Description

1 SPRING RATE

IMPORTANT: Use IPS units for ALL answers on this assignment. Include units on ALL answers. SolidWorks gives mass in units of pounds.
1. What are the Young’s Modulus and Shear Modulus of Plain Carbon Steel in IPS units?
Property Value Units
E 30457924.91 psi
G 11457981.28 psi

2. What is the calculated spring rate 𝑘 using the analytical equation?
k = 71.26 [lb/in]
3. What is the resultant reaction force on the end of the spring from the simulation?
Fr = 1.47 lbs.
4. What is the spring rate 𝑘 found using the Finite Element Method?
k = 73.5 lb/in
5. Assuming the FEM solution is correct, what is the %error of our analytical solution?
error = 3.04%
6. Fill in the mass (in pounds) and density values below:
Value Units
Spring mass 0.3343 pounds
Material density 0.2818 pounds / in^3

2 MODAL ANALYSIS

1. What is the calculated mass of the sphere in pounds?
m = 3.9838 lbs.
2. Using the Mass Properties tool, what is the mass of this configuration (with the sphere) minus the mass of the previous configuration?
m = 3.9834 lbs.
3. What is the calculated natural frequency of the system in Hz? – watch your units!
f = 4.3 Hz.
4. What is the frequency of the axial stretching and compression mode of the spring mass system found using SolidWorks Frequency analysis?
f = 13.407 Hz.
5. What is the frequency associated with the rotation of the sphere?
f = 12.655 Hz.

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MEMS 3110 Machine Elements Lab Worksheet LAB 6
3 NONLINEAR DYNAMIC STUDY

1. What advantages does the Eigenvalue Frequency study have over the Nonlinear Dynamic study? the eigenvalue frequency study is a more accurate method of determining frequency.
2. What advantages could the Nonlinear Dynamic study have over the Eigenvalue Frequency study?
Although the eigenvalue frequency is a better method for the solution, the nonlinear dynamic model requires less parameters to solve the problem thus allowing a faster run time than the eigenvalue frequency.
3. Paste the plot of your simulated spring-mass system displacement using the provided Matlab code (label your axes):

4. What is the roughly estimated frequency of this system and how does it compare with the value obtained using modal analysis?
The estimated frequency is 1/P so f = 25. It is a higher frequency, roughly double that from the modal analysis.

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