Session: 09-01-01: Curriculum Innovations, Pedagogy and Learning Methodologies

Paper Number: 69500

Start Time: Monday, 11:45 AM

69500 - Using Wireless Pasco Smart Carts to Demonstrate Vibration Principals 

In a typical vibrations course, students learn mathematical models to predict the motion of vibratory systems. Often, students have trouble visualizing what they are calculating with the equations. The goal is to have a visual example of the motions that the students calculate. Because of in-person meeting restrictions, demonstration experiments were recorded before class time, and the analysis was also completed before class.

The PASCO wireless smart cart is a great tool in creating demonstrations. The cart provides a Bluetooth link to a computer, sending position measured from the wheel encoders, acceleration from a built-in accelerometer, and force from the connector on one side of the cart. With wireless data transmission, accurate position and force information are easily read by the computer and analyzed.

With the force sensor and wheel encoder measurements from the cart, the spring constants of the springs can be determined, and the damping coefficient from the magnetic damping element. These can be used to predict the transient motion of the cart. From the log-decrement response, students can calculate the damping ratio and natural frequency and compare values to those calculated from the measured forces. From the force sensor measurements, the cart's position can be calculated when the cart is flipped to demonstrate transient vibrations with Coulomb damping. Also, the effect of changing mass, stiffness, and damping coefficient on the natural frequency and damping ratio can be observed.

For one degree of freedom forced vibrations, a second cart can monitor the input to the system. The PASCO mechanical oscillator pulls the input cart in an approximate sinusoidal function. The input cart was connected to the output cart by a spring, forcing movement from the input cart motion. From measurements of the input and output positions, the magnitude of the input and output can be calculated along with the phase difference between the two. This can be compared to the theoretical response equations for magnitude and phase.

For general periodic input problems, the higher frequency components of the input from the mechanical oscillator and the cart's output can be determined using an FFT analysis. The system frequency magnification factor was seen in both the fundamental cart frequency and the higher frequency components of the input. Runs were performed at different frequencies to demonstrate the number of higher frequency terms necessary based on the natural frequency and damping ratio of the system.

To demonstrate the convolution integral for a nonperiodic input, the input cart was moved by hand, while the position and force on both carts were recorded. The output motion was calculated by numerically integrating the convolution integral in MATLAB for the different times in the experimental data.

For two-degree-of-freedom systems, mode shapes and natural frequencies can be calculated from the measured spring constants. Initial conditions matching the mode shapes were used to demonstrate the two ways that the system wants to oscillate. Also, the transient response can be calculated based on arbitrary initial conditions, and the system can be excited with those initial conditions. Using a shim standardize the magnetic damping height, the response from modal analysis can also be determined. Finally, the mechanical oscillator can demonstrate the forced response of the system at different frequencies.

Overall, the predicted response for all the experiments closely matched the physical response from the carts. This helped students visualize what the equations were calculating and developed their confidence in the equations' validity. Students were surveyed, and students indicated that they found the demonstrations helpful and improved their understanding of the material.

Presenting Author: Keith Hekman California Baptist University

Authors:

Keith Hekman California Baptist University