Energy Efficiency and Power Transmission Analysis of a High-Ratio Gear Reduction System

Abstract

This study presents the design and experimental performance evaluation of a custom-built high-ratio gear reduction system composed of four shafts and six spur gears. The gear arrangement consists of three transmission stages: 2:1 (Gear 1–2), 10:1 (Gear 3–4), and 5:1 (Gear 5–6), resulting in a total theoretical speed ratio of 1:100. The gears were manufactured with tooth counts ranging from 10 to 100 and diameters between 36?mm and 316?mm. The gearbox was tested under five different input conditions, with input rotational speeds ranging from 0.281 to 0.391 RPM and torque levels from 2.5 to 27 Nm applied at the driver shaft. RPM and torque were measured at all four shafts to evaluate transmission performance. The maximum recorded output speed at shaft 4 was 40.281 RPM, corresponding to an actual speed multiplication factor of approximately 103:1, which closely aligns with theoretical expectations. Power at each shaft was calculated using the equation P=???. Input power ranged from 0.07?W to 1.10?W, while output power varied from 0.047?W to 0.76?W. The system demonstrated efficiencies between 63.9% and 87.8%, with the highest efficiency observed at moderate torque inputs (6–23 Nm). Energy losses were primarily due to friction, backlash, and minor alignment deviations. The results confirm that the gearbox performs reliably and efficiently for high-ratio speed conversion applications. This configuration is suitable for systems requiring compact form, low input speed, and high output speed, such as laboratory instrumentation, automation mechanisms, or kinetic energy recovery setups

Introduction

Gear systems, especially spur gearboxes, are widely used in mechanical power transmission due to their reliability, compactness, and precision. However, efficiency drops in multi-stage gearboxes due to losses like friction, backlash, and shaft misalignment. This study evaluates the kinematic performance and power efficiency of a three-stage spur gearbox designed to achieve a 100:1 gear ratio, aiming to quantify performance deviations and suggest improvements.

?? Gearbox Design

• Configuration: 3 stages, 6 gears, 4 shafts

  • Stage 1: 2:1 ratio (60T to 30T)

  • Stage 2: 10:1 ratio (100T to 10T)

  • Stage 3: 5:1 ratio (50T to 10T)

• Total Theoretical Ratio: 100:1

• Materials: Hardened steel gears, aluminum frame, ball bearings

• Manufacturing: Involute profile, 20° pressure angle

???? Methodology

• Testing: Input torque levels: 2.5–27 Nm; Input RPM: 0.281–0.391

• Measurements:

  • RPM: Non-contact tachometers (±1% accuracy)

  • Torque: Strain gauge sensors (±0.5% accuracy)

• Power Calculations:

  • Power P=τ⋅ωP = \tau \cdot \omegaP=τ⋅ω, ω=(2π⋅RPM)/60\omega = (2\pi \cdot \text{RPM}) / 60ω=(2π⋅RPM)/60

  • Efficiency per stage: η=PoutPin×100%\eta = \frac{P_{\text{out}}}{P_{\text{in}}} \times 100\%η=Pin?Pout??×100%

???? Key Results

• Actual Output Speeds: 25.1–40.3 RPM

• Actual Ratio: ~89:1 to 103:1 (±10% deviation from theoretical)

• Efficiency Range: 63.9% to 87.8%

  • Highest efficiency at mid-range torque (23 Nm)

  • Lowest at low torque (2.5 Nm), due to proportionally higher frictional losses

• Input Power: 0.07 – 1.10 W

• Output Power: 0.047 – 0.76 W

???? Key Findings & Discussion

• RPM Analysis: Output RPMs closely follow input RPMs with a near-linear trend; slight deviations due to mechanical imperfections and losses.

• Torque Analysis: Strong linear relationship between input and output torque (R² = 0.960). Output torque remains low due to speed-focused design.

• Efficiency Analysis:

  • Peak efficiency occurs at moderate load due to optimal balance of mechanical resistance and power input.

  • Efficiency drops at both low and high torques, confirming effects of friction and misalignment.

?? Energy Loss Sources Identified

1. Gear mesh friction

2. Bearing and shaft resistance

3. Backlash in gears

4. Shaft misalignment

5. Torsional deflection of shafts

6. Inadequate lubrication (suboptimal EHL conditions)

These are consistent with findings from existing literature (Dogan, Tian, Veciana, Gonzalez-Perez, etc.), placing the results within expected real-world performance bounds for multi-stage spur gear systems.

Conclusion

This study presented the design, construction, and experimental evaluation of a multi-stage spur gearbox system with a theoretical speed ratio of 100:1. The gearbox demonstrated reliable kinematic performance, achieving an actual output speed ratio of up to 103:1, with minimal deviation from theoretical predictions.conclusions from the experimental results are as follows: Output speed increased proportionally with input speed, confirming accurate gear meshing and alignment. A linear regression between input and output RPM yielded a strong correlation with an R2R^2R2 value of 0.854. System efficiency ranged between 63.9% and 87.8%, peaking at mid-range input torque levels. Efficiency decreased under very low and very high torque, indicating the influence of mechanical losses. Output torque showed a positive correlation with input torque, though the relationship was not perfectly linear. The torque transmission ratio ranged from 0.666% to 0.896%, averaging 0.756%, which is consistent with the expected trade-off in high-speed gear systems. A linear regression of torque data produced a high coefficient of determination (R2=0.960), confirming a strong predictive relationship between input and output torque

References

[1] O. Dogan, “Performance Evaluation of Low- and High-Contact Ratio Spur Gears,” J. Vib. Eng. Technol., vol. 10, pp. 1337–1347, Jun. 2022. [Online]. Available: https://doi.org/10.1007/s42417-022-00450-x [2] J. M. Veciana, M. Vives, M. Egusquiza, and F. Martinez, “Analysis of Energy Efficiency in Spur Gear Transmissions: Cycloidal Versus Involute Profiles,” Machines, vol. 12, no. 12, p. 943, Dec. 2024. [Online]. Available: https://doi.org/10.3390/machines12120943 [3] X. Tian, G. Wang, and Y. Jiang, “A New Calculation Method for Instantaneous Efficiency and Torque Fluctuation of Spur Gears,” Strojniški vestnik – J. Mech. Eng., vol. 70, no. 1–2, pp. 55–69, Jan. 2024. [Online]. Available: https://doi.org/10.5545/sv-jme.2023.709 [4] I. Gonzalez-Perez and A. Fuentes-Aznar, “Improvement of the Transmission Efficiency in Electric Vehicles by Using Double Staggered Helical Gears,” Forsch. Ingenieurwes., vol. 87, pp. 1081–1094, Sep. 2023. [Online]. Available: https://doi.org/10.1007/s10010-023-00707-1 [5] TikTech, “Gear Backlash: Understanding Its Effects on System Performance,” TechMeStuff, Mar. 2024. [Online]. Available: https://techmestuff.com/gear-backlash-impact-performance [6] Nisuka Industries, “Shaft Misalignment’s Impact on Gearbox Performance,” Industrial Insights, 2025. [Online]. Available: https://nisukaindustries.com/common-problems-in-gearboxes-and-how-to-solve-them

Copyright

Copyright © 2025 Agus Margiantono, Titik Nurharyanti, Muhammad Sipan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.