### Question #: 862

Question:
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What maximum weight will my motor torque be able to lift? Effort = Sf + (Load/(2 x pi x (R/p) x Se)) In this formula, is Sf (static force) include gravity? how much usually is static force? can you please give one example to calculate max. weight Z-axis can carry?
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**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-inCustomer Response:thank you so muchAdditional 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**

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### Other Possible Solutions to this Question

**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)

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**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 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.**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.

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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.

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

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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.**Click the link to respond:**

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.**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.

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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**Click the link to respond:**

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**How can i calculate how much can carry my stepper motor? i have these informations: (Detent Torque: 2.2N.cm; Rotor Inertia: 54g.cm2; Holding Torque: 40N.cm). It's a nema 17**The holding torque will provide the best information for the calculation on how much your stepper motor will carry. But first, when you say carry, do you mean how much weight it can lift, how much inertia it can withstand during an acceleration and deceleration state or how fast it can accelerate or velocity it can maintain under load from the milling process?

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How can i calculate how much can carry my stepper motor? i have these informations: (Detent Torque: 2.2N.cm; Rotor Inertia: 54g.cm2; Holding Torque: 40N.cm). It's a nema 17**How can i calculate how much can carry my stepper motor? i have these informations: (Detent Torque: 2.2N.cm; Rotor Inertia: 54g.cm2; Holding Torque: 40N.cm). It's a nema 17**The holding torque will provide the best information for the calculation on how much your stepper motor will carry. But first, when you say carry, do you mean how much weight it can lift, how much inertia it can withstand during an acceleration and deceleration state or how fast it can accelerate or velocity it can maintain under load from the milling process?

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How can i calculate how much can carry my stepper motor? i have these informations: (Detent Torque: 2.2N.cm; Rotor Inertia: 54g.cm2; Holding Torque: 40N.cm). It's a nema 17**Hi, I’m purchasing an ox build workbee cnc router from China but I need to purchase the spindle mount, router and all cables/wires. Please can you give a list and quote of what I will need? I am purchasing the electrical pack with it but it doesn’t come with the cables and all other bits I need. Thank tou**Hola puedo venderte una maquina nueva completa chocofrutfc@yahoo.es

**Since I am using normal all-thread lead screw 13 TPI 1/2" for the book build cnc, what can be the maximum feed rate of machine and how can I change the mechanical setup in mach 3? I am using 1/4" steel carbile endmill with 2 flutes and router is 2 HP with variable speed**Book build (scratch build), feedrates and recommendation.

Using standard allthread will provide around 20-30 ipm using 36 volts. Although it allows for a working CNC machine, the RPM of the spindle/router will need to spin at the lowest setting to provide the beat efficiency and life for the end mill at 1/4" cut diameter and higher. The speeds may be fine for smaller end mills.

If you would like faster speeds, you should change the lead screws on the CNC machine to the 1/2" 5 start 10 TPI which translates to 2 turns per inch which means, the stepping motor will not need to turn as fast to produce faster motion. That is to say, the stepping motor will only need to turn two revolutions for the machine to travel one inch and with the allthread, the stepping motor will need to turn 13 times to reach one inch.

Link to the lead screw and other mechanical parts needed:

https://www.buildyourcnc.com/CNCMachineMechanicalParts.aspx

To change the lead screws you will need (for each axis):

1. The lead screw for that axis.

2. Two 1/2" collars to keep the lead screw axially stable.

3. One Antibacklash nut.

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20**FIRST OF ALL, THANKS FOR DESIGNING A WONDERFUL SITE. MY QUESTION IS: HOW DO YOU CALCULATE EME (ELECTROMAGNETIC EMISSIONS) AROUND THE TRANSMITTER (ANTENNA) AT ANY GIVEN POINT AND WHAT ARE MEASURES TO KEEP IT UNDER SAFETY CODE?**Conceptually it is straightforward to predict the radiofrequency (RF) exposure intensity at any point in the vicinity of a cellular radio base station antenna. Simply multiply the effective radiation power times the inverse square of the distance times the relative gain of the antenna in the direction of the interest. The relative gain in different directions is know as the antenna radiation pattern and is usually available from the antenna manufacturer in graphical or tabular form.

Unfortunately, in real life the calculations involved in base station antenna evaluations are quite complex and require expert knowledge and experience to deal with the many parameters that are involved. An excellent reference summarizing this process is the Federal Communications Commission OET Bulletin No. 65 titled "Evaluating Compliance With FCC Guidelines for Human Exposure to Radiofrequency Electromagnetic Fields," available on the Federal Communications Commission (FCC) website.

To assess the RF hazards associated with handheld cell phones it is necessary to predict the rate of absorption in the body of radiofrequency energy, a parameter called the specific absorption rate (SAR). This is a very complex calculation, and cell phone manufacturers often rely on measurements of SAR in fluid-filled cylinders or plastic containers in the shape of a head. The FCC requires cell phone manufacturers to provide this data to FCC. You can obtain the data for your model phone on the the FCC's website. Unfortunately only cell phones manufactured in the last couple years are listed here.

As to your question about keeping RF exposures within the safety code, please read the other questions posted on this website this matter. Cellular radio products that meet FCC requirements will be within the guidelines established by safety standards organizations for users' and public exposure to RF radiation fields.

Gary H. Zeman, ScD, CHP**Click the link to respond:**

FIRST OF ALL, THANKS FOR DESIGNING A WONDERFUL SITE. MY QUESTION IS: HOW DO YOU CALCULATE EME (ELECTROMAGNETIC EMISSIONS) AROUND THE TRANSMITTER (ANTENNA) AT ANY GIVEN POINT AND WHAT ARE MEASURES TO KEEP IT UNDER SAFETY CODE?**I bought a 'BuildyourCNC V1' relay board to go with my mach3 usb controller. I have been sent a 'Songle' relay. It's not the one in your picture and it's got different connections, for which there isn't a wiring diagram. The one I ordered says it is 5v, this one seems to be saying it's a 24v unit. Can you please explain what has happened? Thanks**The Mach3 USB interface board requires 24V relays externally. There are no relays on the mach3 usb board. If you use an external relay on the mach3 usb board, the relay connects to the V+ which is 24V and the output pin is the return.

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I understand what you are saying. Does your relay board work with the Mach3 USB board? If not, what relay board do you suggest to work with this usb controller?

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Our relay board works with our parallel breakout board. An off the shelf SSR (Solid State Relay) made for 24V should work fine.**I bought a 'BuildyourCNC V1' relay board to go with my mach3 usb controller. I have been sent a 'Songle' relay. It's not the one in your picture and it's got different connections, for which there isn't a wiring diagram. The one I ordered says it is 5v, this one seems to be saying it's a 24v unit. Can you please explain what has happened? Thanks**The Mach3 USB interface board requires 24V relays externally. There are no relays on the mach3 usb board. If you use an external relay on the mach3 usb board, the relay connects to the V+ which is 24V and the output pin is the return.

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I understand what you are saying. Does your relay board work with the Mach3 USB board? If not, what relay board do you suggest to work with this usb controller?

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Our relay board works with our parallel breakout board. An off the shelf SSR (Solid State Relay) made for 24V should work fine.**can you please tell me what is supported voltage and amperage for this combo connector https://buildyourcnc.com/item/electronicsandmotors-connector-round-female-male-4pin**The 4 pin male and female motor connectors are rated by their manufacturer at 100VAC and 2A.

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can you please tell me what is supported voltage and amperage for this combo connector https://buildyourcnc.com/item/electronicsandmotors-connector-round-female-male-4pin**I am looking at one of your electronics packages as a replacement for my excisting electronics. I have a old table top CNC that has a bad electronics pack, but the motors, and the mill are in good shape. could your system be adapted to work in this case?**Depending on the type of motors and connection type, you could adapt your motors to work with our electronic packages, but you will receive additional motors since our kit is complete.

Now you will have to take into affect the actual motors you have and compare or get accurate replacements(Ex. our 425 oz motor(1/4" input shaft) will have to be same size or similar entry holes)

Your Controller board will be the major issue, due to its wiring and processing manner, you can view the connections for our breakout boards to compare with yours! (parallel: https://www.buildyourcnc.com/item/electronicsAndMotors-parallel-breakout-relay#prettyPhoto/2/)(USB: https://www.buildyourcnc.com/item/electronicsAndMotors-electronic-component-USB-Controller-Breakout#prettyPhoto/2/)

Email(customerservice@buildyourcnc.com for further help)**I got the plans and hardware from you guys and im almost ready for the stepper motor part of this build. what size motors are good to use for this build? the size of cnc will be 2x4 when finish or what size will not work? thanks**We recommend our electronics combo for the scratch build kit, which you can find on our site here: https://buildyourcnc.com/item/electronicsAndMotors-3axis-425-elcombo. This is our standard general purpose 3 axis electronics system, and includes (3) NEMA 24 425 oz-in stepping motors, (3) Drivers (3.0Amp 24-40 Volts, with 1-1/64 microstepping), (1) 36v 8.8a Power Supply, (1) Interface Board either USB or Parallel. (The USB version requires PlanetCNC software; the parallel interface board gives you a variety of options, Mach3 being one popular choice.)

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I got the plans and hardware from you guys and im almost ready for the stepper motor part of this build. what size motors are good to use for this build? the size of cnc will be 2x4 when finish or what size will not work? thanks**Hi i am interested in the greenBull 6x with Hybrid Laser/Spindle Head (includes Spindle/VFD and Laser Components) - USB Interface (Long Z). I was wondering how much it would cost to get this machine to NZ?**You can use our shopping cart to determine the shipping. Add the machine and the parts you want to purchase, enter your shipping address and click on the Calculate Shipping Button to get a price for shipping. The shipping charges are determined directly from the carriers at the time of pressing that button.

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Hi i am interested in the greenBull 6x with Hybrid Laser/Spindle Head (includes Spindle/VFD and Laser Components) - USB Interface (Long Z). I was wondering how much it would cost to get this machine to NZ?**I am going to build a CNC 4x4 plasma table. The frame is made of 1 1/4" pipe and the gantry will be made of either 2"x 2" or 2"x 3" tubing. What size stepper motors do you suggest?**We recommend our electronics combo for the scratch build kit, which you can find on our site here: https://buildyourcnc.com/item/electronicsAndMotors-3axis-425-elcombo. This is our standard general purpose 3 axis electronics system, and includes (3) NEMA 24 425 oz-in stepping motors, (3) Drivers (3.0Amp 24-40 Volts, with 1-1/64 microstepping), (1) 36v 8.8a Power Supply, (1) Interface Board either USB or Parallel. (The USB version requires PlanetCNC software; the parallel interface board gives you a variety of options, Mach3 being one popular choice.)

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I am going to build a CNC 4x4 plasma table. The frame is made of 1 1/4" pipe and the gantry will be made of either 2"x 2" or 2"x 3" tubing. What size stepper motors do you suggest?**My Z-axis seems to be reversed on a fully assembled machine... I've tried reversing it in the config settings on Mach 3, but to no avail. What do I need to do? IS this a wiring issue that was not done correctly at the factory?**If your Z axis is moving in the opposite direction, go into Mach3, click on config, ports & pins, then click on the motor outputs tab. You will see the axes labeled on the left and the parameters labeled on the top of this dialog box. Toggle the dir low active for the z-axis.

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What if I'm having the same issue on a different axis?

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You can follow the same procedure as with the z-axis. When you get to the motors outputs tab, toggle the dir low active checkbox for the axis that you would like to change.

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sdf

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My Z-axis seems to be reversed on a fully assembled machine... I've tried reversing it in the config settings on Mach 3, but to no avail. What do I need to do? IS this a wiring issue that was not done correctly at the factory?**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**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.**In my 4'x8' Blackfoot rig, there is a maximum wire length of 16" between drivers, breakout board, and power supply as well as a maximum wire length of 10' from drivers to motors. What AWG wires should I use to connect power supply to drivers, drivers to motors, and drivers to breakout board?**What we intend our customers to use for wiring the motors to the drivers will be 4 conductor 20 AWG cable, now for the PSU to Drivers; 16-18 Gauge wire should be used, and drivers to BB(Breakout Board) should be a 24 AWG wires.