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# How to calculate a dynamic load due to changing acceleration at the end of a cantilever?

## How to calculate a dynamic load due to changing acceleration at the end of a cantilever?

(OP)
I am working on an application that involves a cantilevered tube. At one end the tube is fixed to a roller assembly that can move the entire cantilevered tube along another tube that is 90 degrees to the cantilevered tube. Think of a T where the middle I is the cantilever tube and it can move along the fixed rail (see here for a concept http://imgur.com/a/b30re). The cantilevered tube will have another carriage (not pictured) that will roll along it's length that will hold a tool. I want to calculate how much 'whip' will occur at this carriage when it is all the way at the end of the cantilever and it experiences maximum deceleration, stops, then goes into maximum acceleration in the opposite direction. Once I have this maximum load I should be able to calculate the worst case deflection to see if I can live with the results or if I need to stiffen where necessary. The relevant parameters are below. Even a rough simplified estimate will help me immensely since I do not know how to perform this type of analysis.

Effective Cantilever Length: 29 inches
Cantilevered tube cross section size: 2" x 3" x 0.083 wall thickness steel tubing
Total Carriage Weight: 5 lbs
Carriage Length: 4"
Maximum Acceleration/Deceleration: 0.040 G or 40 milligee
Maximum Velocity: 300 inches per minute
Loading Scenario: Carriage is at the very end of the cantilever. The cantilever is moving at 300 ipm then decelerates to a stop at 40 milligee then accelerates to 300 ipm at 40 milligee.

Any input or relevant equations would be immensely helpful!

### RE: How to calculate a dynamic load due to changing acceleration at the end of a cantilever?

(OP)
Is the max load really this low? Intuition would lead me to believe that the load would be much higher.

### RE: How to calculate a dynamic load due to changing acceleration at the end of a cantilever?

As long as your acceleration is correct. Having problems visualizing your mechanism, but if the trolley is required to go from 300ips to 0ips in 29" your acceleration/deceleration is more like 4g's

### RE: How to calculate a dynamic load due to changing acceleration at the end of a cantilever?

This appears to be an X-Y carriage? You haven't given us the tool weight, only the carriage weight.

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