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GYRATORY CRUSHERS: THEORETICAL CAPACITY

Basic Operating Principles

Gyratory crushers operate based on the simple concept of a conical crushing surface, the mantle ,gyrating with an eccentric motion within an inverted conical crushing surface, the concaves . The spacebetween the mantle and concaves forms the crushing cham er . The width of the opening between themantle and concaves at the discharge point of the crushing chamber is termed the setting of the crusher.

As the mantle gyrates within the crushing chamber, it moves from the maximum to the minimum settingfor every 180 of eccentric rotation. This cycle creates a crushing motion unli e any other. Although atany specific point within the crushing chamber the crushing motion is strictly reciprocating, the crushingmotion for the crushing chamber as a whole is a continuous com!ressive action .

The setting of the crusher is defined by the eccentricity of the drive. The minimum setting is termed theclose" si"e setting !".#.#.$, and the maximum setting is termed the o!en si"e setting !%.#.#.$. Theopen and closed side settings are related to the eccentricity of the crusher according to the followingrelationships&

!'(. 1$

!'(. )$

The open side setting of the crusher determines the expected product si*e and is customarily stated inhalf+inch increments.

hen material is fed to the crusher, either by a feeder or by direct dump, it is grabbed or -nipped at acertain level within the crushing chamber. The ni! angle is defined as the included angle between themantle and concaves. The maximum nip angle of a specific application depends on the coefficient of friction for the material being crushed and typically varies between )) and /0 . Generally, harder materials such as granite, trap roc and taconite re(uire maximum nip angles from ) to ) . . #ofter materials such as limestone typically re(uire a maximum nip angle of )2 . #lippery materials such asmica bearing shale re(uire tighter nip angles, even though these materials may be relatively soft.3ractically, the nip angle of a specific crusher model is limited by the geometry of the shells !#ee 4igure1$.

At any instant during operation, material is crushed on the closed side of the crushing chamber. "rushingoccurs throughout the crushing chamber, however, the maximum crushing effect is located at the bottomwhere there is greater motion of the mainshaft. The crushed material in this area falls to the next level, or crushing *one, as the crushing chamber opens. As the crushing chamber closes, the material in this areais once again nipped and crushed.

Theoretical Volumetric Capacity

4rom the above discussion, we would intuitively relate the theoretical volumetric ca!acit# of thecrusher to the maximum volume of material which can pass through the crushing chamber during a singlegyration and the fre(uency at which the crusher gyrates from the closed side setting to the open side

setting. This relationship can be defined by four variables& 5antle 6iameter

%pen #ide #etting

'ccentric Throw

Gyrations 3er 5inute

CRUSHI$G %I&ISIO$ 1

O S S C S S EccentricThrow. . . . . =

EccentricThrow Eccentricity= 2

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W C

S Gi =

2 59.

. .

hen a new crusher is designed or when an existing crusher design is modified, a !ro"uct "iagramwhich represents the crusher at both the open and closed side settings is developed using the geometryof the crushing chamber !#ee 4igure )$. This geometry is defined by the radial feed opening, the openside setting, the nip angle, the curvature of the mantle, and the curvature of the concaves. %nce thegeometry of the crushing chamber is defined, the lowest five crushing *ones are evaluated. The crushing*one with the minimum cross sectional area is termed the cho'e !oint . ith straight concaves andmantle, the cho e point coincides with the discharge point of the crushing chamber where maximumcrushing motion occurs. ith Tra#lor curve" non(cho'ing concaves , the cho e point is moved to apoint above the discharge point of the crushing chamber, reducing the tendency of the material to pacwhile being crushed. 7y multiplying the cross sectional area of the cho e point by the circumference of the mantle in this region, the maximum volume of material which can pass through the crushing chamber during a single gyration is determined. This value is multiplied by the gyrations per minute to determinethe theoretical volumetric capacity of the crusher. This theoretical value can be changed by altering anyone of the four variables listed above.

All other variables being e(ual, the effect of increasing or decreasing the mantle "iameter would be torespectively increase or decrease the relative cross sectional area of the crushing chamber. The crosssectional area of the cho e point would also increase or decrease with an approximately linear effect ontheoretical volumetric capacity. Thus, the maximum theoretical volumetric capacity of a 09 gyratorycrusher with a 11/9 mantle diameter exceeds that of a 09 gyratory crusher with a 1109 mantle diameter

which, in turn, exceeds that of a 09 gyratory crusher with an 8:9 mantle diameter.

#imilarly, the effect of increasing or decreasing the o!en si"e setting alone would be to respectivelyincrease or decrease the relative cross sectional area of the crushing chamber. "hanging the open sidesetting would also have an approximately linear effect on theoretical volumetric capacity. ;oo ing at theattached product diagram, increasing the open side setting would be roughly analogous to pulling themantle and concaves apart, while decreasing the open side setting would be roughly analogous topushing the mantle and concaves together. Thus, the maximum theoretical volumetric capacity of a 09 x1109 gyratory crusher designed for a 10 inch !) mm$ open side setting exceeds that of a 09 x 1109gyratory crusher designed for an 8 inch !)0/ mm$ open side setting which, in turn, exceeds that of a 09 x1109 gyratory crusher designed for a 29 !128 mm$ open side setting.

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W W

P

W

F i i

= 10 10

80 80

where " impact strength in foot+pounds per inch thic ness

#.G. specific gravity

This value is obtained empirically from test samples of the material.

)$ The +or' or energy re(uired to reduce the nominal si*e of the material is determined from thee(uation&

!'(. $

where 380 screen si*e in microns which willpass 80= of the product

480 screen si*e in microns which will

pass 80= of the feed

The expected capacity in short tons per hour of crushed product does not include thefraction of crusher feed which already meets the product si*e re(uirement. Thepercentage of feed material which is finer than the 380 is termed the *all(through*actor .

/$ The Theoretical Process Po)er is calculated from the e(uation&

!'(. $

where B the expected capacity in short tonsper hour of crushed product

hen si*ing a crusher for a specific application, a 10= service factor is typically added to the theoreticalprocess power to obtain the theoretical motor !o)er which is used to confirm that the crusher drivemotor is suitably rated.

Summary

Gyratory crusher capacity can be evaluated both in terms of the maximum theoretical volumetric ca!acit# and the theoretical !rocess !o)er re(uired. The theoretical volumetric capacity of a gyratorycrusher is determined by the geometry of the crushing chamber, the setting, the eccentricity and theoperating speed. The theoretical process power is determined by the crusher wor index, feed si*e anddesired product si*e of the material. The concepts and calculations presented in the above discussionare generally accepted by the crushing industry and apply to all gyratory type crushers.

CRUSHI$G %I&ISIO$ 3

HP W Q= 1 34.

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-IGURE .: CO//O$ $IP A$GLES

COMMON NIP N!"#S$ % &'()* 22'3+

$ % )',,* 23')&

$ % )'2)* 2&'-.

$ % )'),* 2)'.1

$ % )'()* 2-'+)

$ % -',,* 2.',(

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-IGURE 0: TYPICAL PRO%UCT %IAGRA/

CRUSHI$G %I&ISIO$ )