Lead equal to Pitch multiply Starts. Velocity and Accuary
Lead Screw or Ball Screw
If you are trying to find out the math of lead screw or ball screw, here we are.
Common Sense:
Pitch is the distance between corresponding points measured from one thread to the next parallel to the centerline, it's resolution, main factor of accuracy.
Lead is the distance a screw thread advances along the centerline in one turn, it's travel per revolution, main factor of Velocity.
Start, or starts.
Threads per inch TPI are the number of threads per inch measured parallel to the centerline.
1/2"-10
This lead screw is ½ inches in diameter and contains 10 threads per inch. The information above does not specify the lead or number of starts.
Velocity or speed is related with the lead. Using a stepper motor to drive lead screw, lead is travel per revolution, if the microstepping is fixed, it's positive correlation with pulse per second PPS.
Accuracy is related with the pitch. Use a stepper motor with lead screw, pitch is the resolution, if PPS is fixed, accuracy is positive correlation with microstepping and pitch.
steps per mm = (motor_steps_per_rev * driver_microstep) / thread_pitch*starts
Tr8*8 2mm pitch 4 starts, 400 steps per mm, 1 step 0.0025mm, frequency 4, resolution is 0.000625mm
Tr8*12 2mm pitch 6 starts, 266.7 steps per mm, 1 step 0.00375mm, frequency 6, resolution is same 0.000625mm
Tr10*2 2mm pitch single start, 1600 steps per mm, 1 step 0.000625, frequency 1, then resolution is 0.000625mm
Faster you need a high torque stepper motor (also powerful stepper driver with higher voltage power supply), nema17 60mm stepper with leadscrew Tr8*20 will be great result for high speed 3d printing or other automations.
More readings:
http://odin.me.memphis.edu/ugs_docs/NX3/mfgturning/turning/turn_td_pitch_lead_tpi.html
http://www.roton.com/identify_threads.aspx#number
