# Don't let vibratory separators shake you up

## Understanding a few key points simpifies setup and operation, and leads to optimum screening patterns. These include adjusting vibratory motion and optimizing separator performance.

A standard round vibratory separator uses a screen cloth enclosed in frames. The frames are vibrated by a motion generator consisting of a vertically mounted double-end shaft motor with eccentric weights on its top and bottom (Figure 1). The motor rotates counterclockwise (CCW) when viewed from the top. As the motor rotates, the weights generate a radial centrifugal force that causes the spring-mounted machine to vibrate.

The top weight has an adjustable force output and a fixed angular orientation on the motor shaft. The bottom weight also has an adjustable force output but includes a variable angular orientation in relation to the top weight.

There are three independent variables or adjustments to a vibratory separator: top force, bottom force and lead angle, which is the angular weight setting. The output variables are horizontal motion amplitude, vertical motion amplitude and phase angle, which is the measured delay between the maximum vertical and horizontal amplitudes.

Figure 1:

Eccentric weights on the top and bottom of the vertically mounted motor generate vibration.

To simplify discussion, let's first consider only the top motor weight. The top motor eccentric weight is designed to be at the center of gravity (CG) of the vibrating machine. Force acting at the CG of a mass will cause uniform planar motion in that mass. In other words, the top weight force spinning at the CG will create a uniform horizontal radial motion of the machine without any torque around the CG.

Figure 2:

An eccentric weight located at the center of gravity of the body causes horizontal motion.

Visualize a separator as a solid cylinder, as shown in Figure 2. The top eccentric weight force acts at the CG of the body. When a force acts at the CG, horizontal motion of the body will occur in the direction of the top weight force.

Figure 3 depicts the same body at two different positions. The first, shown in gray, occurs when the force is pointed left. As the motor rotates 180 Degrees , the force will point to the right and cause the cylinder to translate horizontally to the right position, shown in the black outline. The horizontal motion generated is the distance the separator moves with 180 Degrees of motor rotation.

Figure 3:

As the motor rotates 180 Degrees , the separator moves horizontally from its initial position, shown in gray, to a new position, shown in black.

As the motor continuously spins the weights, we can visualize the cylinder moving through a horizontal radial motion following the eccentric weight force orbit. It is important to note that only the motor and weights rotate, not the cylinder. Because the top weight force acts at the CG, the cylinder will always remain horizontal. Variable horizontal motions will occur as the magnitude of the top force is varied.

Now, if we add another eccentric weight, FBW, as shown in Figure 4, to the bottom of the motor below the machine CG, this weight will induce a torque about the CG that creates vertical motion as the machine tilts from the vertical axis. The result of these weights is a cylinder tilted off the vertical axis. Adding more bottom weight yields more vertical motion.

Figure 4:

An eccentric weight on the bottom of the motor creates vertical motion.

Figure 5 depicts the same cylinder in two different motor positions with the weights rotated 180 Degrees . The drawing shows the resultant horizontal and vertical motions that are generated by the eccentric top and bottom weight forces.

As the motor rotates CCW, the maximum amplitude generated will occur in the direction in which the force points. During rotation, the direction continually changes; elliptical motion in three axes is generated by one rotation of the motor.

In Figure 5, the top and bottom forces are vertically aligned with the maximum horizontal and vertical motion occurring in the same vertical plane or angular position.

Figure 5:

Both horizontal and vertical motions are generated as the weights rotate 180 Degrees .

In vibratory separators, lead angle is defined as the CCW angle between the top and bottom weight when viewed from above. When the weights are vertically aligned, there is a 0 Degrees lead angle. When the bottom weight is 120 Degrees CCW from the top weight and the motor is spinning CCW, the bottom weight leads the top weight. This means the maximum vertical motion generated by the bottom weight will occur 120 Degrees of motor rotation before the maximum horizontal motion generated by the top weight.

Figure 6 shows the bottom weight leading the top weight by 120 Degrees . Note that the vertical and horizontal motion no longer occur at the same time.

Figure 6:

With the bottom weight leading the top weight by 120 Degrees , vertical and horizontal motions no longer occur at the same time.

Lead angle is the parameter that gives a round vibratory separator the unparalleled ability to control material flow pattern. We will discuss the proper setting of lead angle later.

Key measurements

Properly analyzing the motion of a separator requires measurement of vibration amplitudes and phase angles.

A vibration gauge sticker easily measures vibration amplitudes. These stickers are attached to the outside frame diameter of the machine near the screen level and provide a visual indication, usually in 1/16-in. increments, while the machine is running. If amplitude stickers are not available, use a felt-tip marker to make a dot on the frame. A ruler can be used to measure the horizontal and vertical amplitudes of the motion.

Motion amplitudes vary with the distance from the CG of the machine. When comparing machines, ensure that measurements are taken in equivalent locations closest to the most critical screen in the separator.

The next question is how to measure the phase angle between the horizontal and vertical motions. The simple answer is merely to reference the lead angle between the weights; this normally suffices in one- and two-screen machines of the same diameter. However, the lead angle does not predict the vibratory motion or the motion of particles on the screen in units with tall frame stack-ups. Lead angle also is not representative when comparing machines of different heights and diameters. When lead angle is not appropriate, phase angle should be measured.

Phase angle is the measured delay between the maximum vertical and horizontal motion. Measuring this requires a computer monitoring system, which can provide data on horizontal and vertical displacement, motor speed and directional accelerations, as well as phase angle, thereby allowing precise setup and troubleshooting of vibratory separators.

Figure 7:

Material fed onto the center of the screen moves toward the edge.

Particle motion

Now that we understand the function of machine input parameters -- top weight, bottom weight and lead angle -- and the resulting separator motions, we can discuss how to control the motion of a particle. Figure 7 shows material fed onto the center of the screen moving to the outside edge while Figure 8 shows material fed at the edge running to the center. Let's now look at why these material flow patterns occur.

Figure 8: Material fed on the edge of the screen moves toward the center.

The two key concepts of particle motion are:

1. The maximum vertical amplitude occurs directly above the bottom weight. This means that a particle on the screen will be launched vertically when the bottom weight rotates directly beneath that particle.

2. The maximum horizontal radial amplitude occurs in the direction of the top weight. As the top weight rotates toward a particle on the screen, the horizontal radial motion increases to a maximum when the top weight is pointed at the particle. As the weight rotates away from the particle, the horizontal radial motion decreases.

For the first example, let's analyze a machine set up with the top and bottom weights at 0 Degrees lead angle. Consider one particle on a screen directly above both of the weights. This particle will be launched vertically directly above the top and bottom weights at the position of maximum vertical and horizontal radial motion. While the particle is in flight above the screen, the weights will continue to rotate and move the screen underneath the flight of the particle. When the particle lands on the screen, it will be in a new position on the screen.

If, for simplicity, we assume that a particle is in flight for 180 Degrees of motor rotation and the weights are set at a 0 Degrees lead angle, the particle will leave the screen vertically and land closer to the screen edge. By choosing 180 Degrees rotation, the particle, depicted by the double-ended arrow in Figure 9, leaves the screen at the point of maximum horizontal radial motion, shown in the gray outline, and lands at the point of minimum horizontal radial motion, shown in black. The particle will appear to travel radially outward from the screen's center.

Figure 9:

With a 0 Degrees lead angle between the weights, particles will travel outward.

With the weights set at 0 Degrees lead angle, the particle will always travel radially outward, even if the particle is in flight for only 1 Degrees of motor rotation. Because the particle left the screen at the point of maximum radial displacement, it will land at a point of lower radial displacement. This means the particle always will land closer to the edge of the screen.

For the second example, let's analyze the opposite extreme -- when the bottom weight is advanced to a 180 Degrees lead angle. Here, the vertical motion occurs before the maximum horizontal radial motion; therefore, the particle will be launched vertically before the maximum radial motion occurs.

To continue the analogy, let's again assume that the particle is in flight for 180 Degrees of motor rotation, only now the lead angle is set to 180 Degrees . The particle will leave the screen vertically above the bottom weight, be in flight above the screen for 180 Degrees of motor rotation, and land again directly above the top weight. This is shown in Figure 10, with the particle leaving the screen shown in the gray outline and landing in the black outline screen position. When the particle left the screen, it was at the location of minimum horizontal radial displacement and landed at the location of the maximum radial displacement. The particle has landed farther from the outside edge of the screen and appears to travel radially inward.

Figure 10:

When the lead angle is 180 Degrees , particles will move inward.

Using the same arguments, with the weights set at a 180 Degrees lead angle, the particle will always travel radially inward, even if the particle is in flight for 1 Degrees of motor rotation. Because the flight of the particle begins when the separator is at the minimum horizontal radial distance, the particle must land at a point of greater radial distance.

These two extremes show how the lead angle is the controlling parameter in particle flow direction in a vibratory separator.

In reality, particles are not in flight for 180 Degrees of motor rotation. By only considering the 180 Degrees positions we have ignored the second horizontal axis motion. When the motor has rotated 45 Degrees , the screen position will have moved in two dimensions in the horizontal plane, as shown in Figure 11. A particle more realistically will move in two horizontal dimensions, with both radial and angular displacements.

Figure 11:

When the motor has rotated 45 Degrees , screen position will have moved in two horizontal dimensions, with both radial and angular displacements.

Figure 12 depicts the complete range of material flow patterns that can be obtained by adjusting the lead angle in a round vibratory separator.

As the lead angle is raised from 0 Degrees toward 50 Degrees , the horizontal radial particle displacement diminishes. This means that the radial velocity of the particle will decrease because the horizontal tangential motion is increasing. This yields an increasing spiral path to the flow pattern.

Figure 12:

At a 60 Degrees lead angle setting, the material appears to travel only tangentially. This can be explained by a particle being launched vertically 60 Degrees before the top weight and landing 60 Degrees after the top weight in the same radial position on the screen. Material will not readily discharge from the spouts at this setting.

Once the lead angle exceeds 60 Degrees , the inward radial displacements rise. These patterns are explained simply by at what time the particle lands on the screen. If the particle lands after the maximum radial displacement, it will move radially outward. If the particle lands before the maximum radial displacement, it will move radially inward.

Optimizing separator performance

So, what does this all mean? There are hundreds of products that run through vibratory separators and each material can require different motion settings based on its individual physical properties. The following guidelines can help you optimize machine operation.

Low bulk-density materials require less vertical amplitude because lighter materials will have longer flight times. A material that is above the screen cannot go through the screen, reducing overall capacity.

Conversely, high bulk-density materials require additional vertical amplitude to allow the material to move efficiently from screen opening to screen opening.

If capacity needs to be increased, use higher amplitude. The higher the amplitude, the faster the material travels -- and the shorter the residence time on the screen.

If too much good product is leaving with the oversize material, increase the lead angle to raise the screen residence time. Higher lead angle will boost the spiral path length, exposing the material to more screen openings.

Always remember these six key points:

1. Top weight force controls the horizontal amplitude.

2. Bottom weight force controls the vertical amplitude.

3. Lead angle governs the material flow pattern and direction.

4. Horizontal and vertical amplitudes can be easily measured to evaluate and understand separator motion.

5. To raise capacity, increase the material velocity and decrease the residence time in the machine.

6. To improve separation accuracy, decrease the material velocity and increase the residence time in the machine.

Eric Johnson, P.E., is chief engineer for SWECO, Division of M-I LLC., Florence, Ky.