help on this spring analysis

[cboughton]

Please see the sheet I have attached. Table shows my calculated values. See notes for formulas used and diagram to show application. Something about my calculations does not seem right and I think the error may be in my Solidworks simulation of the deflection. I used a 10 lb normal force to simulate the deflection and used the deflection to calculate the stiffness. From there, I calculated the Force based on the stiffness and the d2 value created when the media is installed. The holding force is the force in the x direction that pushes against the media. Does this method look correct?spring_analysis.doc

[JAlberts]

I cannot comment on the accuracy of your initial deflection vs. load simulation because I am not familiar with nor have used Solidworks and this determination obviously critical to your whole design.
However, one immediate calculation error I see is using F/A formula for calculating the stress in the spring. The length of the spring where the media load is applied is essentially a t thick x .5 wide flat "beam" with its length being the distance between the bend in the center of the spring and tangent point to the circular bend on the lower right. From your diagram it appears your load point is in the center of this "beam" between those two end points. While it is complicated to determine the actual max stress point on your total spring due to its shape, it would appear that the point of contact of the media load on spring is a probable location for the springs maximum bending stress. If that is true, then the stress at that point can be conservatively determined by using the classic formula for a rectangular beam with both ends simply supported and a load at the beam's center point. That formula is: s = 3*F*L / 2*b*d^2 where:
F is the media load (lbs),
L is the length of the beam (in.) (in your case, the above described distance between the top spring bend and the tangent point to the circular bend on the lower right)
b is the spring width (in.) (your stated .5 in)
d is the spring thickness (in.) (.015 or .020 on your table)

I would caution you that assuming this calculated stress as the maximum stress point for your complete spring may or may not correct; and if your load contact is not in the center of the assumed "beam" span then another formula for the maximum stress of the "beam" section is required. The above beam formula basis and it variations can be found in a number of mechanical design reference and Strength of Materials course text books and I would recommend you review those sources.

[wilsonr]

The stiffness will not be linear in this example. As the previous poster pointed out what you essentially have is a beam. If you were to apply that load in another location with the same amount of force you can't expect the same amount of deflection.