Stepper Motion Budget Calculation Audit
Stepper Motion Budget Calculation Audit
Ada re-derives this chapter’s own numbers step by step, at full precision
ADA · CALCULATION AUDIT
Stepper Motion Budget Calculation Audit
A NEMA 17 at 200 steps/rev driving a 2 mm lead screw resolves 0.01 mm — 10 micrometres — per full step, so a 50 mm move is 5,000 steps that finish in 6.25 s at 800 steps/s. That tidy count looks like proof the axis will arrive on time. This audit re-derives the angle, travel, torque, and speed figures and asks whether the constant-speed step count really settles the move, or whether ramp time and the 12.5 N cm torque target still have the last word.
Companion to the chapter Stepper Motors — every number here comes from that chapter.
A stepper plan is only as exact as its count ledger. Keep the math visible from motor steps to millimetres, then check the physics path: load force, screw pitch, efficiency, torque margin, and whether the acceleration profile can actually reach the assumed speed.
See the relationship before changing it
The figure reads from left to right. The blue card is move distance. The middle card applies this page's rule. The green card is constant-speed move time. Walk the arrows once: set the input, apply the rule, then read the result with its unit.
The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only move distance, so the numeric fixture does not switch without explanation.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline is 50 mm.
- 2
Name the relationship. time = distance / 0.01 mm per step / 800 steps/s
- 3
Substitute with units. 50 / 0.01 / 800 = 6.25 s
- 4
Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.
Predict, then change move distance
Try Predict the direction of time = distance / 0.01 mm per step / 800 steps/s. Test another move distance, then compare constant-speed move time.
Observe The step count fixes ideal travel time before acceleration and missed-step margins are added. Reset move distance to 50 and compare constant-speed move time.
Explain The step count fixes ideal travel time before acceleration and missed-step margins are added.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
The worked checks
| Check | Arithmetic from this chapter | Review result |
|---|---|---|
| Full-step angle | 360 deg / 200 steps = 1.8 deg/step | The 200-step NEMA 17 value matches the stated 1.8 deg step angle. |
| Lead-screw resolution | 2 mm/rev / 200 full steps = 0.01 mm/step = 10 micrometres/step | The carriage calculation preserves the physical screw pitch, not just the motor angle. |
| Microstep resolution | 200 steps/rev x 16 = 3,200 microsteps/rev; 2 mm / 3,200 = 0.000625 mm = 0.625 micrometres/microstep | Microstepping improves command granularity; it does not by itself prove torque or no missed steps. |
| 50 mm move time | 50 mm / 0.01 mm per full step = 5,000 full steps; 5,000 / 800 steps/s = 6.25 s | This is a constant-speed estimate, so a real motion record must add ramp time if acceleration limits matter. |
| Lift torque example | F = 2 kg x 9.81 m/s^2 = 19.62 N; T = 19.62 x 0.008 / (2 x 3.14159 x 0.4) = 0.0625 N m = 6.25 N cm; safety margin x2 = 12.5 N cm | The stated 40+ N cm NEMA 17 holding torque clears the static sizing target, before derating for speed, heating, and missed-step risk. |
Use the table as a design audit, not as a guarantee. If the load changes, the screw pitch changes, or the motor runs near resonance, rerun the count, torque, and ramp checks with the actual measured values.
Every number above is taken from the chapter’s own examples and re-derived step by step.
Audit result
The constant-speed count is correct, but actual duration and position require a motion profile and torque margin.