12 Replies Latest reply on May 3, 2012 5:21 PM by Bengt Gustafsson

    Fill 1/2 Cylinder Volume with Bottle Cap Shaped Parts

    Mark Horne

      I am trying to calculate the number of pieces that would fill 1/2 of the volume of a cylinder, 9"dia x18"long.  The parts are close to the shape and size of a bottle cap. Actual size is a bit larger. I searched here and the web without finding relevant discussion.

      This job will run millions of parts a year, so a good close number without doing the over simplified "cyl volume/part volume" is required to find the number of stations we need.  We only have one sample finished part so we can not just pour them in and count.


      We have SolidWorks 2012 Premium and Simulation Professional.





      Perhaps this would be better handled in another section of this forum.

        • Re: Fill 1/2 Cylinder Volume with Bottle Cap Shaped Parts
          Adrian Tayne

          I am not sure SW can help you with this one...a hand calc seems like the way to go.


          Considering there is an uncountable number of arrangements the parts could take, you'll have to simplify it in a way that gives a reasonable "packing factor" which will be a close approximation to the average number of parts that will occupy the volume. The way I would do it is assume the parts are stacked in discrete layers with all of the parts being oriented on the flat side (thinking bottle caps here) and touching one another. Calculate the ratio of the volume occupied to the total volume of that layer. This gives you a packing factor. Find the volume of half the cylinder. Multiply the packing factor by the half-cylinder volume to find total volume of the parts. Divide that by the volume of one part.


          This actually comes out to the maximum number of parts that you could fit into the volume.

            • Re: Fill 1/2 Cylinder Volume with Bottle Cap Shaped Parts
              Adrian Tayne

              And actually now that I think about it, SW would make it easier to find the number of caps that would fit in one layer within the circular walls of the container.


              Sketch out a circle to represent the part. Make a linear pattern at 30 degrees down and to the right.

              Then make a linear pattern vertically with part diameter as the spacing

              Make this 2D pattern big enough that you can sketch a circle that has the diameter of your cylinder container on top of it.

              See how many whole circles fit inside the larger circle.

              packing factor.JPG

            • Re: Fill 1/2 Cylinder Volume with Bottle Cap Shaped Parts

              Hi mark,


              The fill pattern might be able to aid you in this - seem like it has everything you might need.





              • Re: Fill 1/2 Cylinder Volume with Bottle Cap Shaped Parts
                Jerry Steiger



                If the cylinder is oriented with the axis vertical, then Adrian's method should give you a reasonable upper bound on how many parts you can fit. How close you get to that number will depend on the weight of the parts, the friction between them, vibration levels and a probably a bunch of other factors.


                If the cylinder is oriented with the axis horizontal, then it is a much harder problem. The same basic idea would work, but now you are filling the space with little rectangles and they may tilt, making it much harder.


                Jerry Steiger

                • Re: Fill 1/2 Cylinder Volume with Bottle Cap Shaped Parts
                  Bengt Gustafsson

                  Hi Mark.

                  It is possible to do a motion simulation that will calculate one possible solution for, let's say, 1000 of your "caps" falling into a cylinder, taking into account that they bounce against the cylinder and into each other. However, unless you have a line into one of the mythical super-mega-machines doing teraflops for breakfast, this would not be practical.


                  If you simplify the problem using, say, half a cylinder or a third, and limit the items to perhaps 50 or so, it is workable. Sure, it does take some time to calculate, but you can decrease the accuracy quite a lot since you are not after the exact movemen of the capst. You just want to see how they may end up, laying at the bottom.

                  I did a test with some 30 pieces, and it took about one hour to calculate - 120 fps, 3d contact set low.


                  After the simulation, it is just a simple task of measuring how high the 50 pieces have reached and multiply until you reach half the cylinder, assuming that the cylinder is upright - axis pointing upward.

                  This should give you a fairly accurate idea of the total amount of pieces fitting into your cylinder.