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Mass Property Analysis

Mass Property Analysis. The size, weight, surface area, and other properties available from a solid model are most often part of the design constraints your design must satisfy. The following are mass property calculations available in today’s solid modelers: Volume Density Mass

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Mass Property Analysis

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  1. Mass Property Analysis The size, weight, surface area, and other properties available from a solid model are most often part of the design constraints your design must satisfy. The following are mass property calculations available in today’s solid modelers: Volume Density Mass Surface area Centroid Moment of Inertia Product of Inertia Radii of Gyration Principal Axes Principal Moments

  2. Volume • Volume is the amount of three-dimensional space that an object takes up. • Design engineers use this value to determine the amount of material needed to produce a part. V = H x W x L V = 4 x 4 x 8 V = 128 in3 4 8 4

  3. Density • Density is defined as mass per unit volume. • Density is different for every material and can be found in a machinist handbook.

  4. Mass • Mass is the amount of matter in an object or the quantity of the inertia of the object. • Many materials are purchased by weight; to find weight, we need the mass. Polypropylene has a density of .035 lbs/in3 Mass = Volume x Density Mass = 128 in3 x .035 lbs/in3 Mass = 4.48 lbs. Using the volume from the previous example. (128 in3)

  5. B C A D F E Surface Area • Surface area is the squared dimensions of the exterior surface. • Surface area is important when determining coatings and heat transfer of a part. A= 4in x 4in = 16 in2 B= 4in x 8in = 32 in2 C= 4in x 8in = 32 in2 D= 4in x 8in = 32 in2 E= 4in x 8in = 32 in2 B= 4in x 4in = 16 in2 A + B+ C + D+ E + F = 160 in2

  6. Centroid • A 3D point defining the geometric center of a solid. • Do not confuse centroid with the center of gravity. • The two only exist at the same 3D point when the part has uniform geometry and density.

  7. Moments of Inertia • An object’s opposition to changing its motion about an axis. • This property is most often used when calculating the deflection of beams. = Integral (Calculus) I = Moments of Inertia r = Distance of all points in an element from the axis p = Density of the material dV= Division of the entire body into small volumeunits.

  8. Products of Inertia • Is similar to moments of inertia only that products of inertia are relative to two axes instead of one. • You will notice an XY, YZ, or ZX after the I symbol when defining products of inertia compared to moments of inertia.

  9. Radii of Gyration • A dimension from the axis where all mass is concentrated, and will produce the same moment of inertia. K = Radius of gyration about an axis M = Mass I = Moments of inertia

  10. Principal Axes • The lines of intersection created from three mutually perpendicular planes, with the three planes point of intersection at the centroid of the part. The X, Y, and Z axes show the principal axes of the ellipsoid.

  11. Principal Moments • Principal moments are the moments of inertia related to the principal axes of the part.

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