Characterization

For our initial analysis we decided to first measure the vibrational response of a drum stick strike on a conventional drumset. However, we first needed to characterize the voice coil given to us by Prof. Gillespie. Below shows how the force provided by the voice coil varies with current. The slope of the line is used as our motor constant (16.74 N/A). The y-intercept of the graph (-1.1287 N) corresponds the weight of the armature and internal friction. A current of nearly 70mA must be supplied to overcome this load. The winding resistance of the motor was measured to be 8 ohms and the inductance was neglected. Damping for a linear motor is exceedingly difficult to measure. Since there armature does not rotate, the conventional measure for damping, observing the oscillation decay, is not possible. The motor came equipped with bearings, and given the weight and orientation of the armature our team decided to neglect measuring damping. Instead damping was left for tuning in the closed loop system.



Next, our team set out to measure the force and oscillation of a drum. This test was done using an ADXL 203 accelerometer and LabView. We encountered some issues here with sampling rates for various components which vibrate at a minimum of 30 Hz to 5000Hz. Our research shows that bass drum have the lowest frequency and the cymbals tend to have the highest. So we decided to test the toms which have the second lowest frequency range of around 50Hz to 2kHz and the snare drum with a frequency range of 70Hz to 2kHz. Our initial problem was that the LabVIEW was not sampling anywhere near the acoustic frequency range output of the drum. Our LabVIEW code was stripped down of all the Express VIs in an effort to run faster. Our final LabVIEW, which achieved sampling rates of 1 kHz (the maximum allowable for computer sampling) is shown below. Prof. Gillespie had mentioned using a microphone and the PCs internal sound card to capture data at an even higher sampling rate. However, the changes to our VI seemed to work fairly well for the low frequency drum components.



Eventually, after many trials and error we were able to achieve a sampling rate close enough to the frequency of each drumhead. The following plots show the response we recorded and imported into Matlab for analysis. Data was captured on three axes, where the Z axis was orientated perpendicular to the drum membrane and the X and Y axes fall in the plane of the drum membrane. Note that similar vibrations were captured in all directions but vibrations in the Z direction are the most pronounced. Our team decided to only replicate the vibrations in the Z direction, since our motor could only actuate in one direction and this was the most important to user force perception.

Then using this data we were able to determine the decay rate and peroid of oscillation. From these values we were able to determine the transfer function below and produce a simulation of an impulse response. The time for decay and peroid of oscillation compares well between the data and the model. The scaling is off because the MATLAB produces and ideal impulse (infinite intestiny, zero pulse duration).