383 directly relatable to classic parameters of imbalance coupled with bearing “goodness” (similar to longstanding static/dynamic rotating assembly methods), and since larger unbalance (very generally) causes a  2nd-order growth of all noise components as rotation rate builds, an alternate means of absolute/relative  “geometric” error was sought. Setting aside design- specific harmonic ratios, an equation form is desired  that can be reverted to classic unbalance- runout types of values/assessments. Also, unlike primary  unbalance, its value is to enable directly relating bearings independent of rotor mass. A summary treatise,  reference perspective, derived relationship, and example values for this methodology/criteria follows below.  

Table 10.  101-Type Bearing Set Basic IV Tested/Tracked/Reported Harmonic Ratios   Theory -  Based  Ratio    Empirically -  Established  Ratio  Description of Root Source/Cause Sig.  Figures  Known   0.3862 0.385 RATIO OF BEARING CAGE/RETAINER SPEED TO ROTOR SPEED  2  0.6138 Detection   RATIO OF BEARING CAGE/RETAINER SPEED TO OUTER RING PASSAGE  2  1.0000  1.00 MISALIGNMENT OF ROTOR CENTER -OF-MASS & SHAFT ROTATION POINT AS PRECISE  AS RWA    2.0000  2.00 SECOND HARMONIC OF 1.0 (RACE-TO-RACE MISALIGNMENT /WHIRL) AS PRECISE  AS RWA    3.8623  3.88 10 (# OF BALLS ) TIMES 0.39  (BALL PASSAGE ON OUTER RACE) 3  4.0000  4.00 THIRD HARMONIC OF 1.0 (RACE MISALIGNMENTS /COMPOUND  WHIRL) AS PRECISE  AS RWA    6.1376 6.14 10 (# OF BALLS ) TIMES 0.61 (BALL PASSAGE ON INNER RACE) 3  -- 7.17 CAUSE NOT KNOWN WITH CERTAINTY ; ONLY EMPIRICALLY DERIVED  ~2  7.7246  7.72 SECOND HARMONIC OF 3.85  (BALL PASSAGE ON OUTER RACE) 3  8.0000  8.00 FOURTH HARMONIC OF 1.0 (RACE MISALIGNMENTS /COMPOUND WHIRL) AS PRECISE  AS RWA      Geometric- Based -Error Method Allow ing Direct Comparison o f Harmonic Disturbance Magnitudes  

Based on empirical  HST RWA  IV dataset s plus a quest for comparing similar configuration bearings with  other sizes  (i.e., varied  harmonic ratios ) and local directions , a quantity termed “Equivalent Geometry Error”  (EGE) was established as a straight forward approach for analytical evaluation based on a least -squares  best-fit-curve methodology imposed on IV second- order equations,  facilitating  direct comparisons related  to amplitudes present in compound harmonic IV signal s’ data . It was  intended to apply to any RWA dat a  acquired by  similar test  criteria and number of data points ( i.e., via computing curve -fit second- order  coefficients ). Fundamental EGE is computed for a chosen harmonic  ratio via the following formula:   𝐸𝐸𝐺𝐺𝐺𝐺 𝑛𝑛= 𝐶𝐶𝑛𝑛 𝛴𝛴 (𝐹𝐹𝑛𝑛𝑛𝑛∗𝜔𝜔𝑛𝑛𝑛𝑛^2) 𝛴𝛴 (𝜔𝜔𝑛𝑛𝑛𝑛^4)  Where 𝐶𝐶𝑛𝑛 is a varying constant for a  particular harmonic ( 𝑛𝑛) and, for HST RWAs,  is equal to the following  4 key values when wheel speed ( 𝜔𝜔𝑛𝑛𝑛𝑛) is expressed in revolutions -per-minute (RPM), output sinusoidal force  peak amplitude ( 𝐹𝐹𝑛𝑛𝑛𝑛) is expressed i n pounds (lb), and E GE (𝐸𝐸𝐺𝐺𝐺𝐺 𝑛𝑛) is expressed in inches (in).   C1.0 = 821.5 ; C2.0 = 205.3 ; C2.8 = 103.3 ; and C5.2 = 30.6  When derived in stated parameter units, resulting units are in/lb-min2. Note these are also relatable  independent  of DOF . As derived from IV datasets, the number of points used needs  to be enough for   reasonably consistent computation stability  (varies  by frequ ency  range), yet not so many  to interpose   distorting  effects of RWA/ fixture resonances ; points typically range 4-20. T his may require insightful  judgment/iterations for the optimum  number of points for calculations while rejecting data outliers.   

Induced Vibration  Harmonic Ratios  Basis in RWA Spin -Axis Torque /Moment Primary Direction    Spin-axis harmonic ratios  are governed by an entirely separate set of physical effects compared to other  IV DOFs . Design -specific drive motor physics/construction  creates minute fluctuations (termed torque