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### Question #: 14023

Question: How to determine lead screw length needed. My Thomson 1 1:4 rails are 60 inches long roughly for the router I’m building. I know I have to have it long enough to couple up with the stepper motor of course but does it matter if it’s a little long on the other end

Current Solution

It generally does not matter if it is longer at the other end as long as the lead screw provides the desired travel for that axis. The lead screw will only need to be long enough for the travel, plus any structure and lead-nut positioning.

For example:
- The motor that will turn the lead screw will need to be mounted at some position (generally at one end of the axis). In many cases, this positioning will be mounted where some of the lead screw will not be used (the lead nut will not be able to moved close to the coupling of the lead screw to the motor shaft). Add some of the length of the lead screw to be inserted into the coupling.

- If the lead screw will contain bearings at either end of the travel, that portion of the mechanical assembly will need to be considered in the lead screw length.

- The lead-nut will need to be mounted in a position on a structural member of the part that is to move. The distance from the part of the structure that will extend closest to the motor will have some distance to the position of the lead nut. This distance will need to be added to the lead screw length.

Add these discrepancies to the length of the lead screw and the travel length and you will have the final length.

Respond:

### Other Possible Solutions to this Question

• BUILDING ONE OF YOUR GREENBULL 6X LONG AND 2.2 KILOWATT SPINDLE DOES NOT FIT. SEEMS LEAD SCREW YOU SENT WITH KIT IS SHORT 42" LOOKS LIKE IT NEEDS TO BE 5 OR 6 INCH LONGER. THIS CORRECT? WHAT THE NEEDED LENGTH FOR UNIT?

The leadscrew length for the greenBull long Z-axis is 47 inches.

• Building one of your greenBull 6X Long and 2.2 kilowatt spindle does not fit. Seems lead screw you sent with kit is short 42" looks like it needs to be 5 or 6 inch longer. Is this correct? What is the needed length of lead screw for this unit?

The leadscrew length for the greenBull long Z-axis is 47 inches.

• hello there, i am using servo motor for my X and Y Axis but i dont know how to calculate steps/mm for that, the lead screw i am using is have pitch of .5 mm. please helpme on this i have done everything only this point is pending.

The formula for finding the steps per mm is found in the units itself. First, you mentioned that the motor is a servo. This needs to be clarified as a servo is different than a stepper motor. Some servos behave similar to a stepper motor, so I will continue with this in mind.

The formula is (steps/mm):

You need to find the steps. The stepper motor has a natural number of steps per a full revolution. This is typically 200 steps per revolution.

The driver for the stepper motor allows you to increase the number of steps per revolution by adding a specified number of steps between each step. For instance, if you set the driver to 1/4 microstepping, then instead of having 200 steps per revolution, you would have 200 x 4 = 800 steps per revolution.

So now we have the first part of the formula:

Steps / mm = (200 x 4) / mm

Lets determine the mm side of the formula:

You mention that the pitch is 0.5 mm. Check to insure that the lead is also 0.5 mm. This could be a multiple start lead screw where the pitch is different than the turns per mm. If in this case, that the 0.5 mm is the travel for one full revolution, then you can simply plug this into the formula as:

mm = .5 mm

Otherwise, determine how fat the travel is for one complete revolution.

Therefor, with what we know and the driver is set at 1/4 microstepping and the stepper motor has a natural step count per revolution at 200:

steps / mm = (200 steps x 4) / 0.5 mm = 800 steps / 0.5 mm = 1600 steps / mm

If your travel for one revolution is not 0.5 mm, then plug in your travel distance instead.

i know about steps/mm calculation for stepper motor, because i am using servo motor that why i asked about that. please tell for servo motor.

because its my first time with servo motor i have no idea about calculation of parameter with servo.

Have you attempted to contact the manufacturer or seller of the servo? We typically respond to customers of our products on this customer service area, unless we have extensive knowledge of the subject and can answer the question efficiently.

• can you please specify how to connect the collar/nut and bearings to prevent the axial movement of lead screw. Do I have to put that next to the stepper motor /coupling assembling or on the other side where the lead screw comes out. Or is there any way I can make the flexible coupling rigid so it does not come out of the middle spider?

You would use a combination of bearings and collars to prevent your lead screw or rod from being able to move back and forth. Without it being able to move back and forth, you shouldn't have the couplings coming apart, because the motor is solidly mounted and unable to move as well.

I will try to draw a picture using symbols, with a key to define what each part is.

--CB|--------------|BC}{M

- = Lead Screw or Rod
C = Collar
B = Bearing
| = Wood, the frame of your machine
}{ = Coupling
M = Motor

On the example above you could replace the collar on the motor side with one half of the coupling, putting it right upside of the bearing to hold it in place instead. Like this:

--CB|--------------|B}{M

You could also place the bearings on the inside as follows:

----|BC----------CB|--}{M

• Building the 2'x4' CNC from the Woodsmith plans and want to use a router with 1/2" collet. Will your stepper motor kit with 2 NEMA-23 and 1 NEMA-34 be sufficient for a Bosch 1617 router motor, or will it be too heavy?

You will be fine with using 2 NEMA 23/24 (425 oz-in) and 1 NEMA 34 (651 oz-in) motors with the Woodsmith CNC build with a large heavy router with a 1/2" collet. Specifically, the Woodsmith CNC build uses lead screws for each axis and this will provide mechanical advantage allowing the motors along with the drive mechanics (lead screws) an increase in torque.

• 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.

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)

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

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

Pls

1m 16mmdiameter ball screws calculations

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.

1

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.

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

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)

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

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

Pls

1m 16mmdiameter ball screws calculations

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.

1

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

• I am building your "Green Bull' 6 foot wide kit and I am at the stage of attaching the motor and drive chain. I would like to know if you have an modification kit available to put the 1/2" ACME screw on the Y-axis?

Currently we do not have that modification kit, our set up is fixed for our greenBull only modification kit we have for this model is the long z-axis kit(Designed for Foam cutting).

• I bought a Blacktoe 2 x 8 three years ago and have always had a problem with the Zid axis. No matter how tightly I've calibrated the axis it always cuts to deep. Can I put a larger Stepper motor on Z-axis using the same motion electronics that came with the original machine.

Modifying the Z-axis to accommodate a larger motor will be a worth while task and is possible, however we have not calibrated the z-axis therefore using the 1600 Steps-per inch in the motor tuning on our machine in our shop. We have not noticed any significant depth increments from not calibrating the z-axis but only from zeroing the z axis too close to the material. Also in your design did you specify the actual depth and the length of tool (end mill/ bit) that you are using?

• 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.

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! (

).
Here is a default setting that you might be able to tune and adjust accordingly: 1600 steps, accel 400.02, velocity 5.

• If i can get the autocadd drawings of the building mdf peices that need to be build are the plans detailed enough for me to make my own autocadd drawings? I have access to another machine to build my own.

Yes, the plans are detailed sufficiently enough to produce CAD drawings. If you wish to create AutoCAD drawings from the plans that we provide, we ask that the information conform to the creative commons license established on this site.

If i can get the autocadd drawings of the building mdf peices that need to be build are the plans detailed enough for me to make my own autocadd drawings? I have access to another machine to build my own.

• I would like to build the 2’x 4’ blackToe2x4v40 CNC router. I have your book. I want to build the latest model blackToe2x4 v40. Are those the correct plans on your web book page ? Is there a bill of materials? If I use a Porter Cable 3-3/4 router motor what size stepper motors do I need?

The blackToe 2'x4' cnc machine is sold as a kit only. We offer plans for the scratch (book) build machine that can be found here for purchase and also comes with a DVD showing the build process: http://www.buildyourcnc.com/cnckitintro.aspx and the plans for build in the book is on the CNC book page: http://www.buildyourcnc.com/Book.aspx.

You can use the same size stepping motors referenced in the book: http://www.buildyourcnc.com/category/elcombo

• I'm trying to build my CNC router 3m*1.3m, but i'm not sure what is the type of stepper motor i should pay, all my CNC body is Al. I need to bay 4 Stepper motors, 4 drivers, spindle, inverter, and i don't know what is the type of controller ?

The size of the stepper motor is measured in holding torque, generally oz/in. You will determine the torque loads of your axes when selecting steppers. Once you know which stepper you need, the drivers and controller board are simple to pair with them.

• Building the 5x10 GreenBull, I went to install the ribs on the mid section of the gantry and you say in the video to skip a spot for the motor to sit, but I have 3 sections that are going to blank not just one like you show in the video. Do I skip more than one, am I missing ribs?

We apologize for the confusion! The current greenBull kit in the video is a 4' x 8' gB CNC machine, so we currently have a shorter Y-axis length, compared to the 5X/6X kits. However with the gB 5X you should skip every other section(or something similar so it is symmetrical), since we added the option for you to increase the number of ribs if you wish, but is not necessary for the CNC machine.

• 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.

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.

• 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

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)

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

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

Pls

1m 16mmdiameter ball screws calculations

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.

1

• 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 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.

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

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

• What side of the x and y axis do you mount the stepper motor to? If it does not matter what side, do I have to change something in mach3?

It is usually best to mount the motor in a way so it is spinning clockwise to avoid confusion.

ok, but lets say the motors turn clockwise. if you mount it to ether side of the y axis it will pull to that side so what are the correct positions of the stepper motors. is it the left side or the right side of the y axis and also is it the front or back of the x axis?

cw250 with mach3 controller

What side of the x and y axis do you mount the stepper motor to? If it does not matter what side, do I have to change something in mach3?

• Does "Additional Length" for the Lead Screw mean Additional Length in inches? So for the 4' x-axis I have to choose Additional Length=52?

So you will need to add the total length which will be 98" in total!

If this is for the scratch build kit (book CNC) the total length (98") of lead screw you will need for this machine is the three axes added together:

X-axis: 52"
Y-axis: 32"
Z-axis: 14"

You will have to specify the dimensions you require by sending a email (with your order details) or call to: customerservice@buildyourcnc.com or 281-815-7701

Does "Additional Length" for the Lead Screw mean Additional Length in inches? So for the 4' x-axis I have to choose Additional Length=52?

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