calculation motor requirements

Im planing to use dual drive motor on my x axis with rack and pinion set up
5x9 table.
Estimated mass of gantry = ~150 lbs
Pinion gear = 1” in diameter 20 teeth
rack 24 diametrial pitch 20° pressure angle
7.2:1 gear ratio on motor



need some help figuring out some of these calculation ?



Target rapid transverse = ~1000 ipm
Estimate stepper RPM = on pinion and motor?
Available torque = 800~1200 oz-in........ need help finding a good supplier for this range i seen some torque charts with bad curves....


Acceleration = calculation
Available peak force at pinion radius = ?

rapid transverse = calculation?
Time to achieve rapid transverse = ?

[Richards]

Let's do the easy part and see how far that takes us. With a 20-tooth spur gear that has a one-inch pitch diameter, the axis is going to move 1 X pi or 3.14159 inches for every rotation of the spur gear. The gear ratio of 7.2:1 reduces that movement to 3.14159 / 7.2 or 0.4363 inches of axial movement per rotation of the stepper motor's shaft. Assuming that you'll be using a Gecko stepper driver, the axis will move 0.4363 / 2000 steps or 0.000218 inches per step. Now, let's take the reciprical of 0.000218 which is 1 / 0.000218 or 4,583.66 steps per inch of axial movement. Depending on your computer, you can expect that Mach 3 can produce somewhere between 45,000 and 60,000 + steps per second. So, with that spur gear and that gear ratio, you're looking at about 10 inches per second or 600 inches per minute of axial movement. To get that speed with that spur gear and that gearbox, you'll need to spin the motor at about 1,375 RPM. That's pretty fast for a stepper of that size. I usually like to think of 1,000 RPM as being my upper limit, but I have gone much much faster (with much much higher heat). By going to a 30-tooth spur gear, you'll automatically be getting an increase in speed to around 15-ips or around 900-ipm. Personally, I would probably use the 30-tooth spur gear and look for a top speed of about 700-ipm. That would require about 1,069 RPM. (By the way, that's about the jog speed at which I run my Shopbot PRT-Alpha. Sorry, but I only have room for one machine in my little shop, but that doesn't stop me from studying every aspect of the MechMate for future use.)

Mechanically, with a 7.2:1 gearbox, you'll get 7.2 X the torque of the same motor without a gearbox. Assuming that you first look at the Oriental Motor PK296-03AA motor, you'll see that it puts out about 300 oz*in of torque without a gearbox. Multiply that by 7.2 and you'll get about 2160 oz*in or 135 lb*in of torque. Of course, the gearbox limits the amount of torque that can actually be transmitted to the axis, but, from what I understand, there are several thousand CNC routers that use the PK296 sized geared motor with a 3.6:1 ratio that move gantrys that would be similar in size and weight to the one you're planning.

Mach 3 has provisions to tune each motor, including excellent ramp control. So, regardless of the motor that you choose, Mach 3 will let you get the most out of it.

By the way, if you've been following some of the discussion on this forum about stepper motors, stepper drivers, power supplies, etc., then you already know that a six-wire stepper motor can be wired either as Bipolar Series (full-coil) or half-coil. With your desire to jog at 1,000 inches per minute with a 7.2:1 gearbox, I believe you'll have to use half-coil connections to get the motor to spin that fast with any meaningful torque.

I'm afraid that I can't answer any mechanical engineering questions, but I can assure you that what you're hoping to do is very similar to what I do everyday. My machine cuts sheets that are five feet wide by ten feet long. I've never weighed the gantry, but it is heavy enough that two of us can barely lift it back onto the rails when I get careless and cause it to jump the track.

Just today I was testing a PK299-F4.5 motor on my machine. It used a 3:1 belt-drive gearbox, a 25.6VDC power supply, a 30-tooth spur gear and a Gecko G203v stepper driver. The amber light on the G203v started to flash constantly at 9-ips, showing that the motor was getting some really good use out of the power supply. However, the motor easily jogged the axis at 20-ips. At 9-ips, that motor and gearbox was just shuffling along at 343.7 RPM. That means that the motor was producing more than 800 oz*in of torque and that the multiplied torque was 2,400 oz*in or 150 lb*in. With a 35VDC power supply, I probably could have driven that axis at about 11-ips before the amber light came on. That is a powerful motor that is designed to run hard and fast. At low speeds, it is noisier than its six-wire cousins.

I guess what I'm trying to say is that the proper motor with the proper driver, the proper power supply and the proper gear ratio can do more than most people imagine.

[Gerald D]

Eloid, although I am a mechanical engineer, I wouldn't waste time on all those calcs, because there is too much guessing involved. Just some notes:

"Pinion gear = 1” in diameter 20 teeth
rack 24 diametrial pitch 20° pressure angle"
20 teeth on 1" means 20DP - this won't run on a 24DP rack. The DP's have to match.

You mention wanting "800~1200 oz-in" from the stepper and not being able to find curves. See this thread:
http://www.mechmate.com/forums/showthread.php?t=255
If you meant curves for a motor with reduction, then I don't know of any standard stepper_motor_gearboxes in this range. You would have to build your own to find your own curves.

[smreish]

Eloid,
The question you ask is a calculation of drawbar. The force necessary to move an object with reference to slope/rolling resistance/friction/durometer of wheel/wheel diameter/weight above wheels/number of wheels carrying the load. Then once you have calculate breakover friction and got the component up to a constant velocity, you have to stop it. Additionally, the speed at which you cutting and what you are cutting directly affects the force that is counteracting the force you just calculated. I guess what i am trying to say is...the math is pretty significant to proof something that already works.
For the record, I did do the rough math based on a 150# gantry, max speed of 500 ips, 4 rollers steel on steel, 20 rack, 1" DP spur and worked backward to a power requirement of 49.7 volts to drive the gecko's. I did this to verify the need for a 56 V transformer or 70V transformer. 56V was fast enough for me!
It's pages of calcs. Each machine is different. MY MM is based on a net 5' x 10' cutting area. Similar is size to Gerald's.

Good luck.
Sean

[Gerald D]

With 2 x-motors, the load is not shared equally between them. Most of the mass and rolling resistance is split 50/50 but the mass of the y-car and the cutting resistance could be way off center.

A huge factor with stepper motors is "jerk". These calcs normally assume instantaneous change of acceleration (jerk) but a stepper doesn't do that (it will slip instead). Bottom line experience is that the accel setting (in Mach) for the much lighter y-car is very similar to the setting used for the x-motors driving the much heavier load. The experience also is that, once Mach's motor tuning is all set up for peak performance, you can add 40 pounds to the gantry and it still goes as well as before. At this point you tear up all the calcs. Or start wondering where S-curved accel. (factoring in rate of change of accel) with Mach Quantum fits into the "traditional" calcs. . . .

Let's do the easy part and see how far that takes us. With a 20-tooth spur gear that has a one-inch pitch diameter, the axis is going to move 1 X pi or 3.14159 inches for every rotation of the spur gear. The gear ratio of 7.2:1 reduces that movement to 3.14159 / 7.2 or 0.4363 inches of axial movement per rotation of the stepper motor's shaft. Assuming that you'll be using a Gecko stepper driver, the axis will move 0.4363 / 2000 steps or 0.000218 inches per step. Now, let's take the reciprical of 0.000218 which is 1 / 0.000218 or 4,583.66 steps per inch of axial movement. Depending on your computer, you can expect that Mach 3 can produce somewhere between 45,000 and 60,000 + steps per second.

Just want to be clear? how did u get 10 inchs per sec? 45,000/4583.66=9.817 inchs

So, with that spur gear and that gear ratio, you're looking at about 10 inches per second or 600 inches per minute of axial movement. To get that speed with that spur gear and that gearbox, you'll need to spin the motor at about 1,375 RPM.

how did u get this number 1,375? explain plz .


thanks gents.....


That's pretty fast for a stepper of that size. I usually like to think of 1,000 RPM as being my upper limit, but I have gone much much faster (with much much higher heat). By going to a 30-tooth spur gear, you'll automatically be getting an increase in speed to around 15-ips or around 900-ipm. Personally, I would probably use the 30-tooth spur gear and look for a top speed of about 700-ipm.

So 30 teeth 1"od on spur gear still?


That would require about 1,069 RPM.

im guessing you calculated same way as above?


(By the way, that's about the jog speed at which I run my Shopbot PRT-Alpha. Sorry, but I only have room for one machine in my little shop, but that doesn't stop me from studying every aspect of the MechMate for future use.)

Mechanically, with a 7.2:1 gearbox, you'll get 7.2 X the torque of the same motor without a gearbox. Assuming that you first look at the Oriental Motor PK296-03AA motor, you'll see that it puts out about 300 oz*in of torque without a gearbox. Multiply that by 7.2 and you'll get about 2160 oz*in or 135 lb*in of torque. Of course, the gearbox limits the amount of torque that can actually be transmitted to the axis, but, from what I understand, there are several thousand CNC routers that use the PK296 sized geared motor with a 3.6:1 ratio that move gantrys that would be similar in size and weight to the one you're planning.

Mach 3 has provisions to tune each motor, including excellent ramp control. So, regardless of the motor that you choose, Mach 3 will let you get the most out of it.

By the way, if you've been following some of the discussion on this forum about stepper motors, stepper drivers, power supplies, etc., then you already know that a six-wire stepper motor can be wired either as Bipolar Series (full-coil) or half-coil. With your desire to jog at 1,000 inches per minute with a 7.2:1 gearbox, I believe you'll have to use half-coil connections to get the motor to spin that fast with any meaningful torque.

I'm afraid that I can't answer any mechanical engineering questions, but I can assure you that what you're hoping to do is very similar to what I do everyday. My machine cuts sheets that are five feet wide by ten feet long. I've never weighed the gantry, but it is heavy enough that two of us can barely lift it back onto the rails when I get careless and cause it to jump the track.

Just today I was testing a PK299-F4.5 motor on my machine. It used a 3:1 belt-drive gearbox, a 25.6VDC power supply, a 30-tooth spur gear and a Gecko G203v stepper driver. The amber light on the G203v started to flash constantly at 9-ips, showing that the motor was getting some really good use out of the power supply. However, the motor easily jogged the axis at 20-ips. At 9-ips, that motor and gearbox was just shuffling along at 343.7 RPM. That means that the motor was producing more than 800 oz*in of torque and that the multiplied torque was 2,400 oz*in or 150 lb*in. With a 35VDC power supply, I probably could have driven that axis at about 11-ips before the amber light came on. That is a powerful motor that is designed to run hard and fast. At low speeds, it is noisier than its six-wire cousins.

I guess what I'm trying to say is that the proper motor with the proper driver, the proper power supply and the proper gear ratio can do more than most people imagine...

i agree, do have a pic of your gear box set up want a close up
of the gearing and the mechancial hold down of pinion for frw rev direction


thanks your post cleard up a lot question, plz just explain the few comments above
so if i add the 30 teeth pinion the gear ratio is still 7.2 just slower rpm?

PK299-F4.5 motor wowwwwwwwwwwwwwwww that thing flys looked at torque curve at 72v.... and 36 v

so here anthere question... do most people have 72v supply with dc regulator to tweek the voltage "down" to find
the sweet spot of there set up or motor?

a half-coil connections is.... unipolar or bipolor?

[Richards]

Eloid,

You are correct 45,000 / 4583.66 = 9.817 inches per second. I used rounding to show the approximate speed. (If you use an oscilloscope to watch the pulse train from a parallel port driven by Mach 3 you'll see a lot of jitter, meaning that 45,000 may not be 45,000; however, Art has written the software so that all axes are affected the same and no quality issues are involved.)

1,375 RPM was computed using this formula: 1-inch spur gear diameter X pi / 7.2 gear ratio = 0.43633 linear inches of axial movement per revolution of the stepper motor's shaft. Then 600 inches per minute / 0.43633 inches traveled per RPM = approximately 1,375 RPM.

The diameter of the gear is related to the diametral pitch of the rack. On my machine, a 20-tooth gear has a working diameter of one inch. A 25-tooth gear would have a working diameter of 1.25 inches and a 30-tooth gear would have a working diameter of 1.5 inches. As the number of teeth increases, the diameter of the gear increases. This is necessary for the gear to fit the rack. So, once you know the number of teeth on a gear that has a working diameter of one inch you divide the number of teeth on the spur gear that you want to use by the number of teeth of the spur gear that has a working diameter of one inch, i.e. 30 / 20 = 1.5, 25 / 20 = 1.25, etc.

1,069 RPM is NOT correct. (I don't know how I came up with that number. I must have miskeyed the calculator and then failed to cross check the result- sorry.) The correct number would be 1375 / 1.5 = aprox 917 RPM. You could also compute that with this formula: 600 RPM / (1.5 spur gear dia. X pi / 7.2) = 916.732 RPM

There are several photos showing belt-drive transmissions on the forum. You'll find them under the heading "Reduction Drive by belt - Designs". Please note that the highest practical gear ratio with a single stage belt-drive is 3.6:1. That is because the smallest gear that can be used on a 1/2-inch shaft is 20-tooth and the largest readily available gear has 72 teeth. So 72 / 20 = 3.6. To get a 7.2:1 gear ratio with a belt-drive, you would have to design a multi-stage gear box.

We'll have to assume that the gear ratio relates to the gearbox or belt-drive that you have attached to your stepper motor. We'll also have to assume that the spur gear that you use may multiply that ratio depending on the spur gear's working diameter. So, when you use a 30-tooth spur gear that has a working diameter 1.5X the diameter of the specified 20-tooth gear, the distance traveled per rotation of the gearbox's output shaft will be 1.5X greater. That means that the motor will turn slower to move the axis the same distance in a specified time period.

On your last post you referenced the PK299-F4.5 motor. The MAXIMUM voltage that you should use with that motor when the motor is connected using Bipolar Parallel wiring (all eight wires used is 50V. That is based on the induction rating of the motor and Mariss's formula: 1000 X SQRT(inductance) = maximum voltage. So, 1000 X SQRT(0.0025) = 50V. Be aware that, at 50V, that motor is going to run extremely hot. A much more comfortable voltage would be 35V. If you connected the motor using Bipolar Series wiring, the inductance would change to 10mH, so 1000 X SQRT(0.010) = 100V, but the Gecko stepper drivers are limited to 80V, so the maximum voltage that you could use would be 80V. However, a quick look at the torque curves with the PK299-F4.5 motor connected Bipolar Series will show you that the Bipolar Series wiring connections are designed for low speed applications and that Bipolar Parallel wiring connections are designed for high speed applications.

Half-coil is NOT the same as Unipolar. A Unipolar stepper driver uses all six wires on a six-wire motor. However, a six wire motor has two coils and each coil has a center-tap wire. If you use one of the end wires and the center-tap wire, you'll be using half of the coil - and that's why we call it a half-coil winding. In the case of the Oriental Motor stepper motors, one coil has Black, Yellow and Green wires, with the Yellow wire being the center-tap wire. The other coil has Red, White, and Blue wires with the White wire being the center-tap wire. So you could use the Black wire and the Yellow wire OR the Yellow wire and the Green wire on one coil. You could use the Red wire and the White wire OR the White wire and the Blue wire on the other coil.

[guri]

I working about 3´x 5´ router table. Is good for me the G203 V with Nema34 600 oz/in Stepper Motor Model # RS34-600 (from homeshopcnc). Is possible to use direct drive (XL kevlar belts) or is best a 3:1 timing belt reduction for axis movement. Is a good motor? do you recomend other motors?

[Richards]

Guri,
I use the G203v stepper drive and prefer it to any other stepper drive. I have never used the RS34-600 motor, so I don't have any experience with it. (I prefer Oriental Motor stepper motors, mostly because I have used them for more than twenty years without a single failure.) I have never used a kevlar belt drive. There has been discussion on the CNCZone showing kevlar belt driven machines. Personally, I use a 3:1 timing belt reduction on my X-axis motors and on my Y-axis motor. That works very well for me.

[guri]

Richards,

thanks for you reply. I desire to know how is your recomendation about a oriental steper motor of aprox. 600 ozin without geared reduction for G203V. Is important for G203V a breakout board?

[Richards]

Guri,
I like the PK299-F4.5A motor from Oriental Motors. When wired Bipolar Parallel (all eight wires connected), it produces more than 800 oz*in of holding torque and still has 400 oz*in of torque when running at 800 RPM. That is the motor that I will be using when ever I need a non-geared motor. I also have a PK299-02AA motor that is very smooth and quiet at lower speeds. The F4.5A motor likes to work at higher speeds - meaning that it is louder at lower speeds than the 02AA motor. All stepper motors resonate at low speeds (usually below 50 RPM), so it's best to add gearing so that the motor runs at least 100 RPM. With direct drive, you might experience unnecessary roughness when cutting 3D at low speeds. By adding a 3:1 belt-drive you would probably not have that problem.

I would recommend that you always use a breakout board. The G203v stepper driver only requires 2.5mA per signal line to operate and voltages can range from 2.5V to 5V, so a parallel port could directly drive the G203v, but using a breakout board is easier. Also, the PMXD-122 board has a lot of other features that would add a lot of value to your controller. (I've never used other brands of break-out-boards, so I can't comment on them.)

[smreish]

Mike,
I have a current set resistor question. I have just finished reading *again* the G203V-release 5 manual. After doing the calculation math, I seem to come up with. R (in kilo-ohms) = 47 * I / (7 – I), thus :. 47 *2.1 / (7-2.1) = 20.14 Kohms or 20K resistor. Am I correct in sizing the resistor for terminals 11 & 12? Thanks in advance. Of course, there have been conflicting advice on the yahoo gecko forum that suggest with the G203V that I don't even need the limiting resistor.
I am using the PK296a2a-7.2 as you suggested in an earlier post which suggests 2.1A/phase (also the same that Gerald has just ordered for MM #3)
Sean

[Richards]

Sean,
When you use the PK296A2A-SG7.2 motor using Bipolar Series wiring, you would use a 20k 1/4W resistor. If you used half-coil wiring, you would use a 30k or 33k resistor. (I use the PK296B2A-SG3.6 wired half-coil with excellent results.)

I must have missed the posts on the yahoo gecko forum about not requiring current limiting resistors. When I just did several searches, I couldn't find the thread that you're refering to. As far as I'm aware, any of the Gecko drives will attempt to force 7A through a motor's coils if no resistor is used. I have supercharged a few stepper motors by forcing about 150% of their rated current through the drives and ended up with excess heat, so, I'm fairly certain that the current limiting resistor should be used to protect the stepper motor. The G203v won't be hurt if 7A is being drawn through the stepper driver, but the stepper motor may be permanently damaged.

[Gerald D]

There is often confusion between the external current limiting resistor and the internal jumpers/dip-switches for current settings found in some drives. The external resistor is non-negotiable - it must be fitted for motors rated below 7 Amps.

[smreish]

Gerald and Mike,
I am certain this was my confusion on the external vs. internal. To many late nights and early mornings without coffee I tried my best to find the post I read about "not" needing the resistor and it may have been on CNCzone or Yahoo groups...I get so many forum feeds it gets a little confusing sometimes. Anyway, thank you for the clarification and I will be purchasing the resistors tomorrow. For some reason I don't have the garden variety of 1/4 watt resistors I usually have on hand for such "emergencies" Back to the store.
Sean

[domino11]

Mike,
Do you notice any power decrease in having the stepper in half coil vs full coil? To me it would seem like you would only get half the power output? Or is it just a matter of where that power comes in on the speed torque curve?
thanks

[sailfl]

Is the resister shown on the drawings? I was going to say I also read that a resistor was not needed but it is the fuse that is not needed when you use the Grecko G230V.

[Gerald D]

The "not-needed" fuse, and the "not-needed" capacitor add further dimensions to the G203V confusion. Apparently Mariss still "recommends" these devices.

The external, current set resistor, across terminals 11 & 12 has never been in doubt.

Printed on the cover of my drives. Leave terminals 11 & 12 open (no resistor), the drive will pump 7 Amps:

[Richards]

Heath,
Using the half-coil wiring method gives you about 70% of the low-end torque when compared to bipolar series wiring; however, you'll still have substantial torque at 3X to 5X the speed of the bipolar series wired motor (depending on the motor, the power supply and how you've set the current limiting resistor). This is one time that the SQRT(2) applies. Many times computations in electronics use the SQRT(2) as their basis, which means that we will either multiply something by 1.41 or by its inverse, 0.707, to get the correct answer.

[Gerald D]

The long reason for the 1.41 or 0.7 factor. The short reason is that the blue area is 1.41 times as big as the red area (for "sine waves" like our alternating current AC)

Clipboard01.gif

[domino11]

Mike, Gerald
Thanks for the reply. Yeah I should not have said half power, I was really wondering what the performance of your machine was with respect to full or half coil. How did it affect how the machine cut and feed rates and or cut quality. Sometimes the most power or the fastest feed rates dont always mean the best solution.

[guri]

Mike,
thank for your recommendation. I buyed 3 gecko 203 today and I am studing the PMXD-122 manual, but I not understand if the example about gecko conections is ok for gecko 203 because the manual not naming this Gecko drive.

[Richards]

Guri,
Look at the PMDX-122 manual's section 2.2 which shows the PMDX-122 being using with COMMON GROUND signals. The G203v uses COMMON GROUND signals. JP1 must be jumped for COMMON GROUND.

[guri]

thanks mike!!

[McMark]

Guri, did you buy from homeshopcnc.com? If so, how was the service? Did you buy the rs34-600 as well? They offered good deals on the Geckos if you bought the motors as well. I stumbled upon them about 2 weeks ago and was considering buying the motors and drives from them and building timing belt reductions.

Thanks
Mark

[J.R. Hatcher]

Mark I'm interested in the design of the timing belt reductions? Maybe several of us could work together.

[guri]

Mark,

I buyed the geckco directly from geckodrive. I have not motors still, I am studing about them.

[McMark]

Originally Posted by J.R. Hatcher

Mark I'm interested in the design of the timing belt reductions? Maybe several of us could work together.

JR, I dug around everywhere for the prints that I had drawn when I built a belt reduction for a machine at work. Can't find them anywhere, but I can take my camera to work and grab a pic. Nothing fancy, toothed belts and pulleys from Mcmaster, open frame mounting with bearings on each end of each shaft. I had used thrust bearings in between the aluminum framework and the toothed pulleys, then machined the standoffs to give these a little pre-load removing any endplay.

On another note, have any of you guys ordered from homeshopcnc.com? I was thinking about getting the drivers and motors from them.

[J.R. Hatcher]

Mark sounds good looking foward to the pics. I have not ordered from homeshopcnc.com, sorry.