Machine vibration - Know and control mechanical vibrations

Whether damping, diverting or using them in a targeted manner: Mechanical vibrations can usually be controlled using suitable technical measures. If you understand the causes of vibration, components, machines and systems can not only be protected, but also specifically optimized. In this article, you will learn how mechanical vibrations can be influenced and the role of vibration types, damping components and modal analysis in mechanical engineering. You also gain insight into avoidance strategies, from limiting degrees of freedom to the targeted use of vibration dampers to designing vibration paths.

Mechanical vibrations and vibration types

What is a vibration? A mechanical vibration is a periodic movement of a body around a stable equilibrium position, also called a resting position. After the period duration T has elapsed, the body is again in the same state of motion. Vibrations are classified as harmonic, linearly damped and forced. In a harmonic vibration, the movement of the vibrating body describes a uniform circle. This always also means that the restoring force acting on the vibrating body is opposite to the deflection and its magnitude is proportional to the body’s distance from its resting position. A linearly damped vibration is a vibration in which the amplitude decreases continuously over time due to linear damping (e.g., friction proportional to speed). A forced vibration occurs when a vibratory system is excited by an external periodic force to a vibration of stable or increasing amplitude.

According to the type of excitation, a further distinction is made between:

• Free: Free vibrations occur when a vibrating system is set in motion once and then vibrates without further external influence. In particularly simple systems without friction or damping, it is called an undamped vibration. In reality, a vibration is always damped by friction. The amount of friction has a direct influence on the vibration behavior. Depending on the damping, the system returns from the original vibration to its rest state, decaying quickly or slowly. The resulting vibration frequency is called the natural frequency. If the system has several degrees of freedom, it also has several natural frequencies.
• Forced: Forced vibrations occur when a system is stimulated to vibrate by an external, usually periodic force, typically with a so-called excitation frequency. In addition to the short-term free vibration (with the natural frequency), a forced vibration forms, whose amplitude remains constant after the transient period or increases due to resonance effects until the system is destroyed. Particularly in the case of harmonic excitation, a resonance with a greatly enlarged amplitude can occur when the natural and excitation frequencies coincide.
• Self-excited: Self-excited vibrations occur when a system maintains its vibrations through feedback. The energy supply is controlled by the vibration process. They are called oscillators. An example is the vibration of a glass when rubbing its rim. The amplitude continues to grow until losses and energy supply are balanced or the system is destroyed.
• Parameter-excited: Parameter-excited vibrations occur when system parameters such as mass, stiffness, or damping change periodically. This type of vibration differs from forced vibrations in that no external force acts, but excitation occurs via internal system changes.

6 possible degrees of freedom of a solid

The six degrees of freedom of a solid (three translations and three rotations) determine which directions and about which axes vibrations can occur. By combining the translational and rotational degrees of freedom, a solid can reach any possible position. Depending on the type of support and excitation, certain degrees of freedom may be suppressed or preferentially excited, which significantly affects the vibrational behavior. This results in complex natural frequencies and vibration modes, especially in non-symmetric or elastic systems.

The vibration itself counts as another degree of freedom. More specifically, each natural vibration mode represents a characteristic motion that the system can perform without external force. These arise from the elastic deformability of the components and expand the dynamic behavior beyond the purely rigid degrees of freedom. In practical applications, such as in mechanical or vehicle engineering, these natural vibrations significantly influence the operational strength and noise generation. If they are not taken into account, they can lead to resonance phenomena that overload or damage machine components. Therefore, modal analysis is a central tool in product development. Modal analysis is a method for determining the natural frequencies, mode shapes, and damping ratios of a mechanical system. Typical natural frequencies result from bending, torsional, or longitudinal vibrations (depending on geometry, material, and support). The analysis is carried out either experimentally (e.g. with impact hammers and accelerometers) or numerically via FEM simulation (cf. stiffness comparison). The objective of modal analysis is to identify critical frequency ranges that could correspond to operating frequencies or excitation frequencies (i.e., involve a so-called resonance risk).

Limitation of degrees of freedom

An option to avoid damage caused by uncontrolled movements due to different degrees of freedom is their targeted restriction. Double and triple pendulums are classic examples of mechanical systems with multiple degrees of freedom that exhibit nonlinear, chaotic motion behavior due to their kinematic coupling. A double pendulum consists of two articulated masses, and a triple pendulum consists of three. Both types of pendulums are extremely sensitive to changes in initial conditions, even for small deflections. Such so-called chaos pendulums serve as models for dynamically unstable systems in theoretical physics, but are undesirable in practical engineering design. In mechanics, such behavior is specifically prevented by reducing degrees of freedom through suitable bearings, guides or couplings and by specifying stabilized trajectories. Especially for highly dynamic machines or robots, chaotic behavior would significantly affect predictability, repeatability and process safety.

There are various design and control engineering options to limit the degrees of freedom of a system:

• Bearings, e.g. joints, guides, for motion limitation on a defined axis.
• Mechanical couplings, e.g. levers, cam discs, for coupling movements between bodies.
• Kinematic guide systems, e.g. cross tables, that specifically exclude movements in certain degrees of freedom.
• Guide profiles, e.g. rails, grooves, guide tracks, which specify a defined direction of movement.
• Form- and force-locking fixations, e.g. clamping systems or clamping mechanisms, which temporarily or permanently fix a body.

Vibration, Transmission and Mass

The natural frequency of a system decreases as mass increases, making it less sensitive to high-frequency excitation. At the same time, however, the moment of inertia increases, which can prolong the reaction time. In vibration engineering, this is referred to as the principle of vibration transmission, in which mass, spring stiffness and damping are specifically coordinated to avoid or filter critical frequency ranges. This principle is implemented in vibration isolators, machine foundations and multi-layer damping systems, among other things, in order to keep vibrations targeted away from the structure or only to transmit them in a controlled manner.

Vibration superposition - what is it?

Superposition of vibrations refers to the physical principle that multiple vibrations acting simultaneously in a system are added, with their deflections overlapping at any time. This produces a resultant vibration, the shape and amplitude of which result from the summation of the individual movements. This is especially true for linear systems. It is possible to calculate the superposition of vibrations.

Vibration Reduction

Targeted design of vibration paths and damping elements allows unwanted vibrations to be dissipated from the system in a controlled manner, preventing harmful effects. Increasing the moving mass or changing the system stiffness can reduce the natural frequency and thereby reduce the transmission of unwanted vibration energy. At the same time, a lower excitation energy can be achieved by decoupling or damping, thereby reducing the overall vibrational behavior.

Materials with high internal friction, such as rubber, PUR or viscoelastic plastics, convert vibration energy into heat. Such damping materials are used specifically in intermediate layers, machine feet or tool holders.

Below are some components that contribute to vibration reduction:

Positive use of vibration: Suspension and Damping

A damped spring pendulum is a classic example of the targeted use of vibration in mechanical systems, e.g. for suspension in vehicles or vibration isolation in machines. Vibration conveyors also use vibrations to transport workpieces or bulk materials via defined tracks. The coordinated interaction between mass, spring stiffness and damping creates a directed movement.

Depending on the ratio between spring constant, mass and damping, different vibration cases occur, which can be used or avoided by design:

• Vibration case (subcritically damped): The system performs damped, periodic vibrations whose amplitude decreases over time. This form is often desired in engineering, e. g. in shock absorbers, as it dissipates energy but allows a quick return to rest.
• Aperiodic limit case (critically damped): The system returns to the rest position the fastest without vibration. This is ideal for high-precision applications, e.g. in measuring systems or sensitive machine guides.
• Creep case (overcritically damped): Return to equilibrium is slow and without overshoot. This is intentionally used when maximum rest and stability are more important than responsiveness, e.g. in vibration-isolated machine foundations.