Kneumatik

Servo Motion Profile Calculator

Calculate motor requirements, optimize system parameters, and verify performance for servo-driven motion systems.

Calculator

Usage Guidelines

Motor Selection

Enter motion requirements (distance, cycle time)
Input load characteristics
Set initial gear ratio
Review required motor specifications
Verify thermal requirements (RMS torque)

Payload Capacity

Enter motor specifications
Input motion requirements
Set mechanical parameters
Calculate maximum allowable payload
Verify inertia ratio

Gear Ratio Optimization

Enter system parameters
Run optimization
Review resulting inertia ratio
Verify torque and speed requirements
Select nearest standard ratio

Overview

This calculator helps you design and validate servo motion systems by:

Determining required motor specifications from motion requirements
Calculating maximum payload capacity for a given motor
Optimizing gear ratios for best performance
Analyzing system dynamics and energy consumption

Motion Profile

The calculator uses a triangular velocity profile which provides:

Minimum peak velocity for given move time
Balanced acceleration/deceleration phases
Simple energy calculations
Clear performance requirements

The profile consists of:

Acceleration phase (0 to peak velocity)
Deceleration phase (peak velocity to 0)
Dwell time (stationary period)

\[v(t) = \begin{cases} a_{max}t & 0 \leq t \leq \frac{t_m}{2} \\ a_{max}(t_m - t) & \frac{t_m}{2} < t \leq t_m \\ 0 & t_m < t \leq t_c \end{cases}\]

Where:

$t_m$ = move time
$t_c$ = cycle time
$a_{max}$ = peak acceleration
$v_{max}$ = peak velocity

Key Calculations

Inertia Ratio

The inertia ratio ($\lambda$) is a critical parameter for servo system performance:

\[\lambda = \frac{J_L}{J_M \cdot i^2}\]

Where:

$J_L$ = load inertia
$J_M$ = motor inertia
$i$ = gear ratio

Recommended range: $\lambda \leq 10:1$

Required Torque

Peak torque requirement includes inertial and dynamic loads:

\[T_{req} = \frac{(J_M + J_{L,reflected}) \cdot \alpha \cdot i}{\eta}\]

Where:

$J_{L,reflected} = \frac{J_L}{i^2}$ = reflected load inertia
$\alpha$ = angular acceleration
$\eta$ = mechanical efficiency

RMS Torque

For thermal calculations:

\[T_{RMS} = \sqrt{\frac{1}{t_c}\int_0^{t_c} T(t)^2 dt}\]

For triangular profile:

\[T_{RMS} = T_{peak} \sqrt{\frac{t_m}{3t_c}}\]

Important Notes

Keep inertia ratio below 10:1 for best performance
Verify mechanical resonance frequencies
Consider thermal requirements for continuous operation
Account for friction and external loads if significant
Add safety margin for acceleration requirements
Consider standardized motor/gear combinations

References

Servo Motor Sizing Fundamentals (Kollmorgen)
Motion Control Design Guide (Yaskawa)
Inertia Matching for Servo Applications (ASME)