Thread: Time-effective alternatives in sharpening

Derek,

I defer to the people who really know, but I don't think your conclusion is correct. Fence Furniture was making the comparison at the two different rpm I used and came to the same conclusion as me, about 45%.

For the same angular velocity (rpm), according to my calculator:
a 6" wheel at 2850rpm has a tangential velocity of 3.5625 metres per second,
an 8" wheel at 2850rpm has a tangential velocity of 4.7500 metres per second.

The 8" is faster by 33%, just as 8 is 33% larger than 6.
Yes, 6 is the base for these % comparisons.
If we want to talk about slower, the base becomes 8.
Either way, the 6" speed is 0.75 of the 8" speed.

Regards,
Mark

FF your circumference are not accurate (not that it makes any difference when working with ratios) as you have been using radii and not diameters. Eight inch wheel has a circumference of 16 times pi making it nearly fifty not 25.
Cheers,
Jim

Originally Posted by MarkInBoatshed

Derek,

Either way, the 6" speed is 0.75 of the 8" speed.

Regards,
Mark

And if the 8" is half the speed of the 6" which is what the original remark by Derek stated then the 6" goes at 1.5 times the speed as I said.
Cheers,
Jim

Originally Posted by jimbur

FF your circumference are not accurate (not that it makes any difference when working with ratios) as you have been using radii and not diameters. Eight inch wheel has a circumference of 16 times pi making it nearly fifty not 25.
Cheers,
Jim

Hi Jim, there's a bit of confusion going around atm! This time it's your turn - circumference is Pi times diameter, area is Pi times radius squared. And yes it does make a very big difference in ratios when squares or square roots are involved, but not in this case. As Mark said earlier it's "linearly proportional".

Derek, the water-ski-ing analogy doesn't affect anything. The maths are simple. Circumference is in a linear relation to radius. Double the radius and you double the circumference, hence with two wheels, one twice the radius of the other and the same revs, the smaller has half the circumferential velocity of the other.
Cheers,
Jim

Yes I understand that Jim, but my calcs are spot on.

Originally Posted by FenceFurniture

Yes I understand that Jim, but my calcs are spot on.

Yes was thinking of 8" radius etc
Cheers,
JIm

Funny, that's exactly the emoticon I thought I would see! It's too easy to get your head locked into a path with this stuff.

Originally Posted by FenceFurniture

Funny, that's exactly the emoticon I thought I would see! It's too easy to get your head locked into a path with this stuff.

Too right. At least we aren't trying to explain the maths of the outside of a car wheel in motion.
Cheers,
Jim

Originally Posted by jimbur

Too right. At least we aren't trying to explain the maths of the outside of a car wheel in motion.
Cheers,
Jim

If you are referring to Simple Harmonic Motion (the tracing of the motion of a fixed point on a circumference when viewed from a profile), and the associated mathematics - I LOVED that at school. It was part of three subjects that I did for the HSC (waaaaay back in 73) - Science, Maths, and the Mechanics strand of Industrial Arts. By the time we got to IA I was doing it with my eyes shut (literally - all 3 studies were within a few months of each other, so I was happy naps).

An example of SHM is the vertical path that a cyclist's feet trace. And just as a bit of whimsy - the sexiest maths I ever studied was Integration by Parts - just a beautifully elegant solution to an unsolvable problem.

If everything else is constant, the heating effect on a tool being sharpened depends on v^2 .

This is because KE = 1/2mv^2 , a doubling of speed produces a 4 times greater KE, while a 50% increase in speed produces a 2.25 times more KE and more heat.

Of course the overall rise in temperature also depends on contact time and pressure so for higher speed grinders, compensations can be made using a shorter contact time and less pressure. Likewise grit size and type, (and to a lesser extent the type of steel) can be used to advantage.

Even when taking all this into account, local (ie immediate contact area) heating effects are still greater for higher speeds. just how much this is, difficult to say.

Does it help if you blow on it Bob?

FF. no what I was referring to was the fact that in theory the part of a wheel in contact with the road (unless it is skidding) comes to a stop for a fraction of a second and accelerates to twice the speed of the car at the top of its travel.
Cheers,
JIm

Originally Posted by jimbur

FF. no what I was referring to was the fact that in theory a wheel (unless it is skidding) comes to a stop for a fraction of a second when it contacts the road and accelerates to twice the speed of the car at the top of its travel.
Cheers,
JIm

Ah, I see. Well straying off topic but I think that is also the same set of equations as SHM. The cyclist's foot is also stationary at the bottom and top of the cycle (referring to vertical motion only).