Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

Torsional Spring Oscillation: Lab Report for EGR 345 at Grand Valley State University - Pr, Lab Reports of Engineering

A lab report detailing an experiment conducted in the egr 345: dynamics systems modeling and control course at grand valley state university. The report focuses on the oscillation of a torsional spring system, using both theoretical models and experimental data collected using labview. Calculations for the natural frequency, spring constant, and comparison of theoretical and measured values.

Typology: Lab Reports

2009/2010

Uploaded on 02/25/2010

koofers-user-a6m
koofers-user-a6m 🇺🇸

10 documents

1 / 8

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Grand Valley State University
Padnos School of Engineering
EGR 345: Dynamics Systems Modeling and Control
Dr. Hugh Jack
Lab 7: Oscillation of a Torsional Spring
Dale Slotman
Partners:
Brad VanderVeen
Joel Knibbe
Eric VanderZee
Ryan Jeffries
Leanne Newman
10-3-02
pf3
pf4
pf5
pf8

Partial preview of the text

Download Torsional Spring Oscillation: Lab Report for EGR 345 at Grand Valley State University - Pr and more Lab Reports Engineering in PDF only on Docsity!

Grand Valley State University

Padnos School of Engineering

EGR 345: Dynamics Systems Modeling and Control

Dr. Hugh Jack

Lab 7: Oscillation of a Torsional Spring

Dale Slotman

Partners:

Brad VanderVeen

Joel Knibbe

Eric VanderZee

Ryan Jeffries

Leanne Newman

Purpose:

The objective of this laboratory exercise was to study torsional oscillation using

both theoretical models and actual data collected using Labview.

Theory:

Figure 1: General Torsional Spring Model

Given a torsional spring as shown in figure 1, a general response can be

calculated using the equations:

M

 T J

M

and

T

J

A

G

L

where T is the torque applied to the mass,

Jm is the mass moment of the mass,

JA is the area moment of the spring,

L is the length of the spring,

and G is the shear modulus of the spring.

Combining these equations yields the differential equation:

J

M

J

A

G

L

Figure 2: Torsional Spring Setup

Calculations of natural frequency:

Area Moment of the Torsional Spring:

D 0.25 in

J A

2

D

2

4

 

J A 1.596 10

 10  m

4 

Spring Coefficient:

L 30.75in

G

Steel

9   Pa

K

s

J

A

G

Steel

L

K

s 15.328N m

Mass Moment of Inertia for Square Tubing:

Outside_Depth 2.016 in Inside_Depth 1.535 in W .526  m M 4.18 kg

Cross_Sectional_Area Outside_Depth

2 Inside_Depth

2  

Volume Cross_Sectional_Area W Density

M

Volume



Mass_Solid Outside_Depth

2  W Density Mass_Inner Inside_Depth

2  W Density

J M

1

12

Mass_Solid Outside_Depth

2 W

2    

1

12

Mass_Inner Inside_Depth

2 W

2      

J M 0.098kg m

2 

The natural frequency is:

The natural frequency is then:

f

J

A

G

L J

M

f 1.992Hz

2. A Labview program was set up to record a voltage input from a potentiometer.

The program is shown in figure 3.

Figure 3: Labview Program for Accepting Potentiometer Voltage Input

3. The potentiometer was calibrated using multiple readings of angle turned and

voltage output. The relationship between angle turned and voltage output is:

Output Voltage = 0.081*Radians Turned + 0.

4. The data collection rate of Labview was calculated to be 150.3 samples per

second.

5. The torsional spring was mounted onto an overhead beam using a c-clamp. The

potentiometer was connected to the mass by setting it on an adjustable wood base

and applying hot glue to the knob when inserted into the hole on the bottom of the

mass.

Discussion:

The theoretical and measured spring constants are 15.328 Nm and 16.131Nm,

respectively. The theoretical and measured frequencies are 1.992 Hz and 2.067 Hz,

respectively. These values are similar and the small error can be accounted for by

inaccuracies in the properties of the materials. Replacing the shear modulus of the

spring material with 80Mpa yields a theoretical frequency of 2.06 Hz, which matches

the measured yield. Since the steel used in the lab was thin rod, possibly an extruded

rod, the shear modulus may have been increased by work hardening.

The actual response of the system matches the theoretical response almost

exactly. The theoretical and measured responses are graphed simultaneously in figure

Measured and Theoretical Oscillations

Time (sec)

Radial Displacement

Measured

Theoretical

Figure 5: Measured and Theoretical Oscillations

Conclusions:

An undamped theoretical torsional spring system will accurately model a physical

torsional spring. The laboratory exercise showed that both spring constants and

natural frequencies can be calculated using an undamped theoretical system.