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# Mass inertia with racks and pinions in the picture

How do we determine the right servomotor-gearbox combination? And how do we choose the right rack and pinion? In practice, the answer to these questions is depending from the application. In this article we therefore share a video that shows you why. We simulate a simple application with linear guidance performed in 3 ways and discuss the impact on the choice of both servomotor and gearbox. And of course this is followed by the selection of rack and pinion.

In the following animated video, we see a container of liquid moving linearly at an average speed of 1.5 meters/second. Each time, 12 meters are covered in exactly 8 seconds. The difference between the three is due to the acceleration and maximum speed.

Each of these examples calls for a different size for the motor and gearbox. But which of these examples best suits your application?

Given the response of the fluid, a triangular acceleration graph gives the best result with the highest productivity and minimum vibration. This reduces the peak load on the installation, which benefits the lifespan. The disadvantage of this movement profile is that a relatively larger gearbox with a lower transmission ratio is required. And this again requires a relatively large servomotor.

## Constant speed

The second and third motion profiles are better for short-distance motions or applications requiring a long constant speed. An additional advantage is that we can save energy because the required motor is relatively small and the gearbox with a larger transmission ratio, so that the mass inertia ratio is better. (IL/i2 <= 4 IM).

There are also applications where a complex motion profile has to be followed, for example a vertical packaging machine that requires high speed and relatively minimal vibration.

## Mass inertia of racks and pinions in practice

Do you often design sizing for a rack and pinion application and the speed is ultimately lower than hoped? And as a result, does the servo motor has to run too fast and does the servo controller malfunction due to overload? If yes, then the answer is:

1. Selection of a motion profile that fits the application we need.
2. Maximum speed is 1.5 times to 2 times the average speed, in this case rack and pinion is the best choice with a maximum speed up to 6 m/s.

With these 3 examples we will probably make clear why so many of our questions are about the application before we advise a gearbox, rack and pinion combination. We help our customers to select the right gearbox combination and the right racks and pinions. Of course we can also deliver these, often within 3 weeks because we deliver from stock.