As the core component of mechanical transmission system, the reliability is directly related to the normal operation of equipment. In the long-of gear service, root stress (Root Stress) is one of the main factors affecting its failure. In this paper, we will deeply analyze the calculation method of tooth root bending stress, and discuss the analysis method of gear breaking and failure, so as to help engineers to better understand and prevent the snapping problem of gear, and improve the service life of gear.

1. Definition of tooth root bending stress

Root stress refers to the maximum stress caused by bending in the root area when the gear is under load. Because the tooth root is the weakest part of the gear, its stress concentration effect is strong, so it becomes the main area of gear breaking and failure. The excessive root stress may lead to the initiation and expansion of fatigue cracks, and eventually lead to gear breaking.

2. Calculation method of tooth root bending stress

The root bending stress is generally calculated by Lewis formula (Lewis Equation) or ISO 6336-3 standard formula.

2.1 The Lewis formula

Lewis formula is a simplified method of root stress calculation suitable for preliminary estimation of gear strength:

among:

σ F: Root Bending Stress (MPa)

Ft: tangential force acting on the gear surface (N)

B: tooth width (mm)

M: modulus (mm)

Y: tooth shape coefficient, related to tooth number and pressure angle

✅ This formula assumes that the root of the gear is in the bent state of simple support beam, without considering the stress concentration effect, and it is only applicable to low precision calculation.

2.2 ISO 6336-3 standard formula

For more precise root stress calculation, refer to the formula specified in ISO 6336-3:

among:

KF: Load distribution coefficient

KA: Applied load coefficient

KV: the dynamic load coefficient

YF: tooth shape coefficient

YS: Stress concentration coefficient

✅ ISO 6336-3 calculation method considers the actual working conditions, such as load distribution, manufacturing error, etc., and is suitable for high-precision gear design.

3. Gear break and failure analysis

Gear breaks is usually caused by fatigue failure or overload failure. the following are common failure modes:

3.1 Root Fatigue Break (Bending Fatigue Fracture)

Features: Cracks originate from the root and expand along the root, eventually causing the gear to break.

cause:

Long-term propagation load leads to fatigue crack extension

The tooth root stress is too large, and the stress concentration effect is significant

Insufficient fatigue strength of the material

Rx:

Root root angle was optimized to reduce stress concentration

To carburize or bolen to improve the surface strength

3.2 Overload Break (Overload Fracture)

Features: The fracture port shows brittle fracture characteristics, and the crack expands rapidly.

cause:

Overload impact resulting in instantaneous fracture

Root material defects, such as inclusions, cracks

Rx:

Use high-toughness materials to improve the impact resistance

Ultrasonic flaw detection was performed to detect the internal defects

4. Optimization design of rail transit gear

In the design of rail transit gearbox, it is crucial to improve the root strength. Common optimization measures include:

Case 1: High-speed EMU gear

Large tooth root and rounded corners are used to reduce stress concentration.

Conduct surface shot shot treatment to improve fatigue resistance.

Case 2: Subway gearbox

High-strength carburizing steel is selected to enhance the wear resistance.

The tooth root was optimized to improve the load distribution.

Root stress is the key factor to determine the failure of gear breaking. Reasonable calculation and optimization design can effectively improve the service life of gear.

ISO 6336-3 standard provides a more accurate method of root bending stress for high precision gear design.

Gear break failure mainly includes fatigue breaking and overload break. The fatigue resistance should be improved by optimizing the root structure and strengthening the surface treatment.

The rail transit gear box should be made of high strength materials and combined with modern testing technology to ensure the long-term stable operation of the gear.