Component Mode Synthesis (CMS)
Component Mode Synthesis (CMS): Theoretical Foundations
What is the CMS Method?
Professor, what is the CMS method?
CMS (Component Mode Synthesis) is a technique that divides a large-scale structure into substructures (components), reduces the dynamic characteristics of each component using modal coordinates, and then assembles the whole.
"Divide, reduce, and assemble"?
For example, directly solving a full-vehicle model (millions of DOF) requires enormous computation. With the CMS method:
1. Divide into substructures like body, engine, suspension, etc.
2. Reduce each substructure using eigenmodes + constraint modes (to hundreds of DOF)
3. Combine the reduced substructures and solve the whole system
Millions of DOF are reduced to thousands!
Computation time can become less than 1/100. Particularly effective when many substructures are used repeatedly (e.g., different vehicle body variations).
Craig-Bampton Method
The most widely used CMS method is the Craig-Bampton method (1968). Each substructure is represented by two types of modes:
- Fixed-Interface Eigenmodes β Internal eigenmodes with the interface fixed
- Constraint Modes β Static deformation when each interface DOF is given a unit displacement
.
So eigenmodes represent internal vibration, and constraint modes represent interface deformation.
Displacement of each substructure:
$\{q\}$ are modal coordinates (tens to hundreds), $\{u_b\}$ are interface DOFs. Total DOFs are reduced to $\sum (n_{modes} + n_{boundary})$.
Advantages of the CMS Method
| Advantage | Explanation |
|---|---|
| Significant reduction in computation time | Reduces total DOFs to 1/10 to 1/1000 |
| Parallelization | Each substructure can be computed independently |
| Efficient design changes | Changing one substructure does not require recalculating others |
| Intellectual property protection | Suppliers can provide only reduced models without disclosing internal structure |
Interesting that it can be used for IP protection.
In the automotive supply chain, suspension manufacturers provide CMS reduced models to OEMs. OEMs can perform full-vehicle vibration analysis without seeing the internal structure.
Summary
Let me organize the CMS method.
Key points:
- Divide large-scale structures into substructures and reduce β DOFs to 1/10 to 1/1000
- Craig-Bampton method is standard β Eigenmodes + Constraint modes
- Significant reduction in computation time β Essential for full-vehicle NVH analysis
- Flexible for design changes β Changes possible per substructure
- IP protection β Share reduced models without disclosing internal structure
Hurty and Craig's Invention of "Solving by Parts"
The CMS (Component Mode Synthesis) method was developed by Hurty (1960) and Craig & Bampton (1968). It's a technique that divides large-scale models into substructures, reduces them using the eigenmodes of each part, and then couples them. The Craig-Bampton method combines fixed-interface modes (internal DOF reduction) and constraint modes (boundary DOF retention) and remains the most widely used CMS formulation today.
Computational Methods for Component Mode Synthesis (CMS)
Implementation of the Craig-Bampton Method
Please explain the implementation steps of the Craig-Bampton method.
Step 1: Substructure Definition
- Divide the structure into logical components
- Define interface DOFs (connection points between components)
Step 2: Reduction of Each Component
- Eigenfrequency analysis with fixed interface β Fixed-interface eigenmodes $[\Phi_f]$
- Static analysis giving unit displacement to each interface DOF β Constraint modes $[\Psi_c]$
- Calculate reduced mass/stiffness matrices
Step 3: Assembly of the Whole
- Combine reduced matrices of each component via interface DOFs
- Solve the overall eigenvalue problem
Nastran
```
SOL 103
CEND
SUBCASE 1
METHOD = 10
BEGIN BULK
$ Superelement definition
SELOC, 100, ... $ Substructure definition
SECONM, 100, ... $ Reduction
```
Nastran's superelement functionality is the industry standard for CMS.
Abaqus
```
*SUBSTRUCTURE GENERATE
*RETAINED NODAL DOFS
interface_nodes, 1, 6
*FREQUENCY
50, ,
*END STEP
```
Ansys
Substructuring analysis type in Workbench allows CMS reduction setup via GUI.
Is Nastran's superelement the industry standard?
For automotive and aerospace CMS analysis, Nastran's superelement has overwhelming track record. There is an industry-standard format (OP2/OP4 files) for exchanging reduced matrices.
How to Determine the Number of Modes to Retain
How many fixed-interface eigenmodes should be retained?
Retain modes up to 1.5 to 2 times the frequency of the range of interest. For example, for full-vehicle analysis up to 500 Hz, retain modes up to 750~1000 Hz for each substructure.
Summary
Let me organize the numerical methods of CMS.
Key points:
- Craig-Bampton method β Reduction using fixed-interface eigenmodes + constraint modes
- Nastran superelement is industry standard β OP2/OP4 format
- Number of modes = up to 1.5~2 times the frequency of interest β Balance accuracy and computational cost
- Interface DOF definition is key β Appropriate interface selection affects accuracy
Craig-Bampton Reduction Procedure and Accuracy Verification
The Craig-Bampton method involves three steps: β Eigenmode calculation for internal DOFs (typically 0~f_max range) β‘ Constraint mode calculation by applying unit displacement to boundary DOFs β’ Assembly of reduced matrices. The standard procedure is to incorporate the reduced model into the full system, calculate eigenvalues, and verify accuracy within Β±1% compared to the full FEM. The cutoff frequency for internal eigenmodes uses 1.5 to 2 times the evaluation upper limit.