On Wednesday, July 19, 2017 at 2:29:31 AM UTC-7, robert bristow-johnson wrote: (snip, I wrote)> > In the case of wheel lug nuts, you want them evenly tightened > > around the wheel. If you tighten them sequentially to full > > torque, one side will be much tighter than the other.> > You still don't want to go full torque at once, but with a star > > pattern over five bolts, and maybe all to half torque and then > > all to full, it is pretty even. This works best for an odd > > number, but if you do six in a 1 4 2 5 3 6 pattern, it probably > > isn't so bad. The five nut 1 3 5 2 4 pattern is nice, as you > > just advance two each time.> this is what i had always thought about it. > it's how i would tighten lug nuts when changing a tire.> i've thought that 3-blade windmill propellers were > more stable than 2-blades. > > as for how an odd-number balances, you can make an > argument from symmetry. if the 5 lug nuts are equally > spaced around the circle, how is the direction that the > balance tips to be predicted? why should it tip in one > direction rather than another?You can get more interesting cases with five, though. Consider that two and three balance, and so will any linear combination of two and three. Three blades at 0, 120, 240 degrees balance. Two blades at 90, 270 degrees balance. Five blades at 0, 90, 120, 240, 270 degrees balance. Note that the latter aren't equally spaced. Or, rotate the two blades a little more, and get five blades at 0, 100, 120, 240, 280. As well as I understand it (not very well) some of these are used to make helicopters quieter. By using a less uniform spacing of the rotor blades, the frequencies are mixed up somewhat, and so there is less at one peak, presumably at (number of blades)*(rotor rotation rate). I suspect that if you allow different blades sizes, you can do even more. You can also do it in 3D. Consider a solid cube, which you can easily see should balance, (that is, static balance), and rotate smoothly (dynamic balance) rotating around an axis through the center perpendicular to any face, or through the main diagonal. It turns out, though, that a cube will rotate smoothly through any axis through the center. The same math explains why cubic crystals are not birefringent. The index of refraction of a cubic crystal is the same along any axis. (In the first case, the moment of inertia tensor is proportional to the identity matrix, in the second, the polarizability is proportional to the identity matrix. Any rotation gives the same matrix.) Hexagonal but not cubic, HCP in crystallography, doesn't have this property. This is why cubic zirconia, and not the alternative HCP zirconia, is used for jewelry. Every object, no matter how strange the shape, has three perpendicular axes through the center of mass that it will rotate (dynamic balance) through. Those axes that diagonalize the moment of inertia tensor. As for wheels, this is why you need dynamic balancing. They can be static balanced, with center of mass in the center of the axle, but not dynamic balanced.
Hah! Why 5-lug wheels balance
Started by ●January 20, 2017
Reply by ●July 19, 20172017-07-19
Reply by ●July 20, 20172017-07-20
On Tue, 18 Jul 2017 16:15:29 -0700, herrmannsfeldt wrote:> In the case of wheel lug nuts, you want them evenly tightened around the > wheel. If you tighten them sequentially to full torque, one side will be > much tighter than the other. > > You still don't want to go full torque at once, but with a star pattern > over five bolts, and maybe all to half torque and then all to full, it > is pretty even. This works best for an odd number, but if you do six in > a 1 4 2 5 3 6 pattern, it probably isn't so bad. The five nut 1 3 5 2 4 > pattern is nice, as you just advance two each time.Oh, god. No no no. That'll screw it up for sure. You need to advance THREE each time. Seven if you want to be thorough. Jeeze. Theoretical guys and their practical mistakes. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Reply by ●July 20, 20172017-07-20
On 7/19/2017 23:01, Tim Wescott wrote:> On Tue, 18 Jul 2017 16:15:29 -0700, herrmannsfeldt wrote: > >> In the case of wheel lug nuts, you want them evenly tightened around the >> wheel. If you tighten them sequentially to full torque, one side will be >> much tighter than the other. >> >> You still don't want to go full torque at once, but with a star pattern >> over five bolts, and maybe all to half torque and then all to full, it >> is pretty even. This works best for an odd number, but if you do six in >> a 1 4 2 5 3 6 pattern, it probably isn't so bad. The five nut 1 3 5 2 4 >> pattern is nice, as you just advance two each time. > > Oh, god. No no no. That'll screw it up for sure. You need to advance > THREE each time. Seven if you want to be thorough. > > Jeeze. Theoretical guys and their practical mistakes. >A good point. :-D -- Best wishes, --Phil pomartel At Comcast(ignore_this) dot net
