- June 01, 2007, By Timothy J. Walker, TJWalker & Assoc. Inc.
Mr. Starcevic taught my 8th grade algebra class and was one of my most memorable teachers. He quizzed us every week, and as he passed out our graded results, he would announce with his fairly thick Slavic accent a commentary on your performance for all to hear. If you didn't do so well, you usually got one of two comments, either “That's a red eff” or even worse, “Mr. Walker, that was a bonehead answer.”
Mr. Starcevic may no longer be with us, but if he graded my March 2007 column, Under Pressure (Revisited), I think I'd be hearing about the thickness of my skull. I have been hesitant to print equations or calculations in this column due to just this possibility, but my eagerness to share a valued concept gave me the courage to share some results of my analysis of how to combine nip load and footprint calculations to find nip pressure.
Fortunately, an alert and insightful reader spotted my mistake and sent me an email. Paul Alexander an engineer for Miasolé, a thin-film solar cell manufacturer in Santa Clara, CA, wrote “What jumped out at me was the values of pressure in the table…specifically, that at constant load, pressure appears to increase with increasing roller diameter. For the general case with rolls of a solid single material, pressure is inversely proportional to (radius). Does the rubber cover change this relationship?”
Paul is correct about the relationship with solid materials, essentially what is considered Hertzian contact, and he is also correct that my table had an error. His instincts served him well, and I thank him for sending me a note. In answer to his question, there is a difference between solid rollers and rubber-covered rollers. The relationship among indentation, radius, and pressure is much more convoluted.
Errors are human, and I am definitely human. Once printed, an error looks much larger, especially when it goes out to tens of thousands of readers. My mistake was not in my equations but in my spreadsheet. To find average pressure, you simply (ahem) divide the nip load per width by the footprint length. These equations are quite cumbersome, including many fractional powers.
In my spreadsheet, I calculate load per width and footprint and divide one into the other to get average pressure. My spreadsheet error had new load calculated with new diameter but calculated the footprint from the wrong diameter, thus getting the pressure value wrong. (Oh, dopey me!)
Lucky for me, my spreadsheet errors affected both tables and one paragraph of my March column. The corrected column is online at www.pffc-online.com, but here are the main changes.
For a fixed indentation or engagement, nip pressure is a direct function of rubber covering thickness but independent of roller diameter. If indentation is fixed, larger diameters don't change nip pressure. The main difference with larger nips is it will take more load per width to get to the desired pressure and indentation, and larger nips will have longer footprints and longer residence time in the nip for a given speed.
For a fixed nip load (e.g., 10 PLI), there is an interaction of covering thickness and diameter on pressure. If you run your nipped process by load, which many people do, a lab machine with 0.25 in. of rubber on a 3-in. roller will create the same pressure as a production machine with 0.5 in. of rubber on a 12-in. roller. In other words, to keep pressure vs. load constant, if you double the covering thickness. you need to quadruple the roller diameters.
Several readers followed up on my offer to send these equations out by email. This offer still stands with a nice PDF file of equations and graphs ready for anyone send me a request. I appreciate the interest this column generated, and I'm glad that Paul wrote me and didn't worry about a “shoot the messenger” response.
Maybe now I can re-earn the remark Mr. Starcevic saved for my good performances. He'd say “That's why your father calls you son…you're so bright.”