Hi mechatronics fans!

Welcome to the latest post on the Sinadrives blog.

May 2022

In today’s post we’re going to discuss the calculation of a perfect motion. We’ve got some useful tips for machinery manufacturers whose equipment must perform linear or rotary motions. Getting from point A to point B is not merely a movement at constant speed; it’s a complex movement composed of phases of acceleration, deceleration or braking, and movement at constant speed.

We’re going to discuss the best way to make the most of the available power and to achieve a clean motion, enabling us to meet our proposed goals in terms of speed, acceleration and precision, avoiding problems of resonances and vibrations.

Normally, when we’re presented with a positioning task, we need to have some starting data. This is usually based on distance or movement and the positioning time. Let’s say, for example, that we have to travel 100 mm in 0.2 seconds or travel 3,000 mm in 2 seconds. The next step is to decide whether or not we need to follow a specific trajectory during this motion.

In Pick & Place, palletizer or assembly machine applications, a specific trajectory is not usually necessary.

However, the need to follow a certain trajectory may be applicable in the case of cutting, CNC or printing machines. When the trajectory is important, we must bear in mind that sudden changes in speed and acceleration can increase the tracking error and, in turn, reduce the motion precision. In other words, the calculated trajectory and the actual trajectory differ, hence the tracking error. The end result may be that the required accuracy is not achieved or the process is no longer performed correctly.

Applications operated by means of a linear motor and linear motor stages are characterized by a tiny tracking error which is ten times smaller than in classic transmission equipment such as timing belts or spindles.

When we start a motion from speed 0, we have to accelerate in order to reach the required speed. When we complete a motion and have to stop the application, we must decelerate or brake in order to return to speed 0.

There are three types of ramps that serve both to accelerate and decelerate: trapezoidal ramps, sinusoidal ramps and trapezoidal ramps with jerk control. The perfect ramp doesn’t exist; it depends on the application and on the required speed.

Image 1 is a speed-time graph of a positioning comprising 3 phases: 1. Acceleration; 2. Movement at constant speed; and 3. Deceleration. It’s a classic example of a trapezoidal ramp.

Image 2 is a speed-time graph of a positioning comprising 2 phases: 1. Acceleration; and 2. Deceleration. In this type of positioning, there’s no phase of motion at constant speed.

Image 3 is an acceleration-time graph of a positioning with a trapezoidal ramp.

We advise using trapezoidal ramps when the acceleration does not exceed 10 m/s2; that is, the value of the necessary speed divided by the acceleration time must not exceed 10 (A = S/t). In this case, it doesn’t matter what speed is reached; what really counts is the acceleration value.

As we’ve explained in point 2.1, in the case of sinusoidal ramps the motion may comprise 2 or 3 phases. The difference is that acceleration or deceleration ramps have a sinusoidal shape. Image 3 is a speed-time graph comprising 3 phases and sinusoidal ramps.

It’s easy to spot the difference, as there’s a non-constant change of speed during the acceleration phase. The speed shift corners are rounded and different from those of trapezoidal ramps.

Image 4 is an acceleration-time graph of a positioning with a sinusoidal ramp.

When are sinusoidal ramps used? Based on our experience, we advise using sinusoidal ramps for motions with accelerations greater than 10 m/s2. The use of this type of ramp softens the bumps and vibrations of machinery.

This type of ramp is a combination of the trapezoidal and sinusoidal ramp, with the difference that the acceleration value is modified only on the corners. It’s necessary to determine the maximum change of the acceleration value in time. This value can’t be exceeded at any time.

Today, thanks to the available ramp configuration options in servo controllers, these types of ramps tend to be used more frequently.

If you require a motion that does not generate vibrations or resonances anywhere in the machinery assembly, we recommend using sinusoidal ramps or trapezoidal ramps with jerk control, which enable a smooth, uniform motion with no resonances.

In this section we’ll try to explain the most suitable way to distribute the acceleration and deceleration ramps in order to make the most of the available power and prevent the premature wear and tear of components.

As a general rule, when analysing the phases of a motion, it’s advisable to use the ratio of ⅓; that is, ⅓ of the total time for acceleration, ⅓ for constant speed and ⅓ for deceleration.

Table 1 summarizes the simulation cases of a positioning application of 2,000 mm in 1.8 seconds with different acceleration and deceleration times. The only value we’re going to modify is the “Acceleration time”:

Table 1: Relation of acceleration time and power required

* These values have been calculated with an MLE20210HS linear motor stage with a 240N peak force motor, with horizontal motion and a payload of 10 kg.

In case 3, where the acceleration and deceleration time corresponds to ⅓ of the total positioning time, we can see that both the motor temperature and the required power are more favourable than in the other cases. The central phase at constant speed allows the motor to cool down to a certain extent. As such, we can conclude that this distribution of times is the one that comes closest to a perfect or ideal motion.

In case 1, where the acceleration time is extremely short, the acceleration ramp requires plenty of additional force and, consequently, greater power, which has a negative impact on the consumption and temperature of the motor.

In case 5, where the acceleration time is ½ of the total time, greater power is required because the motor is constantly accelerating and decelerating. This generates greater consumption and power, since it’s necessary to reach a higher maximum speed in order to perform the motion.By using linear motor stages, you’ll get the best performance in terms of speed, acceleration, accuracy and repeatability, reduce tracking errors and eliminate maintenance. Our technical department is at your disposal.

The selection of acceleration ramps and, above all, the distribution of the phases of a motion are extremely important. An error may lead to unnecessary costs when selecting motors, and to increases in energy consumption, heat generation, resonances and vibrations.

At SINADRIVES, our experts are on hand to help you select the most suitable motor for each application. Make the most of your equipment and build fast, lightweight and competitive machines.

By using linear motor stages, you’ll get the best performance in terms of speed, acceleration, accuracy and repeatability, reduce tracking errors and eliminate maintenance. Our technical department is at your disposal.

If you have an application in which you’re keen to improve the performance of your machine, be it in terms of speed, dynamics, precision or simply reducing maintenance needs, please contact us.

Our specialists in Direct Drive technology and Linear Modules with linear motor technology will be happy to advise you free of charge.

Draw your own conclusions. Decide which innovation you want to implement in your machine to be competitive. We can help you.

Your SINADRIVES Team.