# What is the Calculation for Finding Gear Ratio in a Multi-Gear System?

• TSN79
In summary, the problem asks for the number of teeth and mid tooth-diameter for four gears in a gear train. The first gear has a gear module of 5 mm and a mid tooth-diameter of 95 mm. The second gear, attached to the first, drives a third gear, which then drives a fourth gear with a module of 8 mm. The fourth gear is supposed to run at 80 rpm and have a diameter less than 700 mm due to space constraints. To find the number of teeth for the second gear, the book takes the square root of the ratio between the two gear speeds, which is 18.125. This is then used to calculate the number of teeth for the second gear, which is

#### TSN79

A motor runs at 1450 rpm. Attached is a gear that has a gear module of 5 mm, and a mid tooth-diameter of 95 mm. This wheel is toothed up with a second wheel who's shaft drives a third wheel. This third wheel is then toothed up with the fourth and last wheel who's shaft runs let's say dryer, which is supposed to run at 80 rpm. This last gear has a module of 8 mm. The last gear's diameter must be less than 700 mm 'cause of space. I'm supposed to find the number of teeth and the mid tooth-diameter for each gear. Here what my book does to begin with:

The ratio is calculated as

$$\frac{1450}{80}=18,125$$

$$z_1=\frac{d_1}{m_1}=\frac{95}{5}=19$$ (the number of teeth on the first gear)

Now my book does something I don't get. It finds:

$$\sqrt{18,125}=4,26$$

This number is then used to find the number of teeth on the second wheel:

$$U=\frac{z_2}{z_1} \Rightarrow z_2=U\cdot z_1=4,26 \cdot 19=81$$

As I said earlier, I can't see why the square root of the ratio is calculated...

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Obviously the diameter of the first gear is 95 mm. Is there anything else you have failed to mention? How about writing out the entire problem so we know exactly what we have to deal with?

I've updated the problem above to include the whole thing now...

## 1. What does "rpm" stand for?

"Rpm" stands for revolutions per minute, which is a unit of measurement used to describe the rotational speed of a motor.

## 2. Is 1450 rpm considered a fast speed for a motor?

It depends on the type of motor and its intended purpose. Generally, 1450 rpm is considered a moderate speed for a motor, but it can vary greatly depending on the size, design, and function of the motor.

## 3. How is the speed of a motor measured?

The speed of a motor is typically measured using a tachometer, which is a device that measures the rotational speed of a motor's output shaft. It can also be calculated by measuring the number of rotations per minute using a stopwatch and dividing by the number of revolutions per minute.

## 4. Can the speed of a motor be adjusted?

Yes, the speed of a motor can be adjusted by changing the amount of voltage or current supplied to it, changing the gear ratio, or using a variable frequency drive. Some motors also have built-in speed control mechanisms.

## 5. What factors can affect the speed of a motor?

The speed of a motor can be affected by various factors, such as the type and quality of the power source, the load or resistance on the motor, the temperature and condition of the motor's components, and any speed control mechanisms in place.