An Introduction to Transfer Path Analysis

Siemens Phenom Siemens Phenom
Siemens Phenom

(view in My Videos)

tpa_icon.png

 

Transfer Path Analysis (TPA) is a technique used to break down a noise or vibration problem into its key contributors. These contributers are identified using source loads and transfer functions to the response at a target location. 

 

To understand the response at the target, the following are used:

  • Source: Characterized by forces, the source creates the input loads into the system.
  • Transfer: Transfer functions (Frequency Response Functions) characterize how noise and vibration is transferred from the source to the target location. 
  • Target: Location where an unwanted vibration or noise is perceived. The examples in this article use sound pressure at a target location, but the technique is equally applicable to vibration.

 

Transfer Path Analysis can be used with physical measurements, simulation data, or a combination of the two.

 

Index:

  1. Terminology and Basics

     1.1 Quantities

     1.2 Transfer Functions

     1.3 Operational Forces

  2. Airborne versus Structureborne Paths

  3. Defining Paths

  4. Interpreting Results

  5. Mount Stiffness Force Estimation

  6. FRF Matrix Inversion Force Estimation

  7. Simcenter Testlab Transfer Path Analysis

     7.1 TPA Model

     7.2 TPA Loads

     7.3 TPA Results

  8. Conclusion

 

1. Terminology and Basics

 

In Transfer Path Analysis (TPA):

  • The loads from the source are identified
  • The transfer functions between the source and the target are identified

Understanding the source loads and the transfer functions allows the levels to be calculated at the target location.

 

1.1 Quantities

 

These loads and transfer functions are frequency based.  The following letters will be used in this article to describe the quantities used in these functions:

  • F = structural force, often expressed in Newtons (N) or pounds force (lbf)
  • A = acceleration (structure response), commonly in g’s
  • P = sound pressure (acoustic response) in Pascals
  • Q = acoustic force, expressed in m3/s2
  • P/F = transfer function from structure-borne force location to a pressure
  • P/Q = transfer function from airborne force to a pressure
  • A/F = transfer function from structureborne force to a vibration
  • Fo = operational force at source attachment location to the structure, subscript o indicates operational conditions
  • Qo = operational acoustic force at source attachment location to the structure, subscript o indicates operational conditions
  • Ptotal = predicted total sound pressure from TPA model at an acoustic target location, this is the sum of path contributions
  • Pmeasured = measured sound pressure at an acoustic target location

 

1.2 Transfer Functions

 

In Figure 1, transfer functions (P/F) to an acoustic target are shown. This is for a simplified, two path structureborne noise model.

 

structure_frf.pngFigure 1: Transfer functions, or FRFs, are used to characterize the structure and target attached to the source.

Acoustic transfer functions relate force (F) to sound pressure at a target (P).  These functions can be calculated by:

These loads are applied while the source is not operating. They are strictly to characterize the transfer functions. In this example, the transfer functions characterize the structure that holds the source.

 

1.3 Operational Forces

 

The operational forces, often expressed as a frequency spectrum (vs Hz) or an order (vs rpm), are quantified under the condition of interest (Figure 2). These can be structural forces (F) or acoustic forces (Q).

 

operating_forces.pngFigure 2: Operational forces from the condition of interest at the source/structure attachment locations.

In this case, there are two mechanical structureborne forces acting on the object.

 

To understand which operational loads and transfer function pairs contribute the most to a target, they are multiplied together as shown in Figure 3.  These functions can consist of amplitude and phase.

 

path_summing.pngFigure 3: Operational forces are multiplied by their corresponding transfer functions to determine the biggest overall contributing path to a target noise or vibration.

The quantities P1 and P2 would be evaluated to determine the largest contributor.  The amplitude and phase of P1 and P2 vary with frequency.

 

For a complex structure, there are typically more potential paths.  In the simplified example presented, only one direction was considered at each attachment. In real life applications, there can be several directions to consider at each attachment: translational movement (X, Y, and Z) and rotational movements (RX, RY, and RZ).

 

2. Airborne versus Structureborne Paths

 

Heard the terms airborne and structureborne?

 

Paths can be considered either airborne or structureborne. The term “borne” refers to how forces originate from the source.

 

In the case of structureborne noise, the source imparts forces through a mechanical attachment to the structure as shown in Figure 4.

 

structureborne.pngFigure 4: Structure borne noise is generated through a mechanical attachment between source and structure.

In the case of airborne noise, the source imparts forces acoustically as shown in Figure 5.

 

airborne.pngFigure 5: Airborne noise radiates through the air from the source.The terms airborne and structureborne are only concerned with how the forces originate from the source. This can be confusing as both airborne and structureborne sources can be perceived as sound at the target:

  • Structureborne source imparts vibrations into the structure, which eventually radiate out as noise. So even though the forces originate structurally, part of the path is in the air.
  • Alternatively, the airborne noise source only imparts acoustic force (no initial structural component). This acoustic force can interact with the structure before arriving at the target.  It is still called an airborne path because the forces originated from the source through the air.

 

A transfer path analysis can include both airborne and structureborne paths in the same analysis.

 

3. Defining Paths

 

When performing a Transfer Path Analysis, it is helpful to make a single, continuous “cut” that separates the source and structure. Paths are defined as any attachments that cross the cut, as shown in Figure 6.

 

twelve_path_tpa.pngFigure 6: The source (outlined in cyan) is defined as the motor. This makes the structure the frame and cab (outlined in red). The result is a twelve path transfer path analysis (4 attachment locations and 3 directions each).

In Figure 6, the cut is through the four motor mounts that attach the source to the frame.  If three translational directions were considered at each mount, the result is a twelve path transfer path analysis.

 

Instead of cutting around the motor, the cut could be applied around the cab, as shown in Figure 7.

 

fifteen_path_tpa.pngFigure 7: Source is defined as the motor and frame, resulting in a fifteen path transfer path analysis.

Instead of twelve structureborne paths, there are now fifteen structureborne paths to consider.  These are two different analyses that require different data, despite the fact they are on the same object.

 

Why choose one cut versus the other?

 

If the cab mount rates can be changed, while the motor mount rates cannot be changed, then cutting around the cab might be the preferred way to do the transfer path analysis. On the other hand, if the motor mounts can be altered, then it makes sense to define the cut around the motor.

 

Yet another cut on the same object could make the TPA consist of all airborne paths as shown in Figure 8.

 

five_path_airborn.pngFigure 8: Source is defined as the interior panels of the cab, resulting in a five path airborne TPA model.

In an airborne path analysis, operational Q forces would be needed, and P/Q transfer functions.

 

Each cut defines a different transfer path analysis model. The forces and transfer functions required for each analysis are different, as defined by the respective cuts. 

 

4. Interpreting Results

 

There are many ways to view the results of a Transfer Path Analysis in the Simcenter Testlab software.  One of the most popular is the contribution display.

 

In the contribution display, horizontal color bars represent the amplitude of each path as shown in Figure 9.  Paths with the highest contributions are colored in red, while the lowest contribution levels are colored blue.

 

contribution_display.pngFigure 9: In the TPA contribution display, colored bars indicate dominate paths.

There are three types of bars in the display:

  • Top Bar: Measured data at the target location.
  • Second Bar: Sum of all the calculated paths.
  • Rest of Bars: Individual path contributions. Each individual path bar is the result of multiplying the transfer function times the force.

 

In Figure 9, it can be seen that the path “body:1:+Z” is the largest contributor at 4800 rpm. Every transfer path analysis is different.  While in this example one path is responsible for the issue, often multiple paths contribute to a problem rpm or frequency.

 

If all the paths are summed together, they should equal the measured total at the target (Figure 10).

 

sum_verification.pngFigure 10: Left – Measured and calculated total do not match, some paths were not identified properly. Right – Calculated and measured total match.

If the calculated total and measured total do not match, then some important paths were not identified properly.  Ideally, the calculated and measured totals should match, indicating that all important paths were identified.

 

5. Mount Stiffness Force Estimation

 

Transfer functions are relatively easy to measure via impact testing, or to estimate using structural finite element analysis. 

 

Determining the forces acting on a structure from a source can be a bit harder.  From a measurement point of view, inserting a load cell in place of a mount disturbs the dynamics of the system. 

 

A popular alternative is to place accelerometers on each side of the mount (on the active and the passive sides).  These accelerations are double integrated and subtracted to derive the displacement across the mount (x) as shown in Figure 11.

 

mount_stiffness.pngFigure 11: In the mount stiffness force estimation method, the displacement from the active side (a) to the passive side (p) of the mount is calculated and multiplied by the mount stiffness (k).

The displacement across the mount is multiplied by the mount stiffness to derive the operational force from the source.  This is known as Hooke’s law, where F = kx.

 

In this method, the stiffness must be determined under the correct displacement, preload, and temperature that the mount experiences during actual operating conditions.

 

6. FRF Matrix Inversion Force Estimation

 

For hard connections between the source and structure, the mount stiffness method does not work well. Small experimental errors result in large changes in the force, since there is relatively little displacement across the attachment.

 

An alternative to the mount method is FRF matrix inversion.  In this method, a local FRF is measured at the mount attachment as shown in Figure 12.  This local FRF is also sometimes called a driving point FRF.

 

matrix_force1.pngFigure 12: In the FRF inversion method, the local FRF (A/F) at the source-structure attachment is inverted and multiplied by the operational accelerations to calculate operational forces.

This local FRF is inverted and multiplied by the operational accelerations to calculate operational forces.  The equation to get the operational force is (A/F)-1 * Ao = Fo.

 

At a specific frequency, this local FRF may have an anti-resonance, where the FRF value approaches zero.  This would cause the inverted FRF to have a very large value, approaching infinity. This is not realistic.

 

For this reason, a single FRF is not used in the inversion, but rather a several FRFs (a full matrix of FRFs) as shown in Figure 13

 

matrix_force2.pngFigure 13: Multiple FRFs should be used and inverted simultaneously in the FRF matrix inversion method.

By using multiple FRFs in the inversion, the chances of a single frequency approaching infinity is greatly reduced.  The idea is that the same frequency does not approach zero in all the FRFs.  At a minimum, all cross FRFs of the paths should be measured and used in the force calculation.

 

Additionally, cross-coupling between paths is not taken into account when using a single FRF. 

 

Other FRFs can be added that are not part of the path to ensure a well-conditioned result.  The software shows a condition number which should be as low as possible at each frequency.  Typically, twice as many additional FRFs need to be measured than path data FRFs. 

 

7. Simcenter Testlab Transfer Path Analysis

 

To get started, turn on “Transfer Path Analysis” under Tools -> Add-ins in the main Simcenter Testlab menu as shown in Figure 14.

 

tpa_addin.pngFigure 14: Under “Tools -> Add-ins” turn on “Transfer Path Analysis”

Simcenter Testlab Transfer Path Anlaysis uses 98 tokens. After turning on the add-in, three workbooks are added:

  • TPA Model – Defines the paths, targets, load conditions, and any mount relationships.
  • TPA Loads – Calculates the loads according to different methods.
  • TPA Results – Allows the highest contributing paths to be identified and understood.

The Transfer Path add-in does not acquire data.  The appropriate operational and FRF data must have been already acquired.  The Transfer Path software allows the data to be organized and an analysis to be performed.

 

7.1 TPA Model

 

In the TPA Model workbook (Figure 15), the path information is defined based on the names of data to create a Transfer Path Analysis model definition.

 

tpa_model.pngFigure 15: The TPA Model workbook allows a Transfer Path Analysis model to be defined based on the point identifications and measurement functions of the data.

First, all the data (operational, FRFs, mount stiffness, etc) to be used are placed in the Input Basket.  Then in the TPA Model workbook, the “Read Input Basket” button in the upper left should be pushed.  The list of Available Points should be filled in as shown in Figure 16.

 

available_paths.pngFigure 16: Push the “Read Input Basket” from the upper left and the available point identifications can be assigned to either the target, path, or indicator areas.

From this list, point identifications can be assigned to the target, path, and indicator areas:

  • Target – The location of the noise or vibration experienced by the receiver on the receiving structure.
  • Path – The attachment locations defined between the source and structure.
  • Indicator – Any measurement used to indirectly calculate the loads or forces from the source. For example, accelerations used to calculate loads using the mount stiffness method.

 

The names of the point identifications are important as they are used to match the FRFs (the reference id) to the corresponding operational forces:

  • Directions: Any data must have a direction defined for it to be used. In the case of acoustic data, the direction field should be “S”.
  • Names: If the names are different, the software will not match the FRFs and forces to each other automatically. Be aware that names like “Body:1:+Z” are different than “body:1:+Z” because the names are case sensitive.  If the names are different, rather than renaming each individual measurement, an alias table can be created that maps the names to each other.

 

With the identifications selected, the next step is to identify the type of load or force case from the source (Figure 17).  A case is based on the type of function: orders, spectrums, autopowers, and more….

 

operational_cases.pngFigure 17: Click on Operational load cases are selected from the available cases on the left.

In the Operational Data cases section:

  1. The data type is selected from the pulldown under “Operational Data Type”.
  2. After pressing “Read Input Basket” any matching data is listed.
  3. Available cases can be moved to Select cases as desired.

 

Below the operational data cases area, in the mount table area, the active and passive side connections at attachment locations can be paired (Figure 18).

 

mount_table.pngFigure 18: In the Mount table, the active and passive sides of the mounts can be paired.

To pair the mounts:

  1. Select paths from the passive side list by clicking on row numbers.
  2. Use the arrow keys to move these paths to the mount table.
  3. Highlight the active side areas to match up.
  4. Highlight the paths from the active side.
  5. Use the arrow keys to move the paths from the active side to the mount table.

With the model defined, then the minor worksheets “FRF Selection” and “Operational Data Selection” can be used to select the actual data as shown in Figure 19.

 

frf_selection.pngFigure 19: In the “FRF Selection” and “Operational Data Selection” minor worksheets, cells will turn green indicating data is selected for analysis when pressing “Add from Input Basket”.

In the two minor worksheets:

  1. Select the desired minor worksheet.
  2. Press on the “Add from Input Basket” button.
  3. The corresponding cells for the data turn green when the data is selected to be used in the TPA model.
  4. Highlighting the green cell columns or rows will display the data on the right side.

 

7.2 TPA Loads

 

When all the data is selected and identified, move to the TPA Loads workbook.  In this workbook, loads can be calculated from indicator measurements.  For example, the mount stiffness method (Figure 20) can be used to calculate forces, or the FRF matrix inversion method can be utilized.

 

tpa_loads.pngFigure 20: In the TPA Loads workbook, the Mount Stiffness method can be used to calculate operational forces using accelerations and mount stiffness curves.

For example, in the mount stiffness minor worksheet:

  1. Select the Mount Stiffness minor worksheet at the top of the TPA Loads workbook.
  2. In the lower left menu, click on “Search Mount Stiffness data” button to select the stiffness data.
  3. Press the “Apply to Load Table” button to perform the load/force calculation.
  4. Click on the rows in the upper left to display the load calculation results.

 

After the loads are calculated, the results of the TPA analysis can be displayed.

 

7.3 TPA Results

 

After the loads are calculated, the TPA Results worksheet displays the results (Figure 21), allowing the dominant paths to be identified.

 

tpa_results.pngFigure 21: In the TPA Results workbook, the target and case can be selected on the left side. The display type to show the results can be selected from the middle pulldown.

In the TPA Results display:

  1. Highlight the target on the left side.
  2. Highlight the load case on the left side.
  3. Push the “Update Display” button.
  4. From the pulldown above the display in the middle of the screen, select “Contributions at case (path or group vs rpm or frequency)”.

 

To understand why a path is a big contributor, the Path Specific minor worksheet can be used as shown in Figure 22.

 

path_specific.pngFigure 22: In the TPA Results workbook, click on the “Path Specific” minor worksheet to understand if the source load (upper right) or the structural sensitivity (middle right) contributes significantly to the total (lower right).

All the data for a selected path can be shown: structural FRF, the source forces, mount stiffness, and other indicators. 

 

To use the path specific worksheet:

  1. Click on the Path Specific minor worksheet.
  2. Select a target on the left side.
  3. Choose a path of interest on the left side.
  4. Choose the load case.

With the path data displayed, it is easy to tell if the loads (upper right) or the structural sensitivity (middle right) contributes to the total (lower right).

 

If desired, “TPA Component Editing” can be used to modify the parts of the path to simulate mitigating the problem.

 

8. Conclusion

 

With Simcenter Testlab Transfer Path Analysis, noise and vibration issues can be easily diagnosed.  Either simulation and test data can be used, or a combination of both.  Enjoy!

 

Questions?  Email peter.schaldenbrand@siemens.com, post a reply, or contact Siemens PLM GTAC support.

 

Related Links: