[La-Trovanti]

I am building my first CNC and have been through many websites trying to gather information on this subject.
Essentially there are few approaches to this subject
-The first mostly used is the mechanical approach when we try to calculate forces( torque) necessary to overcame friction, the force for grinding the material or to provide acceleration when start/ stop or making corners. This path is very scholastic and requires advanced knowledge.
-Second is something experimental when we build a machine or try to copy somebody else’s machine and realize it has to be improved and start looking for solutions.
And the third method I shall name it value for money; we try to choose the best parts we can afford for a given budget. The idea was borrowed from Tom’s hardware web site- building the best desktop PC for a budget.
I have chosen 4 stepper motors from e-bay and we will compare them:

Model	Current(A)		Resistance(Ω)		Inductance (mH)	Holding torque(oz.in)	Connection	Price
23HS9430B	3		1.6		6.8	425	4 leads	30GBP
57BYGH41-401A		2.8		0.7	1.4	76	4 leads	16.5GBP
57BYGH627		3		1.6	3.5	270	4 leads	27GBP
23HS45-3008D		4.2		0.4	1.7	354 bipolar parallel	8 leads	39GBP
		2.12		1.6	6.8	240 bipolar serial	8leads	39GBP

The torque produced by the rotor is directly proportional to the current in the armature windings. The proportionality constant is the torque constant of the motor.
M_o = I x K_m
M_o = torque developed at rotor
k_M = motor torque constant

Therefore 23HS9430B at half of maximum current will have half torque 212 oz.in and so on.
But we have to consider we always need the dynamic torque, when the motor is spinning.
Now comes into play the inductance which starts limiting the current.
U=L x ∆I/∆t or considering only amplitude U=ώLI ; Ohm’s law for inductance
We choose the power supply 36V and f=1000hz. To simplify I am going to ignore the resistance
ώ=2πf=2x3.14x1000hz.
I(6.8mH)=36/(6.28x6.8)= 0.84A
I(1.4mH)=36/(6.28x1.4)=4.09A
I(1.7mH)=36/(6.28x1.7)=3.37A
I(3.5mH)=36/(6.28x3.5)=1.63A

The torque at 1000hz is: maximum torque x current/maximum current
23HS9430B 425x0.84/3=119 oz.in
57BYGH41-401A (the limit current is 4.09A greater than maximum current) 76 oz.in
57BYGH627 270x1.6/3=144 oz.in
23HS45-3008D bipolar parallel 354x3.37/4.2=284 oz.in
Bipolar serial 240x0.84/2.12=95 oz.in
This is the torque we are interested of:

Model	Torque 0hz	Torque 1000hz	Price	Torque/price(bigger is better)
23HS9430B	425	119	30GBP	3.96
57BYGH41-401A	76	76	16.5GBP	4.6
57BYGH627	270	144	27GBP	5.3
23HS45-3008D	354 parallel	284	39GBP	7.28
	240 serial	95	39GBP	2.4

In conclusion the best performer value for money is 23HS45-3008D parallel connection. Also is the most powerful at 1000 Hz. As you can see 23HS9430B despite being “the most powerful” comes last.
Wish I was helpful
Contact address at Cazare Pensiunea La Trovanti Horezu

[daniellyall]

just do it backwards what you are moving, force required to move an object there is a couple of good online calculators just look up force calculator there a some that include gravity as well.

it make life simple doing this way no need to do big sums

[La-Trovanti]

I have read about an experimental approach when force was evaluated with a spring scale pulling the gantry.
Have to answer to Daniellyall that a comprehensive mechanical evaluation of a stepper dynamic is difficult for me(friction, acceleration, resonance).
Similar performance motors to 23HS45-3008D are 8 leads 23HS45-3008D and 23HS33-4008D.

[daniellyall]

it does not need to be hard all you need to know is the forces required using a spring scale to work it out.

use a on line calculator to work out how many Nm you need to move that weight you just need to make sure the forces calculation is in a + number at the end that tales you what size stepper you need then the rest is what will run the stepper motor at your desired speed ,power supply, driver once you have done a couple of times and have not been wrong its very simple in the end for some good info look up gecko they have some good info for selecting stepper motors, power supply's and drivers.

taking a guess on what you need is a wast of time