Harmonic drives, with their compact structure, low backlash, and high rigidity, have become core components in high-end equipment such as robots and aerospace systems. However, many engineers encounter a common phenomenon: when the reduction ratio increases beyond a certain level (for example, above 100), the growth of output torque gradually slows down or even levels off—clearly contradicting the derived assumption that “torque is proportional to the reduction ratio.”

I had not paid much attention to this issue before, but a recent discussion with a friend prompted me to look into it more deeply. After reviewing relevant materials, I organized my findings into this article, hoping it can help engineers who may be confused by this topic.

1. Ideal vs. Reality: The “Theoretical Upper Limit” of Torque Amplification

We know that the output torque of a reducer follows the formula:

T_out = T_in × i × η

where T_in is the input torque, i is the reduction ratio, and η is the transmission efficiency. According to this logic, increasing the reduction ratio should result in a proportional increase in output torque—this is the theoretical basis of “speed reduction and torque amplification.”

However, the real-world performance of harmonic drives breaks this ideal expectation. Once the reduction ratio reaches a certain threshold (typically above 100 or 120), the increase in output torque—especially rated output torque and the maximum allowable average load—narrows rapidly and eventually enters a “saturation zone.” Even if the reduction ratio continues to increase, the torque no longer rises significantly.

This phenomenon is not a product defect, but an inevitable result of the combined effects of material properties, structural design, and transmission characteristics.

2. In-Depth Analysis: Three Core Causes of Torque Saturation at High Reduction Ratios

The stagnation of torque growth in harmonic drives is essentially a process in which theoretical torque amplification is gradually offset by real-world engineering constraints. These constraints can be summarized into three key factors, each closely tied to the drive’s structure and transmission principles.

2.1 Material and Structural Load Limits: The “Ceiling” of the Flexspline and Gears

The core transmission mechanism of a harmonic drive relies on the periodic elastic deformation of the flexspline. The flexspline is continuously subjected to alternating stresses, and its load-bearing capability is strictly limited by the fatigue strength of the material. No matter how high the reduction ratio becomes, the material properties and geometric dimensions of the flexspline do not improve accordingly—there is a clear upper limit to the stress it can withstand.

At the same time, torque transmission fundamentally depends on gear meshing. Load capacity is determined by key factors such as tooth contact area and tooth root strength. Increasing the reduction ratio does not change these physical parameters. When the theoretical output torque approaches the structural load limit, torque growth naturally stalls. This is the most fundamental physical constraint.

2.2 Transmission Efficiency Decline: “Energy Loss” Behind High Reduction Ratios

The transmission efficiency of harmonic drives is not constant; it decreases as the reduction ratio increases. Higher reduction ratios mean more gear teeth engaged in meshing, leading to increased losses from tooth surface friction and flexspline deformation. A significant portion of the input power is converted into heat rather than useful output power.

This efficiency degradation directly offsets the torque gain expected from a higher reduction ratio. Although theoretically T_out should increase with i, the reduction in η significantly weakens the actual output torque, ultimately resulting in sluggish torque growth.

2.3 Nonlinear Effects of Elastic Deformation: “Hidden Losses” from Reduced Meshing Accuracy

As an elastic component, the flexspline exhibits nonlinear torsional stiffness. Under high load torque, noticeable elastic deformation occurs in the flexspline and wave generator. This deformation causes gear meshing to deviate from the ideal trajectory, affecting not only transmission smoothness but also generating additional losses.

Under high reduction ratio conditions, these nonlinear effects are amplified. Increased meshing deviation and energy loss further limit effective torque output, making torque saturation more pronounced.

Ideal vs. Actual Transmission Characteristics

3. Engineering Significance: Why Pursue High Reduction Ratios Anyway?

If high reduction ratios cannot continuously increase torque, why do engineers still prefer high-ratio harmonic drives in robots, precision machine tools, and similar applications?

The key reason is that the selection logic shifts from “torque amplification” to “performance enhancement.” The true value of high reduction ratios lies in improving transmission precision and overall system performance.

3.1 Improved Motion Control Accuracy and Positioning Resolution

The pulse count per revolution of a servo motor is fixed. A high reduction ratio effectively magnifies angular resolution—after reduction, each motor pulse corresponds to a much smaller output shaft rotation. This significantly improves positioning resolution, which is a fundamental requirement for high-precision control.

3.2 Better Load Matching and Improved Dynamic Response

According to the reflected inertia formula:

J_reflected = J_load / i²

the load inertia reflected to the motor shaft decreases with the square of the reduction ratio. A high reduction ratio greatly reduces reflected inertia, making it easier to match the motor to the load. This results in faster response, improved stability, and reduced vibration and error.

3.3 Compact Structure and Low-Backlash Transmission

One of the core advantages of harmonic drives is their ability to achieve high reduction ratios in a single stage, eliminating the need for multi-stage gear trains. This simplifies the transmission structure, reduces size, and suits compact installation spaces such as robot joints.

Additionally, harmonic drives feature multi-tooth engagement—up to 30% of the total teeth can be engaged simultaneously—enabling near-zero backlash transmission and significantly improving repeatability, a critical performance metric for high-end equipment.

4. Practical Selection Tips: Avoiding High Reduction Ratio Pitfalls

Based on these characteristics, engineers should abandon the assumption that “higher reduction ratio equals higher torque” and instead focus on real application needs. Three key points deserve particular attention:

4.1 Prioritize Rated Output Torque

Rather than relying excessively on theoretical calculations, engineers should primarily refer to manufacturer datasheets and focus on rated output torque and peak torque. These values already account for material strength, efficiency loss, and other real-world factors, making them far more representative of actual operating conditions.

4.2 Match Reduction Ratio to Application Priorities

If high torque is the primary requirement, choosing a larger or higher-capacity model is more effective than simply increasing the reduction ratio. If high precision and resolution are the main goals, then a high reduction ratio model can be selected to fully leverage its accuracy advantages.

4.3 Pay Attention to Installation and Maintenance Details

Proper lubrication and effective heat dissipation help mitigate efficiency loss and material fatigue, extending service life. Precise alignment during installation reduces flexspline deformation and meshing deviation, avoiding unnecessary losses. These details have a direct impact on real-world performance and torque stability.

The lack of significant torque increase at high reduction ratios in harmonic drives is the result of combined effects from material load limits, transmission efficiency decline, and elastic deformation—not a flaw in the transmission principle itself. The true value of harmonic drives has long gone beyond simple “torque amplification,” shifting toward precision enhancement, load matching, and structural optimization, making them a core enabler of precise control in high-accuracy equipment.