Why One Density Gives the Wrong Assembly Mass: A Worked CAD Example

Prepared by an AI assistant on behalf of CADProps for technical sharing. This is an analytical example, not an independent product review or a measured CADProps test.

A CAD assembly can have the correct total volume and still produce the wrong mass estimate. The missing input is often the distribution of that volume across materials. Multiplying the whole assembly by an aluminium density does not account for its steel components.

A five-solid check you can reproduce

Create five separate, non-overlapping rectangular solids in any CAD system. This deliberately simple arrangement checks the arithmetic and component count, rather than representing a manufactured assembly.

• One block: 40 × 25 × 20 mm. Assign an example density of 2.70 g/cm³.

• Four identical inserts: 10 × 10 × 5 mm each. Assign an example density of 7.85 g/cm³.

The density values are illustrative assumptions for aluminium and steel. They are not material certificates or values inferred from a file. For a real calculation, use the specified alloy and a documented density source.

Place the block at X = 0 to 40 mm. Place the inserts at X = 50 to 60, 65 to 75, 80 to 90, and 95 to 105 mm, all with Y = 0 to 10 and Z = 0 to 5 mm. The gaps make it easy to confirm that no volumes overlap. The block occupies Y = 0 to 25 and Z = 0 to 20 mm.

Calculate each material contribution

Because 1 cm³ = 1,000 mm³, the working equation is:

Mass in grams = quantity × volume per component in mm³ × density in g/cm³ ÷ 1,000.

The block volume is 40 × 25 × 20 = 20,000 mm³. Its mass is 1 × 20,000 × 2.70 ÷ 1,000 = 54.00 g.

Each insert has a volume of 10 × 10 × 5 = 500 mm³. Four inserts contribute 4 × 500 = 2,000 mm³. Their combined mass is 4 × 500 × 7.85 ÷ 1,000 = 15.70 g.

The expected total is therefore 22,000 mm³ and 69.70 g, under the stated density assumptions. These values follow from the specified dimensions; no imported model was measured to obtain them.

Two errors that look plausible

Using one aluminium density: 22,000 × 2.70 ÷ 1,000 = 59.40 g. The volume is correct, but the mass is 10.30 g low, about 14.8% below the component-by-component result.

Counting the insert definition only once: 54.00 + 500 × 7.85 ÷ 1,000 = 57.925 g. A CAD file may store one part definition and reuse it four times. Count included occurrences, not just unique part names. Also check whether a volume already includes quantity before multiplying again.

These are separate checks. Fixing the density does not repair a missing occurrence, and fixing the count does not repair a material assignment.

Why an “average density” is fragile

The example has an effective density of 69.70 ÷ 22 = approximately 3.16818 g/cm³. Applying that density to this exact assembly volume reproduces its mass.

That number is a volume-weighted result for this composition. It is not a material property. Add another steel insert, remove the aluminium block, or change the included configuration, and it must be recalculated. Keeping separate component contributions makes those changes visible.

A practical review record

For each component type, retain the file revision, included quantity, volume per occurrence, volume unit, density, density source, calculated mass and result status. Mark missing or unresolved geometry as incomplete rather than assigning it zero mass.

Before accepting a total, check one known dimension, solid closure, the expected occurrence count and whether any parts overlap. For ordinary mass accounting, each physical component contributes its own material; an unintended interference deserves investigation rather than silently fusing the model and calling the result correct.

CADProps' calculation notes state that assembly totals count occurrences, do not subtract overlapping material, and are not changed merely by hiding a part. Its STEP weight guide describes component-level material inputs. These documented assumptions should be checked against the scope of the files actually loaded. Use separately identified component volumes for a mixed-material calculation instead of treating a whole-model density setting as proof of material assignment.

Finally, a geometric mass estimate is not a scale measurement or shipping weight. Coatings, adhesive, omitted hardware and packaging need their own justified entries. A useful handoff preserves the assumptions and missing items alongside the total.