I have trouble with your shorthand as I am not as good in Mathcad as you are. I relate to the longer equation. I know that is not efficient but I am not experienced enough.

The benchmarks are the only spots where I needed a large degree of accuracy. The left and right slopes can generally be anything as long as they go up and then down smoothly. As x = 0, 1 .. 480, 29 is where the curve accelerates upward, 173 is the peak, and 470 is where the curve levels off.

Sorry to say, but the two 'benchmarks' t(i) and v(k) are no good to accurately determine the curve. There are infinite possibilities to create a curve that hits the top u(j) and both t(i) and v(k) with different widths and skewness of the curve.

It will take some time to test yours as I have to use Win10 Virtual Disk to allow use of my Mathcad 11. PTC will not register it anymore as they unilaterally negated their contract with the legal owners of it. So I have a version of it on disk already that WinXP adapted to via the VDisk.

Selecting the best grease for an important job requires knowing some important things. All lubricant applications are the same and not all grease...

In situations where high operating temperatures mesh with a need for effective grease lubrication, choosing the right grease is a critical decision...

I just read up on lognormal distribution and it just so happens that I did choose that equation after much trial and error. So my equation is the lognormal distribution, albeit in an edited state and a longer version than dlnorm.

Is there no variable or other function that could be added to my original equation that would push the left side further left while the peak is allowed to travel to the right; due to the left side and the peak generally moving together? I tried different log bases and many other iterations. Hopefully you or someone else will be able to recognize a possibility.

The curve that uses the three data points in the 2:28 PM Reply looks great but I need data from 0 through 480. Can that worksheet be adopted to use x = 0,1 .. 480?

I could not get your graphs to work and I could not get your equation, g(x), to graph when I entered it in myself either. I got a positive and a negative array of results. The g6(x) graph looked like it could work with a more asymptotic start to it and a start at 0 and and ending at 480. x must equal 0,1 .. 480.

As of now, the starting(blue) and finishing(cyan) points are good. It is the peak(green) that must move to the right without sacrificing the other positions.

In situations where it is critical to make sure these are right, a customer will contact the grease manufacturer and arrange for bench testing of the specific greases in question to confirm these points.

Greases are considered to be compatible if certain specifications of both greases are similar. Some specifications like copper strip corrosion (whether the grease will contribute to corrosion of metal surfaces) or oxidative stability (how well the grease stays together and resists reaction with prolonged exposure to air) are important but don’t affect their compatibility with other greases. But three specifications do play important roles as to whether two greases are compatible.

Please pardon my Mathcad ignorance but I am not familiar with genfit. Can genfit be converted into an equation that will insert into php?

When I tried a dlnorm() fit of the curve on the three points, using a solve block, it (also) found the green dot somewhere on the slope instead of on the top.

You mention that you need asymptotes for the point t(i) and v(k). It would help if they're not exactly zero, but slightly positive.

> The benchmarks are the only spots where I needed a large degree of accuracy. The left and right slopes can generally be anything as long as they go up and then down smoothly.

As you see I had added a few other points to your three before I tried with your function (slightly modified by adding a parameter for vertical offset.

I also arrived at a solution too. I introduced another variable of x into the base of the larger exponent. By doing this I am able to progressively increase the output at the end of the curve in a non-linear fashion and apparently slow the front part of the curve.

What’s the point of doing this? It may be more important than you think. If the two greases are incompatible, you run a much higher risk of grease lubricant failure. What makes greases compatible vs. incompatible? Which ones work well together and which ones don’t?

Whether two different greases are compatible will depend mostly on the compatibility of the thickener used in the two products (although base oil compatibility can also be a consideration). Back in the old days, they used simple soaps and clay as the most common thickeners, and compatibility was easy to determine because you had a lot fewer combinations to consider. Soaps made from simple lithium and calcium were compatible with each other, but not compatible with clay.

Ah, with this kind of shape you will want to use the lognormal distribution. Why? Distribution Fitting - Chemical Yield Analysis

Gary: Why aren't there more data points? If all you require is those three points, than a triangular shaped curved would do just as well! You must have more points if your intent is to find a bell-shaped skewed curve.

One thing that you will see on the chart is that polyurea greases seem to have the most compatibility problems. This may be because polyurea grease can be made from lots of different kinds of components, and react together to form something that falls under the umbrella of being called polyurea. So not all polyurea greases are the same and therefore there’s a lot more variance in their compatibility with other types of greases than you would first suspect.

If f(29)=0 we dont have an asymptotic behaviour as you demanded earlier. Did you mean the the slope at 29 should be zero?

I have no idea why g_ is labeled as "constant" when defining that function and I have no idea why genfit works even though g_ is labeled as "variable" here. I would have expected the undefined error you describe.

The top benchmark is very close but the other two have been squeezed into the middle. Can the left side be pushed back 60 points and the right side be pushed ahead 120 points; to the benchmarks? I did have the ln function in the equation. Please pardon me for not being heavy into the statistical jargon, although I am somewhat familiar with it.

I see that I should also include needing an equation that I can adopt into php coding. I don't know if php will accept dlnorm language?

Incidentally, I didn't choose the lognormal distribution by chance. I know that many biological processes closely match a lognomal distribution (e.g. the length of people), and specifically looked for an indication that chemical processes may be also well modelled with a lognormal distribution. That's where I found the article.

Yes, thats the error in the first call of "genfit" in my sheet (I made a comment about this in the file) and that also was the motivation for adding some (more or less) arbitrary additional points.

Mathcad 11 allows to choose the solving method.... for solve blocks. For genfit() the solving method is Levenberg-Marquardt, no other choice is possible.

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To be able to attach files you will first switch to "Advanced Editor" (upoer right corner of edit window) and then you ar offered the option "attach" at the lower right.

Without seeing the sheet, a distribution function that is often used to mimic many kinds of distributions is the Beta distribution.

If I open the sheet in Mathcad 11 I get an error on the 4th parameter of the call to genfit(): Mathcad claims it is undefined. Closer inspection reveals that g_ here is a 'variable' type, while its definition uses g_ as a 'constant' type. After that is aligned, Mathcad complains that there must be more data points than variables to solve for, which I think is a reasonable requirement.

Would you all inspect my equation and advise me on whether it can be edited to fit the Benchmark dots on the graph. Maybe another variable can be inserted into the equation? If, not, can you recommend a new equation? The curve slopes are not as critically important as the start, finish, and peak positions and values.

I did explain three or four times about the benchmarks but maybe I did not translate and explain them fully. I wish that I had.

Your configuration was close but did not fit. The variable var6 at the end of the equation disrupts the start of the equation. It needs to start at 0 and it CAN end at a non-0 number, as long as it is close to zero(preferably under 5). I was working on this last night. I managed to zero in on my version again but it is still not acceptable.

The situation is more complex today because there are so many more options to make high-performance advanced greases. Below is a compatibility chart that will give you a good idea of which kinds of greases play well with each other and which do not.

The whole thing is VERY sensible, not only concerning the guess values but also concerning the coordinates of those additionally added points.

I finally tweaked it to where I can use it. I appreciate your work as you pushed me to innovate the original equation. Here is the result.

I might also insert a 'node' at the lower left of the curve which would allow me to vary the upward onset; similar to what I did at the end of the curve with the downward finish.

With only start, peak and end its hard to fit a suitable bell curve. You can also fit a perfect paraobola to run through those 3 points.

Hmmmm - thats strange! When I reopen the worksheet save in MC11 format, genfit throws an error (regression does not converge).

You could also use a solveblock with minerr (or even minimize) to get the "optimal" parameters mimizing the sum of squares of the errors. (least squares fit).

Grease compatibility comes into play when grease is being considered for use that may be different than the grease that was previously used. In these situations, the best practice is to clean out as much of the old grease as possible before introducing the new one. This can often be done by dispensing the new grease into the space, where it will displace the old product.

What would you expect from the world’s best wheel bearing grease? The answer to that question might differ from person to person, as no one grease...

It would be much better defined if you had one point on each of the slopes of the curve instead, I'd guess ideally halfway the height so at a rate/level of about 500. But more datapoints would help even better.

I am trying to get a skewed bell curve to represent a chemical in a reaction via an equation. This first bell curve will be subtracted from another skewed bell curve that represents a second chemical in the reaction. I have tried many equation types and have settled on the one that I am currently using. The trouble is that I cannot manipulate the equation variables enough to attain the configuration that is needed.

Here polynomials of third and sixth order. The provide not just an approximation but a perfect fit at your benchmarks and the polynomial of sixth order provides a slope of zero at all three benchmarks. You never answered the question as to if this would be important to you.

That looks great! As I have Mathcad 11, I will copy your variables into my worksheet. Your notation is much neater and organized than mine so with your permission I will adopt your style.

Grease compatibility is a key consideration when selecting a lubricating grease for an application. This is especially important in business and industrial situations where lubricant failure can have a particularly grievous price tag. Getting it right is important because of the cost of getting it wrong.

I have been working very hard on finalizing this issue. I had posted a file earlier(weeks ago) that at that time was going to be the one. Since then I have taken a closer look at a file that Luc posted that back then wasn't close enough to what I needed. I have made his method work great for me. I found that I also needed the variability that his methodology affords. I can easily move the nodes around by changing the node's x,y values.

In other words, if you examine the Worked Penetration, the NLGI Grade under elevated temperature storage, and the dropping points, if the two greases to be mixed have specifications that are close to each other, they’re more likely to be compatible.

You and Luc are impressive with your knowledge of math and Mathcad. I have only infrequently messed with both. The last time I used heavier math was in college in Calculus II, Physics, and Engineering Chemistry. I have since forgotten most of it.

Mixing incompatible greases can have dire consequences. They may react together and cause a separation of the base oil or oils from the thickeners of the two greases. When this happens, the base oil can no longer stay in place and you get a messy situation – oil oozing or running out of the area where it was applied. You can probably guess the potential consequences for the equipment that might follow from this happening.

I added a lognormal function at the beginning of my equation and have gotten very close. I am still tweaking although I feel I have reached the point of diminishing returns for this newer equation. I wish there was another function or variable that I could insert that would move the left slope to the left and move the peak to the right.

There are more than 3 data points; x = 0, 1 .. 480. The 3 points that I call out are only benchmarks made to denote the start, the peak, and the end of the skewed bell curve.