emachines 0.3.0

Analytical electromechanical machine design library

emachines

Analytical electromechanical machine design library.

emachines is the core physics and mathematics engine behind emdesignlabs.com. It provides well-documented, tested, and citable implementations of the analytical models used in electric motor design.

Scope

• Winding analysis — winding factors (kp, kd, kw), star-of-slots phasor method, slot/pole geometry, coil matrix
• Magnetics — BH curve models (Fröhlich), iron loss (Steinmetz, Modified Steinmetz, Bertotti), electrical steel database
• Motor models — PMSM dq-frame, surface-PM analytical design

Every function documents the equation it implements and its bibliographic source.

Installation

pip install emachines

For development (editable install alongside emdesignlabs):

pip install -e path/to/emachines

Quick Start

from emachines.winding.factors import winding_factor
from emachines.winding.sos import (
    get_basic_params, build_coil_matrix, winding_factor_sos,
    check_symmetry, get_valid_coil_spans
)
from emachines.magnetics.iron_loss import bertotti, fit_loss_model
from emachines.magnetics.electrical_steel import SteelDatabase, SAMPLE_LOSS
from emachines.motors.pmsm import PMSMParams, torque

# ── Winding factors ───────────────────────────────────────────────────────────

# Integer-slot: 24s/4p, 5/6 chording (closed-form kp × kd)
kw1 = winding_factor(nu=1, Q=24, p=2, coil_span=5)
print(f"kw1 (24s/4p chorded) = {kw1:.4f}")   # → 0.9330

# FSCW: 12s/10p, tooth-coil (star-of-slots phasor, auto-dispatched)
kw1 = winding_factor(nu=1, Q=12, p=5, coil_span=1)
print(f"kw1 (12s/10p FSCW)   = {kw1:.4f}")   # → 0.9330

# FSCW: 9s/8p
kw1 = winding_factor(nu=1, Q=9, p=4, coil_span=1)
print(f"kw1 (9s/8p FSCW)     = {kw1:.4f}")   # → 0.9452

# Winding geometry: classify a slot/pole combination
params = get_basic_params(Q=12, P=10)
print(params['winding_type'])    # → 'concentrated'
print(params['q'])               # → Fraction(2, 5)
print(check_symmetry(12, 10))   # → True

# Slot-conductor occupancy matrix (2 layers, tooth-coil span)
matrix = build_coil_matrix(Q=12, P=10, m=3, layers=2, w=1)
# matrix[layer, slot] = ±phase_index (1-indexed), shape (2, 12)

# Full harmonic spectrum via phasor method
from emachines.winding.sos import winding_factor_sos
for nu in [1, 3, 5, 7]:
    kw = winding_factor_sos(nu, Q=12, P=10, layers=2, w=1)
    print(f"  kw(ν={nu}) = {kw:.4f}")

# ── Iron loss ─────────────────────────────────────────────────────────────────

# Bertotti forward model at 400 Hz, 1.5 T
loss = bertotti(f=400, B_peak=1.5, k_h=0.02, k_e=1e-4, k_a=1e-3)
print(f"Total loss = {loss['total']:.2f} W/kg")
print(f"  Hysteresis: {loss['hysteresis']:.2f}  Eddy: {loss['eddy']:.2f}  Anomalous: {loss['anomalous']:.2f}")

# Fit Bertotti coefficients from measured data
import numpy as np
f_arr    = np.array([50, 100, 200, 400])
B_arr    = np.array([1.0, 1.0, 1.0, 1.0])
loss_arr = np.array([1.2, 2.8, 6.5, 15.1])
result = fit_loss_model(f_arr, B_arr, loss_arr, model="Bertotti")
print(f"k_h={result['k_h']:.4f}, k_e={result['k_e']:.2e}, R²={result['r2']:.4f}")

# ── Electrical steel database ─────────────────────────────────────────────────

# Load from manufacturer datasheets (data_dir is your local folder)
db = SteelDatabase("path/to/datasheets")
grade = db.load("M270-50A")
print(grade.loss_at(freq=200, B=1.5))   # W/kg interpolated from datasheet

# Built-in reference data — no files required
print(SAMPLE_LOSS["M-19"])   # DataFrame: loss vs frequency and flux density

# ── PMSM motor model ──────────────────────────────────────────────────────────

motor = PMSMParams(p=3, Ld=5e-3, Lq=8e-3, psi_m=0.15, Rs=0.1)
Te = torque(motor, id=-3.0, iq=10.0)
print(f"Torque = {Te:.2f} N·m")

Modules

emachines.winding

Module	Contents
winding.factors	pitch_factor, distribution_factor, winding_factor — integer-slot (closed-form) and FSCW (auto-dispatch to sos)
winding.sos	build_star_of_slots, build_coil_matrix, assign_phases, winding_factor_sos — star-of-slots phasor method for all winding types; get_basic_params, check_symmetry, get_valid_coil_spans, is_valid_combination

Winding factor dispatch in winding_factor():

• q ≥ 1 (integer-slot) → closed-form kp × kd
• q < 1 (FSCW) → star-of-slots phasor sum, double-layer convention (matches emetor.com)

emachines.magnetics

Module	Contents
magnetics.bh_models	Fröhlich analytical BH model and curve fitting
magnetics.iron_loss	steinmetz, modified_steinmetz, bertotti forward models; fit_steinmetz, fit_modified_steinmetz, fit_bertotti, fit_loss_model dispatcher
magnetics.electrical_steel	SteelGrade dataclass, SteelDatabase (Voestalpine Excel + ThyssenKrupp/SURA pickle loaders, LRU-cached), SAMPLE_BH and SAMPLE_LOSS reference data

emachines.motors

Module	Contents
motors.pmsm	PMSMParams, back_emf, torque (excitation + reluctance), dq_currents

Design Philosophy

• Equations first — every function documents the formula it implements with LaTeX notation
• Cited — every formula traces back to a specific reference (textbook, paper, standard)
• Tested — validated against published datasets and reference tools (emetor, SWAT-EM)
• Dependency-light — only numpy, scipy, and pandas required

Test Coverage

Release	Tests	Status
0.3.0	92	✅ All passing
0.2.0	36	✅ All passing
0.1.0	18	✅ All passing

Changelog

[0.3.0] — 2026-05-09

• winding.sos: complete star-of-slots module — build_star_of_slots, build_coil_matrix, assign_phases, winding_factor_sos, get_basic_params, check_symmetry, get_valid_coil_spans, is_valid_combination
• winding.factors: winding_factor() now dispatches to star-of-slots for FSCW (q < 1)
• winding/__init__.py: all sos symbols exported at package level
• 92 passing tests, 0 xfailed — FSCW winding factors fully supported
• Validated against emetor.com: 12s/10p → 0.933, 9s/8p → 0.945, 12s/8p → 0.866

[0.2.0] — 2026-05-08

• magnetics.electrical_steel: SteelGrade, SteelDatabase, SAMPLE_BH, SAMPLE_LOSS
• magnetics.iron_loss: fit_bertotti, fit_steinmetz, fit_modified_steinmetz, fit_loss_model
• pandas>=1.5 added as runtime dependency

[0.1.0] — 2026-05-07

• winding.factors: pitch_factor, distribution_factor, winding_factor (integer-slot)
• magnetics.bh_models: Fröhlich BH model and fitting
• magnetics.iron_loss: steinmetz, modified_steinmetz, bertotti
• motors.pmsm: PMSMParams, back_emf, torque, dq_currents

Status

0.3.x — Alpha. API may change between minor versions.

License

MIT