# gear tooth strength calculator calculation for Calculations

29 Mar 2024

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# Gear Tooth Strength Calculator

This calculator provides the calculation of gear tooth strength for involute spur gears based on the Lewis equation.

## Explanation

**Calculation Example:** The Lewis equation is a widely used empirical formula for calculating the strength of gear teeth. It is based on the assumption that failure occurs due to bending or compressive stresses at the tooth root. The Lewis equation takes into account the tangential force acting on the gear tooth, the circular pitch, the Lewis form factors, the ultimate tensile strength of the gear material, and the factor of safety.

## Related Questions

**Q: What is the importance of gear tooth strength calculations?**

**A:** Gear tooth strength calculations are important for ensuring the safe and reliable operation of gears. By calculating the stresses acting on the gear teeth, engineers can design gears that are strong enough to withstand the loads they will be subjected to.

**Q: How does the Lewis equation account for different gear tooth geometries?**

**A:** The Lewis equation incorporates the Lewis form factors, Yp and Ys, to account for the different geometries of pinion and gear teeth. These form factors are based on the tooth profile and the pressure angle of the gears.

## Variables

Symbol | Name | Unit |

| —— | —- | —- |

Ft | Tangential Force | N |

Pd | Circular Pitch | m |

Yp | Lewis Form Factor for Pinion | - |

Ys | Lewis Form Factor for Gear | - |

Sut | Ultimate Tensile Strength | MPa |

SF | Factor of Safety | - |

## Calculation Expression

**Tangential Stress:** The tangential stress acting on the gear tooth is given by St = Ft / (Pd * Yp * Ys * b).

```
Ft / (Pd * Yp * Ys * b)
```

**Bending Stress:** The bending stress acting on the gear tooth is given by Sb = St * Ka

```
St * Ka
```

**Compressive Stress:** The compressive stress acting on the gear tooth is given by Sc = Sb * Kc

```
Sb * Kc
```

**Ultimate Tensile Strength:** The ultimate tensile strength of the gear material is given by Sut.

```
Sut
```

**Factor of Safety:** The factor of safety is given by SF.

```
SF
```

## Calculated values

Considering these as variable values: Sut=600.0, SF=1.5, Pd=0.025, Yp=0.35, Ys=0.4, Ft=1000.0, the calculated value(s) are given in table below

Derived Variable | Value |

| —— | —- |

Factor of Safety | 1.5 |

Bending Stress | (285714.28571428574*ka)/b |

Tangential Stress | 285714.28571428574/b |

Compressive Stress | (285714.28571428574kakc)/b |

Ultimate Tensile Strength | 600.0 |

## Sensitivity Analysis Graphs

**Tangential Stress:** The tangential stress acting on the gear tooth is given by St = Ft / (Pd * Yp * Ys * b).

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## App in action

The video below shows the app in action.