- March 01, 2007, By Timothy J. Walker, TJWalker & Assoc. Inc.
(Corrected April 27, 2007)
If I have any repeating theme to understanding web handling, it is to follow the stresses and strains. In nipped processes, you need to follow the compressive stress (aka pressure).
What is the pressure in your nip? How does one set of nips compare to another? What if you change roller diameters, rubber hardness, or covering thickness? If you want to double the pressure in the nip, how much do you need to turn up the load?
Most nipped processes aren’t run with the actual nipping pressure in mind. It is rare for anyone to try and calculate the actual force per area that the web endures within the nip contact zone. Instead, most nips are run based on air pressure to loading air cylinders or how many turns of a screw are just right.
When I want to understand something on an engineering level, I usually dig into my past Proceedings from the Intl. Conference on Web Handling (IWEB). For this column, I’m digging into a good paper from the 2001 IWEB by Dr. Keith Good titled “Modeling Rubber Covered Nip Rollers in Web Lines.”
In this paper, three things can be put together to answer most of the questions I posed in paragraph two. First, there is a review of classic Hertzian contact equations relating indentation and contact length of two cylinders. Second, the paper cites a few authors of past research showing how pressure varies in the machine direction through footprint contact length. Third, Dr. Good graphs out data from his experiments confirming a strong correlation to the theoretical equations.
Almost teasingly, this paper shows the trend between nip load (in force per width) and rubber indentation, but not pressure. As with many academic papers, either intentionally or not, some work is “left to the student.”
Sometimes a set of what-if scenarios is better than looking at a complex equation. The table is for nipping steel and 60 Shore A rubber-covered rollers of equal diameters. The tables below show average pressure. In Hertzian contact, the maximum pressure at the center of the nip footprint will be 4/p times higher than the average, or 27% more.
|Average Pressure vs. Diameter and Covering Thickness|
|Pressure vs. ConstantIndentatin (Indentation=10 mils)||Pressure vs. Load (Load/Width=10 lbf/in.)|
|Diameter (in.)||Diameter (in.)|
|0.25||39 psi||39 psi||39 psi||11 psi||8 psi||7 psi|
|0.50||20 psi||20 psi||20 psi||17 psi||13 psi||11 psi|
|1.00||10 psi||10 psi||10 psi||25 psi||21 psi||17 psi|
|Durometer is 60 Shore A (or IRHD). For Compliant Roller on Steel Roller of Equal Diameter|
From these two tables you can see that nip pressure for a fixed indentation or engagement, the pressure is a strong function of rubber covering thickness, but independent of roller diameter. For a given indentation (10 mils), larger diameter nips will have a longer footprint and residence time, but the pressure is constant. It is also interesting to see at a fixed nip load (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 a 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.
Rubber modulus is an exponential function of hardness, so small changes can have a big effect. For a given penetration, the force and pressure will go up directly with modulus. If you hold penetration constant, but decrease hardness by 10 Shore A, the force and pressure will drop 43%. If you increase hardness, they will go up 76%.
If you combine the equations for load per width and contact length, you find that average pressure goes up as a function of load per width to the two-thirds power. Doubling load per width only increases pressure by 60%. If you want double the pressure, increase the load by 2.8x.
If after all this you are interested in the jumbo equations, please contact me and I’ll send them to you.
Timothy J. Walker has 20+ years of experience in web handling processes. He specializes in web handling education, process development, and production problem solving. Contact him at 651/686-5400; firstname.lastname@example.org; tjwa.com.