Two of the most common engineering failures in legacy balancing software are conflating rotation direction (CW/CCW) with mass polarity (ADD/REMOVE), and blindly inverting ill-conditioned 2×2 influence matrices. Developed under clean-room software engineering rules by the Rootcastle R&D team, the REI DSP Kernel enforces formal mathematical contracts at every stage.
Our solver performs Hermitian eigendecomposition to compute the Complex SVD (σ_max, σ_min) of the 2×2 influence matrix H, gating on the condition number (κ(H) = σ_max / σ_min) and numerical rank (rank=2). Furthermore, it propagates a 10-component uncertainty budget — from sensor calibration (UNC-001) and tachometer jitter (UNC-002) to trial mass/angle tolerances (UNC-005..006) and matrix inversion amplification (UNC-007) — to certify ISO 21940-11 compliance with expanded uncertainty (U_exp, k=2).
Benefits
Explicit phase & polarity contracts
CCW angle mirroring (θ → −θ) and REMOVE polarity inversion (θ → θ + 180°) are strictly separated, eliminating sign errors in the field and on the test bed.
Complex SVD & rank-2 gating
High cross-plane coupling or weak trial runs are caught via κ(H) thresholds before erratic correction masses can be applied.
10-component GUM / ISO 21940-14 uncertainty budget
Residual unbalance is reported with a ±U(k=2) confidence interval and guard-banded acceptance decision.
Fail-Closed CMP-Safety state machine
Over-vibration, tach loss, ADC saturation or mechanical impact immediately transitions the system to SAFE_STOP.
Process
Phase-locked DFT / IQ demodulation
Instantaneous angular velocity ω(t) and phase φ_ref(t) are tracked from the tacho pulse train to extract the synchronous 1X phasor V_1X over integer revolutions.
Complex SVD & conditioning analysis
Singular values σ_max, σ_min and κ(H) are computed via H^H·H; warning (κ > 15) and block (κ > 50) gates protect the solve.
Discrete blade sine-law projection
Free correction vectors W_c are decomposed onto discrete blade angles with det(A) = R·sin(θ_2 − θ_1) verification.
Analytical & Monte Carlo uncertainty propagation
UNC-001..010 input distributions propagate through the solver to yield standard uncertainties (u_m, u_θ) on the correction vector.
Deliverables
- REI Studio Desktop & Embedded DSP Solver Kernel
- Complex SVD (σ_max, σ_min, κ(H)) & Influence Matrix Report
- ISO 21940-14 & GUM Measurement Uncertainty Budget (UNC-001..010)
- Flexible Rotor (ISO 21940-12) & Multi-Plane Least-Squares R&D Consulting
- Custom Test Rigs & Joint Industrial/Academic R&D Projects
Applications
- High-precision (G0.4 / G1.0) defense, aerospace and machine-tool spindles
- Supercritical / flexible-rotor turbine and compressor test stands
- Embedded DSP algorithm licensing for series balancing machines
- Academic rotor dynamics laboratories and metrology institutes
Frequently asked questions
Why must CW/CCW rotation and ADD/REMOVE polarity never be combined into one toggle?
Reversing rotation mirrors the angle across the reference axis: θ_CCW = (360° − θ_CW) mod 360°. Switching from adding mass to removing mass (drilling/grinding) negates the vector: θ_REMOVE = (θ_ADD + 180°) mod 360°. At 30°, CCW gives 330° whereas REMOVE gives 210° — conflating them introduces a 120° phase error.
At what condition number κ(H) does a two-plane solve become unsafe?
κ(H) = 1 represents perfectly orthogonal planes. κ(H) ≤ 5 is excellent, and 5 < κ(H) ≤ 15 is acceptable in field conditions. Above κ(H) = 15, a 1% phase/amplitude measurement noise amplifies into a 15%+ correction error; above κ(H) = 50 the matrix is numerically singular and trial planes/masses must be reconfigured.