How to Select a Linear Shaft Motor: A Step-by-Step Engineering Guide

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

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.

Peak force determines what the motor must be capable of momentarily. Continuous (RMS) force determines what the motor must sustain thermally over time. Many motors can provide high peak force for short durations but cannot maintain that force continuously 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.

The continuous force rating is thermal in nature — it represents the force at which the motor reaches thermal equilibrium at its maximum rated winding temperature. If the motor will operate in an elevated ambient temperature, the continuous rating must be derated.

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

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

With peak force, continuous force, speed, and stroke defined, select the motor from the datasheet:

Selection criteria (in order of priority):

1. Peak force rating > F_peak_design (with safety factor)
2. Continuous force rating > F_rms (at ambient temperature)
3. Maximum speed > v_max (with 20-30% margin)
4. Shaft available in required length
5. Force constant (N/A) matches available current from selected servo drive
6. 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.

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.