Motor Shaft Voltage & Bearing Currents Calculator

Capacitive charging

All voltages are relative to the motor frame unless marked end-to-end. $u_{CM}=(u_a+u_b+u_c)/3$. For nonconducting oil films, charge balance gives

This is the circuit of Ahola et al. (2019), Eq. (1), attached manuscript p. 3, and Liu et al. (2022), Eqs. (2), (12). Cwf is a direct winding-to-frame path and does not enter BVR. The sensitivity curves vary one baseline capacitance group at a time.

NDE insulation replaces $C_{NDE}$ by $C_{NDE}C_{ins}/(C_{NDE}+C_{ins})$. Shaft BVR then refers to shaft-to-frame voltage. The NDE oil film sees only $C_{ins}/(C_{NDE}+C_{ins})$ of that voltage; the remainder appears across the sleeve/coating. The DE film still sees the full shaft voltage.

Brush and imposed edge

The transient is derived here from Kirchhoff's current law: $C_\Sigma\dot v+v/R_{br}=C_{wr}\dot u_{CM}$, with zero initial shaft voltage. During a linear ramp of duration $t_r$, the peak is $BVR\,\Delta U_{CM}\,F$, where $F=(\tau/t_r)(1-e^{-t_r/\tau})$ and $\tau=R_{br}C_\Sigma$. A brush then discharges the shaft exponentially; without it the ideal capacitors retain charge. Filtering scales the excursion by kv and stretches the ramp by kt. The animation is prospective: an EDM arc would collapse the calculated voltage.

DE capacitive ramp-average current is $C_{DE}v(t_r)/t_r$, not its leading-edge peak. Motor CM ramp-average current follows charge conservation: $[C_{wf}\Delta U+C_{wr}(\Delta U-v(t_r))]/t_r$.

Conditional first EDM arc

If the prospective DE voltage reaches Vbd, the first arc starts with $v=V_{bd}$ and $i_{arc}=0$ at the threshold-crossing time of the same pre-arc charging solution. The transient is derived here from
$C_\Sigma\dot v=C_{wr}\dot u_{CM}-G_{br}v-i_{arc},\qquad L_{arc}\dot i_{arc}=v-R_{arc}i_{arc}.$
The remaining linear common-mode ramp continues to inject current until its rise time ends, then $\dot u_{CM}=0$. An active brush retains $G_{br}=1/R_{br}$ throughout the arc; without a brush $G_{br}=0$.

The closed-form, piecewise-constant-forcing solution finds the first positive arc-current maximum before or after the ramp ends. It handles underdamped, critical and overdamped responses. Below the entered threshold the conditional current and energy are zero; that is not proof that a real installation cannot discharge.

The energy card is only the initial capacitive energy $C_\Sigma V_{bd}^2/2$ at firing. Continuing excitation can supply additional energy, so this value is neither total arc energy nor an upper bound on the forced peak. The separately named isolated-capacitor reference gain is used only for natural-response property checks, not for the EDM output.

Conducting circulating loop

This separate estimate assumes conducting oil films and an independent sinusoidal end-to-end shaft-voltage component. Peak current is $U_{loop}/|R_{loop}+j\omega L_{loop}|$. NDE insulation adds $-j/(\omega C_{ins})$. The brush-only comparison takes no credit for interrupting the loop. Filtering scales its source by kl, separately from kv. Inductance and insulation can resonate. Never add this result to the capacitive or EDM currents.

The defaults are illustrative circuit parameters, not a catalog motor or guaranteed mitigation performance. Use measured capacitances at relevant operating conditions or an appropriate electrostatic model. The nominal threshold of 15 V is a scenario input, not a universal safe value.

The shaft starts discharged before one isolated zero-to-excursion ramp. The motor frame is the ideal high-frequency reference, and the specified waveform is imposed at the motor terminals. The model does not compute the waveform from a DC bus or a cable model.

The brush is purely resistive during both charging and the first arc. The EDM branch is a fixed series R-L approximation, with no nonlinear arc-voltage law, brush lead inductance, simultaneous second bearing arc, or subsequent restrikes. Firing occurs at the entered threshold without overshoot; the computed peak belongs to the first positive pulse with zero initial arc current. The imposed ramp continues to completion and then holds. Initial energy at firing does not include later source energy or predict a discharge repetition rate.

The loop model describes a conducting circuit state at one frequency. It does not derive magnetic shaft voltage from the capacitive BVR. A sleeve or coating has finite high-frequency capacitance; a DC insulation-resistance rating cannot replace Cins. Both-insulated or ceramic rolling-element topologies are outside this particular comparison.

For lumped, linear capacitances and a known motor-terminal common-mode excursion while the oil films remain nonconducting. Breakdown threshold, bearing capacitance and arc impedance depend on lubrication, speed, temperature, load, pulse duration and contamination. The displayed voltage is prospective, including when it exceeds the threshold.

Cable reflections, frame-to-earth rise, distributed resonance, brush/contact inductance, coupled machinery paths and bearing-life/current-density criteria are outside this model. Zero conditional EDM current means only that this ideal event does not reach the entered threshold. Filtering performance must be measured or specified for the actual motor, cable and operating spectrum. Near loop resonance use measured frequency-dependent impedance instead of a single R-L-C fit.

Reference checks reproduce published numerical BVR results using rounded capacitances and independently integrate the physical arc/brush nodal ODEs with SciPy DOP853. Cases cover continuing excitation, an active brush, a ramp ending before the peak, and multiple damping regimes. They verify this lumped circuit implementation, not the assumed default threshold, nonlinear bearing arc physics or vendor mitigation performance.