[ARCHIVED THREAD] - Impossible math problem (Page 1 of 3)
Posted: 6/26/2012 6:42:00 AM EDT
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A I know girl who just graduated with a BS in math.
Her boss asked her to develop a formula for accurately determining the weight of a milling cutter. He told her it should be a simple formula based on the shank diameter, tool length, number of flutes, and density of stock. I think it is impossible as there are too many variables. The biggest one being how to determine the volume of material removed with the initial cut of the helix. I gave up and said she should buy an accurate balance. She said her boss wants to use this formula to determine bulk quantities of tools that are still on paper. I think this goes beyond geometry. |
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Quoted: Define "simple". Posted Via AR15.Com Mobile I suck at math, but even I can see that "simple" and the proposed formula will never meet. Sounds like each cutter should be given a part number and weighed. Then the person can just look up the specs from typing the PN into a data base. |
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Theoretically it should be a simple process. Determine maximum area (shank diameter, tool length), subtract area of removed bits (number of flutes), multiply by density.
In practice, she's going to need a lot more information, like flute depth, flute length, flute width. Whether the fluting is uniform or tapers, minimum flute depth vs maximum flute depth and the angle between the two, etc. And that's just on the flutes, assuming that the material is otherwise a perfect cylinder. |
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A I know girl who just graduated with a BS in math. Her boss asked her to develop a formula for accurately determining the weight of a milling cutter. He told her it should be a simple formula based on the shank diameter, tool length, number of flutes, and density of stock. I think it is impossible as there are too many variables. The biggest one being how to determine the volume of material removed with the initial cut of the helix. I gave up and said she should buy an accurate balance. She said her boss wants to use this formula to determine bulk quantities of tools that are still on paper. I think this goes beyond geometry. As you noted, most milling heads are cut with a helix pattern, that right there makes the "simple" thing impossible. Now, you could make a complex formula, but it wouldn't be anything the average Joe would be able to make heads or tails from. |
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It is easy.
You know the density of the steel. You know the volume of the un-cut stock. You know the length and dimensions of the cut portion. It's a two-step problem. The first step is to determine the cylinder coefficient of the cut portion of the tool. Ccyl = 1 means an uncut cylinder. You'll need the diameters OR the radii of the overall cylinder plus each of the helical cuts. Ccyl = (Dstock^2 - [Dflute/2]^2 * NO. of Flutes / 2) / Dstock^2 mt = (Luncut + Lcut * Ccyl) * Dstock ^2 / 4 * Pi * pstock where: mt = mass of each tool Luncut = uncut length of tool stock Lcut = fluted/cut length of tool stock Ccyl = cylindrical coefficient Dstock = outer diameter of tool stock pstock = density of stock in unit weight per unit volume (note: density and dimensional units must agree, or else you'll need an additional conversion factor in there) Test the formula with existing tools, and use empirical values to slightly adjust the Ccyl value. Since the helical cuts are not going to be perfect half circles in cross-section, you'll find that your initial Ccyl estimates will be low. Develop a table of Ccyl values for the type of fluting, since you know you'll only really be using a handful of different options. Alternatively, take a horizontal cross section of the fluted portion in whatever software you're using to design the tool. Take the outer perimeter and block it into a single polyline. Take the polyline and generate a surface with it. Use your area tool to determine the area of that surface (or look it up in SurfProp). That area divided by Pi /4 * Dstock^2 equals Ccyl. You're welcome. |
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It's not impossible; it's impractical. I mean, it's a solid object of fixed volume and known material density. The negative volume of the flute cuts can be closely approximated by knowing about the tools and processes used to make those cuts. Seems like the manager is looking for a simple formula to describe a complex process. The result of a simple formula will be an approximation, not an exactitude.
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Her boss is an idiot. The real solution to his problem is a counting scale. Tare the bin that holds the parts. Then throw ten parts in an empty bin on the scale. Weigh the sample. Put the full bin on the scale and it tells you how many parts you have. http://www.scalesgalore.com/global/images/product_2/303/30303_250X250.jpg? The tools haven't been made yet. |
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Her boss is an idiot. The real solution to his problem is a counting scale. Tare the bin that holds the parts. Then throw ten parts in an empty bin on the scale. Weigh the sample. Put the full bin on the scale and it tells you how many parts you have. http://www.scalesgalore.com/global/images/product_2/303/30303_250X250.jpg? One of the requirements is that she has to know the weight of items that only exist on paper. |
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It's not impossible; it's impractical. I mean, it's a solid object of fixed volume and known material density. The negative volume of the flute cuts can be closely approximated by knowing about the tools and processes used to make those cuts. Seems like the manager is looking for a simple formula to describe a complex process. The result of a simple formula will be an approximation, not an exactitude. I wonder from the sound of things if this is some of the point? Her boss wants to see if she is capable of communicating with him to find out the ballance between "simple" and "exact" that will make him happy? |
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It's not impossible; it's impractical. I mean, it's a solid object of fixed volume and known material density. The negative volume of the flute cuts can be closely approximated by knowing about the tools and processes used to make those cuts. Seems like the manager is looking for a simple formula to describe a complex process. The result of a simple formula will be an approximation, not an exactitude. Boss wants something good-looking that he can put in a PowerPoint presentation. A good, young engineer will give him that, making sure that the formula always errs on the side of lowest cost increase. She wants a good looking table to determine Ccyl properties - put number of flutes on the column headers and the relative depth of flutes (depth of cut divided by the radius of the stock) on the row headers. You'll have a short table that lists various cylindrical coefficients and then a simple formula that will predict the weight of the tool using that value. If you want to be extra awesome, add in Ccyl values for tapered, hex, and keywayed tool ends - note that you can deal with multiple different sections of tool length in the above formula, you just sum all of the Lcut*Ccyl values. It'll look good, it'll work, it'll be easy to use, and OP's acquaintance can use all the time I just saved her to put up pictures of herself on ARFCOM. Everybody wins. |
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It'll look good, it'll work, it'll be easy to use, and OP's acquaintance can use all the time I just saved her to put up pictures of herself on ARFCOM. Let's hope she looks as good as your equation 
Hey, she's apparently just graduated. So, what, 21, 22 years old? As long as she's got a BMI under 20, chances are high that she's in the top quartile of American women in terms of looks. Which, I've covered this before, but that's absolute bullshit. Our society has gotten to the point where all you need to do to be attractive is just not be fat. It's fuckin' shameful is what it is. But, in fairness, that's not the fault of the pretty ones. I guess what I'm trying to say is: No fat chicks. It's the law. 
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Get your Archimedes on. Weight it and then weigh it in a graduated cylinder full of water. With dry weight, floating weight and volume of displacement you can figure it all out. Hard to do if it's only on paper. Paper still displaces water. Yeah, but it gets all soggy and hard to read. |
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Get your Archimedes on. Weight it and then weigh it in a graduated cylinder full of water. With dry weight, floating weight and volume of displacement you can figure it all out. Hard to do if it's only on paper. Paper still displaces water. And beats ROCK. |
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Draw it up in CAD and evaluate the properties (weight, volume, etc) with the correct density. Viola. As for the formula, it's not impossible math. But it is waaay too complicated for what they're trying to achieve. Not worth it. http://www.harrystone.net/posted/viola.jpg This reminds me of the time when I was about 7 years old, and finally realized people weren't saying "a wall ago." They were actually saying "a while ago".
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Draw it up in CAD and evaluate the properties (weight, volume, etc) with the correct density. Viola. As for the formula, it's not impossible math. But it is waaay too complicated for what they're trying to achieve. Not worth it. http://www.harrystone.net/posted/viola.jpg This reminds me of the time when I was about 7 years old, and finally realized people weren't saying "a wall ago." They were actually saying "a while ago". I was 26 years old before I realized that Whitesnake song's lyrics were actually, "Like a drifter, I was born to walk alone..." All that time, I thought it was "like a twister..." 
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Draw it up in CAD and evaluate the properties (weight, volume, etc) with the correct density. Viola. As for the formula, it's not impossible math. But it is waaay too complicated for what they're trying to achieve. Not worth it. http://www.harrystone.net/posted/viola.jpg This reminds me of the time when I was about 7 years old, and finally realized people weren't saying "a wall ago." They were actually saying "a while ago". I was 26 years old before I realized that Whitesnake song's lyrics were actually, "Like a drifter, I was born to walk alone..." All that time, I thought it was "like a twister..."
Yeah, I could write a book on all the lyrics I've screwed up in my life.
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Quoted: It is easy. You know the density of the steel. You know the volume of the un-cut stock. You know the length and dimensions of the cut portion. It's a two-step problem. The first step is to determine the cylinder coefficient of the cut portion of the tool. Ccyl = 1 means an uncut cylinder. You'll need the diameters OR the radii of the overall cylinder plus each of the helical cuts. Ccyl = (Dstock^2 - [Dflute/2]^2 * NO. of Flutes / 2) / Dstock^2 mt = (Luncut + Lcut * Ccyl) * Dstock ^2 / 4 * Pi * pstock where: mt = mass of each tool Luncut = uncut length of tool stock Lcut = fluted/cut length of tool stock Ccyl = cylindrical coefficient Dstock = outer diameter of tool stock pstock = density of stock in unit weight per unit volume (note: density and dimensional units must agree, or else you'll need an additional conversion factor in there) Test the formula with existing tools, and use empirical values to slightly adjust the Ccyl value. Since the helical cuts are not going to be perfect half circles in cross-section, you'll find that your initial Ccyl estimates will be low. Develop a table of Ccyl values for the type of fluting, since you know you'll only really be using a handful of different options. Alternatively, take a horizontal cross section of the fluted portion in whatever software you're using to design the tool. Take the outer perimeter and block it into a single polyline. Take the polyline and generate a surface with it. Use your area tool to determine the area of that surface (or look it up in SurfProp). That area divided by Pi /4 * Dstock^2 equals Ccyl. You're welcome. wow. |
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Get your Archimedes on. Weight it and then weigh it in a graduated cylinder full of water. With dry weight, floating weight and volume of displacement you can figure it all out. Hard to do if it's only on paper. Paper still displaces water. Yeah, but it gets all soggy and hard to read. You win. |
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Her boss is a moron and doesn't know what he's doing. For a lot of reasons; if this was important it should have been done by the tooling designer, most likely a mfg. eng. They sill use paper and not solid models, they need to leave the '80s. Maybe even get a network!! I think he's just giving her stupid shit as to do work, she needs to find a better job. |
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It is easy. You know the density of the steel. You know the volume of the un-cut stock. You know the length and dimensions of the cut portion. It's a two-step problem. The first step is to determine the cylinder coefficient of the cut portion of the tool. Ccyl = 1 means an uncut cylinder. You'll need the diameters OR the radii of the overall cylinder plus each of the helical cuts. Ccyl = (Dstock^2 - [Dflute/2]^2 * NO. of Flutes / 2) / Dstock^2 mt = (Luncut + Lcut * Ccyl) * Dstock ^2 / 4 * Pi * pstock where: mt = mass of each tool Luncut = uncut length of tool stock Lcut = fluted/cut length of tool stock Ccyl = cylindrical coefficient Dstock = outer diameter of tool stock pstock = density of stock in unit weight per unit volume (note: density and dimensional units must agree, or else you'll need an additional conversion factor in there) Test the formula with existing tools, and use empirical values to slightly adjust the Ccyl value. Since the helical cuts are not going to be perfect half circles in cross-section, you'll find that your initial Ccyl estimates will be low. Develop a table of Ccyl values for the type of fluting, since you know you'll only really be using a handful of different options. Alternatively, take a horizontal cross section of the fluted portion in whatever software you're using to design the tool. Take the outer perimeter and block it into a single polyline. Take the polyline and generate a surface with it. Use your area tool to determine the area of that surface (or look it up in SurfProp). That area divided by Pi /4 * Dstock^2 equals Ccyl. You're welcome. What about the area where the flutes taper to meet the shank? That is where my brain melted. |
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I would think you'd need a precise blue print or 3D rendering to do that. There is no way I could possibly set up the integrals required to do that, but I have a math minor. A math degree is going to be too theoretical for someone to be able to set that up right. An engineering major would have better luck. |
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Her boss is a moron and doesn't know what he's doing. For a lot of reasons; if this was important it should have been done by the tooling designer, most likely a mfg. eng. They sill use paper and not solid models, they need to leave the '80s. Maybe even get a network!! I think he's just giving her stupid shit as to do work, she needs to find a better job. Actually, her real job is a diamond grinding wheel dresser. 3rd shift weekends. Her hubby is in the air force, and she will only be staying here another 11 months. So she was happy to get this job since it is short term anyway. (although it pays poorly, and doesn't suit her education) I think her boss just thought "hey, a person who knows math. Can you make me a formula..." |
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I don't remember the math majors looking like this. In fact, I don't remember too many women, pretty or not, being in the hard sciences. The problem, as someone has no doubt mentioned, is solvable. "Simple", on the other hand is a sliding scale - to someone who designs propellers, dealing with the helix for the flutes is straightforward. |
| You need to find the weight for a base unit, for instance 3 lbs per 1 square inch of metal or whatever it actually is- based on the materials being used to produce the item. Ask her to get the raw materials for the production of the components. Then it's just a matter of figuring out the diameter of the cutter heads, diameter of the shafts etc. and then divide that number by the base unit. This is more of a geometry question. As far as weight of material removed per cut, that depends on the depth of the cut, width of the cut and of course again, the weight per unit of the material being removed multiplied by the surface area removed. As far fluted surfaces and cutting surfaces are concerned, she needs the inside diameter measurements after the dept of the fluting, then would need to calculate the area removed from each of the flutes/cuts whatever. I'm thinking her boss thinks he made a mistake hiring her, already knows the answer to this equation and is simply wanting to can her. But that's how I would see such a ridiculous request. |
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As someone with a BS in Math (back before the invention of sliced bread or graphing calculators)...
1) No one in my classes looked close to that good 2) There were only 2 women in any of my highest math classes. 3) The last two years of classes, we rarely used a number. 4) That formula could be created but it would not be close to simple if it was "spot on" accurate. It could be pretty simple if is was "close to" accurate. 5) I am so glad I also got a BS in Computer Science too so I do not have to spend all my days doing stuff like this. |