Force Interaction
Mechanical architectures frequently exhibit unintended displacement in secondary axes when a primary load is applied due to geometric or material asymmetries. Within micromachined gyroscopes or accelerometers, cross-axis stiffness coupling causes a response on the quadrature or signal channel that mimics a physical input. The condition persists as long as the structural beams remain non-orthogonal or exhibit stress gradients from the manufacturing phase.
Geometric Error
Deviations from perfect rectangular cross-sections in support beams typically initiate the energy transfer between modes. While the design target assumes zero interaction, actual etching profiles create trapezoidal footprints that foster cross-axis stiffness coupling throughout the sensor cycle. Side-wall angles from deep reactive ion etching vary by several fractions of a degree across a single wafer.
These variations change the orientation of the principal stiffness axes relative to the sense combs.
Calibration Boundary
Correction algorithms subtract the predictable component of the interaction during factory final testing. Measurements taken at multiple tilt angles determine the magnitude of the cross-axis stiffness coupling for each individual unit. Once mapped, the error is treated as a deterministic bias.
Sudden physical shocks can alter the internal mounting strain and shift the coupling coefficients beyond their original storage table values. Accuracy relies on the rigidity of the package remaining within tight tolerances over time.
Dynamic Consequence
Instability in the sensor feedback loop follows if the off-diagonal terms of the stiffness matrix grow too large. Resonators may lock onto the wrong vibration mode if the cross-axis stiffness coupling provides enough gain to bridge the frequency gap between specific modes. Filtering cannot always distinguish these mechanical ghosts from genuine signals.
High-bandwidth applications require the highest possible modal separation to mitigate the risk.
