There are two main questions that we can answer with respect to motor torque and the mechanical advantage of lead screws, 1) What torque motor do you need to lift a particular weight, or 2) What maximum weight will my motor torque be able to lift.

This formula uses Newtons (N) as it's final unit. Use this with the included radius (R) to determine the torque. Newtons can easily be converted to lbs or ounces using online conversions.

Effort = Sf + (Load/(2 x pi x (R/p) x Se))

where:
p = pitch of the screw
Se = screw efficiency = Standard lead screw will be between 20% (.2) and 40% (.4)
Sf = static force. This is the force that is needed to start the movement. The number may be eliminated, but it is good to use a number in the 5 N to 20 N range.
Load = the expected load that the effort will need to carry (i.e., the router and the included axis assembly that the motor will need to lift)
R = radius of the lead screw


This formula is based on the "law of the machine"

The final effort amount with its unit of newtons and R will be the torque. For example, if the effort comes to 100 N (newtons) and the R is .5 inches, then you can assume that the effort is 50 N-in since it would take twice the effort to turn form the one inch mark from the center of the shaft.

Example:

Load = 90 N (20.2 lbs)
R = 1 inch since that is the length from the center of the shaft that the motor is rated
p = 1 inch / 13 = .08 inches

Effort = 5 N + (90 N / (2 x 3.14 x (1 / .08) x .2))
Effort = 5 N + (90 N / (6.28 x 12.5 x .2))
Effort = 5 N + (90 N / (15.7))
Effort = 5 N + (5.73 N)
Effort = 10.7 N = 2.4 lbs = 38.4 oz-in

I am putting the oz-in on the end because the formula considers the distance from the center of the shaft to be one inch.

Therefore, a 425 oz-in motor would be able to lift a 20.2 lb Router with its accompanying assembly. If the assembly and router is heavier, plug in the numbers and determine the effort required.

With a bit of algebra, the formula can be rewritten to find the load:

Load = (Effort - Sf) x (2 x pi x (R/p) x Se)

Another formula that does not consider friction at all:

Effort = (Load x p) / (2 x pi x R)

Lets see if we get similar results:

Effort = (20 lb x .08 inches) / (2 x 3.14 x 1)
Effort = 1.6 / 6.28 = .255 lbs = 4.08 oz-in

The results from both formulas appear to be very small because a 13 TPI screw will have enormous mechanical advantage.

It is evident that the first formula that does consider friction that we are loosely estimating is far more conservative than the second formula. Either way, even the most conservative formula shows that the 425 oz-in motor will handle very large weights. If you are using a lead screw with only two turns per inch, .5 inch pitch, you can determine the requirements with the first formula.

Example for a 10 TPI 5 start (2 turns per inch) lead screw:

Load = 90 N (20.2 lbs)
R = 1 inch since that is the length from the center of the shaft that the motor is rated
p = 1 inch / 2 = .5 inches

Effort = 5 N + (90 N / (2 x 3.14 x (1 / .5) x .2))
Effort = 5 N + (90 N / (6.28 x 2 x .2))
Effort = 5 N + (90 N / (2.512))
Effort = 5 N + (35.83 N)
Effort = 40.828 N = 9.18 lbs = 146.88 oz-in

Customer Response:
thank you so much

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how do i calculate torque of stepper motor if lead screw coupled to motor shaft and load applied by lead screw on plate is 100 kg by vertically

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Pls


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1m 16mmdiameter ball screws calculations


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What is the max load that 2 NEMA 17 stepper motors (spaced 2 feet apart, both will be pushing up on the same gantry) can lift while using a rod with the following specifications T8 OD 8mm Pitch 2mm Lead 4mm for each motor.

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1

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thank you for the reply. I would be really good to know the calculation. The lead screw is 1/2" diameter with 13 TPI. Please provide the calculation for determing the maximum weight motor can handle on Z-axis on book build cnc. And one more question. If I am cutting 18mm MDF with 6mm cutting bit (so 6mm pass), what can be the maximum speed rate of cutting and spindle speed of router? thank you

The motor is helped by the mechanical leverage of the screw. The 425 oz-in motors that are included in the standard electronics combo has very high torque for that type of machine. You will have no problem using that motor for the book machine.

We use that motor for very heavy spindles on the blackToe and blackFoot CNC Machine kits.

You will need to do the mechanical leverage calculation along with the torque of the motor to determine the actual weight it will lift. The calculation will need to consider the type and pitch of the screw and it would also consider the gravity constant of 9.8 m/s/s.

If you need me to determine this formula and work out the calculation based on the screw you are using, please let me know.

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thank you for the reply. I would be really good to know the calculation. The lead screw is 1/2" diameter with 13 TPI. Please provide the calculation. And one more question. If I am cutting 18mm MDF with 6mm cutting bit (so 6mm pass), what can be the maximum speed rate of cutting and spindle speed of router?
thank you

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I received the electronics for book build cnc machine. I need to know how much weight the z-axis motor can hold since my (craftsman) router seems to be heavy. It is 2HP with variable speed

The greenLean vertical CNC is stable enough to handle large-scale production on a daily basis. We use 3/4" MDO plywood, which is equivalent to about 19mm. The gantry is designed to hold a 2.2kW Spindle, with a maximum of 24,000 RPM.

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Hello. I like your vertikal router. Is then router stabil enogh for the need of a Carpenter? Are you using 21mm Plywood or 21mm MDF. What type of spindel (KW) is maximum allowed and whatbis the maximum feed (6mm cutter) in oak. Thank you, Veit

The book (scratch build) will be able to cut at very high rates of speed, but the speed is partly determined by the mechanical setup. Cutting wood is generally recommended between 60-200 ipm depending on the end mill and spindle being used. The larger the end mill (with increased chip load capacity) the faster the feedrate.

If you are using a standard allthread, you will not be able to have these high feedrates. You will need to purcahse high lead leadscrews: https://www.buildyourcnc.com/item/mechanical-leadscrews-leadnuts-!5-5-starts-10-tpi

The stepping motors need to turn 13 times to travel one inch using standard allthread (1/2-13 TPI - threads per inch). The higher lead leadscrews shown in the link provided will move one inch with only two turns allowing the machine to move many times faster.

These speeds are especially important if you are cutting materials that have low melting points like aluminum and thermoplastics like acrylic, Plexiglas, etc. These materials require high feedrates and smaller depth per passes.

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I just made the book build Cnc machine with the feed rate of 11.19 inch/min as suggested in book. Can I increase it to 20 inch/min? I have 2hp of router attached

The best way to determine the cutting speed is to determine this with respect to the edge quality you desire. This recommendation generally comes from the major end mill manufacturers.

The feedrate (travel speed) should be determined by the chip load of the end mill, the number of flutes, material of the end mill (Solid Carbide, HSS - High Speed Steel, Cobalt, etc.) and the RPM of the spindle. You will need to see the manufacturer's specifications of the end mill to determine this information.

Formula:
Chip Load = (feed rate IPM)/(Spindle RPM x Number of Flutes)

or

Feed Rate IPM = Chip Load x Spindle RPM x Number of Flutes

Once you find this information, apply this to the material at the full depth of the end mill. If you find that your edge condition is aberrant, pull back on either the speed, or the depth per pass. If the edge condition is acceptable, then push the speed higher until the edge condition starts to deteriorate in quality and then pull back to the accepted level.

Using this method, you will be able to reduce the wear on the end mil which will be the most expensive consumable on the machine.

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If I am cutting 18mm MDF with 6mm cutting bit (so 6mm pass), what can be the maximum speed rate of cutting and spindle speed of router?

The maximum length we can ship is a total of 78" inches. However we can send your required length in portions. Please refer to adding the total items you require to your cart to get a visualized amount and shipping cost.

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Regarding 1/2" 5 start and 10 TPI ACME precision lead screw, what the maximum length you can ship within USA? I'm looking for something like 100" and I could use a 1" screw if available. Please include estimated price. Thanks.

The settings that will have to be change will be your steps per inch in motor tuning (mach 3), or settings/axes(planetCNC). But we do not have the actual numbers/specs that will fit your 10 TPI 5 start lead screw, here is a tutorial video which explains how to get the exact numbers you need! (

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On the Book Build: I'm changing the 13TPI 1/2" lead screw with the 1/2" 10 TPI Acme screw with the anti backlash nut. This is for the Z axis only. What should I know about installing it and what are the numbers I need to plug into the motor tuning area.

If you are using Mach3, the setting for the input pin 10 may be enabled as a default for use with the Emergency Stop. If there is no emergency stop on that pin, the reset will trip every time.

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I have the redleaf system for my black toe machine I have wired my limit switches in series NC after setting up in mach 3 I still get limit switch tripped after apply and ok setup can only run if I disable what am I doing wrong

Use a clamping collar (if you are using an ACME lead screw) or a couple of 1/2 nuts (if using an allthread) against the bearing to keep the bearing in place and make sure there is no axial play.

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How do I secure the non-motor end of the lead screw for my 'Book' machine build? Does it just sit inside the bearing or do i use a nut to lock it in place? I did not see any instructions for this in the book.

Dealing with our scratch Build kit/BYO CNC Book Kit, you will use our basic 3 axis electronics kit (https://buildyourcnc.com/item/electronicsAndMotors-3axis-425-elcombo). Now dealing with the Breakout Board, the book specifies the parallel port BoB, but you can use the USB BoB and use Planet-CNC rather than using Mach 3 or Linux-CNC as your control software.

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Correct kit of motors and electronics, I bough a book in Amazons kindle to build a CNC, this book mention a kit of motors and electronics for parallel port, I want to use USB, can you suggest me the correct kit fot this machine.

As long as the bearing has a minimum thickness of 1/4" and 9/32" is a bit thicker, there will be no problem with the book build using the bearing that is 1/32" thicker. There is actually more surface area which is better.

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I am building the CNC in your book - Build you own CNC Machine. One of the bearing thicknesses is 1/4" I can't find that bearing online. I can find 9/32, will that be a problem. Do you have a source? Thx

Decreasing the speed of acceleration in the cutter? Meaning of your router/spindle?, To modify the speed of a router will be going to the router itself and modifying the speed, but if a spindle is being used modifying it will be done either manually in the VFD (VFD Setup:
Change PD001 to '0' (source of run commands)
Change PD003 to 300 (main frequency - Hz)
Change PD004 to 300 (base frequency - Hz)
Change PD005 to 400 (max operating frequency - Hz)
Change PD006 to 2.5 (intermediate frequency - Hz)
Change PD008 to 220 (max voltage - V)
Change PD009 to 15 (intermediate voltage - V)
Change PD010 to 8 (minimum voltage - V)
Change PD011 to 100 (frequency lower limit - Hz)
Change PD142 to 7 (rated motor current - Amps)
Change PD143 to 2 (motor pole number)
Change PD144 to 3000 (rated motor revolution))<- make sure these are your settings in the VFD. If the spindle is wired to the breakout board and is working through Mach 3 then the modification will be done in your CamBam/Feed rate settings.

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How can I decrease the rapid acceleration of the cutter from a completed cutting operation to a new location so that the stepper motor will not lose its steps and mess up the machine zero settings? I am using CamBam and Mach3 on my machine with a chain drive. what is the best way to reduce accleration

You can use any type of threaded rod, i.e. ACME profile, hi-lead, ball screw, etc. The only change you will need to make is the way the lead nut fastens to the nut mount on the machine. Lead nuts for these non-allthread screws typically have flanges with mounting holes, so the mounting of this type of nut is far better than the standard nut used in the book build.

These better screw options will also allow your machine to move faster and with less backlash.

https://buildyourcnc.com/item/mechanical-leadscrews-antibacklash-nut-!5-5-starts-10-tpi

https://buildyourcnc.com/item/mechanical-leadscrews-lead-screw-!5-5-starts-10-tpi

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Has anyone built the machine from the book plans and made substitutions for the store-bought threaded rod? I wanted to spend a bit more money to ensure smoother/faster/more accurate travel with the lead screws, but i am not sure what to use. Mcmaster Carr has quite a few Acme lead screw options, however the price varies drastically. Any input is appreciated.

if you purchased the USB interface, you will need planet-cnc software rather than Mach3, and you will need a usb cable to connect the usb interface to the computer.

The blackToe 2x4 CNC Machine Kit with optional table will need wire to connect the electronics. Don't forget to get some end mills to use for cutting the intended material.


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If I purchase the [blackToe 2x4 v4.1 CNC Machine Kit - USB Electronics - Table Included] all I would need for this CNC to be fully operational is a laptop with mach 3 software and a router. Is this correct?

The settings that will have to be change will be your steps per inch in motor tuning (mach 3), or settings/axes(planetCNC). But we do not have the actual numbers/specs that will fit your 10 TPI 5 start lead screw, here is a tutorial video which explains how to get the exact numbers you need! (

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On the book build machine I changed the Z axis from a 13 tpi lead screw to an acme 10 tpi 5 start lead screw. What numbers do I put into the motor tuneing boxes.

The lead screw must be held in position axially. In other words, you don't want your lead screw to move back and forth at all. This is the only way the coupling hub that is attached to the end of the lead screw could be moving away from its coupling assembly. Depending on the lead screw that you are using, the combination of bearings and collars/nut keep the lead screw in place.

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I am almost done with the book build Cnc machine, but when I run the motors from mach 3, the 1/2" coupling comes out of the middle spider (the joiner which connects 1/4 and 1/2" coupling. How do I prevent this?

When working with our parallel breakout board, a USB to Parallel converter will not work. You will need the exact 25 pins connected directly to get full functionality from our breakout board. The different board in our book was our older version, but was made more compact. The wiring will still be the same and can be found here (https://www.buildyourcnc.com/item/electronicsAndMotors-parallel-breakout-relay#prettyPhoto/2/).
The USB connection on the board is necessary, since it applies the 5v required to power the main board.

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can i use a 25 pin to usb cable (printer cable) with the 25 pin break out board? ive set everything up correctly reading from the build your own cnc machine book but nothing seems to be working. also the breakout board seems to be a different type then in the book would that change anything? .

Since you are using a ball screw which has a very low coefficient of friction to move your heavy gantry, you will have no problem at all using the 651 oz-in motors, and you are not going against gravity, so if you use screw jack formulas that use the low of the machine, you will not need to use weight which is (mass x gravity 9.8 m/s/s). Instead, it will be more susceptible to the inertia of the gantry and if you have any problems, you can compensate by lowering the acceleration.

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Excellent, thank you for your help.

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How do I go about ordering the redleaf system you have discussed? IS there any lead time? Thanks
again

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My machine gantry weighs about 250lbs, I am going to be using 2 steppers to move it. I am using 2510 ball screw and the steppers will be direct drive, will a pair of 651oz steppers be enough? I will be mostly working with aluminum so my feed rates will be low I just want to make sure I dont loose steps due to not having enough power.

There are two main questions that we can answer with respect to motor torque and the mechanical advantage of lead screws, 1) What torque motor do you need to lift a particular weight, or 2) What maximum weight will my motor torque be able to lift.

This formula uses Newtons (N) as it's final unit. Use this with the included radius (R) to determine the torque. Newtons can easily be converted to lbs or ounces using online conversions.

Effort = Sf + (Load/(2 x pi x (R/p) x Se))

where:
p = pitch of the screw
Se = screw efficiency = Standard lead screw will be between 20% (.2) and 40% (.4)
Sf = static force. This is the force that is needed to start the movement. The number may be eliminated, but it is good to use a number in the 5 N to 20 N range.
Load = the expected load that the effort will need to carry (i.e., the router and the included axis assembly that the motor will need to lift)
R = radius of the lead screw


This formula is based on the "law of the machine"

The final effort amount with its unit of newtons and R will be the torque. For example, if the effort comes to 100 N (newtons) and the R is .5 inches, then you can assume that the effort is 50 N-in since it would take twice the effort to turn form the one inch mark from the center of the shaft.

Example:

Load = 90 N (20.2 lbs)
R = 1 inch since that is the length from the center of the shaft that the motor is rated
p = 1 inch / 13 = .08 inches

Effort = 5 N + (90 N / (2 x 3.14 x (1 / .08) x .2))
Effort = 5 N + (90 N / (6.28 x 12.5 x .2))
Effort = 5 N + (90 N / (15.7))
Effort = 5 N + (5.73 N)
Effort = 10.7 N = 2.4 lbs = 38.4 oz-in

I am putting the oz-in on the end because the formula considers the distance from the center of the shaft to be one inch.

Therefore, a 425 oz-in motor would be able to lift a 20.2 lb Router with its accompanying assembly. If the assembly and router is heavier, plug in the numbers and determine the effort required.

With a bit of algebra, the formula can be rewritten to find the load:

Load = (Effort - Sf) x (2 x pi x (R/p) x Se)

Another formula that does not consider friction at all:

Effort = (Load x p) / (2 x pi x R)

Lets see if we get similar results:

Effort = (20 lb x .08 inches) / (2 x 3.14 x 1)
Effort = 1.6 / 6.28 = .255 lbs = 4.08 oz-in

The results from both formulas appear to be very small because a 13 TPI screw will have enormous mechanical advantage.

It is evident that the first formula that does consider friction that we are loosely estimating is far more conservative than the second formula. Either way, even the most conservative formula shows that the 425 oz-in motor will handle very large weights. If you are using a lead screw with only two turns per inch, .5 inch pitch, you can determine the requirements with the first formula.

Example for a 10 TPI 5 start (2 turns per inch) lead screw:

Load = 90 N (20.2 lbs)
R = 1 inch since that is the length from the center of the shaft that the motor is rated
p = 1 inch / 2 = .5 inches

Effort = 5 N + (90 N / (2 x 3.14 x (1 / .5) x .2))
Effort = 5 N + (90 N / (6.28 x 2 x .2))
Effort = 5 N + (90 N / (2.512))
Effort = 5 N + (35.83 N)
Effort = 40.828 N = 9.18 lbs = 146.88 oz-in

Customer Response:
thank you so much

Additional Information:


Additional Information:


Additional Information:
how do i calculate torque of stepper motor if lead screw coupled to motor shaft and load applied by lead screw on plate is 100 kg by vertically

Additional Information:
Pls


Additional Information:
1m 16mmdiameter ball screws calculations


Additional Information:
What is the max load that 2 NEMA 17 stepper motors (spaced 2 feet apart, both will be pushing up on the same gantry) can lift while using a rod with the following specifications T8 OD 8mm Pitch 2mm Lead 4mm for each motor.

Additional Information:


Additional Information:
1

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I need the calculation to determine the stepper motor torque to find the load that it can withstand in horizontal position using a lead screw at 1/2" diameter with 13 TPI.