Analysis of a mechanism suspension to reduce noise from horizontal

vibrating screens1)

1)	 This is the first paper published in NCEJ on the special

topic of Noise in Mines.

,2)

2)	 The findings and conclusions in this report have not been

formally disseminated by the National Institute for Occupational Safety and Health and should not be construed to

represent any agency determination or policy. Reference

to specific brand names does not imply endorsement by

NIOSH.

David S. Yanteka)

a) NIOSH, 626 Cochrans Mill Rd, P.O.Box 18070,

Pittsburgh, PA 15236; email: DYantek@cdc.gov.

and M. Jenae Loweb)

b) NIOSH, 626 Cochrans Mill Rd, P.O.Box 18070,

Pittsburgh, PA 15236; email: MLowe@cdc.gov.

A-weighted sound levels around vibrating screens in coal preparation plants

often exceed 90 dB. The National Institute for Occupational Safety and Health

(NIOSH) is developing noise controls to reduce noise generated by horizontal

vibrating screens. Horizontal vibrating screen noise is dominated by sound

radiated from the screen body. NIOSH researchers analyzed a mechanism suspension system that could reduce screen body-radiated noise. A finite element

(FE) model of the entire screen was used to analyze the screen with the added

mechanism suspension. The spring rates for the mechanism suspension were

tuned to transmit vibration at the mechanism operating speed while attenuating

vibration transmitted from the mechanisms to the screen body at frequencies

above 100 Hz. The FE results were used to estimate the A-weighted sound

power level radiated by the screen sides and feedbox for various mechanism

suspension spring rates. The results indicate that a tuned mechanism suspension could reduce the A-weighted sound power level radiated by the

screen body due to gear and bearing forces inside the mechanisms by 7 to 18 dB.

VC 2011 Institute of Noise Control Engineering.

1 INTRODUCTION

In an effort to reduce the occurrence of noiseinduced hearing loss in the mining industry, the Mine

Safety and Health Administration (MSHA) modified

its rules regarding noise exposure in 19991

. Instead of

relying on hearing protection devices, MSHA requires

mine operators to use all feasible engineering and/or

administrative controls to reduce the noise exposures

of miners who are overexposed according to MSHA’s

Permissible Exposure Level (PEL) criteria—i.e., a

90 dB(A) time-weighted average sound level for an

8-hour workday using a 5-dB exchange rate1

. Despite

MSHA’s requirement to use noise controls, for many

machines, such as vibrating screens, noise controls that

reduce the operator’s noise exposure below the MSHA

PEL do not exist. In these cases, mine operators must

use booths or administrative controls to reduce worker

noise exposure.

National Institute for Occupational Safety and

Health (NIOSH) data from 1999 to 2004 show that 20

out of 46 coal preparation plant workers had noise

exposures that exceeded the MSHA PEL noise dose2

.

MSHA PEL noise doses up to 220% have been

recorded for preparation plant workers such as stationary equipment operators, froth cell operators, plant

operators, plant controls men, third floor operators, wet

plant attendants, sump floor operators, plant backups,

and plant mechanics. These job classifications require

the worker to spend a significant portion of a shift in

the plant while working around slurry pumps, dryers,

centrifuges, and vibrating screens.

In the United States, there are 879 coal preparation

plants, and 570 of these have been active at some time

between 2008 and 20103

. Twenty-four states have

active coal preparation plants. West Virginia (22%),

Kentucky (22%), and Pennsylvania (19%) have the

most coal preparation plants. There were 8,290 coal

preparation plant workers in 2008 and 8,343 in 2009.

According to MSHA data, 1,170 noise-related injuries
have been reported in mining since 2000. Three hundred fifty-five of these cases (30% of all noise-related

injuries) involve preparation plant employees3

.

Vibrating screens generate A-weighted sound levels

from 90 to 95 dB during clean bituminous coal processing, and from 95 to 100 dB during refuse and anthracite processing4

. Since screens are used to size,

separate, and dewater both coal and refuse (rock) of

various sizes, they may be located on many floors

within a preparation plant. The number of screens in a

processing plant can range from a single screen to

more than a dozen. Consequently, preparation plant

workers can be exposed to high sound levels generated

by screens many times during a workday. Vibrating

screens are a major noise problem in coal preparation

plants because screens are used extensively in the

plants, are usually located in high traffic areas, and can

generate high sound levels5

.

A horizontal vibrating screen (see Fig. 1) is a large

machine used to process clean coal that has been separated from refuse materials using a water-magnetite

mixture.

Fig. 1—A horizontal vibrating screen used to

process coal viewed from (a) feed end

and (b) discharge end.

The magnetite is recovered so that it can be

reused in the processing plant, and because it lowers

the heating value of coal. The screen body has two

sides made of steel plates and a screening surface

made of steel wire, which is welded to a frame with

small gaps between the wires. Round cross-tubes are

used at either end of the screen to help stiffen the structure. The screen is supported on a steel coil spring suspension. One or more vibration mechanisms are

mounted to a steel beam that connects the sides of the

screen. The vibration mechanisms, which use eccentric

shafts to generate vibration, are belt-driven by an electric motor. The vibration mechanisms are designed

such that forces are applied normal to the top flange of

the H-beam, which is rotated 45 degrees from vertical.

For the screen that is the focus of this work, the vibration mechanisms are driven at 900 RPM (15 Hz).

When a horizontal vibrating screen is in use, coal

flows from a delivery chute into the screen’s feedbox,

which is made of steel. The screen, which is designed

to vibrate on a 45-degree angle, forces the coal particles to travel across its deck under a water spray that

washes the magnetite from the coal. The liquid and

fine coal particles pass through the gaps in the screening deck as the material flows toward the discharge

end of the screen. Finally, the rinsed coal falls off the

discharge end of the screen, where it enters another

chute for further processing.

Previous NIOSH studies showed that the

A-weighted sound levels around a group of eight horizontal vibrating screens used to process clean coal

ranged from 94 to 98 dB6

. A series of measurements in

the same preparation plant indicated that noise due to

vibration was the dominant noise source, whereas

noise from material flow was less significant. Further

research showed that most of the noise due to vibration

is radiated by the screen body and the mechanism

housings7,8. Screen body noise is the main noise source

below about 1 kHz, while mechanism housing noise is

the primary source above 1 kHz. The sound energy at

frequencies below 1 kHz accounts for about 80% of

the overall A-weighted sound power level. In addition,

operating deflection shape analysis revealed significant

response on the screen sides and feedbox9

. Noise control efforts were split between developing noise controls to reduce noise above 1 kHz from the mechanism

housings and below 1 kHz from the screen body.

To reduce noise above 1 kHz, the NIOSH Office of

Mining Safety and Health Research (OMSHR) applied

constrained layer damping (CLD) treatments to the

mechanism housings and installed an acoustically

treated mechanism enclosure10. Figure 2 shows the

1/3-octave-band sound power level spectra for the

baseline, with CLD treatments on the mechanism housings, and with both CLD treatments and an enclosure
applied to the mechanisms.

Fig. 2—One-third-octave-band sound power level spectra for the baseline screen, for the screen

with CLD treatments on the mechanism housings, and for the screen with CLD treatments and an enclosure applied to the mechanisms.

In the 1–10 kHz frequency

range, which is dominated by mechanism housing

noise, the CLD treatments reduced the A-weighted

sound power level by 3 dB. In addition, the CLD

reduced the overall A-weighted sound power level by

1.2 dB. Adding an enclosure reduced the A-weighted

sound power level in the 1–10 kHz frequency range by

an additional 3.9 dB and the overall A-weighted sound

power level by an additional 2 dB.

In an effort to reduce noise below 1 kHz, the effects

of adding stiffeners to the screen sides and feedbox and

the effects of increasing its damping were evaluated

using an FE model11. The surface-averaged meansquare velocities calculated from the FE results were

used with estimated radiation efficiencies to estimate the

A-weighted sound power level from the screen sides

and feedbox. The study showed that adding stiffeners

would have little impact on the sound power level.

However, a five-fold increase in the modal damping

resulted in a predicted reduction of 7.8 dB.

Due to the screen manufacturer’s concern about the

process required to install constrained layer damping

treatments, the screen manufacturer was interested in

other noise controls that could reduce sound levels

below 1 kHz. Vibrating screens are produced using

cutting, machining, and welding processes. Because

each of these processes generates metal fragments,

screen manufacturing plants are not clean enough for

the surface preparation and bonding required to make

constrained layer damping treatments.

Most screen body noise results from gear noise and

bearing chatter within the mechanism housings12.

Clearance within the bearings allows the bearing components to chatter as the machine vibrates. In addition,

gear vibrations are transmitted from the mechanism

housings to the H-beam. The gear and bearing forces

transmitted to the screen could be reduced by adding a

suspension between the mechanisms and the H-beam.

However, for vibrating screens, the vibratory forces at

the mechanism rotation speed must be transmitted to

the screen to make it oscillate—thus it can separate

coal from refuse and/or products used in coal processing. Given the above constraints, the mechanism suspension system would have to be tuned, so that forces

at the mechanism rotation speed are transmitted, while

forces at higher frequencies due to gear and bearing

forces are attenuated. This tuned mechanism suspension concept to reduce noise emissions below 1 kHz is

the focus of this work.

2	 MECHANISM SUSPENSION ANALYSIS

PROCEDURE

A mechanism suspension is proposed to be added to

the screen to reduce noise radiated by the screen body

due to gear and bearing forces within the vibration

mechanisms. To add a mechanism suspension to the

screen, vibration isolators would be inserted between

the vibration mechanisms and the H-beam. The
vibration mechanisms would be mounted on top of a

large steel plate, or raft. Then, the raft would be

mounted on top of the vibration isolators. The goal of

adding a mechanism suspension is to separate the primary source of mechanical energy from the noiseradiating structure, but without degrading the performance of the screen.

2.1 Analysis Approach

Prior to designing a mechanism suspension, it is

necessary to analyze the dynamic behavior of a screen

with an added mechanism suspension. First, a twodegree-of-freedom (DOF) model was used to examine

the rigid body behavior of the system. Next, a finite

element (FE) model of the screen with an added mechanism suspension was used to examine how the natural

frequencies and mode shapes of the system vary with

the stiffness of the mechanism suspension. The FE

model was then used to perform a forced response

analysis on the screen due to forces input at the vibration mechanisms. Finally, the results from the forced

response analysis were used to estimate the sound

power level radiated by the screen sides and feedbox.

2.2 Two-DOF Model

A simple two-DOF model (see Fig. 3) was used to

gain insight into the behavior of a screen with an added

mechanism suspension.

Fig. 3—A simple two-DOF model used to analyze the screen with an added mechanism suspension.

In the model, m2 represents the

mass of the screen body and m1 represents the mass of

the vibration mechanisms. The stiffness and damping

for the existing screen suspension are represented by k2

and c2, and the stiffness and damping for the mechanism suspension are represented by k1 and c1. The

vibration mechanism force is represented by F1.

The forced response of the above two-DOF system

is given by13

 z1ðjxÞ -m1x2 þ jxc1 þ k1 1⁄4 -jxc1 - k1

-1 

F1ðjxÞ

 

(1) z2ðjxÞ -jxc1 - k1 -m2x2 þ jxðc1 þ c2Þþðk1 þ k2Þ 0

where x is the

p

forcing frequency in units of rad/s and j

denotes the ffiffiffiffiffiffi-1.

ffi The force transmitted from the

vibration mechanisms to the screen body is

Fmb 1⁄4 k1ðz1 - z2Þ þ c1ðz_1 - z_2Þ (2)

and the force transmitted from the screen body to the

ground is simply

Fbg 1⁄4 k2z2 þ c2z_2: (3)

A computer program was used to solve Eqns. (1), (2),

and (3) for a range of mechanism suspension spring

rates to examine how the dynamic behavior of the system changes with the mechanism suspension stiffness.

The displacement responses for the screen body and

the vibration mechanisms, and the forces transmitted

from the vibration mechanisms to the screen body and

from the screen body to the ground, were examined.

2.3 Finite Element (FE) Model

The two-DOF model can be used to examine the

rigid body behavior of the screen with the added mechanism suspension. However, because of the complex 

structural modes of screens, the two-DOF model is too 

simplistic and a more complicated model is necessary

to analyze the dynamic response of the system. An FE

model was developed to analyze the flexible-body

dynamic behavior of the screen with an added mechanism suspension (see Fig. 4).

The FE model was based on a previously developed

FE model of the screen prior to adding the mechanism

suspension11. The first several natural frequencies and

mode shapes predicted by the prior model showed

good agreement with the first several experimentally

determined natural frequencies and mode shapes. In

addition, visual comparisons revealed similarities
between experimentally determined operating deflection shapes and the vibration patterns of a forced

response analysis with the FE model. In the FE model,

the vibration mechanisms were modeled using solid

blocks. The density of the blocks was adjusted so that

the mass of the blocks matched the mass of the actual

mechanisms. The screen deck, which consists of a series of wires with gaps between them, was not included

in the model because it would significantly increase its

complexity, and because it does not contribute substantially to either the mass or the stiffness of the structure.

The A-frame (refer to Fig. 1) used to support the screen

was not included because previous tests7–9 showed that

it is not a significant noise source. The belt guard was

also ignored because it is attached to the A-frame

instead of the screen body.

Several simplifications were made to decrease the

complexity of the FE model. On the actual screens, the

connections between some screen components, such as

the ribs and screen sides, are welded joints, whereas

the connections between other components, for example the screen sides and round cross-tubes, are bolted

joints. In the FE model, all connections were modeled

as bonded joints to simplify the model. This approach

may overestimate the stiffness and underestimate the

damping of the screen. However, the model should still

be adequate for comparison purposes. Another simplification used for the model is that the screen suspension springs were modeled using lumped spring

elements at each of the mounting locations. Three

spring elements were used at each location to model

the spring rates in the x-direction (fore/aft), y-direction

(vertical), and z-direction (lateral). Each suspension

spring was connected to ground with fixed boundary

conditions. Steel was used as the material for the entire

screen.

Fig. 4—FE model of the vibrating screen with

an added mechanism suspension

system.

To model the addition of a mechanism suspension,

the vibration mechanisms were separated from the Hbeam by attaching them to a large steel plate, or raft

(see Fig. 5).

Fig. 5—FE representation of a mechanism

suspension consisting of a raft and

longitudinal springs.

The raft was supported by longitudinal

springs with three degrees-of-freedom at six locations.

Four of the spring locations were near the corners of

the raft, while the remaining two spring locations were

at the midpoint of the raft’s front and rear edges.

The final FE model had a total of 24,145 nodes and

20,649 solid elements. Because most of the screen is

plate-like, shell elements were used to model most of

the screen. A total of 19,045 four-node shell elements

with six degrees-of-freedom at each node—three translations and three rotations—were used in the model.

The remaining 1,604 solid elements were ten-node

solid elements with three translational degrees-of-freedom at each node.

The FE model was used to analyze the mechanism

suspension in two steps. First, the model was used to

solve for the natural frequencies and mode shapes of

the screen with the mechanism suspension. The spring

rates of the mechanism suspension springs were varied

to examine how their stiffness affects the modes. Next,

the forced response of the screen was determined for a

range of mechanism suspension spring rates. For each

case, the displacement responses at 24 points on the

screen sides and 15 points on the feedbox were

exported for subsequent use when estimating the sound

power level radiated from these locations (refer to

Fig. 6). The focus was on the sides and feedbox

because prior beamforming studies showed that the

sides and feedbox were the primary noise-radiating

surfaces8,9. In this analysis, a unit load with a flat frequency spectrum from 0 to 500 Hz was applied at each

of the vibration mechanisms with a direction normal to

the top of the H-beam. A flat frequency spectrum was
used to represent the impact forces due to bearing chatter within the vibration mechanisms for simplicity. The

analysis was limited to this frequency range because

above 500 Hz the modal density was high. The objective of the analysis was to determine the approximate

mechanism suspension spring rates needed to reduce

the vibration transmitted to and the resulting noise

radiated by the screen sides and feedbox.

Fig. 6—Point locations used to estimate the

sound power level radiated by the (a)

screen sides and (b) feedbox.

2.4 Sound Power Level Estimation

The results of the FE model forced response analysis were used to estimate the sound power level radiated by the screen sides and feedbox due to forces

from within the vibration mechanisms. For a vibrating

object, the sound power level radiated can be estimated

by

LW 1⁄4 10 log 2

10h iv s;t

þ10 log10 S þ 10 log10 r

þ 146 dB re 10-12W (4) ( )

where LW is the sound power level, h iv

2

s;t is the

surface-averaged mean-squared velocity, S is the surface area, and r is the radiation efficiency14. Equation

(4) was incorporated into a computer program that carried out all calculations for the screen sides and feedbox on a frequency-by-frequency basis in 1 Hz

increments. For each set of displacement results, the

velocity response at each location was calculated by

v 1⁄4 2pfd (5)

where d is the displacement magnitude as a function of

frequency and f is the excitation frequency in Hz.

The radiation efficiencies of the sides and feedbox

were estimated from the thickness and perimeter of

each part using data from Bies and Hansen14. For the

screen sides, the areas between stiffening ribs were

treated as separate panels (see Fig. 7(a)). The radiation

efficiency of each panel was estimated using its perimeter and thickness. For the feedbox, the rear and sides

of the feedbox were treated as separate entities (see

Fig. 7(b)).

Fig. 7—(a) Individual “panels” used to estimate the sound power level radiated

by the screen sides and (b) portions of

the feedbox used to estimate the

sound power level radiated by the

feedbox.

The perimeter and thickness of each was

used to estimate its radiation efficiency. Within the

program, the radiation efficiencies were estimated by

curve fitting values from the Bies and Hansen data

using a 3rd order polynomial. This provided a simple

means of estimating the radiation efficiency on a frequency-by-frequency basis.

Once the radiation efficiencies were estimated, the

sound power levels for each panel of the screen sides

and for the rear and sides of the feedbox were calculated using Eqn. (4). For the screen sides, the radiation

efficiency of each panel was used with its calculated

surface-averaged mean-squared velocity. Similarly, for

the feedbox, the radiation efficiencies of the rear and

sides of the feedbox were used with their calculated

surface-averaged mean-squared velocity. The total

sound power level for the screen side was calculated

by adding the contributions of each panel and the total

sound power level for the feedbox was calculated by

adding the contributions of the rear and sides of the
feedbox. In the past, the same approach was applied to

examine the sound power level radiated by screens9,11.

Since the MSHA PEL is based on A-weighted

sound levels, the program was used to apply

A-weighting to the estimated sound power levels. The

summation of the sound power levels for the screen

sides and feedbox was found by

LWSþF 1⁄4 10LOG 100:1LWS þ 100:1LWF (6) ( )

where LWS þ F is the estimated sound power level radiated by the sides and feedbox, LWS is the estimated

sound power level radiated by the sides, and LWF is the

estimated sound power level radiated by the feedbox.

For each set of data, the A-weighted 1/3-octave-band

sound power level spectrum was computed by summing the narrowband sound power from the lower cutoff frequency to the upper cutoff frequency for each 1/

3-octave band. One-third-octave bands were used to

simplify the interpretation of the results. Finally, the

overall A-weighted sound power level from 0 to

500 Hz was calculated by summing the A-weighted

narrowband sound power levels.

3 RESULTS AND DISCUSSION

While a simple single-DOF analysis is adequate for

most vibration isolation systems applied to stationary

machines, it is insufficient to analyze a mechanism suspension to isolate higher frequency energy within

vibrating screens. For most pieces of equipment, completely preventing all vibratory forces from being

transmitted from a vibrating component to the surrounding structure would be ideal. But for a vibrating

screen to function properly, the forces generated by the

vibration mechanisms at their rotational speed must be

transmitted to the body of the screen. Therefore, it is

proposed to design a vibration mechanism suspension

that transmits the vibration mechanism forces at their

shaft speed while attenuating higher frequency force

components due to bearing and gear vibrations.

There are several design considerations for an effective mechanism suspension. First, the tuned mechanism suspension cannot substantially decrease the

response of the screen at the vibration mechanism

operating frequency, because this would affect the ability of the screen to process coal. In addition, the vibration amplitude of the vibration mechanisms at the

screen’s operating speed cannot significantly increase,

because this could decrease the life of the gears, bearings, drive belt, and drive motor. Since building vibration is a major concern, the mechanism suspension

must not adversely affect the vibration transmitted to

the building. Finally, the mechanism suspension

should reduce the force transmitted from the mechanisms to the screen body at frequencies where

noise radiation is a concern. A target isolation

frequency of 100 Hz was selected because most of the

A-weighted sound power level is due to frequencies

above 100 Hz.

3.1	 Two-DOF Analysis of Screen with an

Added Mechanism Suspension

The model shown in Fig. 3 was used to examine the

dynamic characteristics of a screen with an added

mechanism suspension while varying the spring rate

for the mechanism suspension, k1, from 8.755 MN/m

to 17,510 MN/m. These values were used so that the

system dynamics could be examined for a wide range

of suspension stiffness with the hope of finding a range

of stiffness values that would isolate operating forces

at audible frequencies from the screen without creating

problems due to suspension modes during startup,

operation, and shutdown. The natural frequencies and

mode shapes, the displacement responses for the

vibration mechanisms and the screen body, the force

transmitted from the vibration mechanisms to the

screen body, and the force transmitted from the screen

body to the ground were calculated for each spring

rate.

Because the model has two degrees of freedom,

there are two natural frequencies and mode shapes for

the model. In the first mode, the vibration mechanisms

and the screen body move in phase with the same amplitude. For the second mode, the vibration mechanisms and the screen body move out of phase with

each other, and the amplitude of the vibration mechanisms is approximately seven times that of the screen

body. Because the second mode gives the appearance

of the vibration mechanisms bouncing on top of the

screen body, this mode is referred to as a “bounce

mode.”

The two-DOF-analysis results showed that when the

bounce mode was in the range of 50 to 70 Hz, the

mechanism suspension attenuated the forces transmitted from the vibration mechanisms to the screen body

above 100 Hz. In addition, the mechanism suspension

did not significantly change the force transmitted from

the vibration mechanisms to the screen body at the

operating speed of the screen, 15 Hz. For subsequent

analyses, the goal was to determine the mechanism

suspension spring rates required to yield a bounce

mode between 50 Hz and 70 Hz, without creating

problems caused by pitching modes of the suspension.

The two-DOF analysis provided good insight into

the behavior of the proposed suspension. Figures 8(a)

and 8(b) show the response of the mechanisms and the
response of the screen body per unit force applied at

the mechanisms. Figures 8(c) and 8(d) show the force

transmitted from the mechanisms to the screen body

and the force transmitted from the screen to the ground

per unit force applied at the mechanisms.

Fig. 8—System response per unit force based on a two DOF model using a unit load applied to

the mechanisms: (a) response of the mechanisms; (b) response of the screen body; (c)

force transmitted from the mechanisms to the screen body; and (d) force transmitted

from the screen to the ground.

The red vertical line represents the operating speed of the vibration

mechanisms, 15 Hz. Because the figures are based on a

two DOF model, two resonant peaks occur. The lower

resonant peak at approximately 2.1 Hz is not affected

by the mechanism suspension spring rate. However,

the frequency of the upper peak decreases with

decreasing spring rate. In addition, the responses of

both the screen body and the mechanisms at the operating speed are affected as the mechanism suspension

spring rate is decreased. As the second resonant peak

approaches the operating speed, the responses of the

mechanisms and screen body at the operating speed

are greatly amplified. As a result, both the force transmitted to the ground and the force transmitted to the

screen body increase substantially.

3.2	 FE Analysis of the As-Built Screen with

an Added Mechanism Suspension

As in the two-DOF model, the frequency of the

bounce mode for the FE model determines the frequency at which isolation of vibration mechanism forces

begins. For the FE model, the bounce mode is identified

by motion of the raft and the attached mechanisms normal to and out of phase with motion of the H-beam top

flange. The bounce mode may also exhibit motion of

other screen components. The mechanism suspension

should have a bounce mode at roughly 50 to 70 Hz,

because the two-DOF analysis showed that systems

with mechanism suspension bounce modes in this range

meet the design requirements discussed above. However, the spring rates from the two-DOF analysis provide only a rough starting point for the FE model,

because adding a raft between the vibration mechanisms

and the top flange of the H-beam in the FE model will

increase the mass supported by the mechanism
suspension. This increase in sprung mass requires an

increase in the mechanism suspension spring rates to

keep the bounce mode in the range of 50 to 70 Hz.

Due to the geometry of the as-built screen, it was

expected that achieving a mechanism suspension

bounce mode of 50 to 70 Hz might result in a system

with a pitch mode, with rotation about the lateral axis

of the mechanism suspension, near or below the operating speed of the vibration mechanisms, 15 Hz. The

top flange of the H-beam on the as-built screen is not

very deep. This limited the spacing of the mechanism

suspension mounting locations to 177.8 mm (refer to

Fig. 9).

Fig. 9—Side view of mechanism suspension,

showing CG of mechanisms and

mechanism suspension spring attachment points for the FE model of the

as-built screen with added mechanism

suspension.

In addition, the mechanisms are mounted so

their centers of gravity are above their mounting surface. Both of these factors contribute to the presence of

a pitch mode at low frequencies. The presence of a

pitch mode near the operating speed could cause problems with the drive belt, bearings, gears, etc. If a pitch

mode occurred below the operating speed, high amplitude motion during start-up and/or shutdown transients

could be problematic.

To examine the modal characteristics of the as-built

screen, the spring rates for each of the six mechanism

suspension springs in the Xs-, Ys-, and Zs-directions

(refer to Fig. 5) were varied from 44 MN/m to 17,510

MN/m. The 17,510-MN/m spring rate represents a

rigid suspension, which would prevent relative motion

between the raft and H-beam. The results, summarized

in Table 1, showed that none of the spring rates

resulted in a suspension that would meet the design

objectives.

Table 1—Summary of mechanism suspension spring rates and resulting pitch and bounce mode frequencies from modal analysis of the as-built screen with an added mechanism suspension. 

Spring rate in Xs-, Ys-, and Zs-directions (MN/m) 17,510 88 44

Fbounce (Hz) NA 73.5 55.6

Fpitch (Hz) 37.8 16.5 12.7

NA Not applicable

For the rigid suspension, the pitch mode of

the mechanisms involved twisting of the entire

H-beam with no deflection of the springs, and the

bounce mode did not exist because the spring rates

were high enough to prevent relative motion between

the raft and top flange of the H-beam. When the mechanisms suspension spring rates were 88 MN/m, the

mechanism suspension bounce mode frequency was

73.5 Hz (refer to Fig. 10), just above the target range,

and the mechanism suspension pitch mode frequency

was 16.5 Hz (refer to Fig. 11). When the spring rates

were 44 MN/m, the bounce mode frequency was 55.6

Hz and the pitch mode frequency decreased to 12.7

Hz. The suspensions with spring rates of 44 MN/m and

88 MN/m would probably cause problems due to the

proximity of the pitch mode to the operating speed of

the screen. To force the pitch mode well beyond the

operating speed of the screen while keeping the bounce

mode in the 50 to 70 Hz frequency range, the design of

the mechanism suspension and the as-built screen must

be modified.

3.3	 Modal Analysis with FE Model of Screen

with Increased Depth of H-beam Top

Flange and Raft

In order to develop a successful mechanism suspension, the suspension’s rotational stiffness about its yaxis must be increased to push the pitch mode far

above the screen’s operating speed. If this is done by

increasing the mechanism suspension spring rates, the

bounce mode of the suspension will be forced out of

the 50 to 70 Hz range, and the resulting suspension

will not begin to attenuate forces transmitted from the

mechanisms to the screen body at 100 Hz. Therefore,

instead of increasing the mechanism suspension spring

rates, the distance between the suspension spring
locations could be increased. This would also require

the depth of the H-beam top flange and the depth of

the raft to be increased.

Fig. 10—Bounce mode of mechanism suspension for FE model of as-built screen

with added mechanism suspension.

Fig. 11—Pitch mode of mechanism suspension for FE model of as-built screen

with added mechanism suspension.

For a simple system supported by linear springs

that undergoes rotational motion about its center

(refer to Fig. 12), the system’s rotational stiffness is

defined by

k

K 2	 rot 1⁄4 L (7) 2

where k is the spring rate and L is the distance between

the springs.

Fig. 12—A simple spring-supported system

that undergoes rotational motion

about its center.

Because the rotational stiffness increases

with the square of the distance between the springs, a

small increase in the distance between the springs will

significantly increase the rotational stiffness.

To improve the rotational stiffness for the mechanism suspension, the depth of the raft and the depth of

the H-beam top flange were increased in the FE model,

allowing the distance between the mechanism suspension springs to increase from 177.8 mm to 431.8 mm

(refer to Fig. 13). From Eqn. (7), these changes

increased the rotational stiffness of the mechanism suspension about its y-axis by a factor of 5.9. The changes

to the raft also increased the mass of the raft and the

mass of the H-beam top flange by a factor of 1.6. These

changes increase the total mass of the screen by a small

percentage.

As before, the FE model was used to perform modal

analysis on the screen with the modified H-beam and

raft for a variety of mechanism suspension spring rates.

Table 2 summarizes the spring rates used and the

resulting bounce and pitch mode frequencies. Case 1,

which used a spring rate of 17,510 MN/m in all three

directions, represents a rigid suspension. For the rigid

case, a bounce mode was not observed, as expected.

Case 2 used a spring rate of 175 MN/m in all three

directions, and Case 3 used a spring rate of 35 MN/m

in all three directions. Both of these cases yielded suspensions that met the target range of 50 to 70 Hz for

the bounce mode. In addition, the pitch modes for each

case were well above the operating speed of the screen.

Some vibration isolation mounts are much stiffer in

off-axis directions. Case 4, which uses the same spring

rate as Case 3 in the Zs-direction and spring rates that

are five times higher in the Xs- and Ys-directions, was

used to examine how these conditions would affect the

modes. As Table 2 shows, the large increases in the

stiffness in the Xs- and Ys-directions (Case 4) had a

minimal effect on the frequencies of the pitch and

bounce modes.

3.4	 Forced Response Analysis and Estimation

of Sound Power Level

After providing a good understanding of how the

frequencies of the pitch and bounce modes change

with the mechanism suspension spring rates, the FE

model was used to perform a forced response analysis

for a range of mechanism suspension spring rates using

the modal superposition method. Table 3 summarizes

the mechanism suspension spring rates used in the

analysis. Case A, which uses a spring rate of 17,510

MN/M in all three directions, represents a rigid
connection. Case B, which uses a spring rate of 175

MN/m in the Zs-direction, has a bounce mode of

approximately 67 Hz. Case C uses a spring rate of 35

MN/m in the Zs-direction, which yields a bounce mode

of 50 Hz. For Cases B and C, the spring rates in the

Xs- and Ys-directions were five times their respective

spring rates in the Zs-direction. The spring rates for

Case B and Case C were selected because they produce

systems with bounce mode frequencies at the extremes

of the desired target range for the bounce mode.

Fig. 13—Comparison of mechanism suspension spring spacing along the depth of the H-beam

for the model of the as-built screen (left) and for the model of the screen with increased

H-beam top flange and raft depth (right).

Table 2—Mechanism suspension spring rates and resulting pitch and bounce mode frequencies for the

modal analysis of the screen with added mechanism suspension and increased H-beam top

flange and raft depth.

Mechanism Suspension Spring Rates (MN/m) Direction Case 1 Case 2 Case 3 Case 4

Fpitch (Hz)

Fbounce (Hz)

Xs

Ys

Zs

17,510

17,510

17,510

54

NA

175

175

175

37.7

67.1

35

35

35

23.4

50.1

175

175

35

24.0

50.2

NA Not applicable

Several assumptions were made to simplify the

model and to enable the use of the modal superposition

technique. In the analysis, the spring rates were considered to have a fixed value as a function of frequency.

In addition, a constant modal damping of 0.002 was

used for all modes. This value was used because previously collected experimental modal data showed that

the as-built screen is lightly damped. In practice, rubber vibration isolators would probably be used for the

mechanism suspension. For rubber vibration isolators,

the stiffness and damping increase as a function of frequency. As a result, the FE model will tend to underestimate the displacements at high frequencies. However,

assuming constant values allows trends to be observed

while allowing modal superposition to be used to solve

the problem instead of explicitly solving for the

response. Due to the large model size, the explicit solution would require significantly more solution time and

computational power.

In the analysis, a unit load with a flat input spectrum

from 0 to 500 Hz was applied to the raft at the center

of each mechanism. These loads represent the impact

forces generated by the interaction of the eccentric

shafts with the bearings. Clearance in the bearings

allows the vibration mechanism shafts to make and

break contact with the bearing’s rolling elements as the

screen vibrates. It is likely that the real force spectrum

is not flat. However, for comparison purposes, assuming a flat input spectrum should be adequate. It is

expected that the actual force spectrum would roll off

at higher frequencies similar to the spectrum of an

impact hammer used for modal testing.

The mechanism suspensions with bounce modes in

the 50 to 70 Hz frequency range, Case B and Case C,
reduced the estimated sound power level in the 0 to

500 Hz frequency range. Figure 14 shows the estimated A-weighted sound power level from the screen

sides and feedbox in 1/3-octave bands as computed

from Eqn. (4).

Fig. 14—Estimated A-weighted sound power

level in 1/3-octave bands for two

mechanism suspensions compared

to a rigid mechanism suspension.

Case A represents the baseline because

its response should be similar to that of a screen with

its mechanisms bolted directly to the H-beam. For

Case A, the spectrum exhibits a hump in the 250 Hz

through 500 Hz 1/3-octave bands. The measured sound

power level, shown in Fig. 2, also exhibits this characteristic. Recall, the results presented in Fig. 14 are

based on a unit force with a flat input spectrum applied

at the center of each mechanism. The real forces

applied to the mechanisms by the bearings will probably not have flat spectra. Instead, the real input forces

would probably exhibit peaks near the bearing frequencies. Therefore, the results should only be used to

examine trends.

The suspensions for Case B and Case C shift the

sound power level spectrum towards lower frequencies. The figure shows that the estimated overall

A-weighted sound power level from 0 to 500 Hz is 74

dB for Case A, 67 dB for Case B, and 56 dB for Case

C. Treating Case A as the baseline (mechanisms rigidly

connected), Case B and Case C reduced the estimated

A-weighted sound power level by 7 dB and 18 dB,

respectively. In a real world application of these mechanism suspensions, it is unlikely that the sound power

level would be reduced by these values. However, the

results show how mechanism suspensions could reduce

the A-weighted sound power level.

With the previously discussed assumptions, the

results indicate that the sound power level radiated by

the screen sides and feedbox decreases as the mechanism suspension spring rate normal to the H-beam is

adjusted to produce mechanism suspension bounce

modes in the 50 to 70 Hz frequency range. In practice,

the screen and mechanism suspension designs must be

modified to ensure that other modes of vibration, such

as the mechanism suspension pitch mode, occur at frequencies well beyond the operating speed of the

screen. Another factor to consider is that the magnitude

of the impact forces generated within the vibration

mechanisms might be affected by the mechanism suspension stiffness. If the displacement of the vibration

mechanism housings increases above the baseline

value, the forces due to bearing slap will probably

increase. If the increase in the bearing slap forces is

equal to the attenuation in the force transmitted, the net

result will be that the sound power level will stay the

same. It is also possible that the increase in bearing

slap forces could exceed the attenuation provided by a

mechanism suspension system. In this case, the sound

power level would increase. As demonstrated, caution

must be exercised when implementing a mechanism

suspension system. A slightly stiffer system could ultimately yield a larger reduction in sound power level

than a softer system.

Table 3—Mechanism suspension spring rates for the forced response analysis of the screen with added

mechanism suspension and increased H-beam top flange and raft depth.

Direction Case A Case B Case C

Mechanism Suspension

Spring Rates (MN/m)

Xs

Ys

Zs

17,510

17,510

17,510

876

876

175

175

175

35

4 CONCLUSIONS

The addition of a mechanism suspension to a vibrating screen was analyzed using a simple two-DOF

model and an FE model. The two-DOF analysis

showed that mechanism suspensions with bounce

modes from 50 to 70 Hz could transmit vibration at the

screen’s operating speed while attenuating vibration at

frequencies above 100 Hz. For the as-built screen with
an added mechanism suspension, FE modal analysis

showed that a mechanism suspension pitch mode

would occur close to the screen’s operating speed for

mechanism suspensions with bounce modes from 50 to

70 Hz. These systems might successfully attenuate

noise and vibration above 100 Hz, but because their

pitch modes would be close to the screen’s operating

speed, these systems could cause undesirable behavior

during screen start-up, shutdown, and steady operation.

In the FE model, changes were made to the H-beam

and the mechanism suspension to increase the rotational stiffness of the suspension to force the pitch

mode to higher frequencies. Increasing the depth of the

H-beam top flange and the depth of the raft allowed

the spacing between the suspension springs to be

increased. For mechanism suspensions with bounce

modes of 50 to 70 Hz, this shifted the mechanism suspension pitch mode to higher frequencies.

The modified FE model was used to estimate the

sound power level radiated by the screen sides and feedbox due to a unit force applied at the center of each

vibration mechanism. The estimated sound power levels

for mechanism suspensions with bounce modes of 50

and 67 Hz were compared to those of a rigid suspension. The estimated A-weighted sound power level from

the screen sides and feedbox was reduced by 7 to

18 dB, depending on the mechanism suspension stiffness. It is important to realize that this analysis only considers noise radiated by the screen sides and feedbox

due to gear and bearing forces within the vibration

mechanisms. In reality, vibrating screen noise is generated from many components. In addition, because these

results are based on several assumptions, these reductions would probably not be achieved in practice. However, even though the FE model was simplified by

assuming non-frequency-dependent spring rates, constant modal damping, and flat force spectra, the analysis

shows that a mechanism suspension could be designed

to reduce vibration-related screen noise due to high frequency forces within the vibration mechanisms.

The analysis revealed several important factors to

consider in the design of a mechanism suspension for

vibrating screens. First, to attenuate noise at frequencies

above 100 Hz without significantly affecting a screen’s

performance, the bounce mode of the screen suspension

must be kept within the range of 50 to 70 Hz. Next, the

spacing between the vibration isolation mount locations

must be increased to force the suspension pitch mode to

higher frequencies where it will not be well-excited during screen start-up, shutdown, or operation. The analysis

used here showed that a suspension system with a 50

Hz bounce mode would reduce noise more than a system with a 70 Hz bounce mode. While the results indicate that adding a mechanism suspension to a screen

will significantly decrease radiated noise, these results

must be verified experimentally. The next phase of this

research will consist of adding a mechanism suspension

to a vibrating screen and measuring the resulting sound

power levels.

5 REFERENCES

1.	 Department of Labor, Mine Safety and Health Administration,

“Health Standards for Occupational Noise Exposure: Final

Rule,” 30 CFR Part 62. Federal Register, (1999).

2.	 E. R Bauer, Personal communication. DHHS, CDC, NIOSH,

PRL, Pittsburgh, PA, (2004).

3.	 Mine Safety and Health Administration. http://www.msha.gov/

OpenGovernmentData/OGIMSHA.asp downloaded December

9, 2010 with the exception of the MSHA Accident data file,

which was added December 27, 2010.

4.	 E. E. Ungar, G. E. Fax, W. N. Patterson and H. L. Fox, “Coal

Cleaning Plant Noise and Its Control”, BuMines OFR 44-74,

(1974).

5.	 M. N. Rubin, A. R. Thompson, R. K., Cleworth and R. F.

Olson, “Noise Control Techniques for the Design of Coal Preparation Plants”, BuMines OFR 42-84, (1982).

6.	 D. S. Yantek, P. Jurovcik and E. R. Bauer, “Noise and Vibration Reduction of a Vibrating Screen”, SME Annual Meeting,

Society for Mining, Metallurgy, and Exploration, (2005).

7.	 D. S. Yantek, H. E. Camargo and R. J. Matetic, “Application

of a microphone phased array to identify noise sources on a

horizontal vibrating screen”, NoiseCon08, (2008).

8.	 H. E. Camargo, P. A. Ravetta, R. A. Burdisso and D. S. Yantek, “Noise source identification on a horizontal vibrating

screen”, Mining Engineering, (2009).

9.	 D. S. Yantek and H. E. Camargo, “Structural vibration as a

noise source on vibrating screens”, ASME 2009 International

Mechanical Engineering Congress & Exposition, (2009).

10. M. J. Lowe, D. S. Yantek, H. E. Camargo, L. A. Alcorn and

M. Shields, “Noise controls for vibrating screen mechanisms”,

SME Annual Meeting, Society for Mining, Metallurgy, and Exploration, Inc., (2010).

11. D. S. Yantek and S. Catlin, “Evaluation of stiffeners for reducing noise from horizontal vibrating screens”, NoiseCon10,

(2010).

12. E. E. Ungar, C. L. Dym, and M. H. Rubin, “Practical Reduction of Noise from Chutes and Screens in Coal Cleaning

Plants”, BuMines OFR 59-77, (1976).

13. Singeresu S. Rao, “Two degree of freedom systems”, Chap. 5

in Mechanical Vibrations – Second Edition., Addison Wesley

Publishing Company, Inc., (1990).

14. D. A. Bies and C. H. Hansen,	 Engineering Noise Control

Theory and Practice. Third Edition. Spon Press, (2003).