How to calculate the bending stress in a double spur gear?

Hey there! I'm a supplier of double spur gears, and today I'm gonna walk you through how to calculate the bending stress in a double spur gear. It's a crucial aspect when it comes to ensuring the gears work well and last long.

Understanding the Basics of Double Spur Gears

First off, let's quickly talk about double spur gears. These gears are pretty cool. They consist of two sets of teeth on the same gear blank, which allows for more load - carrying capacity compared to single spur gears. They're used in a bunch of applications, from automotive transmissions to industrial machinery.

If you're also interested in other types of gears, we've got some great options. Check out our Straight Tooth Bevel Gear, PM Gears, and Tiny Small Gear.

Why Calculate Bending Stress?

Calculating bending stress is super important. When a gear is in operation, the teeth are subjected to forces that cause bending. If the bending stress is too high, the teeth can break or wear out quickly. By calculating the bending stress, we can design the gear to handle the expected loads and ensure its reliability.

The Lewis Bending Equation

One of the most common ways to calculate the bending stress in spur gears is by using the Lewis bending equation. The equation is given as:

$\sigma = \frac{W_t}{FmY}$

Where:

• $\sigma$ is the bending stress (in psi or Pa).
• $W_t$ is the tangential load on the gear tooth (in lb or N).
• $F$ is the face width of the gear (in inches or meters).
• $m$ is the module of the gear (in inches or meters).
• $Y$ is the Lewis form factor, which depends on the number of teeth on the gear.

Step - by - Step Calculation

Step 1: Determine the Tangential Load ($W_t$)

The tangential load on the gear tooth can be calculated using the power transmitted and the pitch line velocity. The formula for the tangential load is:

$W_t=\frac{33000P}{V}$ (in English units)

where $P$ is the power transmitted (in hp) and $V$ is the pitch line velocity (in ft/min).

In SI units, the formula is:

$W_t=\frac{1000P}{V}$

where $P$ is the power transmitted (in kW) and $V$ is the pitch line velocity (in m/s).

The pitch line velocity $V$ can be calculated as:

$V=\frac{\pi dN}{12}$ (in English units, where $d$ is the pitch diameter in inches and $N$ is the rotational speed in rpm)

or

$V=\frac{\pi dN}{60}$ (in SI units, where $d$ is the pitch diameter in meters and $N$ is the rotational speed in rpm)

Step 2: Measure the Face Width ($F$)

The face width of the gear is the length of the tooth along the axis of the gear. It can be measured directly using a caliper or obtained from the gear design specifications.

Step 3: Calculate the Module ($m$)

The module $m$ is defined as the ratio of the pitch diameter $d$ to the number of teeth $N$, i.e.,

$m=\frac{d}{N}$

It's an important parameter that determines the size of the gear teeth.

Step 4: Find the Lewis Form Factor ($Y$)

The Lewis form factor $Y$ is a dimensionless number that depends on the number of teeth on the gear. You can find tables in gear design handbooks that list the values of $Y$ for different numbers of teeth. For example, for a 20 - tooth gear, the Lewis form factor might be around 0.32.

Example Calculation

Let's say we have a double spur gear with the following parameters:

• Power transmitted $P = 10$ hp
• Rotational speed $N = 1800$ rpm
• Pitch diameter $d = 4$ inches
• Face width $F = 1$ inch
• Number of teeth $N_t=20$

First, we calculate the pitch line velocity:

$V=\frac{\pi dN}{12}=\frac{\pi\times4\times1800}{12}=1885$ ft/min

Then, we calculate the tangential load:

$W_t=\frac{33000P}{V}=\frac{33000\times10}{1885}\approx175$ lb

The module $m=\frac{d}{N_t}=\frac{4}{20}=0.2$ inches

From the Lewis form factor table, for $N_t = 20$, $Y = 0.32$

Now, we can calculate the bending stress using the Lewis equation:

$\sigma=\frac{W_t}{FmY}=\frac{175}{1\times0.2\times0.32}\approx2734$ psi

Other Considerations

While the Lewis equation is a simple and widely used method, there are some limitations. It assumes a single point of contact on the gear tooth and doesn't account for factors like dynamic loads, stress concentration, and the effect of tooth profile modifications.

For more accurate calculations, especially in high - performance applications, you might want to use more advanced methods such as finite element analysis (FEA). FEA can take into account the complex geometry of the gear tooth and the distribution of stresses more precisely.

Conclusion

Calculating the bending stress in a double spur gear is an essential part of gear design and analysis. By following the steps outlined above, you can get a good estimate of the bending stress and ensure that your gears are designed to handle the expected loads.

If you're in the market for high - quality double spur gears or any of our other gear products like Straight Tooth Bevel Gear, PM Gears, and Tiny Small Gear, don't hesitate to reach out for a purchase and negotiation. We're here to help you find the best gear solutions for your needs.

References

• Mott, Robert L. "Machine Elements in Mechanical Design." Pearson Education, 2016.
• Shigley, Joseph E., et al. "Mechanical Engineering Design." McGraw - Hill Education, 2015.