Video N°218 COMMENT DETERMINER LE NOMBRE DE DENTS DES PIGNONS D'UN REDUCTEUR

Summary

In this video, the instructor guides viewers through an exercise to calculate the reduction ratio and certain criteria for the gears in a parallel shaft gearbox. Key concepts include determining the reduction ratio using the input and output speeds, and calculating the number of teeth for the gears involved. The video covers the application of formulas for reduction ratio, gear teeth count, and specific calculations using module and pitch. The instructor also demonstrates the importance of matching the correct distances and module values for accurate results in gear design.

Takeaways

• 😀 The video provides a review exercise on calculating the reduction ratio and gear tooth criteria for a parallel-axis reducer.
• 😀 The reducer consists of gears Z1, Z2, Z3, and Z4, with Z1 and Z2 being the input and output gears, and Z3 and Z4 on a common shaft.
• 😀 All four gears have the same module, meaning they share the same size standard.
• 😀 The input speed (n1) is 1500 RPM, and the output speed (n2) is 100 RPM, which are key to calculating the reduction ratio.
• 😀 The reduction ratio (R) is calculated by dividing the output speed by the input speed, giving a result of 0.068.
• 😀 The general formula for the reduction ratio involves the multiplication of the number of teeth on driving gears divided by the number of teeth on driven gears.
• 😀 The speaker explains how the diameter of each gear is related to its number of teeth and the module, using the formula for the primitive diameter.
• 😀 The distance between gears Z1-Z2 and Z3-Z4 is the same, which ensures consistent alignment in the system.
• 😀 The reduction ratio formula involves calculating the product of the teeth counts on each set of gears and their respective modules.
• 😀 The speaker demonstrates the algebraic manipulation of equations to solve for the number of teeth on gears Z3 (26 teeth) and Z4 (76 teeth).

Q & A

What is the main purpose of the exercise in this video?

The main purpose is to practice calculating the reduction ratio and some specific parameters of a gearbox, as well as to apply the concepts learned in the previous video regarding gear teeth count and the reduction ratio formula.

What kind of gearbox is being discussed in the video?

The video discusses a parallel-axis gearbox, where the input and output axes are parallel to each other.

What are the given input parameters for the calculation?

The input parameters include the input speed (1500 RPM), output speed (100 RPM), and the number of teeth on certain gears (Z1 = 17, Z2 = 85).

How is the reduction ratio calculated in this video?

The reduction ratio is calculated as the ratio of output speed to input speed. In this case, it is 100 RPM divided by 1500 RPM, resulting in a reduction ratio of approximately 0.068.

What is the significance of the module in this exercise?

The module is significant because it determines the size of the teeth on the gears. All the gears in this exercise have the same module, which simplifies the calculations.

What formula is used to calculate the reduction ratio of a gear train?

The reduction ratio (R) is calculated using the formula: R = (Z3 * Z4) / (Z1 * Z2), where Z1, Z2, Z3, and Z4 are the numbers of teeth on the respective gears.

What does the term 'anthrax' refer to in this context?

'Anthrax' in this context refers to the center distance between two gears, specifically between the gears Z1 and Z2 or Z3 and Z4. It is crucial for maintaining the proper alignment of the gears.

How is the 'anthrax' distance calculated?

The 'anthrax' distance is calculated as the sum of the diameters of two gears (Z1 and Z2, or Z3 and Z4), divided by two. This ensures the gears mesh correctly.

What are the steps involved in determining the number of teeth on the gears Z3 and Z4?

To determine the number of teeth on gears Z3 and Z4, a system of equations is used based on the reduction ratio and the center distance formula. By solving the system, the values for Z3 and Z4 can be calculated.

How does the parity of the number of teeth affect the rotation direction of the output shaft?

If the total number of teeth in the gear system is even, the output shaft rotates in the same direction as the input shaft. If it is odd, the output shaft rotates in the opposite direction.