How to manage vibration and cycle time in motion-control applications

In many motion-control applications, vibrations emerge when attempts are made to reduce cycle time or increase productivity. These effects have been attributed to insufficient mechanical stiffness. Their origin is often more complex, arising from a direct interaction between structure, motion profile and control.

This phenomenon has become more evident in equipment due to lighter mechanical architectures, higher accelerations and production rates and the widespread use of low-inertia motors combined with servo drives capable of tracking aggressive command profiles. As a result, motion profiles can excite the structure, even when the control system remains stable.

Vibratory modes

Every machine exhibits multiple natural vibration modes. From an industrial perspective, it is particularly useful to distinguish between two main categories: the fundamental mode and structural modes.

The fundamental mode is generally the lowest-frequency vibration mode of the system. It represents the dominant compliance between motor and load and is associated with components such as screws, belts, gearboxes, shafts and couplings.

From a practical standpoint, this mode can often be approximated by a two-mass system connected by an equivalent spring and damper. In many machines, it exhibits relatively high damping, so oscillations decay quickly. It is typically excited by moderate accelerations and manifests as low-frequency oscillations during motion or at the settling phase.

Structural modes are associated with elastic deformation of the supporting structure: frames, gantries, columns, arms and mounts. Unlike the fundamental mode, they do not correspond to a localized compliance but to a distributed flexibility of the entire structure.

These modes occur at higher frequencies and usually exhibit low relative damping. In lightweight, high-dynamic machines, many of these modes fall within the excitation range generated by motion profiles.

Vibration excitation and jerk

Natural modes always exist; whether they become observable depends on the dynamic excitation. In motion-control systems, this excitation is primarily imposed by the commanded motion profile.

Jerk, defined as the time derivative of acceleration, describes how abruptly dynamic forces are applied. High jerk introduces high-frequency components into the excitation spectrum, which are especially effective at activating structural modes.

The combination of mass-optimized structures and fast transitions makes these effects more visible and more limiting than in previous generations of equipment.

Jerk and harmonic content of motion

Jerk does not alter the mechanical structure of the system; it alters the excitation spectrum.

From both a physical and mathematical standpoint, abrupt acceleration transitions lead to a slow spectral roll-off, resulting in a significant presence of higher-order harmonics. With high-jerk profiles, a substantial portion of the motion energy can be distributed outside the fundamental frequency, often on the order of 20–30% in mid and high harmonics.

By contrast, jerk-limited profiles concentrate most of the energy in the fundamental frequency, which becomes clearly dominant, while higher harmonics are strongly attenuated. This behavior is inherent to the motion profile itself and is independent of the servo drive manufacturer.

Why high harmonics prolong vibration

When the motion contains high harmonics, it excites multiple structural modes simultaneously. Many of these modes, particularly at higher frequencies, exhibit low relative damping.

This occurs because frictional and structural dissipation mechanisms are less effective at high frequencies and because local bending and torsional modes can store energy with limited loss. As a result, even if the initial vibration amplitude is small, these modes decay slowly.

In practical terms, vibration persists not because the system is less stiff, but because energy has been injected into modes that dissipate poorly.

What a closed-loop servo drive “sees”

A servo drive does not directly sense mechanical vibration. Its only reference is the set of internal control-loop signals, that is, how vibration is reflected as position error, velocity error or torque/current demand.

The feedback device used, whether for motor control or for reporting position and velocity at different points of the machine, does not change this fundamental principle. It does, however, influence how clearly the disturbance appears in the internal variables, depending on resolution, noise, filtering and its location within the mechanical chain.

Bandwidth and response speed: Before examining the drive response, it is necessary to distinguish two concepts that are often confused.

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Bandwidth is a frequency-domain property. It defines the upper frequency limit of disturbances that the control loop can effectively detect and process.

Response speed is a time-domain concept. It describes how quickly the drive can generate a corrective action once a disturbance has been detected.

These concepts are related but not equivalent. Increasing bandwidth (BW) extends the range of observable disturbances, but corrective action is always constrained by digital delays, filtering and stability margins.

As an order of magnitude, the theoretical minimum response time of a control loop is on the order of 1/(2·BW). This value should not be confused with the actual settling time of the complete system, which is typically dominated by mechanical resonances and by harmonics generated by high jerk.

Sequential drive response to disturbance

With these definitions in place, the servo drive response can be described sequentially:

• Disturbance generation: a mechanical vibration is excited by the motion profile, typically during high-jerk transitions.
• Observability: the disturbance appears in the drive’s internal variables only if its spectral content lies within the bandwidth of the corresponding control loop.
• Error interpretation: the controller interprets this signal as a dynamic error.
• Reaction: the drive generates a corrective action with a finite response speed, related to bandwidth but limited by delays and stability constraints.
• Mechanical interaction: if the corrective action acts on a flexible or resonant dynamic, it may further excite that mode.

With high jerk, spectral components are generated both outside the bandwidth, and therefore unregulated, and near the bandwidth limit, where they are detected with significant phase lag. This can lead to oscillations, audible noise or increased settling time, even in systems equipped with high-performance servo drives.

Practical approach to vibration reduction

From industrial experience, it is often more effective to:

• identify whether the dominant behavior is governed by the fundamental mode or by a structural mode
• observe at which phase of the motion the vibration appears
• adjust jerk and motion-profile shaping before modifying mechanical design or control tuning.

In many cases, appropriate jerk management reduces vibration, improves stability and shortens cycle time without mechanical changes.

Conclusion

In motion-control machines, vibrations are not isolated defects but a direct consequence of how the system’s natural modes are excited. As dynamic performance increases, structural modes become increasingly relevant, and jerk emerges as a critical parameter.

Managing jerk does not mean slowing the machine down; it means aligning motion dynamics with the structural reality of the system and with the real limits of the servo drive, enabling faster, more stable and more efficient motion.

In this context, the use of virtual models or digital twins could simplify design and commissioning phases. The ability to identify structural modes, evaluate the harmonic content of different motion profiles and analyze the interaction with control loops allows more suitable mechanical architectures and motion profiles to be selected at early design stages, reducing subsequent iterations on the physical machine.