Reduction ratio, as the ratio of the input speed to the output speed of the reducer in the servo system, is usually expressed by the value i. Although this parameter seems simple, it has a profound impact on the overall performance of the servo system.
(I) Basic calculation formula
The calculation formula is: i = N₁/N₂ = T₂/T₁×η. Among them, N₁ represents the input speed (motor end), N₂ is the output speed (load end), T₁ is the input torque, T₂ is the output torque, and η is the transmission efficiency .
(II) Three core roles
Torque amplification effect: The output torque is approximately equal to the motor torque multiplied by the reduction ratio, that is, the output torque ≈ motor torque ×i, which can effectively enhance the system’s ability to drive the load.
Speed reduction function: The output speed is obtained by dividing the motor speed by the reduction ratio, that is, the output speed = motor speed /i, which can convert the high speed of the motor into the low speed required by the load.
Inertia matching effect: When the load inertia is converted to the motor shaft, it will be reduced by i² times, which helps to optimize the inertia matching of the system and improve the stability of the system operation.
The influence of the reduction ratio on the five key performances of the servo system
(I) System dynamic response characteristics
The selection of the reduction ratio is directly related to the acceleration capability and response speed of the servo system.
Small reduction ratio (i<10)
Advantages: Fast response speed, suitable for work occasions that require frequent high-frequency start and stop.
Disadvantages: The motor needs to provide greater torque, and the motor performance requirements are high.
Typical applications: indexing plates, high-speed packaging machines and other equipment.
Large reduction ratio (i>50)
Advantages: Significant torque amplification effect, suitable for heavy-load application scenarios.
Disadvantages: The system inertia increases accordingly, resulting in a slower response speed.
Typical applications: heavy-load robot joints, etc.
(II) Positioning accuracy performance
The reduction ratio mainly affects the system accuracy through two mechanisms.Resolution enhancement effect: The encoder resolution will be equivalently increased by i times. For example, when a 17-bit encoder (131072 pulses/rev) is paired with a reducer with i = 50, the equivalent resolution at the load end can reach 2,621,440 pulses/rev, greatly improving the position detection accuracy.
Error reduction effect: The positioning error on the motor side will be reduced by i times when reflected on the load end, but it should be noted that the backlash of the reducer itself will have a reverse effect on the accuracy.
(III) Energy efficiency and temperature rise
An unreasonable reduction ratio will cause significant energy loss.
Improper speed matching: When the motor works in the inefficient speed range (<500rpm), the efficiency will drop by 10-30%, and the temperature rise will increase by 15-40℃, resulting in energy waste and shortened equipment life.
Torque matching imbalance: A small reduction ratio will force the motor to output a large current, increase copper loss, and then increase the winding temperature, affecting the motor performance and reliability.
The system efficiency curve (measured data) under different reduction ratios can intuitively show how the efficiency changes with the reduction ratio (the relationship curve of efficiency vs reduction ratio needs to be inserted here).
Three golden rules in engineering selection
(I) Torque-speed matching principle
The calculation formula is: i = N_motor/(1.2×N_load_max). Among them, 1.2 is the safety factor. This formula can ensure that the motor works in the optimal efficiency area (usually 70-90% of the rated speed), give full play to the motor performance and ensure stable operation of the system.
(II) Inertia matching criteria
The recommended inertia matching relationship is: 0.25 <J_load/(i²×J_motor) < 4. If it exceeds this range:
If the value is too small, the system response will become sluggish and cannot quickly follow the command changes.
If the value is too large, it is easy to cause system oscillation, affecting the operation accuracy and stability of the equipment.
(III) Precision transfer formula
The total positioning error of the system is calculated as: ε_total = ε_motor/i + ε_reducer. In practical applications, it is necessary to ensure that ε_total < allowable error / 3 to meet the system’s requirements for positioning accuracy.
Common selection misunderstandings and solutions
“The bigger the better” misunderstanding
Phenomenon: Some users blindly choose a large reduction ratio when selecting.
Problem: This will cause the motor to run at a low speed for a long time, resulting in obvious torque pulsation, affecting the smoothness and accuracy of the equipment.
Solution: A two-stage reduction method can be used, or the motor power can be appropriately increased to balance the torque and speed requirements.
Ignoring efficiency changes
Phenomenon: Only the theoretical speed ratio is calculated, and the change in efficiency with the speed ratio in actual operation is not considered.
Problem: The actual operating efficiency of the system is lower than expected, increasing energy consumption and operating costs.
Solution: Carefully refer to the efficiency curve provided by the manufacturer when selecting, and comprehensively consider the efficiency performance under different reduction ratios.
Backlash accumulation error
Phenomenon: In the case of multi-stage series reducers, simply add the backlash of each stage to estimate the total backlash.
Correct method: The formula ε_total = √(ε₁²+ε₂²+…) should be used to accurately calculate the total backlash of the system to ensure the positioning accuracy of the system.
Analysis of typical cases of industry applications
(I) SCARA robot joints
Requirement: Achieve a balance between speed and accuracy to meet the efficient and precise operation requirements of robots in tasks such as assembly.
Solution: The first two axes use a reduction ratio of i = 50, and the Z axis uses a reduction ratio of i = 30.
Effect: Successfully achieved a repeated positioning accuracy of ±0.01mm, meeting the requirements of high-precision operations.
(II) CNC turntable
Problem: The vibration is large when directly driven, affecting the positioning accuracy and processing quality of the turntable.
Solution: Use a two-stage planetary reduction scheme with i = 120, and use the torque amplification and speed reduction functions of the reducer.
Results: The angular resolution was increased to 0.0001°, which effectively reduced vibration and improved the accuracy and stability of the turntable.
(III) Packaging machine conveyor belt
Error: The original reduction ratio of i = 5 caused the motor to be overloaded for a long time, resulting in overheating, which affected the life of the equipment and production efficiency.
Correction: Use a reduction ratio of i = 20, increase heat dissipation measures, and optimize system matching.
Improvement: The motor temperature was reduced by 25°C, the equipment life was extended by 3 times, and the stable operation of the packaging machine was guaranteed.
The reduction ratio is crucial to the servo system and is related to the system performance, selection and application. Avoiding misunderstandings and choosing it reasonably can improve energy efficiency and reduce costs. Nowadays, cutting-edge technologies are emerging frequently, and servo systems are developing rapidly. In the future, deepening the understanding and application of reduction ratios will effectively promote its innovation and popularization in various industries.