Simcenter Testing Solutions Rosette Strain Gauges

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Rosette Strain Gauges

A single strain gauge can only measure strain in one direction. In real life applications, this is often inadequate due to the complex nature of most structures and their loads.

Strains and stresses may come in various directions and thus a gauge capable of measuring several different directions simultaneously is necessary. A rosette strain gauge consists of three single direction strain gauges at specific angle increments.  Using mathematical relationships, the full strain field in any direction can be calculated from the individual gauges of the rosette.

This article explains rosette strain gauges:
1. The Challenges with Single Strain Gauges
2. Strain Tensor vs. Principal Strain
3. Rosette Strain Gauge 
4. Delta and Rectangular Rosettes
   4.1 Delta Rosette Gauges
   4.2 Rectangular Rosette Gauges
   4.3 Planar versus Stacked Rosette
5. Biaxiality Ratio
6. Critical Plane Analysis
7. Rosette Gauges in Simcenter Testlab
   7.1 Real-Time Acquisition: Virtual Channels
   7.2 Post Processing: Time Signal Calculator
8. Maximum Shear Strain in Simcenter Testlab
9. Rosette and Critical Plane Analysis in Simcenter Testlab Neo
   9.1 Getting Started
   9.2 Selecting Data
   9.3 Defining Process
   9.4 Rosette Results
   9.5 Critical Plane Results

1. The Challenges with Single Strain Gauges

In Figure 1, would the single, uniaxial gauge capture the strain field correctly?

Figure 1: Three different force loads on a metal cylinder. Only for the axial load case on the left does the uniaxial strain gauge measure properly. For the torsional and bending loads on the right, the uniaxial strain gauge is insufficient.
 

Only the strain gauge on the left properly measures the strain field. A single uniaxial strain gauge only measures the strain field correctly in one direction. To measure more complicated strain fields, a rosette strain gauge may be required.

Most real systems/products have complicated geometries and multi-directional loads that cannot be measured by an individual strain gauge.

Instead of thinking of the strain in a single, uniaxial direction, a planar approach can be used to think of strain in a XY axis system as shown in Figure 2.

Figure 2: For complicated strain fields, a planar approach can be used.

In a plane, strain can manifest itself in three ways:

• Normal strain in X direction (ɛx)
• Normal strain in Y direction (ɛy)
• Shear strain in XY ( ɛxy)

2. Strain Tensor vs. Principal Strain

There are two methods to define strain in a plane: strain tensor or principal strain. Both methods define the same planar strain state at a point on a test piece, but with a different “perspective”:

• Method 1: Strain Tensor - The first method considers three strain components: two normal components (ɛx,ɛy) and a shear component called γxy or ɛxy. The strains are considered in the xy coordinate system as shown in Figure 2 (left side).

 

• Method 2: Principal Strain - Two principal strains and an angle are used. The gauge is “virtually” rotated so that the shear strain is zero, leaving the two largest principal strain components in the plane. The angle of the principal strain indicates how it is rotated relative to the XY axis as shown in Figure 3 (right side).

Figure 3: Left is Strain Tensor, Right is Principal Strain

Correctly identifying the principal (ie, largest) strain is very important. The fatigue life of the part is determined by the largest strain. If a smaller component strain was used in a fatigue life calculation, it would be under-estimated and the part would fail sooner than predicted.

The two principal strains and angle are related to the strain tensor by a series of equations known as the “strain-transformation.”

The “strain-transformation” can be easily visualized with the aid of Mohr’s circle (Figure 4). Mohr’s circle plots the normal strain (x axis) with respect to the shear strain (y axis) and provides a model by which both the principal strain and the maximum shear can be determined.

Figure 4: Mohr's circle

The Mohr’s circle has the following properties:

• A strain tensor consisting of two normal (ɛx, ɛy) strains and a shear strain (ɛxy) are calculated from the measured rosette strain gauge arms ɛ1, ɛ2, and ɛ3 as shown in Figure 6 or Figure 7.
• The average strain is calculated as (ɛx+ ɛy)/2 and plotted on the X axis where the shear strain is zero.
• Using the calculated normal and shear strains, two points (ɛx, ɛxy) and (ɛy, -ɛxy) are plotted on the graph.
• A circle is fit thru the two points (ɛx, ɛxy) and (ɛy, -ɛxy) with the average strain as the center of the circle.
• The two principal strains are the minimum and maximum values where the Mohr’s circle intersects the x axis at zero shear strain.
• The angles of the Mohr's circle are twice the angles of the rosette gauge. Depending on the convention used, the angle will either be between 0 and 180 degrees, or between -90 and +90 degrees.
• Note that Mohr’s circle is constructed with positive shear strain plotted downward. This is done so that the positive rotational direction of the angle in Mohr’s circle is the same (CCW) as for the rosette.

Commonly, the normal strain and the shear strain output of a Computer Aided Engineering (CAE) simulation is based on the strain tensor method. The strain output of a test using a rosette gauge is based on the principal strain method. To compare the output of a CAE simulation to a test, the “strain-transformation” must be used.

3. Rosette Strain Gauge 

A rosette strain gauge can be used to capture multi-directional strain fields and determine the principal (ie, largest) strains at any given location on a test piece at any point in time.

Strain gauge rosettes combine three co-located strain gauges at specific fixed angles to measure the normal strains along the surface of a test part as shown in Figure 5.

Figure 5: Rosette Strain Gauge consists of three co-located strain gauges. A planar delta rosette is shown installed on a metal bar.

Three strain versus time signals are measured.  An example is shown in Figure 6 below:
 

Figure 6: Three strain signals (red, green, blue) from a rosette strain gauge.

The three strain gauge measurements, Young’s modulus of the material, and Poisson’s Ratio are used to calculate the following nine different values from a rosette strain gauge:

• principal stress 1 (SS1) : the maximum principal stress
• principal stress 2 (SS2) : the minimum principal stress
• principal strain 1 (SN1) : the strain in the direction of the principal stress 1
• principal strain 2 (SN2) : the strain in the direction of the principal stress 2
• angle (AG) : the angle from strain 1 to the principal axis
• shear stress (SH)
• engineering shear strain (SNSH) : corresponds to twice the shear strain
• equivalent stress (ES) : the equivalent stress according to von Mises
• biaxiality ratio (BR) : the ratio of the two principal stresses

Three actual measurements give at least nine calculated outputs! That’s a three to one return!

4. Delta and Rectangular Rosettes

Rosette strain gauges have two common configurations: rectangular or delta. These configurations simplify much of the math involved in the rosette calculations.

4.1 Rectangular Rosettes

Rectangular Rosettes separate gauges by 45° placing a strain gauge on both the X and Y coordinate axes as seen in Figure 7.

Figure 7: Rectangular Rosette diagram
 

Due to the placement of the gauges, the math for a rectangular gauge is more simple than a delta gauge. With today’s computers, this is not an important criteria to consider when selecting rosette gauges.

The following formulas are used to calculate the nine outputs of a rectangular rosette gauge:

When calculating angle (AG) the N and D conditions are defined as:

4.2 Delta Rosette Gauges

Delta gauges have a wider coverage versus rectangular gauges. The strain gauges are separated by 60°, and the middle strain gauge is aligned with the y-axis as shown in Figure 8.

Figure 8: Delta Rosette diagram

The following formulas are used to calculate the nine outputs of a delta rosette gauge:

When calculating angle (AG) the N and D conditions are defined as:

 

4.3 Planar versus Stacked Rosette

In theory, the individual strain gauges of a rosette should measure at the same point on the part. This is done by placing the gauges in a tight grouping near the rosette center. The two main positioning schemes for the individual gauges in a rosette are called "Planar" and "Stacked":

• In "Stacked" configurations the individual gauges are placed on top of each other at the exact same point.  This is helpful to measure strain fields with large gradients where a small position change results in a very different measured strain value.  A "Stacked" configuration will not dissipate heat as efficiently as a "Planar" configuration.
• In "Planar" configurations, the individual gauges are offset from each other and not located at the same point.  This configuration will dissipate heat well, and is good for measuring strain fields with small gradients.

Both delta and rectangular rosettes can be either planar or stacked.
 

5. Biaxiality Ratio

When doing the calculations for a rosette gauge, a biaxiality ratio can also be calculated. The biaxiality ratio is the ratio of the two principal stresses (SS1 and SS2) as seen in the equation below (assuming |SS1| > |SS2|).

Biaxiality Ratio is the ratio of Principal Stresses

The principal stress with the largest absolute value is always put in the denominator so that the biaxiality values are always between -1 and 1. The biaxiality ratio can be any value between -1 and 1:

• 0 : If the biaxiality ratio is 0, the stress/strain field is uniaxial tension or compression
• -1 : If the biaxiality ratio is -1, the stress/strain field is pure shear stress or strain
• 1 : If the biaxiality ratio is 1, the stress/strain is equal in all directions

The biaxiality ratio is one of the parameters calculated using the ROSETTE virtual channel calculations in Simcenter Testlab.

6. Critical Plane Analysis

In addition to calculating principal stresses and strains, a rosette gauge can also be used to perform critical plane analysis.

The principal stresses and strains have a magnitude and angle.  The magnitude and angle can change as function of time. In a critical plane analysis, the strain time history is calculated at a specified angle(s). Typically, this is done at 0 degrees, 10 degrees, 20 degrees, up to 170 degrees as shown in Figure 9:

Figure 9: From three measured strains of a rosette (red, blue, green), the strain time history at any angle can be calculated in a critical plane analysis.

Both principal strain and critical plane analyses are useful – one for determining the largest absolute strain (principal) and one for calculating the angle direction with the most potential damage (critical plane).

While the principal stresses and strains indicate the maximum strain a part may see at a given location, it cannot be used to calculate fatigue damage.  The resulting strain time histories of a critical plane analysis can be rainflow counted and translated into damage using material properties.  Using this method, the angle with the highest damage can be determined.  

Critical plane analysis can be performed from either a delta or rectangular rosette strain gauge.

7. Rosette Gauges in Simcenter Testlab

Direct YouTube link: https://youtu.be/DEiqEVPmKcA

Rosette calculation can be performed in real-time while acquiring data (via "Virtual Channels" or post-acquisition using the Time Signal Calculator.

7.1 Real-Time Acquisition: Virtual Channels

Rosette strain gauges can be setup via “Virtual Channels” in Simcenter Testlab (formerly called LMS Test.Lab) to be calculated while acquisition is in progress.

In Simcenter Testlab Signature acquisition, change “Channel setup” to “Virtual Channels” using the pulldown in the upper right of the “Channel Setup” worksheet as shown in Figure 10.

Figure 10: Virtual Channels in Simcenter Testlab Channel Setup worksheet.

After selecting “Virtual Channels” a formula area appears at the bottom of the Channel Setup worksheet as shown in Figure 11.

Figure 11: Function Selection in Virtual Channels via the "f(x)" button

Click on the “insert function” button with the “f(x)” symbol and select “Strain gauges” group of functions. Then, select the type of strain gauge that is being used in the test: delta or rectangular.

In the “Edit formula arguments” menu, enter the three channels of the Rosette strain gauge, Young’s Modulus and Poisson’s ratio (Figure 12).

Figure 12: “Edit formula arguments” menu for Rosette gauge

Note: Young’s modulus is 210000 MPa for a typical steel.

Press the ‘OK’ button on the ‘Edit formula arguments’ menu when finished. Nine new rosette time calculation channels will be created in the resulting time history file as seen in Figure 13.

Figure 13: Rosette Time Calculation channels in Time File

7.2 Post Processing: Time Signal Calculator

Rosette strain gauge calculations can also be performed offline (ie, post-acquisition) using the Simcenter Testlab Time Signal Calculator. An example calculation of maximum shear strain is shown in the next section.

8. Maximum Shear Strain in Simcenter Testlab

The maximum shear strain is not calculated by default in Simcenter Testlab.  To calculate it, the following formula can be used in conjunction with the ROSETTE calculation in the Time Signal Calculator (Figure 14):

Figure 14: Formula for maximum shear strain using output of ROSETTE calculation in Time Signal Calculator.

The maximum shear strain is the difference of the principal strains (SN1 and SN2) divided by two. In the example above, the channel names (Rosette_SN1 and Rosette_SN2) are used.  Channel numbers can be used as well.  In this case, the channel numbers would be CH4 and CH5.

See the knowledge article Time Signal Calculator Tips! for more information on using the Time Signal Calculator.

9. Rosette and Critical Plane Analysis in Simcenter Testlab Neo


Direct YouTube link: https://youtu.be/Idmn8b6ZuKk


The Simcenter Testlab Neo Process Designer has two methods for analyzing rosette strain gauges:

• Rosette (0-45-90 and 0-60-120 degrees): Calculates principal strain, principal stress, shear strain, shear stress, angle, biaxiality ratio and more from rosette strain gauge data.
• Critical Plane (0-45-90 and 0-60-120 degrees): Calculates strain time histories from 0 degrees to 170 degrees in increments of 10 degrees using rosette strain gauge data.

A single rosette strain gauge contains three channels of strain data (Figure 15).  

Figure 15: Strain data collected from a rosette strain gauge with 0-45-90 degree orientation.

Each channel of a rosette strain gauge is from a different degree orientation.

9.1 Getting Started

After opening Simcenter Testlab Neo, go to “File -> Add-ins”.  Turn on “Process Designer” and “Interactive Analysis” add-ins as shown in Figure 16:

Figure 16: The “Process Designer” and “Interactive Analysis” add-ins are needed to perform either rosette or critical plane analysis in Simcenter Testlab Neo.

Click on the tab labelled “Processing” at the bottom left of Simcenter Testlab Neo (Figure 17).  

Figure 17: The processing tab of Simcenter Testlab Neo allows data to be selected for processing.  A custom data analysis process can be defined by combining methods from the method library.  Both input and processed data can be displayed.

This opens the processing workbook which has areas for:

• Data Selection: Allows selection of rosette data to be processed.
• Process: Methods are connected to define data processing.
• Method Library: Catalog of methods that are available to define data processing.
• Properties: Set parameters in individual methods.
• Display: View both input data and processed results.

9.2 Selecting Data

Time data acquired by a rosette gauge can be selected for processing.  This is done in the Data Selection area by one of two means (Figure 18):

• Active Project: Under “Testlab” in the data navigation tree, choose the run in the currently active project.
• This PC: Under “This PC”, navigate to a directory that contains the time file.

After finding the desired time data, right click and choose “Add to Input Basket”.

9.3 Defining Process

In the method library, scroll to the bottom and find the “Combined Methods” section.  Drag and drop the appropriate rosette method (based on angle), into the Process area and connect it to the input basket (Figure 19):
Highlight the rosette method, and adjust the processing parameters in the Properties area (Figure 20): The 0-, 45-, and 90-degree channels need to be identified properly.  This is done by one of two methods:

• Channel ID: Set the field to the appropriate channel number (C1, C2, C3, etc) OR
• DOF ID: Use wild characters with partial names if desired, for example *45* might be used to identify the channel name for the 45 degree position.

The channels only need to be defined by one of the two methods above. The method not being used can be left blank.

Enter the Young’s modulus and Poisson ratio to get proper stress results.

The rosette method can only be used to calculate data from one rosette.  If the data set contains multiple rosettes, create the identical number of result methods, and use the Pass method to send one rosette to each one.

When finished creating the process, execute the Process by pressing the Run button (Figure 21).
 

Enjoy measuring rosette strain gauges! Further questions? Email nicholas.divincenzo@siemens.com  or contact Siemens Support Center.
 

More Fatigue and Durability links:

• Index of Testing Knowledge Articles
• History of Fatigue
• Stress and Strain
• Strain Life Approach
• Neuber's Rule
• Calculating Damage with Miner's Rule
• Rainflow Counting
• Mean Stress Corrections and Stress Ratios
• Difference between 'Range-Mean' and 'From-To' Counting
• Some Thoughts on Accelerated Durability Testing
• Goodman-Haigh Diagram for Infinite Life
• Introduction to Strain Gauges
• Measuring strain gauges in Simcenter Testlab
• Rosette Strain Gauges
• Digital Image Correlation for Static Testing
• Calculating Damage in Simcenter Tecware Process Builder
• Setting up a SN-Curve in Simcenter Tecware
• Simcenter Testlab Neo: Strain Life Method
• Simcenter SCADAS
• Simcenter SCADAS Mobile and SCADAS Recorder
• Simcenter SCADAS RS for Testing in Harsh Environments
• Strain Gauges: Selecting an Excitation Voltage
• Simcenter Testing Durability YouTube Playlist

Other Articles:

• What is an order?
• What is torsional vibration?
• What is sound power?
• What is a Power Spectral Density (PSD)?
• Modal Assurance Criterion (MAC)
• AC versus DC Coupling - What's the difference?
• What is a SN-Curve?