Strain Measurement
As previously mentioned extensive strain gage experience has been obtained. This section describes some capabilities in more detail.
Any Gage, Anywhere, Anytime
Shock Wave Engineering offers a mobile, infield strain gage application service. This requires the application of strain gages in difficult to reach positions. The photo below shows strain gages being applied to the underside of a trailer axle. A steel plate was used to protect the strain gage from rocks and other material being dumped.
Tower testing required the application of gages 50 m above ground. The photo above shows the skip used to access the gage locations. The skip was positioned using a tower crane. Windy conditions added an additional challenge!
The photo above shows the view of the ground 50 m below the gage location.
The photo above shows surface preparation for the application of gages to the rear plate of a bottom dumper. The work had to be conducted while positioned between the open jaws of the bottom dumper. To prevent potential accidents a large steel beam was constructed to hold the jaws open against the force of the pneumatic cylinder.
Kingpin instrumentation and Calibration
This section describes some detail of strain measurements on a bottom dumper. General information about the project is available here. The forces being applied to the structure were required. This included the lateral and vertical forces being applied by the horse to the kingpin i.e. the lateral and vertical forces needed to be measured separately. In this case the kingpin was attached to a longitudinal beam shown in the figure below.
Strain gages were applied to each side of the beam on the top and bottom. The gages on each side were combined into a half bridge for the left and right hand side and measured separately. The sum of the left and right hand side half bridges was proportional to the vertical force and the difference between the left and right hand side was proportional to the lateral force.
In order to calibrate the measured strain into a force, a block and tackle was used to apply a lateral force to the structure. The force was measured using a load cell. The figure below shows the linear relationship between the applied lateral force and the measured strain.
There was a negligible sensitivity of the measured vertical force to the applied lateral load as shown in the figure below. The base value is due to the self weight of the bottom dumper on the horse.
The bottom dumper was loaded using a front end loader. The figure below shows the measured vertical load as the front end loader filled the bottom dumper with a number of loads. The vertical load was calibrated using a weighbridge.
The instrumented and calibrated kingpin was then used to measure the actual loads while the vehicle was moving. The loads were correlated with GPS data. The first two figures below show the GPS position and heading change when the bottom dumper was turned through 90°. The lateral loads required to turn the bottom dumper are shown in the third figure.
Stress Wave Drag Balance with a 20 microsecond Response Time
This section describes the technique used to develop a force balance with a 20 micro-second response time. The requirement for such a balance is described here. Conventional drag balances require that the aerodynamic forces are in equilibrium with the reaction forces on the support. However a shock wave moves so rapidly that equilibrium cannot be achieved. To overcome this challenge the sphere was attached to a long bar as shown in the figure below. The shock wave resulted in stress waves propagating from the sphere into the bar. The stress waves reflect within the sphere and only a portion of the energy is transmitted into the bar at each reflection. This results in a finite balance response time. Using the impulse response of the bar and a mathematical method known as deconvolution the original input forces created by the shock wave could be determined (the stress waves are the convolution integral of the balance impulse response and the input force) i.e. deconvolution is a post processing technique used to reduce the mechanical response time of the balance.
The four figures below are useful for gaining an insight as to how the deconvolution process is performed. The first figure shows a typical impulse response of a balance. The second figure shows the response of the balance to an arbitrary input force. Note that at time = 0 the force = 0. At time = 1, the output is divided by the first value of the impulse response to get the force at time = 1 as represented by the solid vertical line in the second figure. Then this force is multiplied by the impulse response to yield the dashed line seen in the second figure. This is the effect of the force applied at time step 1 on future time steps. At time step 2 the effect of the force from time step 1 is subtracted from the balance output. This value is then divided by the first value of the impulse response to yield the force at time step 2 (see the third figure). This force (represented by the solid vertical line at time = 2 in the third figure) is then multiplied by the impulse response to determine its effect on later time steps (represented by the dashed line starting at time = 2 in the third figure). At time step 3 the effect of the force at time step 1 and 2 is subtracted from the balance output. This value is then divided by the first value of the impulse response to yield the force at time step 3. This process is repeated until the force at all time steps is known. All the forces are then represented together as shown in the fourth figure.
Verifying the results of a normal force balance is very simple. A known load is applied and this is checked against the output of the balance. However, in the case of the Stress Wave Drag Balance the known load needs to be applied within the testing time of the balance. This is a very difficult task. In order to validate the results a special validation rig was built. Shock waves are ideal at providing an instantaneous step up in pressure. This pressure can also be measured easily using dynamic pressure transducers. However, since the purpose of this project is to measure the force as a shock wave moves over a sphere there is no way of verifying the balance in its current configuration. Instead the sphere was replaced with a cylinder. This provided a flat surface for the shock wave to reflect off and thereby produce an instantaneous force increase. If the cylinder was placed in the test section of the shock tube then air would flow past it and reduce the stagnation pressure on its front face. This would result in the known force only being applied for an instant. To overcome this the end plate of the shock tube was modified. A hole was drilled through it and the cylinder was pushed through the end hole such that its front face was flush with the inside of the shock tube. This arrangement can be seen in the figure below. The direction of shock wave propagation can be seen in the figure. When the shock wave hits the end wall of the shock tube it reflects and produces a step up in pressure which acts on the face of the cylinder. This pressure stays at a constant value for far longer than the testing time of the balance. There was a small annular gap between the cylinder and the end plate. This was to eliminate friction between the cylinder and the end plate without being large enough to allow significant leakage of air. Unfortunately the gap was not quite large enough and some friction did occur.
The impulse response using the cylinder would be different to that of the sphere. However, it was desirable to keep the two as similar as possible. To achieve this, the length of the cylinder was chosen to be the same as the length (i.e. diameter) of the sphere. The diameter was also chosen such that the mass of the sphere and cylinder would be the same.
A pressure transducer was also installed in the end plate such that its active face was flush with the inside face of the end wall. This transducer monitored the pressure rise from the shock wave. The pressure was multiplied by the area of the cylinder to determine the force acting on the balance.
The figure below shows a typical result from the validation testing. There is always a constant percentage error present due to the friction. Despite this, there is good agreement between the balance and the pressure transducer. These results also show that the balance output has an error of approximately 20% and a 20 microsecond response time.
The figure below shows the difference between the raw data and the deconvoluted data. From the raw data it is evident that the response time of the balance is approximately 300 microseconds. Deconvolution reduces the response time to 20 microseconds.
The figure below shows the measured drag (deconvoluted) as a shock wave passes over the sphere.
