BLDC Motor Design Calculator: Winding, Kv, Kt and Losses

The model uses an ideal three-phase star-connected radial-flux motor with trapezoidal back EMF and six-step block commutation. Two phases conduct at any instant. All coil turns within each phase are in series; parallel in-hand strands share current within a turn.

Active-conductor estimate. A phase has $N_{ph}=QN_c/3$ series turns. An active side moving through a radial field has $e=BLr\omega$. With two active sides per turn and $D=2r$, the ideal phase flat top is $e_{ph}=k_{flat}N_{ph}BDL\omega$. Therefore the conducting phase pair gives $E_{LL}=2k_{flat}N_{ph}BDL\omega=K_e\omega$. This is a Lorentz/Faraday derivation for an effective field and flat-top factor, consistent with the active-conductor expression in TI SPRABQ7A, p.4. The factor includes pitch, distribution and waveform effects; it is not automatically a fundamental winding factor. Diameter and stack length describe active dimensions, not the motor envelope.

Constants and current. In measured mode, mechanical rpm/V is converted to $K_e$ using one radian per second as an explicit reference. $E_{LL}I=T_{em}\omega$ gives numerically $K_t=K_e$ in SI, per plateau phase ampere. $K_v=60/(2\pi K_e)$ in rpm/V. Required shaft torque is $P_{shaft}/\omega$; rotational loss adds $P_{rot}/\omega$. Each phase carries current for two thirds of a cycle, so $I_{rms}=\sqrt{2/3}I$.

Resistance and losses. Bare copper area per turn is $A_{Cu}=s\pi d^2/4$. NBS Handbook 100 gives annealed-copper resistivity $1/58$ ohm mm²/m at 20 °C and resistance coefficient 0.00393/K. The cold line resistance is $2\rho N_{ph}l_{turn}/A_{Cu}$, multiplied by $1+\alpha\Delta T$ at the assumed copper temperature. In measured mode, keep the measured baseline turns $N_b$, baseline Kv and baseline resistance fixed. For proposed turns $N$, use $K_e(N)=K_{e,b}N/N_b$ and $R_{20}(N)=R_{20,b}N/N_b$, then apply the same copper-temperature correction. This models a rewind with unchanged wire bundle, mean turn length, coil assignment and magnetic geometry. $P_{Cu}=I^2R_{LL}=3I_{rms}^2R_{ph}$. Bus power includes shaft output, supplied rotational/core loss, copper loss, effective inverter $I^2R$ loss and supplied other inverter loss. Average battery current is bus power divided by bus voltage.

Voltage and winding guidance. Required average line voltage is $K_e\omega+I(R_{LL}+R_{drive})$, compared with the chosen usable bus fraction. Slot bare-copper fill is $2N_cA_{Cu}/A_{slot}$. For a fixed-wire rewind, let $a=K_e\omega/N_c$, $b=V_{available}-(IN_c)(R_{LL}/N_c)$ and $c=(IN_c)R_{drive}$. The voltage condition is $aN^2-bN+c\le0$. Its roots, drive-current limit, RMS-density target and slot-fill limit give an integer turn interval. Empty intervals are reported. The speed envelope uses the same line equation with clipped positive motoring current and constant equivalent drag torque. Its shared speed axis includes both current-limit knees, the exact zero-shaft-torque cutoff, the ideal voltage speed and a point beyond it. These are the boundaries of its linear segments, so chart interpolation cannot extend a segment past the calculated cutoff. The animation illustrates ideal commutation with zero inductive overlap; it is independent of sizing.

• Three phases, star connection, symmetric double-layer tooth coils, one coil per slot, all coils in each phase in series. No parallel phase circuits, delta winding or unequal strands.
• Aligned 120° flat-top phase back EMFs and ideal rectangular currents. Instantaneous commutation, no reluctance torque, inductive voltage drop, PWM ripple or field weakening.
• Uniform effective radial field and an explicitly supplied flat-top factor. Geometry-mode constants are preliminary estimates; they do not predict the waveform or establish a manufacturable winding assignment.
• Copper temperature, cooling-related RMS density target, available slot area, fill limit and losses are user assumptions. Defaults are an illustrative 48 V, 500 W trial, not data for a commercial motor.
• Fixed wire size, strand count, mean turn length, coil placement and magnetic geometry during measured-mode rewind evaluation and turn-count guidance. Keep measured baseline turns, Kv and copper resistance fixed while changing proposed turns. A different wire bundle requires a matching baseline resistance; resistance is not automatically corrected for wire changes in measured mode.
• Rotational/core loss is specified at the requested speed. Only its equivalent drag torque is kept constant across the speed envelope. Other inverter loss is fixed at the operating point.
• Radians are dimensionless in SI energy equations. A named one-radian normalization keeps the unit checker consistent without hidden speed-conversion factors.

Use this tool for positive-speed steady motoring and preliminary winding comparisons. A negative voltage headroom or a current-limit warning means the requested point is unreachable under the entered assumptions: displayed loss and efficiency values then describe the demand, not achieved performance. The plotted envelope excludes startup, regenerative operation, field weakening and a thermal duty model. Zero-load efficiency is displayed as zero when no motor input is required.

The slot/pole balance condition is necessary, not sufficient for an acceptable coil layout. Verify phase balance, connections, harmonic content, effective flat-top factor, saturation, demagnetization, cogging, inductance and commutation overlap using a winding model, electromagnetic analysis and tests. Bare-copper fill does not prove physical wire packing. RMS current density does not establish an operating temperature or continuous rating. Copper resistance correction is a simple linear model around 20 °C, used here over a user-entered −60…180 K rise.

Published-source discrepancies. Çetinceviz (2025), p.8, Equations (18)–(19), use a fundamental/RMS style EMF expression alongside the flat-top line equation; these coefficients are not interchanged here. Table 4, p.19, lists experimental 96 V and 30.05 A, whose product is 2884.8 W, while its input-power entry is 2737.372 W. Its current/power convention is therefore insufficiently specified for validating bus current or total efficiency. The paper reference case checks only independently tabulated shaft torque against power and speed. ThinGap TG2340, p.2, lists approximate Kv, Ke and Kt values that differ under exact SI reciprocity; its check states the resulting tolerance explicitly. These differences are documented instead of fitted away.

Measured rewind scope. The separate measured baseline turn count anchors Kv and cold copper resistance. Proposed turns change the evaluated winding and its performance without redefining that baseline. This scaling assumes unchanged wire bundle and mean turn length; changing either requires new or independently adjusted baseline resistance data.