Let's look at the power/price information when designing a linear mechanical system with acme threaded rod and stepper motors. For evaluation I will be using information from Techno Inc, specifically information on their supernut:
For analysis, I've chooses three screws to evaluate, 1/2"-10 single start (.1" lead), 1/2"-10 two start (.2" lead),and 1/2"-4 two start (.5" lead). Threads per inch (TPI) is the number of threads in one inch of screw length. Most people think of TPI and pitch based on single start threads. With single start threads, the pitch is equal to 1/TPI. Here I will be comparing three different pitch screws. First letsl start by analyzing the amount of linear power that will be lost when converted by rotary power for acme threads using the data from Techno Inc (above) we see:
- 1/2"-10 single start 41% efficient pitch =.1"
- 1/2"-10 two start 57% efficient pitch =.2"
- 1/2"-4 two start 75% efficient pitch =.5"
The next element to be included in the comparison is the mechanical advantage of a screw. mechanical advantage is computed by MA= circumference/pitch. The circumference of a 1/2" screw is 1.57". So the mechanical advantage is as follows:
- 1/2"-10 single start 41% efficient pitch =.1" MA = 15.7
- 1/2"-10 two start 57% efficient pitch =.2" MA = 7.85
- 1/2"-4 two start 75% efficient pitch =.5" MA = 3.14
Thus for a given unit of torque we can surmise the following:
- 1/2"-10 single start 41% efficient pitch =.1" MA = 15.7 transferred power = 6.437
- 1/2"-10 two start 57% efficient pitch =.2" MA = 7.85 transferred power = 4.474
- 1/2"-4 two start 75% efficient pitch =.5" MA = 3.14 transferred power = 2.355
Right now you would ask why ever use anything but the single start rod. But we now need to look at the power characteristic of a stepper motor at various speeds. Below is a power curve taken from a Vexta data sheet on one of their motors. If you examine the curves you see how power drops as motor speed increases. This is a natural characteristic of a stepper motor. This characteristic can be improved by a higher coil voltage to supply voltage ratio as show in the dotted line (48V) on the graph verses the solid line (24V), but typically that improvement comes at a cost to the electronics. For the purpose of this explanation the solid line data is used.
For sake of argument, say the machine has a 48" axis. And as a user you would like that machine to be able to rapid 48" in 60 seconds, or 48 ipm. To transverse 48" the above three screws will need to produce the following rpm:
- 1/2"-10 single start 480 revolutions, 480 rpm
- 1/2"-10 two start 240 revolutions, 240 rpm
- 1/2"-4 two start 96 revolutions, 96 rpm
Looking at the data curve from above, we can come to the following conclusion on motor power based on the above 166ozin motor:
- 1/2"-10 single start at 480 rpm the motor will produce roughly 30ozin of torque
- #1/2"-10 two start at 240 rpm the motor will produce roughly 80ozin of torque
- 1/2"-4 two start at 96 rpm rpm the motor will produce roughly 140ozin of torque
Combine that with lead screw efficiency and mechanical advantage when you convert rotary torque into linear force. Torque/ (pitch / 6.28) them multiply by nut efficiency and we get the following linear force from that motor:
- 1/2"-10 single start at 480 rpm, roughly 48.3 lb of linear force
- 1/2"-10 two start at 240 rpm, roughly 89.6 lb of linear force
- 1/2"-4 two start at 96 rpm, roughly 82.4 lbs of linear force
And the power winner in this example is .... 1/2"-10 two start with nearly double more strength over single start, and 1/2"-4 two start close behind.
For comparison at low speed (50rpm)where the motor is delivering it's rated 166ozin:
- 1/2"-10 single start, roughly 267 lb of force
- 1/2"-10 two start, roughly 186 lb of force
- 1/2"-4 two start, roughly 98 lb of force
To look at a broader range of the stepper power band and screw performance I have taken the specification of a Keling KL23H276-30-8B and graphed the produced force utilizing the screw/nut data.
As you see by the graph, the five start (black) screw produces a flatter force curve over the usable range of the motor. Bottom line, select your screw based on the machine and usage. For example the single start screw would be better suited for cutting metal where feed rates are lower. The two and five start screws would be better suited for wood routers, with the two start more suited to an application where the motor torque is less and travels are shorter.
Keep in mind the above illustration is just a specific example for people to consider what they want for performance. A good source for reasonably priced acme leadscrews and nuts: