Measuring Displacement using Optical Methods
Delko van der Walt
Displacement measurements can be of high importance in the vibration industry. The equation of motion of a single degree of freedom system can be expressed as.
M x’’(t) + C x’(t) + K x(t) = F(t)
With a known displacement this equation can be used to analyse system constants such as the mass, damping and stiffness of the system. These unknowns, if determined accurately, can improve any finite element analysis. Measuring displacement can be difficult especially at high frequency when using contact measurement solutions such as a Linear Voltage Displacement Transducer (LDVT) or a potentiometer. Non-contact laser measurements have the advantage of high sampling frequencies and no added friction or mass. In this test, the aim is to obtain the displacement of a transient event and to verify it with another source of measurement like a laser.
An electromagnetic shaker was used to simulate an event that has a change in displacement. Because of the rapid motion of the armature of the shaker, non-contact measurements are preferred because it does not affect the capacity of the shaker. The shaker was set up to give out a shock pulse, which simulates any type of event that can be captured by a high-speed camera. A non-contact triangulation laser was used to enable a direct comparison between these two methods of measurements. High-speed camera analysis can be advantageous over the laser because of its different applications, and measurement range.
Test setup and operation
The setup is a standard closed loop vibration control. The electromagnetic shaker was controlled by a vibration controller which acts as a data acquisition system and a signal generator. The Vibration controller was used to excite a classic shock pulse. The laser analog output was recorded on the vibration controller so it could be compared with the TEMA analysis.TEMA is a market leading advanced motion analysis software which enables motion analysis and enables the user to obtain measurements by analysing video footage. The video was triggered using a mouse click trigger, with an acquisition frequency of 1000 Hz.The camera that was used was an NX4-S1 by IDT Vision. To Compliment this camera, a 50mm f1.4 Kowa lens was used which make use of a c-mount interface. The lighting used was the constellation 120 kit manufactured by IDT vision, which enabled frame syncing with the camera. The markers were used to track the movement of the accelerometer. The motion plane was defined as a single parallel axis, and the distance between the markers was defined. The event was captured using a small pre-trigger. The data from the laser was exported to .csv format and imported into Tema for comparison. The curves can be compared by using the compare curve setting.
Data and Results
The displacement of the 2D tracking using quadrant symmetry can be seen in the purple graph. The shape is typically what can be expected when measuring the displacement of a classic shock pulse. The maximum positive value of around 2mm can be seen. The red curve shows the calculated displacement of the laser. The Laser and the 2D tracking positive direction differ, and thereby the laser results had to be inverted to have the same sign convention. It is very clear the results looks very similar. The 2D tracking, as well as the laser, give very low noise, although the sampling frequency of these methods of measurements appears to be quite high. This states that the analysis done by Tema is correct and accurate as with those of the laser. This means the Tema analysis can be used in the field to calculate the displacement of any event using quadrant symmetry markers given the resolution zoom lightning and acquisition rate is sufficient.
Non-Contact displacement measurements are becoming more popular because it doest not change the load path of the component in question. The laser that was used, ILD 2300-50 has a very high sampling rate typically 20 kHz. With a measuring range of 50mm, only 5mm were used. This laser is manufactured by Micro Epsilon. This means that the laser used was more than adequate for the job. Since most metallic surfaces are reflective, the strobing of the light did influence the laser performance. When the lighting was in a certain direction, the laser count detects the reflecting beam. Tema is a less advanced motion analysis package, for more advanced features, the Track eye package can be used, also offered by Image systems. Tema does need to interface with the camera and needs a normal video file such as .MP4 or .AVI. This indicates that even small machine vision cameras such as the offering from the Basler ace product range can be used for motion tracking analysis.