Calculating Assembly Mass Properties of Different Densities with AutoCAD

[leeminardi]

How to Calculate the Mass Properties of a Group Of Solids (Assembly) with AutoCAD

The AutoCAD massprop command provides a rich collection of mass properties including volume, centroid, moments of inertia and more.  However, it has two major shortcomings, the first is that density of the solid is assumed to be 1.0. The other limitation is that massprop does not calculate the mass properties for a collection of solid objects that have different densities.

Here’s a method that uses standard AutoCAD features for addressing these massprop limitations.

Mass Properties of an Assembly with Components of the Same Density

To calculate the mass or other mass properties of a collection of solid objects simply use the union function to combine all the solids into one object then multiply the massprop results  by the density of the material.  The centroid and center of mass are the same if the material is of uniform density.

Mass Properties of an Assembly with Components of Differing Densities

The mass property of an assembly with components of differing densities can be calculated with massprop by substituting solids with volumes representing the individual masses of each component then using union to get the mass properties of the assembly.

Here’s an example.

Assume an assembly includes three solids we will call A , B, and C. The density of A is 0.1, B is 0.2, and C is 0.6.  We will not include units in this example and will assume units are consistent.

 

Step 1. Use massprop to calculate the volume and centroid of each solid object.  Multiply the density by the volume for each solid to get its mass.  The results may look like this:

Step 2. Create a sphere of radius 0.62035 and place a copy at the centroid for each object. A sphere with a radius of 0.62035 has a volume of 1.0000.

Step 3. Scale each of the spheres by the cube root of their respective mass.  This can be easily done in AutoCAD as follows.

Command: SCALE [Enter]

Select objects: 1 found  -- select a sphere --

Select objects: [Enter]

Specify base point:  -- object snap to center of sphere--

Specify scale factor or [Copy/Reference]: 'cal [Enter]

>>>> Expression: 0.00247^0.33333

Resuming SCALE command.

Specify scale factor or [Copy/Reference]: 0.13517851631567 

[Enter]

Note, a sphere with a radius of 0.13517… has a volume of 0.00247 (the mass of solid A).

Step 4.

After scaling all the individual spheres by their appropriate scale factor union them together.  Although the three spheres may not overlap they can be made into one solid in AutoCAD! 

Step 5. Use massprop on the new solid that includes the three spheres.  This will yield the mass properties of the full collection of objects.  The “volume” in the results is the total mass (or weight if pound mass were assumed).  The other properties (except bounding box) are correct for the assembly.

Mass:                    0.11935

Volume:                  0.11935

Bounding box:         X: 1.19974  --  2.87560

                      Y: 0.43710  --  1.52298

                      Z: 0.44720  --  1.00418

Centroid:             X: 2.36449

                      Y: 0.88545

                      Z: 0.74265

Moments of inertia:   X: 0.17189

                      Y: 0.75230

                      Z: 0.78923

Products of inertia: XY: -0.23949

                     YZ: -0.07974

                     ZX: -0.20797

Radii of gyration:    X: 1.20009

                      Y: 2.51061

                      Z: 2.57148

Principal moments and X-Y-Z directions about centroid:

                      I: 0.00475 along [0.80520 -0.58673 -0.08602]

                      J: 0.02676 along [0.59111 0.80572 0.03755]

                      K: 0.02855 along [0.04727 -0.08109 0.99559]

[maratovich]

Try using this, it is more convenient: 3DSolidBox - Get information from 3D solid

[SEANT61]

Nice procedure.  the only comment I can make has to do with this statement:

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@leeminardi wrote:

. . . .

Step 4.

After scaling all the individual spheres by their appropriate scale factor union them together.  Although the three spheres may not overlap they can be made into one solid in AutoCAD! 

. . . .

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I think that should be:  The three spheres must not overlap before 'Union'ing, else the calculations become skewed.

I am unable to comment on the recommendation in post #2 of this thread.

[leeminardi · Accepted solution]

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@SEANT61 wrote:

Nice procedure.  the only comment I can make has to do with this statement:

---

@leeminardi wrote:

. . . .

Step 4.

After scaling all the individual spheres by their appropriate scale factor union them together.  Although the three spheres may not overlap they can be made into one solid in AutoCAD! 

. . . .

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I think that should be:  The three spheres must not overlap before 'Union'ing, else the calculations become skewed.

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@SEANT61 Thanks for the compliment.  Your sharp eye is correct in that if the spheres that are used to represent the masses of the original objects overlap there will be an error in the calculation of the mass properties as the overlapping volume of the spheres will reduce the total volume used for the calculation.

If the spheres do overlap the user should scale each sphere down by the same scale factor about its center so that there is no overlapping then factor the scaling in the results generated by massprop (after the Boolean union is done on the scaled spheres).

For example, if each sphere is scaled using a scale of 0.1 then the following should be taken into account in the results of massprop.

Mass:                    multiply by 1000 to get true value

Volume:                ignore, the volume has been modified to adjust for the different densities.  

Bounding box:     ignore

Centroid:             correct

Moments of inertia:  multiply by 1000 to get true value

Products of inertia: multiply by 1000 to get true value 

Radii of gyration:    is the true value

Principal moments and X-Y-Z directions about centroid:  scale moment value by 1000, the vector is correct

[AVCPlugins]

What a terrible method 🤐. It is easier to extract 3D-solid volumes into a table and then work only with the table.
Actually AutoCAD objects have a Material property! However, this material only provides texture for rendering, but it has no density. Therefore, the MassProp command and the DataExtraction command always assume that the density is 1, no matter what material you assign. This problem can only be solved with plugins. A cheap plug-in AVC Properties Palette adds density, price and a number of other properties to materials. If you assign such materials to your solids or layers of your solids, then the DataTable or Sawing Table plugin will be able to extract the weight and price data for each of your parts and assemblies as a whole. And the Material Table plugin will extract the total data on the amount of materials needed to manufacture the entire product.

[lamensterms]

Thanks for posting this, seems like a good method based on my brief testing