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

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

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

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)

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 B C D E F A A + B+ C + D+ E + F = 160 in2

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.

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 volume units.

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.

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

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.

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