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Parallel Shaft Gear Transmission in Gear Drive: A Comprehensive Explanation

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Parallel Shaft Gear Transmission in Gear Drive: A Comprehensive Explanation

Overview

Gear transmission is one of the most prevalent methods in mechanical engineering, boasting high efficiency, stable transmission ratios, and strong load-carrying capacity. Among its variants, parallel shaft gear transmission is tailored for scenarios where two shafts are arranged in parallel, finding extensive applications in industrial equipment, automobiles, aerospace, and beyond. This guide elaborates on its working principles, design methodologies, and engineering applications, serving as a practical reference for professionals.

1. Working Principles of Parallel Shaft Gear Transmission

1.1 Basic Transmission Mechanism

Parallel shaft gear transmission relies on the meshing of two gears with parallel axes to transfer motion and power. Common types of parallel shaft gears include:

 

  • Spur Gear: Teeth are parallel to the gear axis, featuring a simple structure. Ideal for low-speed, light-load applications.
  • Helical Gear: Teeth are helically shaped, ensuring smoother meshing and higher load capacity. Suitable for high-speed, heavy-load transmission.
  • Double Helical/Herringbone Gear: Consists of two symmetric helical gear rows, offsetting axial forces. Used in heavy-load, precision transmission systems.

 

Meshing Requirements:

 

  • Identical module (m)
  • Identical pressure angle (α)

 

Advantages Disadvantages
High efficiency (up to 98%) High manufacturing precision requirements
Constant transmission ratio Vibration and noise (more pronounced in spur gears)
Strong load-carrying capacity Requires precise lubrication

1.2 Transmission Ratio Calculation

The transmission ratio i is defined as the ratio of input speed to output speed:(i = frac{n_1}{n_2} = frac{z_2}{z_1}) Where:

 

  • (n_1, n_2) = input and output speeds (r/min)
  • (z_1, z_2) = number of teeth on driving and driven gears

 

For multi-stage transmission, the total ratio is the product of individual stage ratios:(i_{text{total}} = i_1 times i_2 times dots times i_n)

2. Key Design Parameters and Calculations

2.1 Basic Gear Parameters

  • Module (m) Selection: Estimated using torque and speed:(m geq sqrt[3]{frac{2000T}{psi_d z_1 [sigma_F]}}) Where:
    • T = torque (N·m)
    • (psi_d) = tooth width factor
    • (z_1) = number of teeth on the pinion
    • ([sigma_F]) = allowable bending stress (MPa)
    Preferred standard modules: 1, 1.25, 1.5, 2, ..., 18 (mm).
  • Tooth Count Determination:
    • Closed transmission: Pinion teeth = 20–40
    • Open transmission: Pinion teeth ≥ 17
    • Minimum teeth to avoid undercutting: (z_{text{min}} = frac{2}{sin^2 alpha}); for (alpha = 20^circ), (z_{text{min}} = 17).
  • Transmission Ratio Distribution: For multi-stage systems, follow the "small first, large later" principle. Adjacent stage ratios should range from 1.3 to 1.5.

2.2 Gear Force Analysis

  • Circumferential force: (F_t = frac{2000T_1}{d_1} , text{(N)})
  • Radial force: (F_r = F_t tan alpha , text{(N)})
  • Normal force: (F_n = frac{F_t}{cos alpha} , text{(N)})

 

Force Relationships:

 

  • (F_{t1} = -F_{t2}) (opposing circumferential forces)
  • (F_{r1} = -F_{r2}) (opposing radial forces)
  • (F_{t1}) acts against the driving gear’s rotation; (F_{t2}) aligns with the driven gear’s rotation.

2.3 Strength Check

  • Tooth Surface Contact Fatigue Strength:(sigma_H = Z_H Z_E Z_varepsilon Z_beta sqrt{frac{2K F_t}{b d_1 (1 - 1/u)}}) Where:
    • (Z_H, Z_E, Z_varepsilon, Z_beta) = node area, elastic, contact ratio, and helix angle factors
    • b = tooth width; (d_1) = pinion reference diameter; u = gear ratio
    Key principles: Depends on (d_1); excessive tooth width causes uneven loading.
  • Tooth Root Bending Fatigue Strength:(sigma_F = frac{2K F_t}{b m} Y_{Fa} Y_{Sa} Y_varepsilon Y_beta leq [sigma_F]) Where:
    • (Y_{Fa}, Y_{Sa}) = tooth form and stress correction factors
    Key principles: Dominated by module m; pinions require higher-grade materials due to greater stress cycles.

2.4 Shaft Design

Preliminary shaft diameter estimation:(d geq A sqrt[3]{frac{P}{n}}) Where:

 

  • A = material factor (100–110 for carbon steel; 95–105 for alloy steel)
  • Pub Time : 2025-08-01 09:35:30 >> News list
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