Equations for time varying stress profile segments

[JJPEngr]

About the only difficulty I encounter with ALTA 7 Pro is creating equations to define stress profile segments for time varying stress profiles. Some of our products operate in devices with varying temperature profiles. The straight line segments are easy, but some of the segments are sections of a parabola either ramping up or cooling down. Nothing in the ALTA training addresses these complex profile elements. It would help a lot if Reliasoft could provide some equations or examples to create these segments from known end points of time and temperature. It is a lot of time consuming trial and error to create these profiles, and it has to be done for use level and each accelerated level.

[David]

Hi JJPEngr,

I agree that depending on the profile, determining the equation can be a little difficult and time consuming. The vertex form equation for a parabola is given by:

y= a(x-h)^2 + k

where,
k is the stress value at the inflection point (vertex)
h is the time at the inflection point (vertex)

Depending on the profile, it may be necessary to estimate where inflection point might be based on a segment of the profile so that the equation can be determined. Once the stress (k) and time (h) at the inflection point are known, the time at the begining of the parabolic segment can be used to estimate a. It can be a little difficult to match up both ends of the parabolic segment to the previous and following segments. This is the basic method that I have used in the past and I am sure it is not the only one that would work.

Thank you for the suggestion. Hopefully this will help for now and we can try to put some examples together.

I hope this helps.

[JJPEngr]

David,

Thanks for the basic equation. This seems to work for a decreasing segment such as cool down where initial drop is faster and then levels off to form a parabo;lic segment.

However, I still have difficulty applying it to an increasing segment such as heat up that goes up quickly at first and then levels off at a peak also in a parabolic segment. Does this require a sign change anywhere in the equation?

Thank you

[David]

In the vertex equation for a parabola, if a>0 then the parabola opens upward (like a "U"). If a<0 then the parabola opens downward (upside down "U").

I hope this helps.

[JJPEngr]

David,

Thanks for the aditional clarification. Changing the sign to get the correct orientation for the parabolic segment helps. Guessing the inflection point for the parabolic segment is trial and error, but plotting the result and then tweaking the numbers in the equation up or down to move the segment and make it connect works after several trials. So, overall, I am getting this to work reasonably well, but it is tedious and time consuming.

Ideally, it would be great to be able to import a data plot from Excel and use it to create the stress profile, but I realize that may be a significant challenge to program into ALTA Pro. When using these time varying profiles, they are often based on trial runs of the device to see what actual profile can be achieved. The data is captured and plotted in Excel, and if there was a way to convert that to a stress profile in ALTA Pro, that would help a lot - just an idea for a future enhancement to a great tool.

[David]

I agree that it can be tedious and time consuming, particularly for a parabolic step. Thank you for your suggestion and we will certainly look into improving the interface for creating profiles. Your feedback is greatly appreciated! Good luck with your analysis and if you have any additional questions/suggestions just let us know.

Thanks!

[JJPEngr]

David,

Another complication - what if the segment is part of a sideways parabola, with the "U" open to the right or left and the inflection point at or near the start of the segment? I am now struggling with getting an equation to fit that scenario by rearranging terms in the equation, but no luck yet.

Thanks

[David]

The previous vertex equation for a parabola assumes a vertical axis of symmetry. For a horizontal axis of symmetry (opens to left or right), the following equation is used:

x = a(y-k)^2 + h

The vertex is still indicated by (h, k). If a>0 then the parabola opens to the right. If a<0 then it opens to the left. Additional information on parabolas can be found at http://en.wikipedia.org/wiki/Parabola.

I hope this helps.

[JJPEngr]

David,

Thank you once again for the equation and Wikipedia reference.
In my references I found the equation Y^2=2px for a parabola oriented along the x-axis, but I was having difficulty translating that to time and temperature data from a test run to define the profile.
The form you provided helps a lot.

Unfortunately, using the form for a parabola along the horizontal axis results in a form not accpeted by ALTA 7 Pro. Here is what I found:
Using the form x=a(y-k)^2+h, then t=a(S-k)^2+h; I get t=.02442*(S-1199.81)^2+3300.
Putting this into a form to define stress, S as a function of time t, I get (S-1191.81)^2=(t-3300)/.02442.
Then, converting this to S=SQRT((t-3300)/.02442)+1199.81.
But, ALTA Pro will not accept this form, SQRT((t-3300)/.02442)+1199.81. I get the dialog box:
"The stress function could not be evaluated. Valid input variables are [t] and [T]." But the variable is t.
How can I restate this to get ALTA Pro to accept it?

Thanks

[David]

Hi JJPEngr,

We are currently looking into this. What is the interval in which this segment is to be applied? What are the stress values at the start and end points of the segment?

[JJPEngr]

David,

This is a decreasing parabolic segment opening to the right along the horizontal axis. The vertex is assumed just above the start point of the segment. Time, t is the x-axis, Stress, S, is temperature in deg K on the y-axis.

It is defined by these end points:

S1 = 1183.71 deg K, t1 = 3308 seconds
S2 = 498.15 deg K, t2 = 5344 seconds

My assumed vertex is h = 3300 sec, k = 1199.81 deg K.

Thanks for all your help on this.

[David]

Hi JJPEngr,

Thank you for bringing this issue to our attention. The issue has been corrected and I will be sending you the fix via email shortly. This fix will also be included within the next service release for ALTA.

I apologize for any inconvenience and thank you for your patience.