As a core component of modern industrial automation, the performance of servo systems directly impacts equipment motion accuracy and dynamic response. During servo commissioning, stiffness and inertia ratio are two critical parameters that jointly determine system stability and response speed. This article will delve into the concepts of servo stiffness and inertia ratio, their commissioning methods, and practical considerations in real-world applications.
I. Concept and Debugging of Servo Stiffness
Servo stiffness reflects a system's ability to resist external disturbances, typically manifested as the combined effect of position loop gain (PG) and velocity loop gain (VG). A high-stiffness system responds swiftly to commands and resists external disturbances, but excessive stiffness may induce mechanical vibration; a low-stiffness system offers stability but exhibits slower dynamic response.
Debugging Methods:
1. Position Loop Gain (PG) Adjustment
PG determines the system's ability to correct position deviations. Increasing PG enhances rigidity but requires caution to avoid overshoot. The "incremental method" is recommended: Start from a lower value and gradually increase while monitoring equipment vibration. Once slight oscillation appears, reduce the gain by 5%-10%.
2. Speed Loop Gain (VG) Optimization
VG influences speed loop response speed. During debugging, fix PG and incrementally increase VG until speed command tracking error is minimized. In typical scenarios, the VG-to-PG ratio is approximately 1:3 (e.g., when PG=30, VG≈10).
3. Feedforward Compensation Technology
For high-speed, high-precision applications, enable velocity feedforward and acceleration feedforward. Set velocity feedforward to 80%-95% and acceleration feedforward to 60%-80%. This significantly reduces tracking error without increasing vibration risk.
Case Study:
A CNC machine tool exhibited contour errors during arc machining. By increasing PG from 25 to 35, adjusting VG from 8 to 12, and enabling 85% velocity feedforward, contour accuracy improved by 42%. Note that different mechanical structures (e.g., direct drive vs. lead screw transmission) exhibit significant variations in sensitivity to stiffness parameters.
II. Calculation and Matching of Inertia Ratio
The inertia ratio is defined as the ratio of load inertia to motor rotor inertia (JL/JM), directly influencing system acceleration performance and stability. Traditional experience suggests limiting the inertia ratio to within 10:1, but modern servo technology now supports higher ratios (up to 50:1 in certain applications).
Calculation Method:
1. Load Inertia Measurement
● Obtained via motor self-identification functions (e.g., Yaskawa Σ-7 series "One-Touch Tuning").
● Formula calculation: For rotary loads, JL = 0.5mr²; linear motion loads require conversion to motor shaft inertia (JL = m × (v/ω)²).
2. Optimization Strategy:
When inertia ratio > 15, recommend:
a) Increase gear ratio (improves square relationship; e.g., gear ratio 12 reduces equivalent inertia ratio to 1/4)
b) Select high-inertia motor
c) Adjust speed loop integral time (typically increase by 20%-30%)
Special Scenario Handling:
In multi-joint robotic systems, the inertia ratio of each axis varies with posture. For a 6-axis robot where the 4th axis inertia ratio changes from 81 during motion, implement:
● Enable adaptive filtering (e.g., Mitsubishi MR-J4's vibration suppression function).
● Configure multiple gain parameter sets and automatically switch via PLC.
III. Collaborative Tuning of Rigidity and Inertia Ratio
These two parameters are coupled, requiring adherence to the debugging principle of "inertia first, then stiffness":
1. Basic Steps:
● After mechanical assembly, first measure the actual inertia ratio.
● Preset speed loop parameters based on the ratio range (e.g., when inertia ratio > 20, initial VG is set to 70% of the standard value).
● Finally, adjust the position loop gain.
2. Vibration Suppression Techniques:
● Enable notch filters in the 500-800Hz high-frequency vibration range.
● For low-frequency vibrations (<100Hz), appropriately reduce PG and increase the speed loop integral time.
3. Dynamic Testing Method:
Use a trapezoidal velocity curve for testing, observing tracking errors during different acceleration phases:
● Large error during acceleration → Increase VG or add acceleration feedforward.
● Error during constant velocity → Adjust PG.
● Overshoot during deceleration → Optimize deceleration time constant.
IV. Advanced Tuning Techniques and Industry Applications
1. Adaptive Control Technology
For example, the HRV control in Fanuc's 30iB system can identify load changes in real time and automatically adjust gains. In die casting machine applications, it reduces position fluctuations by 60% when inertia ratios fluctuate.
2. Dual-Closed-Loop System Configuration
High-precision grinding machines often employ dual feedback (motor encoder + linear scale). Key considerations include:
● Insufficient mechanical rigidity may cause oscillation in linear scale feedback.
● Set linear scale resolution to 5–10 times that of the motor encoder.
3. Industry Parameter Reference:
| Industry Applications | Typical Inertia Ratio | PG Rating | VG Rating |
| SMT Placement Machine | 3-8 | 40-60 | 15-25 |
| Injection molding machine platen | 15-30 | 20-35 | 8-15 |
| Gantry machine tool | 5-12 | 30-45 | 10-20 |
V. Solutions to Common Issues
1. Low-Frequency Vibration Issue
A packaging machine exhibited persistent vibration at the 5Hz frequency band. Resolved through the following steps:
● Verify mechanical transmission clearance <0.05mm.
● Reduce VG from 12 to 9 and adjust PG from 35 to 28.
● Increase speed loop integral time from 100ms to 150ms.
2. Inertia Recognition Error
When using third-party gearboxes, measured inertia ratios may deviate up to 30% from theoretical values. Recommendations:
● Take multiple measurements at several typical positions and calculate the average.
● Account for equivalent inertia changes caused by gearbox backlash.
3. Rigidity Sudden Change Scenarios
For scenarios like stamping machines experiencing sudden rigidity increases upon contacting workpieces, countermeasures include:
● Configure two parameter sets and switch between them via IO signals.
● Use pressure sensors to trigger gain switching (switching delay must be <10ms).
With the advancement of smart manufacturing, servo tuning is shifting from experience-based to data-driven approaches. Engineers are advised to establish parameter databases documenting optimal parameter combinations under various operating conditions, complemented by vibration spectrum analysis tools for precise tuning. In the future, predictive tuning integrated with digital twin technology will emerge as a new development direction.