There are a few areas where people are afraid to use aluminium bolts. There has to be some wisdom behind it, but I decided to see if I could dispel the myth because they make very good, and more affordable, weight savings over titanium bolts - worth my time considering. It is also very convenient to make these calculations now, considering that I recently learned a lot from revising the sizes of the bolts on the flanges of my vacuum chamber.Firstly, to get an idea of the conventional places where titanium fasteners are recommended over aluminium, Nino's article from 2002 mentioned:
- seatpost clamp bolt
- v-brake brake pad carrier bolts
- stem
- seatpost (saddle mount bolts)
- rotor mount bolts
which seem to be traditionally obeyed, even among the 'pros' (BTP: titanium pad carrier bolts, AX-Lightness: titanium saddle mount bolts, Extralite: titanium stem bolts, M2racer/'M2-lookalikes' and many others: titanium seat clamp bolts). I added rotor mount bolts because I always hear of advice that you can change rotor mount bolts to titanium ones - why not aluminium?
By the way: I've used aluminium brake pad carrier bolts, without lubrication, for 3 years without re-tensioning them. Not advisable to leave them unlubricated, but it certainly suggests that something is wrong with conventional wisdom when the material has put up all this while...
1. Aluminium and its mechanical properties
Now, the first thing I needed to know is, what exactly do you mean by 'aluminium bolts'? There are many grades of aluminium alloys, with significantly (I qualified the use of this adjective on hindsight from completing the calculations - of which I will soon discuss) different properties. For example, I am using a particular aluminium alloy, 6061-T6 on my particle accelerator for good reasons (ease of weldability), and not merely arbitrary choice. A quick check reveals that my source of aluminium bolts (Pro-bolt) CNCs its bolts from the 7075-T73 aluminium alloy.
Next, I looked up for experimental results on the ultimate tensile shear strength of 7075-T73 aluminium bolts: 48100 psi, from a double-shear test (see Bickford, J. H., Nassar, S. (1998) Handbook of bolts and bolted joints, pp. 37-41). This equates to ~332 MPa, which is in the order of magnitude of the tensile strength of aluminium in general. Meaning, the dimensions of these numbers make sense on prima facie examination.
That's all I needed to know.
The bolts can fail from shear or tension, so I've considered both possibilities below.
2. Shear stress
> velocity from jumps, and momentum
Let's make a pessimistic calculation. I suppose that my road bike will be making s=1m (3.3 ft) jumps frequently... let's round up the acceleration of free fall to 10m/s^2, such that my bike reaches a maximum vertical velocity of sqrt(2gs) = sqrt(20) = 4.5m/s from these jumps.
Suppose that I weigh 100kg; and that my bike weighs 5kg, then let's say that we behave as a rigid, point mass with a mass of 105kg. The additional, average force from these jumps will be 105 * 4.5 = 473 N s (momentum) divided by the average time taken to bring my bike to stop (assuming that these jumps decelerate my motion to zero). We know that inelastic collisions between rigid objects usually involve an impulse over a time of 0.5s, so let's just say that the additional load is 2365N (let's pessimistically assume 0.2s instead).
(I didn't consider 'horizontal load', by assumption that horizontal momentum remains practically constant, thereby there is no change in momentum and hence force in the horizontal direction.)
> static load
With a system mass of 105kg, we roughly have 1050N of weight exerted. Of course, we're supposed to distribute this load to different bolts because there's more than 1 bolt acting as a contact point. But let's make it a pessimistic calculation. So each bolt is loaded with 3415N of force.
> pitch diameter
We usually use M5 bolts, which have a pitch diameter of 5 - 3 * sqrt(3) * 1.00/8 mm - that's about 4.35mm.
> cross-sectional area subjected to shear stress
is hence pi*4.19^2/4, that's 1.49e-5 square metres.
> shear stress on 1 bolt
is thereby 7670/1.49e-5 = 229MPa
So... we have a safety factor 332/229 = 1.4 with just 1 bolt! Realistically, even if all this (pessimistic) load went through 3 aluminium bolts: seat clamp, stem x 2, we have a safety factor of 4.2! By contrast, aircraft fuselages have a minimum safety factor of 1.5. Simply put, unless you weigh >100kg, and frequently do >1m jumps, your bolts aren't going to break on you because of the shear stress. There are many other parts on your bicycle (with lower safety factors) that will fail first, before your bolts do.
3. Tension
The minor diameter of a low tolerance M5 bolt is 3.869mm. That of a M6 bolt is 4.596mm. Calculating breaking tension from T/lb-in = pi * shear strength/psi * (d/inch)^3 / 13 yields 41.4 lb-in and 68.9 lb-in for M5 and M6 respectively: without lubrication.
The same calculation yields 50.4 lb-in and 84.5 lb-in for M5 and M6 titanium bolts (59000 psi shear strength). As you can see, the difference isn't phenomenal for a material that is 60% heavier (or rather, more dense) than aluminium. I don't see why you should feel safer with titanium.
COROLLARY: There are 2 myths to consider here. That's not even taking into account that the 'double the strength' tenet is only a comparison to 6061-T6 aluminium: depending on your source *cough *cough Alcoa *cough, 7075-T6 aluminium should have a higher shear strength than most commercial grades of titanium (with perhaps exception to those bolts on a pair of Avid Ti brakes I had which I swear had "8.8" stamped on them, which should imply 800 MPa ultimate shear strength - that's plainly overkill - Ti-6Al-4V?). It is also said that titanium alloys are generally as strong as low grades of steel (400 MPa tensile strength): true! But the same goes to 7075-T6 (469-524 MPa)!
Easton recommends that a torque of 45 lb-in (~8 N m) is adequate for handlebars/stem bolts, and maximum of 70 lb-in - agrees with Syntace's maximum torque recommendation on their F99 stems. The stem is the area of one of the highest bolt torque ratings on the bicycle, and much greater than the other 4 on the list. I'll not consider other values (by a fortiori argument). Another surprising observation from the lists from the link in this paragraph: there's a lot of torque going into crank bolts, chainring bolts etc.: why is aluminium frequently used here? They have a larger minor diameter (this phrase sounds funny), and hence cross-sectional area subjected to shear stress.
Recall that lubrication drastically reduces the tension on the bolt (different from the torque reading on the torque meter as you fasten the bolt), by a minimum of 15%: down to 38.25 lb-in from Easton's recommendation. That means that lubricated aluminium bolts can handle the tension on the stem: no problem!
COROLLARY: There's some shade of grey for the stems (I had to rely on the effect of lubrication), but for the much lower torques on bolts holding other components together, lubrication isn't necessary - though always advised. I cannot emphasize how important it is to lubricate/use a sealant for your bolts! Moreover, it mitigates galvanic corrosion (seizing) - on which matter, I must point out that special 'anti-seize greases' for titanium or aluminium or whatever are nothing special: they have the same function, and they perform just as well as your regular greases (if not worse). Experimentally verified. If you have the extra money, look for PTFE-fortified Krytox grease from DuPont, or Fel-Pro nuclear grade grease (...for whichever reasons).
CONCLUSION: The calculations give us good insurance to use aluminium bolts. Other parts on a typical bike will fail before the bolts do. Lubrication is a good practice; and justifies the use of alumnium bolts. Hence, I (safely) recommend a mass exodus from titanium bolts to aluminium bolts. Make sure you go for 7075-T6, though. Of course, experimentation is the best way to further validate this - I'll be one of the first volunteers, but we need more than one set of results.
I'll be shipping the aluminium bolts for my bike (2 for my AX seatpost, 6 for my stem, 1 for my seat clamp) - you figure out the weight and cost savings, and the custom machined bolts with low outgassing rates soon. ^^
P.S.: You may ask, seeing that my calculations above are for a 100kg rider... Ephedyn, how much do you/your bike weigh? Not 100kg, surely! I weigh 100-115lbs (that's why I have a customized crankset for my weight), depending on how busy my research is during a particular month. And my bike will weigh somewhere around 10.7lbs, a modest weight.
No comments:
Post a Comment