Linear Motor Winding Pitch Selection for Back-EMF Shape

Overview of Technical Issues:

The winding structure with non-optimized pitch selection generates back-EMF with insufficient waveform quality, containing excessive harmonic distortion and non-sinusoidal characteristics, resulting in degraded control accuracy, increased torque ripple, and reduced motion smoothness; the goal is to determine the optimal winding pitch that produces ideal sinusoidal back-EMF for high-performance servo control.

Solution directions generated for this problem

Problem Direction 1 :

ImproveBack-EMF waveform quality
VS
ConstraintWinding design complexity

Inspiration 1 : Cross-domain reference

Application Principle: #1 Segmentation
Cross-domain applicability Assess applicability
System and method for bladder detection using harmonic imaging
Innovative Solution Refine solution

Multi-zone independent coil group winding for harmonic-targeted back-EMF optimization

Divide winding into independent coil zones targeting specific harmonics
How to solve :
  • Partition stator into 3 independent coil zones: Zone A (slots 1-4) with 5/6 pitch targets 5th/7th harmonics, Zone B (slots 5-8) with 4/5 pitch targets 11th/13th harmonics, Zone C (slots 9-12) standard full pitch for fundamental component
  • each zone uses simple integer pitch ratios avoiding fractional slot complexity
  • Connect zones in series with phase-shifted electrical connection (Zone A at 0°, Zone B at 15° electrical, Zone C at 30°) to achieve harmonic cancellation through vector summation rather than geometric winding complexity
  • Manufacture each zone independently using standard automated winding equipment with ±0.3mm tolerance (no precision upgrade needed), pre-wind coils on fixtures with laser-marked pitch templates, insert as modular units
Expected Effect : THD reduced to <5%, design uses 3 simple patterns vs 1 complex pattern, manufacturing tolerance unchanged
Risk Control :
  • inter-zone electrical connection resistance mismatch
  • phase shift accuracy during series connection
  • modular zone assembly alignment deviation

Problem Direction 2 :

ImproveBack-EMF waveform quality
VS
ConstraintWinding manufacturing precision

Inspiration 1 : Cross-domain reference

Application Principle: #2 Taking out
Cross-domain applicability Assess applicability
Multi-bit digital to analogue converter and a delta-sigma analogue to digital converter
Innovative Solution Refine solution

Pre-formed modular coil cassettes with locked pitch geometry for high-quality back-EMF

Separate precision winding from assembly using pre-formed coil modules
How to solve :
  • Wind coils on dedicated CNC coil-forming fixtures with ±0.05mm pitch accuracy, lock geometry with thermosetting resin impregnation at 130–150°C for 2 hours, creating rigid coil cassettes with fixed 5/6 pitch ratio before stator insertion
  • Insert pre-formed coil cassettes into stator slots using standard assembly tooling with ±0.3mm tolerance — pitch accuracy is pre-locked in cassette, eliminating dependency on insertion precision
  • Implement optical inspection of each cassette post-forming: measure coil span at 8 angular positions, accept if deviation ≤0.08mm, reject rate <2%, ensuring THD <3% without tightening assembly tolerances
Expected Effect : THD reduced to <3%, assembly tolerance relaxed to ±0.3mm, back-EMF sinusoidal distortion <5%
Risk Control :
  • resin curing uniformity affecting dimensional stability
  • cassette-to-slot fit clearance causing vibration
  • thermal expansion mismatch between cassette and stator

Problem Direction 3 :

ImproveHarmonic distortion level
VS
ConstraintWinding design complexity

Inspiration 1 : Cross-domain reference

Application Principle: #22 Blessing in disguise
Cross-domain applicability Assess applicability
Electrical system and control method
Innovative Solution Refine solution

Dual-winding harmonic self-cancellation architecture with intentional signature design

Design standard winding to generate known harmonics as control signal
How to solve :
  • Implement dual-layer winding architecture where inner layer uses standard 2/3 pitch (simple pattern) generating predictable 5th/7th harmonics, outer layer uses 5/6 pitch generating inverse-phase harmonics for mutual cancellation
  • Embed harmonic signature encoding by intentionally phase-shifting outer layer coils by 15° electrical angle, creating unique harmonic fingerprint (THD 8-12%) that servo controller uses for real-time rotor position detection and load estimation
  • Deploy adaptive harmonic compensation algorithm in controller that measures back-EMF harmonic spectrum (FFT sampling at 10kHz), extracts 5th/7th/11th components as diagnostic signals, and injects counter-torque commands to achieve effective THD <3% at torque output
Expected Effect : THD reduced to <3%, design complexity unchanged, position accuracy ±0.1° electrical
Risk Control :
  • harmonic phase-shift tolerance ±3° electrical
  • FFT computation latency >2ms
  • temperature drift altering harmonic ratios ±15%

Problem Direction 4 :

ImproveHarmonic distortion level
VS
ConstraintWinding manufacturing precision

Inspiration 1 : Cross-domain reference

Application Principle: #11 Beforehand cushioning
Cross-domain applicability Assess applicability
Microelectromechanical systems microphones, microphone units and electronic devices
Innovative Solution Refine solution

Tolerance-margin winding pitch design with built-in harmonic compensation buffer

Design winding pitch with intentional harmonic margin buffer
How to solve :
  • Implement 5/6 pitch ±2.5% tolerance band design where THD remains ≤5% even with ±0.5mm coil placement variation, eliminating need for precision manufacturing
  • Use dual-tolerance zone specification: nominal pitch 150° (5/6 of 180°) with green zone 147°–153° (standard manufacturing ±0.5mm) and yellow zone 145°–155° (acceptable degraded performance), enabling 95% yield with conventional winding equipment
  • Apply harmonic sensitivity analysis mapping during design phase to identify pitch ranges where THD gradient is minimal (≤0.3% THD change per 1° pitch deviation), selecting these low-sensitivity operating points as nominal design targets to cushion manufacturing variations
Expected Effect : THD ≤5% with ±0.5mm tolerance; manufacturing precision unchanged; 95% first-pass yield
Risk Control :
  • sensitivity mapping accuracy insufficient
  • tolerance band too wide reduces performance
  • batch consistency verification required

Problem Direction 5 :

ImproveServo control accuracy
VS
ConstraintWinding design complexity

Inspiration 1 : Cross-domain reference

Application Principle: #6 Universality
Cross-domain applicability Assess applicability
Robotic-assisted endoluminal surgical system and related methods
Innovative Solution Refine solution

Multi-function winding with integrated sensing coils for servo accuracy enhancement

Standard winding handles torque generation plus sensing
How to solve :
  • Implement standard distributed winding (simple integer slot, full pitch) for main torque generation, eliminating complex fractional slot optimization
  • Install auxiliary sensing coils in 3–6 unused or partially-filled slots, wound with 50–100 turns of 0.2mm wire, dedicated to high-resolution position feedback via back-EMF harmonic analysis
  • Integrate dual-channel signal processing: main winding feeds torque control (tolerance ±0.5mm), sensing coils feed position estimation through FFT-based harmonic extraction (5th, 7th, 11th orders) achieving ±0.1° accuracy
Expected Effect : Control accuracy +40%, design complexity unchanged, THD <8%
Risk Control :
  • sensing coil placement interference
  • signal crosstalk between channels
  • temperature drift in auxiliary coils

Problem Direction 6 :

ImproveServo control accuracy
VS
ConstraintWinding manufacturing precision

Inspiration 1 : Cross-domain reference

Application Principle: #28 Mechanics substitution
Cross-domain applicability Assess applicability
Temperature control circuit, oscillation control circuit, and temperature control method
Innovative Solution Refine solution

Electronic self-calibration servo control with manufacturing tolerance compensation

Replace mechanical precision with electronic compensation
How to solve :
  • Manufacture windings with standard tolerances (±0.5mm coil placement), then implement automated post-manufacturing characterization where each motor undergoes speed sweep testing (100-3000 RPM) to map actual back-EMF harmonic signature across all phases
  • Store unique motor-specific compensation tables in servo controller EEPROM (512-byte lookup table containing THD profile, phase imbalance coefficients, and harmonic amplitude ratios at 20 speed points) for real-time feedforward correction
  • Deploy adaptive control algorithm that applies custom gain scheduling (Kp adjustment range 0.8-1.2×nominal, Ki 0.6-1.4×nominal) based on stored signature, electronically nullifying manufacturing variations to achieve target control accuracy without tightening winding tolerances
Expected Effect : Servo accuracy ±0.02° maintained with ±0.5mm winding tolerance; manufacturing cost -30%; characterization time 45s per motor
Risk Control :
  • characterization equipment calibration drift
  • EEPROM data corruption risk
  • algorithm convergence under high dynamic load
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