Vibration Design Decision Tree

To identify a solution, we must first understand the problem. Below is a basic flowchart to aid in the decision making process based on your particular situation.

Need to measure vibration at the point of interest as well as the near the source of the vibration.  This can be done with specialized equipment like an accelerometer paired with data acquisition system, or even smartphones with vibration measurement apps.  

  • Tonal Disturbances - where a single or multiple disturbance dominates the response and causes vibrations at a certain frequency.  Examples of these may be a motor, propeller, or other actuator that is periodic.

  • Random disturbances exciting system dynamics - where the characteristics of the system will vibrate at the resonant frequency of the structural modes.  For example, a bell will always ring at a certain frequency regardless of the frequency content of the input. Cause

Transmissibility Plots

Transmissibility is the ratio of the payload vibration given a base vibration across a range of frequencies.  A Frequency Response Function (FRF) Transmissibility plot is a crucial tool used to analyze and understand the behavior of a vibration isolation system.

Here's an explanation of how to interpret such a plot:

1. Horizontal Axis (Frequency): The horizontal axis represents frequency and is usually plotted on a logarithmic scale. This means that the frequency values increase exponentially from left to right. Frequencies are typically expressed in Hertz (Hz), which is the number of vibrations or cycles per second.

2. Vertical Axis (Decibels, dB):  The vertical axis represents transmissibility and is measured in decibels (dB). Transmissibility is a dimensionless quantity that indicates the ratio of output vibration amplitude to input vibration amplitude. It characterizes how much vibration is transmitted through the system concerning the input.  To convert between a linear scale and decibels, use the following formulas: x_linear = 10^(x_dB/20) (ex: 2x = 6dB, 10x = 20dB)

3. Interpretation of Transmissibility Values:

  • Regions of Transmission: In the region of transmission, transmissibility values are close to or equal to 1. This indicates that the system efficiently transmits vibration from the input to the output. Vibration levels at the output are nearly the same as the input.

  • Regions of Amplification: In the region of amplification, transmissibility values are greater than 1 (expressed in positive dB values). This implies that the system amplifies vibration at specific frequencies. These amplification peaks can occur due to system resonance or other dynamic effects.

  • Regions of Isolation: In the region of isolation, transmissibility values are less than 1 (expressed in negative dB values). This indicates that the system attenuates or isolates vibrations at certain frequencies, reducing the vibration transmitted from the input to the output.

4. Identifying Resonant Frequencies: Resonant frequencies are frequencies where the transmissibility peaks, i.e., where the system experiences amplification. Resonant frequencies are crucial as they indicate points where the system is most susceptible to vibration amplification, which can lead to structural resonance issues.

5. Optimal Isolation Region: The optimal isolation region is the area where the transmissibility is lowest (negative dB values), representing the highest level of vibration isolation. This region typically corresponds to frequencies below the system's natural frequency and is essential for effective vibration isolation.

6. Design Considerations: For effective vibration isolation, it's important to design the system to have low transmissibility (high isolation) in the frequencies of interest, especially in the region where sensitive equipment or structures might be susceptible to vibrations.  This is primarily accomplished by lowering the isolation frequency (f = sqrt(k/m)/(2pi) ) by using a softer spring (k) or adding mass (m).  However, this will lead to more displacement and more gravity sag so there must be sufficient clearance around the payload.  In addition, adding more damping (c) will reduce the amplification at the isolation frequency.  

By understanding the Frequency Response Function Transmissibility plot, engineers and designers can make informed decisions to optimize their vibration isolation systems, minimizing resonance issues and ensuring optimal performance for specific applications. Proper isolation can lead to improved equipment performance, reduced vibrations, and enhanced operational safety.

Design Guidance

  • Isolation systems work by decoupling the payload body from the base body.  Simply put, a soft connection between two bodies allows them to move independently above the frequency of the isolation mode.  

  • To reduce the amount of vibration experienced by the payload, the isolation mode frequency must be reduced by decreasing stiffness of the isolator or adding mass to the payload.  

  • The isolation constraint is displacement.  First, as the isolator frequency decreases, it will sag more due to gravity.  Secondly, most isolators have a resonance that amplifies certain frequencies and causes more movement, determined by the amount of damping in the system.  Softer isolation systems must be able to move more.  

  • Ideally, the isolation modes should be clustered together as the highest isolation mode will dictate the vibration transmitted to the payload.  

  • Ideally, the isolation plane should be in line with the payload center of gravity to limit cross-coupling (i.e. linear motion results in angular motion).  This may require additional structure

  • If the payload center of gravity is above the isolation plane with a narrow base, it could become unstable and buckle.  Instead, hang the payload center of gravity below the isolation plane.  

  • For payloads where line of sight is important (cameras, etc), angular displacement is far more important than linear displacement.  

  • Finally, typical passive isolation systems provide 3-10x reduction.  Beyond this level, effects like friction, nonlinearities, secondary pathways, and other real-world behavior limit the available isolation.  For further reduction, other techniques are required.