cast Mg wheel of this form when they used inboard disk brakes.

9. Cross section of an aircraft front wheel. Main undercarriage wheels have brakes the front ones do not. These are probably forged from Al alloy blanks, then machined to a finished shape The ‘spokes’ here is a version of section 2 shown on slide 1. This wheel center is like the structure of the wing of an airplane . A wing has skin or plates only at the top and bottom, as far as possible from its neutral axis.

10. A sheet wheel along side a sheet upright. This figure shows that there can be continuity of a similar method of construction.

11. Before all the problems became evident we had imagined that the sheet center could flow smoothly to be assembled with the CF rims, but both have given problems.

12. At left is a 2 mm sheet wheel, attached to a rim and tyre, also modelled from 2 mm Al. At right is the 09 wheel center attached to the same tyre. Where the ribs (ie spokes) are at their least depth, is the location of the highest stress, the level is about 3-4 times that of the sheet wheel. This effect was foreseen on page 6. The high stress in the sheet, at the bend where it meets the hub, can be ‘removed’ by welding the sheet to an appropriately shaped hub. The stress in the sheet wheel is everywhere about 3 times less than the spoked wheel, it was expected to be 60% of its mass.

13. A sheet wheel made from 1.6 mm Al was shown to withstand about 3 times the moment that comes with max lateral acceleration. The production wheel have been made from 2 mm AL

14. Canterbury wheel coupling at left (~ 2008), Ferrari F1 at right (~ 1970). Note just how small the nuts can be made.

15. Some FSAE nuts and hubs. One can rely on students to make imaginative parts

16. The hub and wheel used by us in 2010. The wheel failed because the ends of the hubs were reduced in length by about 3 mm, machining off some of the weld in the process. There was a great deal of uncertainty about the thread in the Al shaft. It in fact withstood a huge torque without failing. These hubs could be reused with much lighter nuts

17. These are wheels on a F1 Lotus from about 1970. The means of attaching the centers to the rims is hard to deduce. It is clear that the hub is attached with many small screws. In those years there was no regular pit stops and wheel changes were probably not permitted. I have been told that these wheels begin as two asymmetrical castings, then machined to shape

18. Stiff wheel centers have been made from a single ‘plates’ provided the plate is not flat. Left is a cast Mg wheel for F-juniors from the 60s. Note that the corrugations effectively increase the second moment of area of the ‘plate’. Wheels like these may be seen on Mini Coopers that have survived from the 60s. Right - Porsche 07. Form slightly ahead of function, but this wheel has to have some ‘style’ to appeal to the public. Each wheel nut has 2 spokes, each spoke has 2 rim screw ! The rim screws may be faked, and maybe these wheels breakdown to 3 pieces. Al alloy almost certainly forged – not cast. All Porsche wheels are moderately good

19. Auckland 05 From many points of view this is one of the best designs: Note the many spokes to make the load nearly uniform at the rim. The spokes split from 6 at the centre to 12 at the rim. And, it is the depth of the spokes that reflects the higher bending moment, not their width. Negative points include that the wheels were cast (the fatigue strength of cast Al is about half that of wrought) and that the wheels were attached by one heavy bolt not by many small light ones on large PCD. Single bolts would make sense if quick wheel changes were a necessity in this competition, which they are not.

20. One of Curtain University’s wheels, at Werribee 2012. The best wheel seen in Australia, except for our sheet Al wheel, of course. At top left is one of our designs similar to Curtain’s wheel, except the 18 spokes are not Siamese into 9.

21. This forged wheel for Ferraris appears to have ribs that are of a T section. A section like an I beam would be better (top & bottom flanges with web between them), a T may be next, a simple flat vertical I beam last. A disadvantage of I and T sections is that they would have to be fully machined. The I beams on the other hand can be cut out with a water jet or a laser profiling NC machine.