Intrinsic Vibration Behavior of Springs

In mechanical engineering, tension and compression springs are an important part of the design of mechanical systems, applications and uses. The properties of springs, such as their return force and spring constant, influence the performance and functionality of machines. In order to understand these properties and the vibration behavior of spring systems, we look in this article at the physical relationships between spring systems and the relationship between the natural frequency and resonance.

Physical Properties of Springs

Tension and compression springs, simply called "springs", are one of the most important elements in mechanical systems. They have the capability to stretch and compress, enabling them to store kinetic energy. This energy is released when the spring returns to its original shape.

The physical properties of springs depend on various factors. The material from which the springs are made, their shape and size as well as the way in which they are loaded are decisive. In addition, external factors such as temperature and humidity can influence the properties of springs.

The intrinsic vibration behavior of springs is determined by their physical properties. These include density, modulus of elasticity, vibration damping and rigidity. The intrinsic vibration behavior of springs is also influenced by the type of application.

Harmonious Vibrations

Harmonious vibrations are undamped vibrations in which the return force is proportional to the deflection of the spring.

When a spring is deflected from its equilibrium position and then released, it starts to vibrate. These vibrations are harmonious when the return force, i.e. the force acting in the direction of the equilibrium position, is always proportional to the deflection. Harmonious vibrations have a fixed frequency and do not stop by themselves after the initial external exertion of a force.

Damped Vibrations

In reality, the vibration of springs, for example, is fundamentally damped because they decrease over time due to external influences such as friction or air resistance. This means that the amplitude of the vibration gradually decreases until the vibration finally stops. The period of oscillation is thus reduced by damping the spring, depending on its physical properties.

The damping influences the intrinsic vibration behavior of the spring by causing energy losses during vibration. When a spring vibrates, it releases energy due to friction and other factors. This causes the vibration to gradually decrease. The damping changes the vibration behavior of the spring by reducing the frequency and amplitude of the vibration. This means that damped vibrations are significantly less susceptible to resonance.

In order to understand the intrinsic vibration behavior of a damped spring, the damping properties of the spring must be taken into account. Damping can be influenced by various factors, such as the shape of the spring, the material and the environment in which it is used.

Industrial shock absorbers can also be used to dampen vibrations in addition to springs.

The spring constant as a decisive parameter

The importance of natural frequency

The intrinsic vibration or natural frequency of a mechanical system describes the frequency at which the system vibrates after a single excitation from the outside. The intrinsic vibration behavior of springs is important to understand the vibration characteristics of mechanical systems.

When a spring is integrated into a mechanical system, it can affect the vibration behavior of the system. In the case of a spring pendulum (also spring swinger), the natural frequency depends on the spring constant k and the mass m of the pendulum body.

Based on the vibration equation, the following formula can be used to calculate the natural frequency of a spring:

Resonance in a spring system

Resonance is an important mechanical phenomenon and can occur in many applications. It is important to understand how resonance develops and the impact it has on optimizing the performance of spring systems. In the design, natural frequencies and resonances of spring systems are of greater importance when it comes to the resulting consequences for the stability and safety of an application.

A resonance occurs when an external force acting on the spring system corresponds to the natural (intrinsic) frequency of a spring. When this frequency is reached, the system begins to vibrate with the greatest possible amplitude. This is called resonance.

Assuming an application consists of a vibration feeder that is mounted on spring-loaded foot jack bolts. In this case, a resonance effect can occur if the frequency of the vibration feeder is close to the natural frequency of the spring-loaded foot jack bolts. This resonance effect could ultimately result in the vibration amplitude of the application increasing further and its stability and safety is no longer given.

The effects of resonance in the spring system can be very serious. If the spring system vibrates too much, it can cause damage to the construction or cause unforeseeable movements.

It can thus be stated that resonances in the construction should generally be avoided.

• All natural frequencies not equal = GOOD
• All natural frequencies equal = BAD

How resonance can be prevented

We have already established that the natural frequency is an important factor for the occurrence of unwanted resonance in an application. How can this knowledge be used in practice?

1. Determine the vibration frequency of the planned application.

   The vibration frequency of the application should be known as part of the design (e.g. technical data of the application). As a result, suitable springs can be selected in the following steps.

2. Determine the natural frequency of the desired spring.

   By inserting a suitable natural frequency into the vibration equation (see calculation formula for natural frequency), spring constants can be determined that are suitable in consideration of the vibration frequency of the planned application.

3. Further damping of the vibration.

   In some cases, it may be necessary to additionally dampen the vibrations of a spring by using dampening materials (e.g. PU dampers) to further reduce unwanted vibrations or noise. A damped spring system reduces vibrations to an acceptable level and increases the stability and safety of the application.

What other measures are there to dampen vibrations?

One option is to use a suitable spring to dampen the application. A spring can absorb a vibrating movement and convert it into heat energy, thus dampening the vibration. This principle is often used in vehicles where shock absorbers made of springs are used to cushion vibrations on the road.

Shock absorbers are another means of damping vibrations. Unlike springs, shock absorbers convert kinetic energy directly into heat energy, thus reducing the extent of movement considerably faster than springs.

A more modern example of an effective damper is a PU (polyurethane) damper. This type of material not only absorbs vibrations due to its elastic properties like other materials; it also has excellent shock absorbing properties and a high resistance to abrasion and wear compared to conventional rubber materials.