Rolling-Bearing Kinematics and Waviness Screening Calculator

Inputs

Results update automatically as values change. Speeds are signed in one reference frame.

Inner-ring speed n_irpm Outer-ring speed n_orpm Element diameter D_bmm Pitch diameter D_pmm Contact angle αdeg Element count Zelements Harmonic count h_maxorders

Screening result

Use calculated lines as engineering guides, not standalone diagnostic proof.

Result—

Harmonic screening lines

Order	BPFO	BPFI	BSF

Equations used

Ring frequencies f_i=n_i/60 and f_o=n_o/60 are in hertz; signed speeds use one fixed reference direction. Define the projected diameter ratio x=(D_b/D_p)cos α, where D_b is rolling-element diameter, D_p is pitch diameter, and α is operating contact angle.

f_c = ½[(1 − x)f_i + (1 + x)f_o]

BSF = |f_i − f_o| D_p(1 − x²)/(2D_b)

BPFO = Z|f_c − f_o|; BPFI = Z|f_i − f_c|

f_c is cage frequency, BSF is element spin frequency, BPFO/BPFI are outer/inner rolling-element pass frequencies, and Z is element count. Harmonic h is h times each fundamental.

f_p = N_wf_r; λ = 2πr/N_w

A_pk,lim = (W/m)/(2πf_p)²

N_w is waves per revolution, f_r rotation frequency, r track radius, W normal load, and m effective supported mass. The unloading displacement is peak amplitude; output is converted from metres to micrometres.

V = V_ref10^L_V/20; v_rms = V/S_v

A_pk = √2 v_rms/(2πf_p); N_w = f_p/f_r

L_V is voltage level in dB, V_ref reference voltage, and S_v calibrated velocity sensitivity. RMS velocity is converted to peak displacement for one sinusoidal component.

Assumptions and limits

Rigid, no-slip rolling geometry and steady operating values are assumed.
Slip, skidding, deformation, load-zone modulation, speed variation and resonance can shift measured peaks.
The inertial threshold is a screening boundary, not a fatigue-life or contact-stress rating.
Frequency coincidence alone must not be used to diagnose a fault.

How to use

Select Bearing kinematics, Waviness screening, or Sensor conversion.
For kinematics, enter signed ring speeds in rpm, internal element and pitch diameters in mm, operating contact angle, element count and harmonic count.
For waviness, enter waves per revolution, surface rotation in Hz, track radius in mm, effective mass in kg and compressive normal load in N.
For sensor conversion, enter dB voltage level, its reference voltage, calibrated sensitivity, passage frequency and surface rotation frequency.
Results calculate automatically after every valid edit; there is no separate Calculate button.
Use Reset example to restore the published example for the active mode.
Interpret pass frequencies and harmonics as geometric screening lines; compare them with speed uncertainty, slip, modulation and structural response.
Correct any red validation message before using outputs. All dimensions, units and RMS/peak conventions must match the labels.
Do not use this model for automatic fault diagnosis, bearing life/rating, transient impact response, nonlinear contact loss, or measurements outside sensor calibration bandwidth.

Reference

Harris, T. A. and Kotzalas, M. N. (2006), Rolling Bearing Analysis, Fifth Edition, Two-Volume Set, CRC Press, Volume I, Examples 10.1, 14.6, 14.7 and 14.9. doi:10.1201/9781482275148. Published example values are rounded; calculations here retain the entered geometry and full floating-point precision.