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bearwen
Wed 05 September 2007, 11:42
Hello,
Well I am building a smaller cnc but will build a mechmate in the near future.
My questions are how do you calculate the torque of a spur gear and rack based on teeth or does it matter? The problem I have is that I can figure the circumferance for distance traveled and I know how fast I want and can spin my motors at a given voltage and torque (of the motor) and I have seen several gears that are the same size but have different number of teeth so how do I decide on the right number teeth whats the formula to figure the torque? I am currently looking at directlly coupling the spur gear to the motor shaft but may use a gear box this is why I am trying to figure out the teeth thing. Also if someone could list all the formulas and perhaps an example for gearing and rack systems for speed and torque (such as ozin of motor through gear of ? to gear box of ratio ? ( or no gear box) to rack of ? gives ?ftlbs of torque at the cuter minus weight of gantry etc.. I would really be greatful. I have a nice DIY router that uses ballscrews but really want to use rack and pinoin on this new one and will have to use it on the mechmate(I might just be in over my head haha but hey I am always in over my head thats the fun part learning to swim once you do you never forget)


Thanks All

Bearwen

Dirk
Wed 05 September 2007, 16:03
I made an Excel spreadsheet a year or two ago that may help. It gives a theoretical cutting force depending on your ratios.
Dirk

bearwen
Thu 06 September 2007, 10:20
Dirk,
Thanks for the calc :) I have one more question on the cutting force this is the amount of ftlbs that are at the cutting bit correct? What about the weight of the gantry and z carriage etc do you really need to take this into consideration since there on bearings the gantry weights 80lbs but doesnt require 80lbs to move it? (my 8yr old pushes it with one finger) (ie z assy weights 40lbs with router and I want 40lbs of down cutting force so do I need to have 80lbs min in the cutting force box of the spread sheet?) I am trying to figure out how fast and with enough force to move the gantry and cutter through material with a given size motor. Any ideas as to how much cutting force you need for different depths and different materials and different speeds any body have a spreadsheet or a link? If I run a 1/4 spiral at 40inmin at3/4 deep in MDF thats fine but how fast and how much cutting force is required to go faster at same depth?(there is a limit to the 2-1/4hp router not sure what that is and also theres a limit to the bit not sure what that is)


thanks
Bearwen

Doug_Ford
Thu 06 September 2007, 20:59
Gerald has recommended using a scale for weighing fish to determine which size spring we will require on our Z axis. If your router is mounted on your Z axis, could you could use a fish scale to pull your gantry while your router is actually cutting wood?

Gerald D
Thu 06 September 2007, 23:50
Bearwen, you ignore the mass of the moving parts while they move at a steady speed. You only use the friction for a calculation

A suggestion on how to find cutting forces is to put a hand router down on a table without any cutting bit. Run a string from the router, over a pulley at the table edge, down to a bucket. Put various weights in the bucket and then imagine yourself routing and lift the bucket off the floor. Check the max weight you will be comfortable to push around for say 10 minutes in every 30 minutes. That is the type of force that a hand router's bearings, collet and cutter have been designed for.

bearwen
Fri 07 September 2007, 07:54
Gerald D,
Never thought about the bucket idea. Correct me if I am wrong but you say to ignore the mass of the moving parts because it moves at a steady speed but dont you need to calculate the mass of the moving parts when you are figureing the motor size to use? Such as if a 269 ozin motor with a 24 pitch 12 tooth gear no reduction drive gives a cutting force of 67.25lbsft now that is most likely plenty for most cuts that are .25" deep or shallower in mdf or softwoods at say 5-10"persec but what about moving the gantry as you are cutting doesnt the mass need to be configured in there as well and if so then you are going to use some of that 67.25 lbs of cutting force to move the gantry from a stand still or reverseing directions which will lower the cutting force you actually have correct? or does the weight of the gantry really not matter as it is on bearings example my 8 yr old can not lift 100lbs but the gantry weighs 100 lbs and he can easilly move it with a light push from one hand (I believe that statement answered my question but still curiouse as to wether you calculate any of the weight of the moving masses at all when choosing a motor size) I am curently finishing up a router not a mechmate and have ran into wether the motors are big enough for the mass and cutting force at the speeds I want to go.

Thanks for the replies.

Bearwen

Gerald D
Fri 07 September 2007, 09:23
The mass of the gantry is only a factor when you have to accelerate or decelerate it (eg, when changing direction). Your motors need torque to get the gantry "up to speed". But once it is at the right speed, you only need torque to overcome friction.

If you cut big rectangles all day (eg doors) then the mass hardly makes a difference. If you are engraving a sign with small letters and details then the mass makes quite a difference.

Dirk
Fri 07 September 2007, 12:59
This past summer I was paid to do some motor testing. There were questions as optimum current set, voltage, makes of drivers and also different motors. Because I was being paid I don’t wish to get real specific. I made some assumptions from experience. A 10# pull at various speeds was sufficient for a dependable jog. A minimum pull of 30#s was sufficient for light cuts and 40#s to 50#s should suffice for the heavier cuts. A PC router will start to choke on a full depth cut of ¾” at about 3.5 – 4” a second. You need to be in the 40 to 50 pound range to reliably cut without loss of steps at this force level. The weight of the gantry has little effect on performance, It may effect your ramping, but since steppers have the most power a low speeds the initial change in inertia from changing directions is overcome with the extra low speed power. This is also assuming with motors disengaged you can easily push the gantry and is doesn’t require much force to keep it rolling.
With these assumptions in mind I set up a test track. The track consisted of two hardened rails and gear rack attached to aluminum T-slot Extrusion. I constructed a small carriage that would ride the track and drive it with the test motor. I used the same gearing as would be used in the final CNC machine. I then attached a cable, which was routed through pulleys to a 5-gallon bucket in which I could add or take away different weights.
This allowed a constant force on carriage through out its 8’ of travel.
I began each test with 10#s of weight and the carriage would be cycled a trip to the end of the track and back. After a successful cycle the speed would be increased and cycled again. The top speed was noted when a cycle completed without the loss of steps, the weight was increased and test repeated. A performance curve then could be generated from that data and give a real worldview of the performance of the combination being tested. One drawback to this test was it could be very abusive to the carriage. When a step motor losses steps it has absolutely no power. With 50#s of weight dangling in the air it will crash to the floor and slingshot the carriage along with it. I went through several rebuilds because of this. Holding torque could be tested easily. One could park motor and add weight to bucket until motor no longer could hold.
I came up with some valuable data and a couple of eye openers.

Bearwin:

The excel sheet is a good start. Find a machine close to what your building and find out what it’s specs are, Or find out what motors they’re using and back figure to ball park what you need. Testing is the only way to tell what different combinations will yield.
One nice thing about the Mechmate is it’s design is already tested.
Dirk

Gerald D
Fri 07 September 2007, 14:02
Another bucket & string guy! :) As crude as it may sound, this is actually a very valid "dynamometer".

Yes, I once loaded about 30kg [66#s] of scrap on top of a 50kg [110#s] gantry to see how much it slowed down. It didn't. And that was my major confirmer that aluminum gantries don't make sense.

bearwen
Sat 08 September 2007, 14:26
Thank you all for your replies I have learned some new things and will try the bucket the biggest reason I asked this question as I have some 269ozin motors and was wondering what they can do geared and direct driven as my wifes uncle wants me to build him a cnc and I figured I would build a smaller 4'X4' cutting area Mechmate and was trying to figure out if the motors would do it or not I believe they will you will just have to ramp to speed but thats fine.

Once again Thankd You All for the quick and informative replies.
Bearwen

Dirk
Sat 08 September 2007, 15:32
bearwen
Looking back over your post I have a few suggestions. I'm assuming you're planning on a full size router on a 4X4 router table. I think a 24 pitch rack is to light and small. I have an older shopbot PR model that has 280 oz in steppers driving it. It works very well especially with Geckos and a 70 volt supply. They are 23 size and have a good torque curve. They are also Hybrid square motors. The gearing is a 3 to 1 timing belt driving a 16 tooth pinion on 20 pitch rack. I think it has all the power you would need for a router.
There's a lot of differences in steppers. If what you have is anything short of a square body hybrid stepper, you're better off getting something else. I think you will be disapointed otherwise. I would be also careful about spending a lot of time and effort along with money building a machine around a part you have on hand. Be sure what you want to do with the machine and plan it fron there. If the motors fit in great.
Dirk

Gerald D
Sat 08 September 2007, 21:51
. . . 269ozin motors and was wondering what they can do geared and direct driven . . . . .

Geared at 3:1 or higher okay, direct driven not okay. I think.

bearwen
Sun 09 September 2007, 12:47
Dirk,
I have the aquare bodied steppers they are 269 ozin and I have a set of 3 Gecko 203 Vampires with a 60 volt power supply ( mymotors are rated @ 3.2 volts so 64 volts is 20 times rated which is about the most you should go)that drive them they came off another router I built a while back (it was my first went through lots of upgrades) so I am looking to build a small mechmate basically so after your replies and doing something thinking and some bucket tests by hand and running my current router (Another DIY but its built from wood this is why I am asking Iwant to build a steel frame) with some bucket loads I feel that this is doable and I will have to gear it which kills the rapids. Here are the numbers I have come up with from the spreadsheet (thanks Dirk) all the gaers are 1/4 inch bore so i copuld keep the possibility of direct drive motors are nema 23 1/4 inch shafts. 24 pitch 12 teeth spur gear 2:1 gearing gives 134lbs cutting force and a rapid speed of 600"min or 3:1 gearing which yields 201lbs cutting force and a rapid of 420"min Just out of curiosity direct drive gives 32 pitch 14 tooth 76lbs cutting force rapid 1020"min but will have to ramp up to speed. The mas majority of the work I will be doing is carving @.05" deep in oak with a 60 degree V-bit so I am thinking the load on the cutter is really low so I should be able to run in the 3-4 hundred inches amin which will put a load on the tool I am guessing to be 30lbs which fits in my numbers I can always slow down for deep cuts and long passes but need speed for the shallow cuts as this is mostly what I do.

thanks again you guys are great
bearwen

Dirk
Mon 10 September 2007, 05:02
bearwen
I think gearing your motors will be strong enough. I think the smaller rack will give you problems. I would try and stay with 20 pitch rack. 24 pitch rack is 1/4 inch square, compared to 20 which we are using is 1/2 inch square. Thats 4 times the steel, 32 pitch is 3/16 square. Even though the ratio shows a multiplication of the power, I don't think gearing with smaller rack is going to handle those forces. I think your only real option is a belt reduction or a gear box.
Dirk

bearwen
Mon 10 September 2007, 05:43
I was thinking the same thing but had hopes oh well thanks for the help and I will let you guys know how it turns out like I said it will be a scaled down mechmate with a few mods do to scaling, cost, needs, etc...

Bearwen