Vibration isolation theory

Summary¶

Motor vibration propagates through a rigid frame into the IMU where it appears as noise indistinguishable from genuine aircraft motion. The flight controller cannot separate the two and attempts to correct for both — degrading control quality and demanding aggressive software filtering that adds control loop latency. A mechanical isolator inserted between the motor and the frame creates a low-pass filter in the structural path: vibration above the isolator's resonance frequency is attenuated before reaching the IMU. This article explains the physics of structural vibration propagation and mechanical isolation. For the libdrone implementation see floating-motor-mounts.

Concept¶

Vibration sources in a multirotor¶

A brushless motor produces vibration at several frequencies simultaneously:

Motor fundamental frequency: one vibration cycle per revolution. At 20,000 RPM = 333 Hz. At 40,000 RPM = 667 Hz.
Blade passage frequency: for a 3-blade prop, three pulses per revolution. At 20,000 RPM = 1000 Hz.
Harmonics: integer multiples of the above, extending to several kHz.
Bearing noise: broadband, centred around bearing resonance (typically 1–5 kHz for small brushless motors).

On a rigid connection between motor and frame, all of these propagate with minimal attenuation. The IMU's gyroscope samples angular velocity typically at 8 kHz or higher — it captures the full spectrum.

How vibration degrades flight control¶

The gyroscope samples the sum of genuine aircraft motion and structural vibration. At 1000 Hz blade passage the gyroscope sees a 1000 Hz signal component that looks identical to very rapid angular oscillation. The flight controller's PID loop treats it as real and generates a corrective motor command — which itself creates additional vibration. The system enters a self-exciting oscillation loop.

Software filters (dynamic notch filter, RPM filter, low-pass filters on gyroscope output) are designed to remove these frequency components. However, every filter introduces phase lag — a delay between when the real motion occurs and when the flight controller sees it. High phase lag means slow loop response: the drone reacts sluggishly to disturbances and pilot inputs.

The fundamental trade-off: more aggressive filtering → less vibration noise → more phase lag → slower loop response. Mechanical isolation before the signal reaches the gyroscope reduces the noise floor, allowing less aggressive filtering and lower phase lag for equivalent noise rejection.

Mechanical low-pass filter model¶

A spring-mass-damper system has a characteristic resonance frequency:

f₀ = (1 / 2π) × √(k / m)

Where: - k = spring stiffness (N/m) — set by isolator Shore hardness and geometry - m = mounted mass (kg) — the motor mass - f₀ = resonance frequency (Hz)

Below f₀: vibration passes through with amplitude gain (near resonance) or unity gain (well below resonance).

Above f₀: vibration is attenuated. A simple spring-mass system attenuates at 40 dB/decade (−40 dB per 10× frequency increase). With damping added (viscoelastic material), resonance amplitude is suppressed and attenuation above resonance is approximately 20–40 dB/decade depending on damping ratio.

For effective isolation, f₀ must be well below the lowest motor operating frequency. If a motor operates from 5,000–40,000 RPM (83–667 Hz), the isolator resonance should be below approximately 50 Hz. This requires a combination of low stiffness (soft silicone) and sufficient mounted mass.

Viscoelastic isolators¶

Rubber and silicone are viscoelastic: their deformation has both elastic (spring-like, energy-storing) and viscous (damping, energy-dissipating) components. The ratio of these components determines the damping ratio ζ.

High ζ (over-damped): resonance amplitude is suppressed but attenuation above resonance is reduced. Good for eliminating resonance peaks.

Low ζ (under-damped): higher resonance amplitude but steeper roll-off above resonance. Can amplify vibration at frequencies near f₀.

Silicone isolators for motor mounts are designed with moderate damping (ζ ≈ 0.3–0.6) to suppress the resonance amplitude while maintaining useful attenuation slope above f₀.

Shore hardness and its effect¶

Shore A hardness is a surface indentation measure that correlates with stiffness k. For a given isolator geometry:

Higher Shore A → higher k → higher f₀ → less effective isolation at lower frequencies.
Lower Shore A → lower k → lower f₀ → better isolation but more compliance (motor positional stability reduced).

Two isolator elements in the floating mount system serve different functions and have different Shore specifications:

O-rings (40–50A): carry compressive load from motor weight and thrust reaction. Firmer durometer prevents motor sag under sustained thrust.
Sleeves (30–40A): provide radial isolation at the bolt shaft. Softer durometer gives more compliance in the radial direction where motor vibration is highest.

Temperature dependence¶

Silicone Shore hardness is relatively stable across a wide temperature range, but does increase at low temperatures. Standard silicone shows significant stiffening below 0°C, raising f₀ and reducing isolation effectiveness in cold weather. VMQ (vinyl methyl silicone) maintains more consistent Shore hardness from −50°C to +200°C and is specified for this reason in libdrone's floating mount. → See floating-motor-mounts §Rationale.

Isolation vs decoupling¶

A mechanical isolator does not eliminate the connection between motor and frame — it changes the character of the connection from rigid to compliant. The motor is still attached. Forces at frequencies below f₀ still propagate. The isolator is not perfect.

For the residual vibration that passes the mechanical filter, software filters act as a second stage. The two stages address different frequency regions: mechanical isolation handles the high-amplitude fundamental and low harmonics; software filters handle the residual and higher-frequency components. Together they achieve lower total gyroscope noise than either could alone.

Reference¶

Isolation effectiveness (approximate, single-axis model)¶

Frequency relative to f₀	Transmissibility
0.1 × f₀	~1.0 (passes through)
0.5 × f₀	~1.1–1.3 (slight amplification)
1.0 × f₀ (resonance)	2–10× (amplification — must not coincide with motor operating range)
2 × f₀	~0.3–0.5 (30–50% attenuation)
5 × f₀	~0.05–0.1 (90–95% attenuation)
10 × f₀	~0.01–0.03 (97–99% attenuation)

Values are approximate and depend on damping ratio. Real isolators deviate from the ideal model, particularly at high frequencies where mass and stiffness of the isolator itself introduce secondary resonances.

Blackbox indicators of vibration issues¶

Symptom	Probable cause
High-frequency noise band on all axes (250–700 Hz)	Motor fundamental / blade passage reaching IMU
Narrow spike at specific RPM	Resonance near motor operating frequency
Noise increases with throttle	Mechanical isolation bypassed (direct contact, worn isolators)
Noise present at idle, not correlated with RPM	Airframe resonance from external excitation

Procedure¶

Rationale¶

Why this article exists separately from floating-motor-mounts¶

The implementation article (floating-motor-mounts) tells a builder what to do: which O-rings, which torque, which lubricant. This article tells a student or contributor why it works: the physics of vibration propagation, the spring-mass model, the frequency domain behaviour. Separating them follows the atom boundary rule — the implementation article links here for depth without repeating the physics. A builder does not need the spring-mass model to assemble the mount; a student studying drone control systems does not need the part numbers to understand isolation.