topic Re: Model with simple frustrum - volume calculation wrong in Creo Modeling Questions
https://community.ptc.com/t5/Creo-Modeling-Questions/Model-with-simple-frustrum-volume-calculation-wrong/m-p/278753#M70692
<HTML><HEAD></HEAD><BODY><P>I think I figured it out. The frustrum equation, though not described as such, must only apply to a square pyramid, i.e. where L and W are the same for each height, z. When that assumption is applied to the integrated solution, the resultant equation collapses to the one from the CRC tables.</P><P></P><P>I wish I'd noticed that earlier.</P></BODY></HTML>Sat, 29 Mar 2014 18:08:28 GMTKenFarley2014-03-29T18:08:28ZModel with simple frustrum - volume calculation wrong
https://community.ptc.com/t5/Creo-Modeling-Questions/Model-with-simple-frustrum-volume-calculation-wrong/m-p/278748#M70687
I make a lot of models that involve pyramidal frustrums (transition of a rectangular section to another rectangular section, linearly). Rather than use the measured value calculated by Creo, I thought I'd have a go at calculating the volume directly from the dimensions.When IFri, 28 Mar 2014 20:36:24 GMThttps://community.ptc.com/t5/Creo-Modeling-Questions/Model-with-simple-frustrum-volume-calculation-wrong/m-p/278748#M70687KenFarley2014-03-28T20:36:24ZRe: Model with simple frustrum - volume calculation wrong
https://community.ptc.com/t5/Creo-Modeling-Questions/Model-with-simple-frustrum-volume-calculation-wrong/m-p/278749#M70688
<HTML><HEAD></HEAD><BODY><P>I think Creo is right. </P><P></P><P>I'm not sure where the formula came from but ...</P><P></P><P>L = l_base - ((l_base-l_top)/delta_z) * Z</P><P></P><P>W = w_base - ((w_base-w_top)/delta_z) * Z</P><P></P><P>A = L * W = </P><P>l_base*w_base</P><P>- (l_base*((w_base-w_top)/delta_z) + w_base*((l_base-l_top)/delta_z)) * Z</P><P>+ ((l_base-l_top)/delta_z)*((w_base-w_top)/delta_z)*Z*Z</P><P></P><P>Integrating: </P><P>V =</P><P>l_base*w_base*Z</P><P>- (l_base*((w_base-w_top)/delta_z) + w_base*((l_base-l_top)/delta_z)) * Z*Z/2</P><P>+ ((l_base-l_top)/delta_z)*((w_base-w_top)/delta_z)*Z*Z*Z/3</P><P></P><P>Plugging it all in I get 11.33...</P></BODY></HTML>Fri, 28 Mar 2014 23:56:31 GMThttps://community.ptc.com/t5/Creo-Modeling-Questions/Model-with-simple-frustrum-volume-calculation-wrong/m-p/278749#M70688dschenken2014-03-28T23:56:31ZRe: Model with simple frustrum - volume calculation wrong
https://community.ptc.com/t5/Creo-Modeling-Questions/Model-with-simple-frustrum-volume-calculation-wrong/m-p/278750#M70689
<HTML><HEAD></HEAD><BODY><P>I should be able to simplify the integral to be the same as the original formula, but so far no luck. I looked at the Wikipedia page that showed the derivation of the original formula, but it doesn't yield terms I can yet convert.</P><P></P><P>I get 11.3182 from the original formula, but don't see the reason for the discrepancy. </P></BODY></HTML>Sat, 29 Mar 2014 01:40:26 GMThttps://community.ptc.com/t5/Creo-Modeling-Questions/Model-with-simple-frustrum-volume-calculation-wrong/m-p/278750#M70689dschenken2014-03-29T01:40:26ZRe: Model with simple frustrum - volume calculation wrong
https://community.ptc.com/t5/Creo-Modeling-Questions/Model-with-simple-frustrum-volume-calculation-wrong/m-p/278751#M70690
<HTML><HEAD></HEAD><BODY><P>I got the original formula from the CRC math tables. A handy book from olden times which has all sorts of nice answers to unusual geometry questions. It's an odd conundrum. One would, reasonably, expect any sound mathematical method to yield the same results.</P><P></P><P>I can see where your integration comes from, and how it gets the number Creo gets. But still, I wonder if I'm missing something crucial about the frustrum...</P></BODY></HTML>Sat, 29 Mar 2014 04:48:22 GMThttps://community.ptc.com/t5/Creo-Modeling-Questions/Model-with-simple-frustrum-volume-calculation-wrong/m-p/278751#M70690KenFarley2014-03-29T04:48:22ZRe: Model with simple frustrum - volume calculation wrong
https://community.ptc.com/t5/Creo-Modeling-Questions/Model-with-simple-frustrum-volume-calculation-wrong/m-p/278752#M70691
<HTML><HEAD></HEAD><BODY><P>I put the integration solution and original into Excel and tried some experiments.</P><P></P><P>Case 1: the top and bottom the same; the original formula and mine agree.</P><P>Case 2: the top dimensions both zero; the original formula and mine agree.</P><P>Case 3: the top length equal to the bottom and the top width to zero the formulas disagree. Since it's simulating a triangle section, the volume should be 1/2 that of Case1. Mine is, but the original formula gives 1/3.</P><P></P><P>What is interesting is that the original formula doesn't distinguish between the case where the top surface area is zero because it is a point and the case where it is a line. </P><P></P><P>It may be that the original formula is built on the assumption that the sides all could extend to a single point and is shape independent while the integration handles sides of differing slopes, but only rectangles.</P></BODY></HTML>Sat, 29 Mar 2014 16:19:20 GMThttps://community.ptc.com/t5/Creo-Modeling-Questions/Model-with-simple-frustrum-volume-calculation-wrong/m-p/278752#M70691dschenken2014-03-29T16:19:20ZRe: Model with simple frustrum - volume calculation wrong
https://community.ptc.com/t5/Creo-Modeling-Questions/Model-with-simple-frustrum-volume-calculation-wrong/m-p/278753#M70692
<HTML><HEAD></HEAD><BODY><P>I think I figured it out. The frustrum equation, though not described as such, must only apply to a square pyramid, i.e. where L and W are the same for each height, z. When that assumption is applied to the integrated solution, the resultant equation collapses to the one from the CRC tables.</P><P></P><P>I wish I'd noticed that earlier.</P></BODY></HTML>Sat, 29 Mar 2014 18:08:28 GMThttps://community.ptc.com/t5/Creo-Modeling-Questions/Model-with-simple-frustrum-volume-calculation-wrong/m-p/278753#M70692KenFarley2014-03-29T18:08:28ZRe: Model with simple frustrum - volume calculation wrong
https://community.ptc.com/t5/Creo-Modeling-Questions/Model-with-simple-frustrum-volume-calculation-wrong/m-p/476706#M111226
<P>Just in the interest of completeness, I needed to document this for some training stuff, so I have a nice illustration of the problem with the mathematical solution employed. Attached is picture of the results.<span class="lia-inline-image-display-wrapper lia-image-align-inline" image-alt="Calculation of Rectangular Frustum Volume.png" style="width: 772px;"><img src="https://community.ptc.com/t5/image/serverpage/image-id/404i339F6D7DF3D94364/image-size/large?v=v2&px=999" role="button" title="Calculation of Rectangular Frustum Volume.png" alt="Calculation of Rectangular Frustum Volume.png" /></span></P>Tue, 11 Jul 2017 11:53:58 GMThttps://community.ptc.com/t5/Creo-Modeling-Questions/Model-with-simple-frustrum-volume-calculation-wrong/m-p/476706#M111226KenFarley2017-07-11T11:53:58Z