BIZOMAT MAKEOS · Mechanics
Linear Move Drive Check (Move Profile, Screw Torque, RMS Torque, Cycle Time)
For a carriage moved back and forth by a motor and screw, how long does each move take, what speed and torque does the motor need, and does it meet my cycle time?
Check of a horizontal screw-driven (or belt-driven) linear axis: the trapezoidal or triangular move profile, move time, peak speed and acceleration force (as the move profile tool), the friction force, the motor speed and the accelerating, running and decelerating torques through the screw lead and efficiency, the RMS torque over an out-and-back cycle with dwells, against the motor’s speed, peak and continuous torque and your cycle time.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Move distance | mm | Length of each move. |
| Speed limit | mm/s | Highest speed allowed for the carriage. |
| Acceleration | mm/s² | Acceleration and deceleration used. |
| Moving mass | kg | Mass of everything that moves with the carriage. |
| Friction coefficient of the guides | Rolling or sliding friction coefficient of the guides. | |
| Dwell at each end | s | Time stopped at each end of the move. |
| Out-and-back cycle time required | s | Time allowed for one move out, one move back and both dwells. |
| Drive and motor | ||
| Travel per motor revolution (screw lead or pulley circumference) | mm | Carriage travel for one revolution of the motor (screw lead, or pulley circumference for a belt). |
| Drive efficiency | % | Efficiency of the screw or belt drive. |
| Motor maximum speed | rpm | Highest speed of the motor. |
| Motor peak torque | N·m | Peak (intermittent) torque the motor can give. |
| Motor continuous torque | N·m | Continuous (RMS) torque the motor can give. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Move distance
- What it is
- The length of one move of the carriage, from start to stop. The tool assumes the same move out and back with a dwell at each end.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 500 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer move takes longer and may reach the speed limit, giving a trapezoidal profile.
- Get it right
- Enter the move distance in millimetres, not the full stroke of the axis if the moves are shorter.
What this means: Speed limit
- What it is
- The highest carriage speed the move may reach. If the move is too short to reach it, the profile becomes triangular and the peak speed is lower.
- Units and format
- Enter a number in mm/s: millimetres per second. The form accepts 0.000001 mm/s to 100000 mm/s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 mm/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher limit shortens the move time on long moves and raises the motor speed needed.
- Get it right
- Enter the carriage speed in mm/s, not the motor speed in rpm.
What this means: Acceleration
- What it is
- The rate at which the carriage speeds up and slows down, taken as the same at both ends of the move. It sets the acceleration force and the accelerating torque.
- Units and format
- Enter a number in mm/s²: mm/s². The form accepts 0.000001 mm/s² to 10000000 mm/s². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5000 mm/s² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Higher acceleration shortens the move but raises the peak and RMS torque.
- Get it right
- Enter it in mm/s²; one g is about 9807 mm/s².
What this means: Moving mass
- What it is
- The total mass that moves with the carriage: the carriage itself, fixtures, tooling and the payload. It sets both the acceleration force and the friction force.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0.000001 kg to 1000000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Acceleration and friction forces, and so every torque, rise in direct proportion to the mass.
- Get it right
- Include the payload at its heaviest; the motor and screw inertia are not included by this tool.
What this means: Friction coefficient of the guides
- What it is
- The friction coefficient of the linear guides or slides carrying the carriage, from the guide maker or a test. Friction force is this times the weight of the moving mass.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Friction raises the running torque and the RMS torque.
- Get it right
- Rolling guides and sliding ways differ greatly; use the value for the guide type you have, including seal drag if the maker gives it.
What this means: Dwell at each end
- What it is
- The time the carriage stays stopped at each end of the move, for example while a part is loaded or a tool works. Two dwells are counted per cycle.
- Units and format
- Enter a number in s: seconds. The form accepts 0 s to 10000 s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.5 s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Longer dwells lengthen the cycle and lower the RMS torque.
- Get it right
- Enter the dwell at one end only; the tool doubles it for the out-and-back cycle.
What this means: Out-and-back cycle time required
- What it is
- The time allowed for one complete cycle: a move out, a dwell, a move back and a second dwell. The calculated cycle time is compared with it.
- Units and format
- Enter a number in s: seconds. The form accepts 0.000001 s to 100000 s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2.5 s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Make sure the required time covers both moves and both dwells, not one move only.
Drive and motor
What this means: Travel per motor revolution (screw lead or pull…
- What it is
- How far the carriage travels for one turn of the motor shaft: the screw lead for a ball screw, or the pulley pitch circumference for a belt drive, including any gearbox between motor and screw.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer lead lowers the motor speed needed but raises every motor torque.
- Get it right
- Lead is not the same as pitch on a multi-start screw: lead = pitch × number of starts.
What this means: Drive efficiency
- What it is
- The share of motor power the screw or belt passes to the carriage, from the screw or belt maker’s data.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 1% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 90% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Lower efficiency raises every motor torque in inverse proportion.
- Get it right
- Type the percentage itself; ball screws and lead screws differ greatly.
What this means: Motor maximum speed
- What it is
- The highest speed the motor is rated for, from its data sheet. The motor speed at the peak carriage speed is compared with it.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 100000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3000 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the rated maximum speed at your supply voltage, not a no-load figure.
What this means: Motor peak torque
- What it is
- The peak torque the motor can deliver for short periods, from its data sheet. The accelerating torque is compared with it.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0.000001 N·m to 100000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Peak torque often falls at higher speeds; check the curve at the motor speed you need.
What this means: Motor continuous torque
- What it is
- The torque the motor can deliver continuously without overheating, from its data sheet. The RMS torque over the cycle is compared with it.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0.000001 N·m to 100000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.5 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Do not compare the continuous rating with the peak torque; it is checked against the RMS value only.
Method and formulas
- Trapezoidal if L ≥ V² ÷ a: t = L ÷ V + V ÷ a; otherwise t = 2√(L ÷ a); acceleration force = m a (as the move profile tool).
- Friction F_f = μ m g; motor torque T = F × lead ÷ (2π η); motor speed = peak speed ÷ lead.
- T_rms = √(Σ T² t ÷ cycle) with accelerating (m a + F_f), running (F_f) and decelerating (m a − F_f) torques and zero torque in the dwells.
- Example: each move takes 0.7 s; the motor turns 2,400 rpm with 0.52881 N·m peak and 0.2637 N·m RMS over a 2.4 s cycle.
Limitations
- Horizontal axis; on a vertical axis gravity adds to the torque one way and needs a brake.
- Rotor and screw inertia are not included; add their share to the moving mass for a servo sizing.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a motor for a pick-and-place axis
- Check whether a faster cycle is possible
- Pick a screw lead for a linear stage
Who it is for
- Automation engineers
- Machine designers
- Controls engineers
What you get
- Move profile, time and peak speed
- Motor speed and torques
- RMS torque and cycle time against the motor and target
Interpreting the result
- Halving the acceleration time doubles the accelerating torque; a coarser lead trades motor torque for motor speed.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 175–180, 155–162. Topic reference; no source tables or recommended settings are reproduced.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Linear Move Drive Check (Move Profile, Screw Torque, RMS Torque, Cycle Time) calculator