Motor-Insight is a steady-state frequency-domain workbench for linear resonant actuators (LRAs). It combines the moving mass, suspension, coil, magnetic circuit, and drive circuit into a linear electromechanical model and calculates displacement and fixture-acceleration responses across a selected frequency range.
What it is for
- Estimate resonance frequency, quality factor Q, and peak displacement;
- Compare the frequency-response effect of mass, stiffness, damping, BL factor, coil resistance, and inductance;
- Identify frequency shift, insufficient drive voltage, or excessive-stroke risk early in design;
- Provide a first-order baseline for prototype testing, parameter calibration, and higher-fidelity digital-twin work.
Solver model
The mechanical side uses a mass-spring-damper model:
$$m\ddot{x}+r\dot{x}+Kx=F_{em}$$The electrical side includes coil resistance, inductance, and back-EMF:
$$u=Ri+L\frac{di}{dt}+BL\dot{x}$$With $F_{em}=BL\cdot i$, the solver converts the equations to a coupled complex-impedance matrix at each sinusoidal sweep point, then calculates current, displacement response, and acceleration Grms.
Model boundary
This tool is intended for linear, small-signal, steady-state frequency-domain trend analysis. It is not a complete FEA model or a nonlinear transient digital twin. Large-stroke $BL(x)$ variation, impacts, nonlinear suspension behavior, saturation, heating, rise time, and active-braking time should be validated with measured data and higher-order time-domain models.
User Guide
1. Intended use
The workbench supports LRA concept studies, prototype comparison, design reviews, and first-pass interpretation of test data. Its purpose is to show how parameter changes influence resonance, displacement, and fixture vibration trends; it does not replace structural or electromagnetic FEA, nor production release testing.
2. Open Parameter Ranges & Production DFM Safety Guardrails
All 11 physical and sweep excitation parameters are fully unlocked for evaluation, backed by automated production DFM safety guardrails. When any parameter exceeds the safe physical envelope, the solver halts calculation and displays an engineering alert:
| Parameter | Allowed Range (Default Baseline) | Engineering Meaning & DFM Guardrail Notes |
|---|---|---|
| Force Factor BL | 0.02 ~ 0.40 N/A (default 0.21) | Electromagnetic conversion factor bounded by gap flux density and active conductor length. |
| Spring Stiffness K | 100 ~ 2000 N/m (default 1510) | Suspension stiffness (too soft causes static droop, too stiff causes fatigue fracture). |
| Moving Mass m | 0.1 ~ 1.2 g (default 0.95) | Equivalent mover mass (<0.1g cannot sustain inertia, >1.2g exceeds micro linear motor scale). |
| Coil DCR R | 0.5 ~ 12.0 Ω (default 9.0) | DC resistance (<0.5Ω risks thermal blowout, >12Ω causes driver voltage saturation). |
| Damping Coeff r | 0.005 ~ 0.060 N·s/m (default 0.045) | Mechanical dissipation constant; $Q > 25$ triggers high-ringing warnings. |
| Coil Inductance L | 0.00 ~ 0.20 mH (default 0.15) | High-frequency reactive component governing high-band roll-off. |
| Fixture Mass M | 80.0 ~ 100.0 g (default 100.0) | Fixture test acceleration reference (standard evaluation jigs typically 80g~100g). |
| Start / End Freq | 1 ~ 100 Hz / 1 ~ 300 Hz (default 50 / 250) | Sweep interval (Start Freq must be strictly less than End Freq). |
| Drive Voltage Vrms | 0.1 ~ 2.0 V (default 1.8) | Sinusoidal RMS voltage; excessive voltage triggers driver overload alarms. |
| Resolution steps | 50 ~ 500 pts (default 250) | Discrete solver evaluation points balancing precision and rendering response. |
💡 Engineering Note: This parameter space precisely matches mass-production micro linear resonant actuators (LRA) across smartphones, gaming controllers, and wearables. For extreme long-stroke modeling and measured data fitting, feel free to join discussions via email.
3. Workflow
- Enter or confirm Moving Mass m, Spring Stiffness K, Force Factor BL, and Coil DCR R.
- Set Start Freq, End Freq, and Drive Voltage Vrms for the intended application.
- Review Resonance Freq f₀, Quality Factor Q, Peak Stroke Xpeak, and Peak Output Grms.
- Check whether displacement and acceleration peaks fall in the target band.
- Change one parameter at a time and validate the trend using measured FRA or acceleration data.
4. Interface outputs and curves
| On-screen output | Unit | How to read it |
|---|---|---|
| Resonance Freq f₀ | Hz | Center resonance position of the frequency response. |
| Quality Factor Q | — | Indicates resonance sharpness and energy dissipation characteristics. |
| Peak Stroke Xpeak | μm | Maximum displacement amplitude within the sweep range. |
| Peak Output Grms | Grms | Maximum effective fixture-test acceleration within the sweep range. |
The page provides the Oscillator Stroke Displacement Response Curve and Fixture Test Acceleration Grms Curve to show the trends behind these indicators.
5. Frequently Asked Questions (FAQ)
Q1: How do I calculate motor resonance frequency f0 and quality factor Q with this tool?
Enter moving mass $m$ (g) and spring stiffness $K$ (N/m). The tool uses the electromechanically coupled natural equation $f_0 \approx \frac{1}{2\pi}\sqrt{\frac{K}{m}}$ combined with electromagnetic force factor $BL$, damping $r$, and coil impedance $Z(j\omega)$ to extract the true loaded peak resonance frequency and quality factor $Q$.
Q2: Why is coupled complex impedance essential for precision linear motor simulation?
When a resonant motor vibrates near resonance, the moving coil cuts magnetic flux and produces Back-EMF ($e = BL \cdot \dot{x}$). Back-EMF feeds directly back into the electrical loop, inducing a substantial impedance spike at resonance. Ignoring this coupling leads to over 40% error in predicted current and Lorentz force.
Q3: How do force factor BL and coil resistance R influence vibration output Grms?
Electromagnetic force is $F_{em} = BL \cdot I$. Under constant drive voltage $V_{rms}$, lower coil resistance $R$ allows higher current, while higher $BL$ converts electrical energy into mechanical thrust more effectively, significantly boosting the fixture acceleration $G_{rms}$.
6. Result interpretation
- $f_0$ too low or high: check moving mass and equivalent stiffness first, then preload and suspension condition.
- Excessively high Q: may increase peak output but also ringing and lot sensitivity.
- Excessive displacement: assess air gap, mechanical stops, and reliability risk.
- Low Grms: do not only increase voltage; check BL, frequency match, damping, and device coupling.
- Non-coincident curve peaks: can be normal because inertia and the measurement reference both affect the response.
7. Engineering Discussion
The public page exposes model inputs, result metrics, and overview-level dynamics. Detailed complex-impedance modeling and numerical methods are elaborated in our technical articles.
For in-depth discussions on coupled complex-impedance formulation, nonlinear $BL(x)$, thermal drift, or measured-data calibration, feel free to contact Tony Chen for engineering exchange.