Random Vibration Procedures and Best Practices

Random Vibration Procedure and Best

PracticesOptiStruct

David M. Aguilar

Tuesday, September 25, 2018

© 2018 Altair Engineering, Inc. Proprietary and Confidential. All rights reserved.

Table of Content

• Random Response Background

• Random Response Inputs

• Random Response Setup in OptiStruct

• Post Processing

• Stresses

• Response Spectrums

• Dynamic Responses

• Drawing Conclusions

• Common Mistakes

• Next Steps and Conclusion


Scope of document

In Scope:

- Background of random response analysis

- Single direction excitation

- Analysis setup

- Key outputs and interpreting results

- Common Mistakes

Out of Scope:

- Creating a PSD input profile from data

- Multi direction excitation

- Random response fatigue analysis

- Test-analysis correlation


Random Vibration Background


Random Vibration Overview

In order to evaluate if a design is robust and meets design margins, engineers use a variety of analytical tools. Often a product’s duty cycle is not perfectly characterized but the statistics of a lifetime of excitation are known.

These excitations can cause fatigue when system level dynamics are excited. It is very important to understand how a system responds to these excitations and how natural frequencies interact with each other.

Power spectral density (PSD) analysis, more commonly known as random response analysis, is used to determine stresses and strains in a system that is subjected to random excitations.

Fender Mounted Vertically on

an Electrodynamic Shaker

(Palve & Roy, 2015)


Random Response Inputs


Material Properties

The following material properties are required for random response analysis.

• Elastic Modulus

• Density

• Poisson’s Ratio

• Damping

OptiStruct Material Card in

HyperMesh**Note: These material properties are provided as an example.

They are not to be used as a reference nor should they be applied

in analysis without independent verification of their validity.


Input Excitation

• The input excitation for a random response analysis is a Power Spectral Density (PSD) profile.

• An input profile is generally provided by test engineers or is part of an engineering test requirement.

• Since PSD input profiles are based on duty cycle, physical data must be available in order to create an input.

Input PSD Profile


Random Response Setup in OptiStruct


OptiStruct Random Response Analysis Flow

Unit Load Frequency

Response Analysis

(Mode Based Solution)

Random

Response

Analysis

• Random response analysis is the result of cascading analyses.

• Frequency response analysis can be performed using modal superposition or a direct solution. This document will use the modal superposition solution.


OptiStruct Random Response Card Flow

SPC

EIGRL

SPCD

TABLED1

FREQi

RLOAD2

Unit Load

Frequency

Response

Analysis

TABRND1

RANDPS

Random

Response

Analysis

Load Collectors

Subcase

Key

TABDMP1

First Subcase

Second Subcase

© 2018 Altair Engineering, Inc. Proprietary and Confidential. All rights reserved.Unit Load Frequency Response Definition

Unit of

Acceleration

Notes:

• 1g (9810 [mm/s^2]) in Y, between 1 and 1000 [Hz].

• The value of uniform damping, 2.5%, is applied as

critical damping which is twice that value (0.05).

• Modes should be calculated for 1.5x to 2x

excitation range.

Excitation

Direction


Random Response Definition

TABRND1

RANDPS

Random

Response

Analysis

8

9

PSD input excitation must

be in log-log


Post Processing


Steps to Reviewing and Interpreting Results

Basic review of random response results should follow these steps: 1. Review stress contours, find high stress areas, and isolate several elements for further investigation.2. Using the elements found in step one, generate stress spectrums. It is not feasible to do this for all

elements in the model due to computer storage requirements. 3. The stress spectrums found in step two will highlight frequencies that contribute the most to the

component's stress. Using the results from the frequency response analysis, animate the dynamic response of influential frequencies and determine ways to modify their behavior.

Stress ContoursStress

Spectrums

Dynamic

Responses


Stresses


Stress in Random Response

Random response results can be viewed per frequency, Power Spectral Density Function (PSDF), or as an ensemble of the entire excitation bandwidth, Root Mean Squared (RMS).

Setting “Random” to PSDF in the stress output card will result in both the PSDF and RMS results being output to the results file.


RMS Stress in Random Response

When looking at RMS stress contours calculated from a random excitation it is important to remember several points:• You are looking at the combination of all response

frequencies across the entire input frequency range.

• The default display shows the limit of stresses that can be expected 68% of the excitation time. A detailed explanation of this can be found on the next slide.

• Response frequencies do no contribute equally to the final RMS value. To truly understand what the stress contours mean, you must determine which frequencies respond greatest to the input excitation.

RMS Von Mises Stress [MPa]


1𝜎 Root Mean Squared Stress

The magnitude of RMS stress can be shown as a one, two, or three sigma value. These values represent increasing standard deviations of the response.

Stresses calculated from a random response analysis have a zero mean. If a one sigma stress is 10 [MPa], then the three sigma stress is 30 [MPa]. There is a 0.7% chance that stresses will be greater than 30 [MPa].

If a system has a one sigma stress of 10 [MPa], there is a 32% chance that stress will exceed that value during the time of excitation. For the same time of excitation, there is a 68% chance that stresses will be at or below 10 [MPa].

Sigma Prob. Of Stress

Within Range

1 68.3%

2 95.4%

3 99.3%

Probability of Stresses Occurring


Selecting Areas of Concern

Areas of concern will typically occur around welds or geometric stress concentrations. Once an area has been identified, record the element number and generate a stress spectrum. The image to the right shows an element that occurs in the toe of a weld. While not the highest stress found in the system, it is still important to evaluate it further.

Details on how to create a stress spectrum can be found in the next section of this document.

1𝜎 RMS Von Mises Stress [MPa]


Response Spectrums


Response Spectrums

Important outputs that give significant insight to the response of a particular element are its response spectrums. Response spectrums will show frequencies at which the element strongly responds to the input. In order to get these graphs, unsupported cards must be created before the solution is calculated. - Navigate to the Analysis Panel and select Control

Cards- On the first page select Case_Unsupported_Cards- Enter XYPLOT or XYPEAK.- E.g. XYPLOT,STRESS,PSDF/ elem#1(Stress

component), elem#2(Stress component), … , elem#n(stress component).

Details on how to use these cards can be found in the help documentation under XYPEAK/XYPLOT

Since stress spectrums are generated for a specific stress tensor, it is important to review each component to determine which are the most excited.

Sxx1 Stress Spectrum

Input Deck Example


XYPLOT Card Explained

Stress Outputs Stress

PSDF The square of stress

302780 Element Number

(3) Normal X at Z1

(10) Normal X at Z2

(5) Normal Y at Z1

(12) Normal Y at Z2


Response Spectrums

The spectrum shows that the two frequencies that respond the strongest to the input and contribute the most to the stress are 29 [Hz] and 96 [Hz]. The motion of the component at these frequencies should be reviewed in order to make design change suggestions.

Problem

Frequencies

1𝜎 RMS Von Mises Stress [MPa] Sxx1 Stress Spectrum


Dynamic Responses


Dynamic Response

After the stress spectrums have been reviewed and a few interesting frequencies have been identified, it is time to study the dynamic response of the system at those frequencies.

In the example plot to the right, 29 [Hz] and 96 [Hz] need to be reviewed further. While these frequency values occur very close to the natural frequencies of the system, reviewing the mode shapes will not give a full picture of the response.

By definition, mode shapes are unforced responses, while the results of a PSD are forced. Looking at frequency response results at problem frequencies will give a complete picture of the system’s problematic dynamic responses.

Sxx1 Stress Spectrum

Natural Frequencies of the system


Component Motion at 96 [Hz]

To review the dynamic response of a system at a

problem frequency, simply select the frequency

response subcase and frequency.

In the example to the right, stresses were

observed in the PSD Z analysis so the FRF Z

results are reviewed. When animated, the vertical

excitation is clearly observed along with the

dynamic response of the system. Knowledge of

how the system vibrates near areas of high stress

can be used to change the design.

Subcase and load selection in HyperView

Forced Dynamic Response of the system at 96 [Hz]


Drawing Conclusions


Drawing Conclusions

The ultimate goal of running a PSD analysis is generating fatigue damage values. In situations where that has not been done, there are several ways to evaluate results. It should be noted that these methods are purely rules of thumb and ways to quickly evaluate results. They should not be used as the final determination of a design’s robustness.

• Ultimate tensile strength by half: If the 3𝜎 RMS VM stress is below 𝑈𝑇𝑆

2then the component should

not fail due to fatigue. This should not be applied to welds. • Stress below fatigue limit: If the 1𝜎 RMS VM stress of a component is below the fatigue limit of the

material, the system should not fail due to fatigue.

Fatigue is the result of stresses repeatedly occurring in a material. Therefore, these rules of thumb are based off the likely hood of the stresses occurring. Since one sigma stresses are more likely to occur, they must be below the lower stress threshold, the fatigue limit of the material. Three sigma stresses are less likely to occur, so they must be below the higher limit, half the ultimate tensile strength of the material.


Common Mistakes


Common Mistakes

- Setting the unit acceleration to 1 rather than setting it to a unit of acceleration in the SPCD card.

- Most input PSD profiles are in [G^2/Hz] which means that the unit load applied in the SPCD card needs to be equal to the gravitational constant of your unit system. If you are working in [MPa] your unit load needs to be equal to 9810 [mm/s^2].

- If your PSD input profile is in [(m/s^2)^2/Hz], the SPCD value would be 1 since the gravitational unit is accounted for in the input profile.

- Linearly interpolating the input PSD profile rather than logarithmically.

- For PSD analysis you must use logarithmic interpolation, which can be set in the TABRND1 card.

- Too coarsely calculating the frequency response.

- PSD responses are calculated by multiplying the result of the FR and the input PSD. Therefore an analyst should use a frequency step of ~1 [Hz] in the FREQi card. This value should be adjusted by considering the input PSD and the number and spacing of the component’s modes.

Setting logarithmic interpolation

for the input PSD profile.

Acceleration load set to the

gravitational constant.


Next Steps and Conclusions


Next Steps

After a basic review of random response results, an analyst may wish to dive deeper into post processing. The next logical step is to calculate fatigue damage values of high stress locations. The information garnered from fatigue calculations will give the analyst a better understanding of if a location is in danger of failing and by what degree.

Detailed information on how to calculate fatigue due to random excitation is outside of the scope of this document.


Conclusions

Random vibration analysis is a tool that can provide powerful predictions on the robustness of a system’s design. There are many pitfalls during setup and post processing but following a well defined procedure will ensure the generation of meaningful results.

PSD Stress Results

Documents

Random Vibration Procedures and Best Practices