# 2" Universal Axis

## Contents

# Introduction

Goal is to make belt-driven heavy duty CNC to fit with the Universal Axis concept which is intended to be used for small and large machines at OSE. This will be challenging, so another version with lead screw or ball screw will have to be used if extra strength is required. However, it is useful to do a systematic study of precision based on the number of belts used - and based on using wide, 3D printed belts. Stretch per force applied will be the critical data that will determine the potential accuracy in large force (1000 lb and up) applications. Precision grinding - which requires less force - is still expected to be feasible using simple 3D printed belt systems.

# Calculations

- Lead accuracy - motion accuracy per foot - [1]. 0.004" per foot for regular, 0.001" for precision, and .0005" for precision ground.
- Here is 0.003" per foot accuracy bar - [2]
- 3/4" is 0.009" per foot accuracy. Only $4/foot - [3]
- 1/2", 5:1 acme - 0.009" per foot lead accuracy - [4]
- Ultra precision lead screw - 0.0006" per inch accuracy. This is much worse than above.
- Centralizing acme thread - is called precision acme - it has less radial play. [5]. Classes are 2C, 3C, 4C.

## Force

- Using the Universal Axis, but with 2" shafts, allows rod deflection precision of 1/2 thousandth of an inch for a 2 foot by 2 foot working bed. By quadrupling dual belts, only 6 mm wide for low cost - a lateral cutting force of 100-200 lb is sought for heavy duty machinine
- Ball screws are 5000 lb for 16 mm ball screw static force, 2300 lb dynamic force

## Ball/Lead Screws + Nuts

- Ball screws are good for 1 thousandth accuracy over 1 foot of distance according to Wikipedia [6]
- Super high precision is obtained by using Invar. It costs $30/foot for 3/8" shafts.
- Lead screws can be used with balls or non-ball nuts - [7] - 3/10 thou per inch runout

## Notes

- Acme nuts can be anti-backlash - 2 halves separated by a spring.

- Comparison of ball to lead screw - [10]
- Comparison of ball to lead to acme -
- Cost of acme screw is slightly higher than ball screw -[11]. Is this in general, or just for this specific company?
- Terminology - it appears that acme screws are used interchangeably with lead screws - which have no balls, whereas ball screws have balls
- There is a patent for a lead screw where the lead screw nut compensates automatically for wear to keep the desired stiffness. See ActiveCAM - [12]
- OpenSCAD library for acme threads - [13] - plus other library parts - [14]

# Notes

Using the Universal CNC Axis - http://opensourceecology.org/wiki/Universal_CNC_Axis - but enlarged so it's using 2" steel rods, and metal plate is also used to clamp the 3D printed parts together- we would like to do heavy duty CNC.

So that means about 200 lbs of lateral force on the tool head. Can we get to 200 lbs of lateral force with a belt drive, with 1/2 thousandth of belt stretch over a 2 foot working bed? That's how much deflection the 2" rods would have for a 2x2 foot working bed of a CNC machine.

Fig 7 here shows 3.35 in-lb per mm of belt width for GT5 belt, at high speed. We need low speed - GT5 has tooth jump torque of 300 in-lb. So it looks promising for heavy duty CNC. However, Fig 10 seems to be the critical one - showing that only GT2 belts give sub-thousandth positioning accuracy. Figure 8 shows max tooth jump torque for a 5 mm wide belt to be 9 in-lb for a small pulley (20 teeth). Extrapolated linearly to a larger pulley, say 40 teeth, or 1" diameter - that would be 18 in-lb. And further extrapolating to 12 mm wide belt - 43 lb. These are common belts. So if we have 5x gear reduction - we get our 200lb tool head torque. But - would a GT2 belt hold this much torque without breaking? I can't find any data on stretch or force limit of GT2 belts. Sounds like we should be able to get about 100 lb from a 1" width of GT2 belt. So doubling up the axis gets us to 200 lb - it should be doable. Thoughts?

Take tooth jump torque of GT2 at 9 in-lb per 5mm wide belt. Thus, 1" of GT2 is 45 lb. Dual axis is 90 lb total. Assume that tooth jump torque is within working limit of belt, and belt can go higher. So at minimum we have 90 lb of tool torque guaranteed even with GT2 belts. We can multiply belts as needed, given the OSE D3D Belt tensioner which is very simple. So GT2 belt-driven heavy duty CNC is possible from first principles.

Cost - 2" shaft is $15/foot. Each axis costs $60 in steel, $40 in bearings, $10 in belt, and $16 in stepers. Rest is 3D printed. As such we have axis cost of about $150 for a minimum of 90 lb cutting torque machines. The limit of the GT2 belts would be their max working capacity.

# Sourcing

## Rod

- 2" A36 steel (lower quality than Cold Rolled Steel) - $13/foot for 10' section - [15]
- 2" 1018 Cold Rolled - $20/ft- [16]
- 0.003" per foot accuracy - Rolled Threads Unlimited - [17]

## Screw

- 1" centralizing acme - $16/foot - [18]

# BOM

- Axes - 32' total (8 rods of 3', 4 rods of 2' for z) - $640
- Frame - 1/2"x6"x6" angle -$20/ft; 4x4x1/2 tube - $30/ft - 36 ' - $720 or $1080
- Oil-impregnated 2" bushing - 8000 lb+ lateral force capacity- $9.41 - [19]

## Precision Drive

- $25/meter for ball screw only -
- 1" ball screw set - $200/2 meter with complete set - [20]
- .6" ball screw complete set, 2 foot travel - $50/foot
- $5/foot for 1" acme screw - [21]

# See Also

# Useful Links

- This one says only 25 lb working tension of GT2 belt per inch. But, breaking strength is almost 700 lb per inch, so working tension << breaking strength. To press the limits, operating at 1/10 the breaking strength appears adequat as a 10x safety factor. This means 68 lb per inch of belt - [22]
- Big Gates manual - [23]