Selecting the wrong motor for an application is expensive — either the motor is undersized and fails prematurely, or it's oversized and wastes cost and space. Linear shaft motor selection follows a systematic methodology that weighs force requirements, duty cycle, thermal limits, speed, and stroke to land on the correct motor specification.
This guide walks through the selection process step by step. For most applications, you need to gather six pieces of information: load mass, required acceleration, friction force, maximum speed, stroke length, and duty cycle. Get those six numbers and the right motor follows directly.
Step 1: Define the Motion Profile
Before calculating any force requirements, fully define the motion profile — the complete description of how the load moves through time.
Trapezoidal profile (most common):
Most automation moves follow a trapezoidal velocity profile: accelerate from rest to peak velocity, cruise at peak velocity, decelerate to rest.
For a trapezoidal profile, you need:
- Stroke length (S) — Total travel distance in meters
- Maximum velocity (v_max) — Peak speed in m/s
- Acceleration time (t_acc) — Time to reach v_max in seconds
- Cycle time — Total time for move + dwell in seconds
From these, you can calculate acceleration:
a = v_max / t_acc
Example:
Stroke = 200mm = 0.2m
v_max = 0.5 m/s
t_acc = 0.1 s
a = 0.5 / 0.1 = 5 m/s²
Step 2: Calculate Peak Force Requirement
Peak force occurs during acceleration. The motor must provide enough force to accelerate the total moving mass at the required rate, overcome friction from the linear guide, and support any external forces on the load.
Peak force formula:
F_peak = (m × a) + F_friction + F_external
Where:
- m = total moving mass (payload + forcer + carriage + cable carrier)
- a = required acceleration (from Step 1)
- F_friction = friction force from linear guide (typically 0.5-2% of normal load)
- F_external = any constant external force (gravity component for vertical axis, process force, spring preload)
Example:
Moving mass m = 2 kg
Acceleration a = 5 m/s²
Guide friction (with 20N normal load) = 0.3N
External force = 0
F_peak = (2 × 5) + 0.3 + 0 = 10.3 N
Add a safety factor of 1.5-2x to handle acceleration transients, cable drag variation, and bearing preload variation:
F_peak_design = 10.3 × 1.5 = 15.5 N
Important: The selected motor's peak force rating must exceed F_peak_design.
Step 3: Calculate Continuous (RMS) Force Requirement
Peak force is what the motor needs to deliver for an instant. Continuous (RMS) force is what it needs to sustain, thermally, over time — and plenty of motors can hit a high peak force briefly but can't hold anywhere near that without overheating.
Calculate the RMS force over one complete cycle:
F_rms = √[(F_acc² × t_acc + F_cruise² × t_cruise + F_dec² × t_dec + F_dwell² × t_dwell) / t_cycle]
For our trapezoidal example with:
- t_acc = 0.1s, F_acc = 10.3N
- t_cruise = 0.2s, F_cruise = 0.3N (friction only)
- t_dec = 0.1s, F_dec = 10.3N (motor braking)
- t_dwell = 0.1s, F_dwell = 0N
- t_cycle = 0.5s
F_rms = √[(10.3² × 0.1 + 0.3² × 0.2 + 10.3² × 0.1 + 0 × 0.1) / 0.5]
F_rms = √[(10.6 + 0.02 + 10.6 + 0) / 0.5] = √[42.4] = 6.5 N
The selected motor's continuous force rating must exceed F_rms at the expected operating temperature.
Step 4: Verify Thermal Performance
The continuous force rating is a thermal spec — it's the force at which the motor settles into thermal equilibrium at its maximum rated winding temperature. Run it in a hotter-than-reference ambient, and that rating has to come down.
Motor datasheets specify continuous force at a reference temperature (typically 25°C ambient). Derate linearly with ambient temperature:
F_cont_derated = F_cont_rated × √[(T_max - T_ambient) / (T_max - T_ref)]
Where:
- T_max = motor maximum winding temperature (typically 100-130°C)
- T_ambient = actual ambient temperature
- T_ref = reference temperature (25°C typically)
If your F_rms exceeds the derated continuous force, you have options:
- Select a larger motor with higher continuous force rating
- Add active cooling to the motor mounting
- Reduce cycle rate (increase dwell time) to reduce duty cycle
Step 5: Verify Speed and Stroke
With force requirements confirmed, verify that the selected motor meets speed and stroke requirements.
Maximum speed:
Linear shaft motors have a maximum velocity determined by the back-EMF constant and available supply voltage. The motor datasheet specifies maximum speed at rated voltage. Verify that your required v_max is below the motor's rated maximum speed, with a 20-30% margin.
Stroke length:
The shaft must be long enough to accommodate the full stroke plus the forcer length. Minimum shaft length:
L_shaft_min = Stroke + L_forcer + 2 × mounting_margin
For strokes exceeding ~1 meter, also consider:
- Shaft deflection under gravity (shaft support bearings may be required)
- Thermal expansion of the shaft affecting end-of-stroke clearances
- Cable management for the moving forcer
Step 6: Select the Motor
With peak force, continuous force, speed, and stroke defined, select the motor from the datasheet:
Selection criteria (in order of priority):
- Peak force rating > F_peak_design (with safety factor)
- Continuous force rating > F_rms (at ambient temperature)
- Maximum speed > v_max (with 20-30% margin)
- Shaft available in required length
- Force constant (N/A) matches available current from selected servo drive
- Motor constant (N/√W) maximizes efficiency for the thermal budget
Motor constant (Km) is a useful figure of merit: higher Km means more force per unit of heat generated. For thermal-critical applications, choose the motor with the highest Km that meets force and speed requirements.
Don't forget the complete system:
Motor selection also determines drive requirements. Calculate required current for peak force: I_peak = F_peak / K_f where K_f is the motor force constant. Verify the servo drive can supply this current. Calculate required bus voltage from motor back-EMF constant and maximum speed.
Common Sizing Mistakes
Experienced engineers make these mistakes less often — but they happen:
- Forgetting cable and connector mass — On long-stroke systems, cable mass can be significant. A 3-meter cable bundle can weigh 0.5-1 kg — 25-50% of the payload in some cases.
- Not including forcer mass in moving mass — The forcer itself is part of the moving assembly and must be accelerated. Forcer mass is typically 0.5-3 kg depending on size.
- Using rated speed at rated voltage without margin — Always maintain 20-30% speed margin. Back-EMF builds linearly with speed; too close to rated speed and available force drops precipitously.
- Ignoring thermal derating for elevated ambient — Machines that pass thermal qualification at 25°C may run into continuous force limits at 45°C ambient in a production environment.
- Under-specifying the encoder — The encoder resolution should be 5-10x better than the positioning accuracy requirement. A 1 µm positioning requirement needs at least 0.1-0.2 µm encoder resolution.
Conclusion
Motor selection here isn't a guess, it's arithmetic. Work through peak force, RMS force, the thermal derating check, and the speed and stroke margins, and whatever motor survives all four is the right one for the application.
Nippon Pulse America's engineering team offers free sizing support: send over your load, acceleration, speed, stroke, and duty cycle, and we'll return a complete sizing analysis with a motor recommendation. The online sizing tools run the same calculation interactively, if you'd rather work through the numbers yourself first.
