## Calculating Static Friction To Eject Parts with Air

In today’s fast-paced world, companies are always looking for ways to do things faster, cheaper, more efficiently without sacrificing safety.

A cereal company had a high-speed system to check the quality of each box of cereal.  When a box did not meet the quality criteria for visual and/or weight, the box would be rejected.  The rejection system that they used was a quick blast of compressed air to remove the box from the conveyor line into a non-conforming bin.  For their first attempt, they tried to use a ¼” copper tube with a solenoid valve attached to a reservoir tank.  When a “bad” box was detected, the solenoid would be triggered, and compressed air would “shoot” the box off the rubber conveyor belt.  The ¼” copper tube can be an inexpensive, common, and easy-to-use device; but they found that the copper tube was very loud (above OSHA limits for noise exposure) and not very effective.  As a note, this company had a safety committee, and they wanted to keep all blowing devices below 80 dBA in this department.  The ¼” copper tube was around 100 dBA.  So, they contacted EXAIR to get our expertise on this type of application.

The cereal company gave me some additional details of the operation.  The box weighed 26 oz. (740 grams) with a dimension of 7.5″  wide by  11″ tall by  2 3/4″ deep (19 cm X 28 cm X 7 cm respectively).  The issue with the ¼” copper tube was the small target area compared to the area of the box.  With any slight variation in the timing sequence, the force would miss the center of mass of the box.  The box could then spin and remain on the conveyor belt.  This would cause stoppage and disruption in the system.  They asked if EXAIR had a better way to remove the defective boxes.

I recommended a model 1122, 2” Flat Super Air Nozzle.  The reason for this style of nozzle was for a variety of reasons.  First, we needed a larger area to “hit” the box.  This Flat Super Air Nozzle has a width of 2” versus the ¼” copper tube.  This increased the target area by 8 times.  So, any small variations in time, we could still hit the center of mass and remove the box.  The second reason was the force rating.  The model 1122 has a force of 22 oz. (624 grams) at 80 PSIG (5.5 bar).  This is slightly under the 26 oz. (740 grams) weight of the cereal box, but we are just sliding the box and not lifting it.  If we can overcome the static friction, then the box can be easily removed.  With Equation 1, we can calculate the required force.

Equation 1:

Fs = ms * W

Fs – Static Force (grams)

m– Static Friction

W – Weight (grams)

From the “Engineering Toolbox”, the static friction between rubber and cardboard is between 0.5 to 0.8.  If I take the worse case condition, I can calculate the static force between the belt and cereal box using Equation 1:

Fs = 0.8 * 740 grams

Fs = 592 grams

The model 1122 has a force of 22 oz. (624 grams), so plenty enough force to move the box from the rubber conveyor belt.

The third reason for this nozzle is the noise level.  The noise level of the model 1122 is 77 dBA, well below the safety requirement for this company.  Noise levels are very important in industries to protect operators from hearing loss, and the model 1122 was able to easily meet that requirement.  I added an additional reason for recommending the 2” Flat Super Air Nozzle; compressed air savings.  Companies sometimes overlook the cost when using compressed air for blow-off devices.  In this comparison, the ¼” copper tube will use 33 SCFM (934 SLPM) at 80 PSIG (5.5 bar) while the model 1122 will only use 21.8 SCFM (622 SLPM).  This is a 33% reduction in compressed air; saving them money.

At the intro, I mentioned that companies are looking to do things faster, cheaper, more effective without sacrificing safety.  For this company, we were able to increase production rates by removing every cereal box from the conveyor belt.  We also saved them money by reducing the compressed air requirement as well as keeping it safe by reducing noise.

If you have an application that needs products to be moved by air, you can contact an Application Engineer at EXAIR to help you with a solution.

John Ball
Application Engineer
Email: johnball@exair.com