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.
The Challenges with Single Strain Gauges
In Figure 1, would the single, uniaxial gauge capture the strain field correctly?
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.
In a plane, strain can manifest itself in three ways:
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 γxyor 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).
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.
The Mohr’s circle has the following properties:
Commonly, the normal strain and the shear strain output of a 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.
Rosette Strain Gauge Calculations
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.
In theory, each strain gauge should measure the strain at the same position on the part. This is done by placing the gauges in a tight grouping near the rosette center. Rosette gauges even come in "stacked" configurations if strain needs to be measured on the exact same point due to large strain gradients.
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:
Three actual measurements give nine calculated outputs! That’s a three to one return!
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.
Rectangular Rosettes separate gauges by 45° placing a strain gauge on both the X and Y coordinate axes as seen in Figure 6.
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:
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 7.
The following formulas are used to calculate the nine outputs of a delta rosette gauge:
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 Equation 1 (assuming |SS1| > |SS2|). 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:
The biaxiality ratio is one of the parameters calculated using the ROSETTE virtual channel calculations in LMS Test.Lab.
Rosette Gauges in Simcenter Testlab
Rosette strain gauges can be setup via “Virtual Channels” in Simcenter Testlab (formerly called LMS Test.Lab). In Signature acquisition, change “Channel setup” to “Virtual Channels” using the pulldown in the upper right of the “Channel Setup” worksheet as shown in Figure 8.
After selecting “Virtual Channels” a formula area appears at the bottom of the Channel Setup worksheet as shown in Figure 9.
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 10).
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 11.
Rosette strain gauge calculations can also be performed offline using the Simcenter Testlab Time Signal Calculator.
More Fatigue and Durability links: