Acme leadscrew vs timing belt getting really high numbers

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Discussion Overview

The discussion revolves around comparing the mechanical performance of an Acme leadscrew and a timing belt system for a CNC project, focusing on the axial force generated by each system when driven by a stepper motor. Participants explore the implications of torque, efficiency, and mechanical advantage in their calculations.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant calculates that a leadscrew with a torque of 30 in-lbs can produce an axial force of 967.7 lbs, which they find excessively high.
  • The same participant calculates that a timing belt system can produce an axial force of 62.67 lbs, which they consider reasonable.
  • Another participant notes that frictional forces at the screw will increase with axial load and seeks advice on how to incorporate this into their calculations.
  • A different participant explains that while the leadscrew provides a large mechanical advantage, it requires many rotations to achieve linear movement, emphasizing the conservation of energy in the system.
  • This participant calculates the energy output of the motor and relates it to the efficiency of the leadscrew, suggesting that the calculations align with the manufacturer's efficiency rating.
  • One participant expresses gratitude for the energy-based approach to solving the problem, indicating a shift in their understanding of the topic.

Areas of Agreement / Disagreement

Participants express differing views on the calculations and implications of mechanical advantage, torque, and efficiency. There is no consensus on the interpretation of the leadscrew's performance or the best approach to account for frictional forces.

Contextual Notes

Participants mention specific efficiency ratings and mechanical properties of the leadscrew and timing belt systems, but the discussion does not resolve the uncertainties related to friction and the calculations involved.

Who May Find This Useful

Individuals interested in CNC design, mechanical engineering, and the analysis of linear positioning systems may find this discussion relevant.

Taiden
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Hey all,

I'm on summer break so my engineering brain is almost completely turned off. So I would not be surprised if I am making some kind of silly error. I'm trying to compare different methods of linear positioning for a CNC project.

------------------------- Part 1

OK, so here's the scenario.

We have a stepper motor that is able to produce 30 in-lbs of torque.
We have a leadscrew whos manufacturers states that 0.031 in-lbs of torque will "lift 1 lb"

(Not used in calculations, but it is a 3/8-12 acme two start with 43% efficiency)

If I do:

30 in-lbs * ( 1 lb / 0.031 in-lb) = 967.7 lbs axial force

This seems astronomically high.------------------------ Part 2

We have a timing belt arrangement producing linear motion by being constrained (from translation) by a drive pulley on the same stepper motor, a free spinning pulley bringing the belt into proper tension, and a cart attached to one "side" of the belt.

The motor produces 30 in-lbs of torque.
The drive pulley has a diameter of 0.900".
The system is 94% efficient.

30 in-lbs * (1/0.450 inch) * 94% = 62.67 lbs axial force

This seems reasonable to me. The answer from Part 1 absolutely does not.------------------------ Part 3

Leadscrew has 0.166 inches of linear movement per rotation
Timing belt assembly has 2.827 inches of linear movement per rotation

The ratio between the two (TB:LS) is 16.87:1 (ignoring efficiency so far)

The ratio between Part 1 and Part 2 (TB:LS) is 15.44:1 (not ignoring efficiency)How is it possible that the linear displacement to angular displacement ratio is vastly different than the axial force to torque ratio? The leadscrew is magically exceeding it's mechanical advantage?
 
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I was ignoring that frictional forces at the screw will increase as the axial load increases.

Anyone know how I can take this into consideration when I go to calculate the axial force produced at the nut with 30 in-lbs of torque at the screw?

Here's the data sheet: nookindustries dot com/pdf/NookInchAcmeScrew.pdf

Page 4 is what you want. On my pdf viewer it's listed as page 21, not sure why.

3/8-12 two start rod with a plastic nut is what we're going for

Thanks all
Luke

PS: sorry for the 10 post link workaround but I figure that's for spam and I need to link to the datasheet for this question
 
Taiden said:
How is it possible that the linear displacement to angular displacement ratio is vastly different than the axial force to torque ratio? The leadscrew is magically exceeding it's mechanical advantage?
Putting torque on a threaded screw provides a huge mechanical advantage. Needless to say, there's a conservation of energy, so although there is a very large mechanical advantage for the lead screw, you have to turn the screw a very large number of times. The screw has to be rotated 12 times to move it just 1 inch.

Take your torque of 30 inch pounds and determine the amount of energy it puts out after rotating 12 times. In other words, your motor is producing 30 inch pounds of torque which is equivalent to a force of 30 pounds, 1 inch from the center line of the shaft. So the total distance the 30 pound force rotates through in one revolution is 30 pounds times the circumference (2" * pi). That gives you 188.5 inch pounds of energy. Multiply by 12 and you have 2262 inch pounds of energy produced. If we use that energy to rotate the screw 12 times, we will have produced some force over a distance of 1 inch. Per your calculation, the screw has produced 967.7 inch pounds of energy, the rest we can assume has been given up as heat due to inefficiency. Now if we divide 967.7 inch pounds by 2262 inch pounds, we get an efficiency of only 43% which is exactly the number given by the power screw manufacturer. Seems to work out! :smile:
 
THANK you for that post. Our engineering professors don't teach us how to solve problems, they teach us how to follow book steps. I never once considered using energy to find the solution but it's obvious now how easy and effective it is. I'm going to look more into this tomorrow afternoon when my brain is awake so I can do it out and follow it 100%

Thank you again
Luke