Wave-Insight is a simulation platform designed for Linear Resonant Actuators (LRA). It integrates transient time-domain differential equations and steady-state complex frequency response sweeps to evaluate actuator performance under both natural resonance and arbitrary off-resonance (non-inherent frequency / wideband haptic) AC drive, reversed-phase braking, and ring-down phases.
Solved Challenges
- Validate Off-Resonance Drive & Non-Resonant Vibration: Enter any carrier frequency $f$ (whether matching $f_0$ or at discrete off-resonance frequencies) to evaluate force transmission, displacement decay, and phase dynamics for wideband haptic cues;
- Simulate Time-Domain Startup & Braking: Simulates dynamic displacement, line current, and acceleration profiles under sinusoidal feedforward, active braking, and free ring-down decay;
- Evaluate Steady-State Energy Distribution: Computes analytical 50Hz - 300Hz sweeps to map resonant peaks, half-power bandwidth, and system damping;
- Fixture Mass Tuning: Unlocks and adjusts the test fixture mass $M$ to convert mover acceleration to the actual G-forces measured on test jigs;
- Avoid Safety Boundary Overrun: Evaluates whether peak stroke $xmax$ exceeds safety limits to prevent internal mechanical collisions.
Mathematical Modeling & Equations
The electromechanical coupling is modeled as a 3rd-order state-space system of ordinary differential equations (ODEs):
$$\frac{dx}{dt} = v$$$$\frac{dv}{dt} = \frac{BL \cdot i - c \cdot v - k \cdot x}{m}$$$$\frac{di}{dt} = \frac{u(t) - R \cdot i - BL \cdot v}{L}$$Where:
- $x$, $v$, $i$ represent mover displacement, velocity, and coil current;
- $m$ is the mover equivalent mass, and $k = m(2\pi f_0)^2$ is the equivalent spring stiffness;
- $c = (2\pi \cdot m \cdot D) / 27.3$ is the damping coefficient derived from the mechanical decay rate $D$;
- $BL$ is the electromagnetic force constant, $R$ is the DC resistance, and $L$ is the coil inductance;
- $u(t)$ is the time-varying drive voltage (sinusoidal carrier during drive at target frequency, followed by reversed square wave during active braking).
The numerical engine performs high-precision adaptive transient time-stepping, with anti-aliasing envelope fidelity rendering on the frontend to eliminate waveform distortion and beat pattern artifacts.
Boundary Conditions
This open-access tool uses a linear, lumped-parameter model for trend assessment. It does not account for large-stroke electromagnetic non-linearities like $BL(x)$ or $k(x)$, eddy currents, temperature-dependent coil resistance drift, or closed-loop driver chip controllers. Commercial projects should calibrate these results against physical test datasets.
Operating Manual
1. Input Parameters
| Parameter Group | Adjustable Parameter | Unit | Description |
|---|---|---|---|
| Actuator Model | Moving Mass $m$ | g | Mover equivalent vibration mass. Works with resonant frequency to determine spring stiffness. |
| Target Frequency $f_0$ | Hz | Resonant frequency, used to calculate equivalent stiffness. | |
| Force Factor $BL$ | N/A | Electromechanical coupling constant (出力系数 and back-EMF coefficient). | |
| Mechanical Damping $D$ | dB/s | Damping loss factor; governs exponential decay and settling time (BT). | |
| Coil Inductance $L$ | mH | Coil self-inductance; slows rate of current rise. | |
| Coil Resistance $R$ | Ω | Coil DC resistance. | |
| Fixture Mass $M$ | g | Test jig baseline mass; used to translate acceleration to G-forces. | |
| Safety Boundary $xlim$ | mm | Maximum allowable single-sided stroke. Exceeding this triggers a warning. | |
| Drive Parameters | Drive Voltage $Vop$ | V | Peak voltage of the sinusoidal AC source. |
| Drive Frequency $f$ | Hz | Carrier frequency of the sinusoidal source. Can be set to natural resonance $f_0$ or any arbitrary off-resonance frequency to assess non-resonant vibration behavior. | |
| Drive duration $On$ | ms | Duration of the sinusoidal drive stage. | |
| Brake duration $Brake$ | ms | Duration of the reversed hard square-wave braking stage. | |
| Thresholds | RT Rise Time Target | % | Percentage of steady amplitude used to calculate rise time (default 90%). |
| BT Settlement Band | % | Percentage of steady amplitude used to determine settling/brake time (default 10%). |
2. Metrics & Outputs
The solver outputs 5 core metrics on the dashboard:
| Metric | Unit | Physical Meaning & Interpretation |
|---|---|---|
| Resonant Frequency f₀ | Hz | Measured mechanical natural frequency. |
| Steady Acceleration Gpeak | G | Steady-state acceleration envelope magnitude at the configured drive frequency (resonant or off-resonant). |
| Peak Displacement xmax | mm | Peak single-sided stroke calculated across the 2.0s solver window. |
| Rise Time RT | ms | Time elapsed for the acceleration envelope to first reach the target percentage (e.g. 90%) of steady amplitude. |
| Brake Time BT | ms | Time elapsed for the acceleration envelope to settle and remain within the target band (e.g. 10%) after drive ends. |
3. Data & Engineering Discussion
This open-access engine provides discrete numerical integration of standard physical differential equations for understanding actuator wave response, rise-time acceleration, and active damping.
For discussions on parameter identification, nonlinear time-domain models, or haptic driver strategies, feel free to join discussions in the comments or contact Tony Chen ([email protected] ).
📌 Recommended Articles & Engineering Handbooks:
- 🧭 R&D Methodology: 👉 From Point, Line, to Plane: Precision Engineering R&D Methodology
- 📖 Formula Reference: 👉 Linear Resonant Actuator (LRA) Engineering Formula Handbook
- 🧲 System Co-Design: 👉 What Determines Smartphone Haptic Feedback? Motor, Structure, and System Co-design
- ⚡ Transient Dynamics: 👉 Transient-Insight Dynamics & Active Reverse-Braking Simulator
- 📊 Impedance FRA: 👉 Motor-Insight Actuator Impedance & Frequency Response Workbench