August 19th, 2012
Some of you know I work for a guy where we manufacture portable band saws. There's about 25 different processes that need to be done to complete each saw, but it's much more efficient to do a large run of each process at a time. Basically that means I have a new but equally boring job every day. One day I might be checking 300 idle wheels for concentricity and the next drilling out 250 elevation handles for set screws.
As you can see, my job affords me ample opportunity to let my mind wander and muse on the deep questions of life, such as how many minutes are left until deer season or the best way to attach a lawnmower engine to a bicycle.
A few days ago I found myself making a batch of blade guides for the band saw. That entails cutting 40 feet of 1/2" diameter brass rod up into 3.5 inch chunks. About halfway through I began to wonder if I could calculate the width of the saw blade by the weight of the resulting sawdust. I did a very thorough job of recovering the detritus and I'd estimate I recovered around 99%.
Cutting out a blade guide blank
I took the sawdust home and found I had 1.004 pounds by weighing it on my dad's sensitive gunpowder scale. Adding on 1% for unrecovered sawdust bumps our total up to 1.014 pounds.
1.004 pounds of brass sawdust
I ended up with 136 blade guides after cutting up the 40 feet of 1/2" diameter brass rod, but I only made 132 cuts since the first blade guide from each of the four 10 foot brass rods still had one factory end.
136 blade guide blanks
Our blade guides are made from C36000 free machining brass which is an alloy consisting of copper, zinc, and lead. It has a density of .307 pounds per cubic inch. Since I've got 1.014 pounds of sawdust and there's .307 pounds per cubic inch, that means I must have 3.303 cubic inches of sawdust.
Next I need to find the length of a 1/2" diameter cylinder that contains a volume of 3.303 cubic inches. Since the height of a cylinder is equal to the volume divided by the area of the base, we can conclude the rod must be 16.822 inches long.
I made 132 cuts with the saw which resulted in 16.822 inches of 1/2" diameter brass rod turning into sawdust. 16.822 divided by 132 results in a saw blade width of .127 inches. I measured the widest tooth on the blade with a micrometer and it checked in at .128 inches on the money. Just one thousandth of an inch off from my calculation! So there you have it. The effort I have to go through to have fun at work.
0.128"
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