3. Design space definition

A design exploration campaign is only as good as the design space it searches. Before any DOE matrix is generated or any optimizer is launched, the engineering team must decide what can vary, how much it can vary, and how those variations propagate from CAD geometry into the CAE model. This chapter covers the practical mechanics of parameterizing four major vehicle subsystems — body, chassis, powertrain, and thermal — and the discipline required to keep the resulting design space both physically meaningful and computationally tractable.

From CAD Parameters to CAE Design Variables

Parameterization begins in the CAD environment but must be validated in the CAE environment. A CAD parameter is a dimension, offset, angle, or feature control that drives geometry regeneration. A CAE design variable is a scalar input that the solver or morphing tool can modify without breaking the mesh or invalidating boundary conditions. The gap between the two is where most campaigns fail.

Three parameterization strategies are common in automotive CAE:

• CAD-driven parameters — dimensions and feature controls exposed in the parametric history tree (e.g., a rail section height, a suspension hardpoint coordinate, a battery pack thickness). Regeneration is exact but slow, and topology changes can break downstream features.
• Mesh morphing — direct node displacement using control blocks, domains, or radial basis functions. Fast and topology-preserving, but limited to shape changes that the morphing domain can accommodate.
• Hybrid approaches — CAD parameters for major architecture decisions, morphing for local shape refinement. This is the dominant practice for full-vehicle campaigns.

Regardless of strategy, every design variable must satisfy four conditions: it must be independent (no redundant variables), bounded (physically and manufacturably feasible), sensitive (it measurably affects at least one response), and stable (small changes produce small, continuous response changes).

Body Subsystem Parameterization

Body-in-white (BIW) parameterization typically targets mass, stiffness, and crash performance. Representative design variables include:

Gauge variables are straightforward: they map directly to shell element thickness and require no remeshing. Shape variables (section height, bead depth) require either CAD regeneration or morphing. A practical rule is to keep gauge variables continuous and shape variables bounded to ±15–20% of baseline to avoid mesh distortion and unrealistic styling departures.

Chassis Subsystem Parameterization

Chassis design variables are dominated by hardpoint coordinates and bushing rates. For a double-wishbone front suspension, the design space might include:

DV_01  lower_control_arm_front_z    -10.0 .. +10.0 mm
DV_02  lower_control_arm_rear_z     -10.0 .. +10.0 mm
DV_03  upper_control_arm_z          -8.0  .. +8.0  mm
DV_04  steering_rack_x              -15.0 .. +15.0 mm
DV_05  lower_bushing_radial_rate    800   .. 1600  N/mm
DV_06  lower_bushing_axial_rate     200   .. 600   N/mm

Hardpoint moves affect camber, caster, bump steer, and roll center height simultaneously. This coupling is the central challenge: a 10 mm move in one hardpoint can improve camber gain while degrading bump steer. The design space must therefore be defined with the kinematic coupling in mind, and responses should include the full suspension characteristic curve, not just a single scalar.

Bushing rates are treated as scalar design variables but must respect manufacturing reality. A common constraint is to limit the ratio between radial and axial stiffness to a range achievable with a single rubber compound, typically 3:1 to 8:1.

Powertrain Subsystem Parameterization

Powertrain parameterization spans structural, thermal, and NVH domains. For an electric drive unit, typical variables include:

• Mount stiffness — three orthogonal rates per mount, bounded by elastomer supplier capability.
• Mount position — fore-aft and lateral coordinates, constrained by package envelope.
• Housing rib thickness and height — affecting radiated noise and structural modes.
• Inverter switching frequency — affecting tonal noise and thermal load.

Powertrain variables often interact strongly with body and chassis variables. Mount stiffness changes affect both driveline NVH and full-vehicle ride. When defining the design space, it is good practice to declare cross-subsystem coupling explicitly rather than letting the optimizer discover it through failed runs.

Thermal Subsystem Parameterization

Thermal design variables govern coolant flow distribution, heat exchanger sizing, and battery thermal management. Representative parameters:

Thermal variables are often constrained by 1D system models rather than 3D CFD, because the design space exploration requires hundreds or thousands of evaluations. A common workflow is to calibrate a 1D thermal network against a small number of 3D CFD runs, then use the 1D model as the campaign surrogate.

Design Space Definition Workflow

The following SVG illustrates how parameters flow from subsystem definitions into a unified design space, with the key validation gates that prevent infeasible or unstable variables from entering the DOE.

Practical Validation Before the Campaign

Before committing to a full DOE, run a small screening study — typically a 2-level fractional factorial with 8–16 runs. The purpose is not optimization but diagnosis. Check three things:

1. Mesh stability — does the mesh survive the full variable range? If elements invert or aspect ratios exceed 5:1, tighten bounds or switch to a more robust morphing domain.
2. Response continuity — do small variable changes produce small response changes? Discontinuities usually indicate contact switching, buckling, or solver convergence issues, not real physics.
3. Variable significance — do any variables show near-zero effect across all responses? If so, remove them. A design space with 20 variables where 8 are inert wastes 40% of the campaign budget.

Design Variable Documentation

Every campaign should produce a design variable table that travels with the model. A minimal but complete entry includes: variable name, subsystem, parameter type (gauge/shape/rate/discrete), baseline value, lower bound, upper bound, unit, CAD or morphing reference, and the primary response it is expected to influence. This table becomes the contract between the CAD team, the CAE team, and the optimization engineer. Without it, variable definitions drift between runs and results become unreproducible.

The design space is not a static artifact. As the campaign progresses and surrogate models reveal which variables matter, the space can be refined — bounds tightened, inert variables removed, new variables added where the response surface suggests unexplored potential. Treating design space definition as an iterative, validated process rather than a one-time setup is what separates a productive exploration campaign from an expensive random search.