Equipment Mass Lumping for Seismic Analysis
Best practice for lumping equipment mass in seismic FEA models, covering point mass placement, offset CG representation, and the preservation of rotational inertia.
When to lump equipment mass
Equipment is typically modelled as a lumped mass rather than with detailed solid elements because the internal structure of the equipment is not the subject of the seismic analysis — the cabinet or frame is. The equipment mass is applied as a point mass at the centre of gravity and connected to the mounting points. This preserves the total mass and the CG location, and if done correctly, the rotational inertia.
Point mass at the CG
The equipment mass is applied as a point mass (a concentrated mass at a single node) located at the equipment centre of gravity. This node is connected to the mounting nodes on the cabinet or frame using rigid links or master-slave constraints. The rigid link ensures that the mass moves with the mounting points as a rigid body, preserving the offset of the CG and the rotational inertia about the mounting points.
Preserving rotational inertia
If the mass is lumped directly at the mounting nodes without a rigid link to the CG, the rotational inertia of the equipment about the mounting point is lost. This affects rocking and torsional modes. For a heavy item with a high CG (e.g. a transformer at the top of a cabinet), the loss of rotational inertia can significantly change the overturning response. The rigid link to the CG node is essential for preserving the correct dynamic behaviour.
Mass moments of inertia
For equipment with significant rotational inertia (e.g. a motor, a rotating machine, a tall transformer), the mass moments of inertia about the three axes at the CG should be included in the point mass definition. Many solvers allow a point mass with six independent inertia terms (three translational mass, three rotational inertia). If the inertia values are not known, they can be estimated from the equipment geometry and mass distribution.
Common errors
- Lumping mass at mounting nodes without a rigid link to the CG, losing rotational inertia
- Not including mass moments of inertia for equipment with significant rotational inertia
- Placing the CG node at the wrong location, producing incorrect overturning moments
- Using a rigid link that is too stiff, causing numerical issues in the eigensolver — use the solver default rigid link stiffness
- Connecting the CG node to the wrong mounting nodes, not reflecting the actual mounting detail