CA2274699C - Archbreaking hopper for bulk solids - Google Patents
Archbreaking hopper for bulk solids Download PDFInfo
- Publication number
- CA2274699C CA2274699C CA002274699A CA2274699A CA2274699C CA 2274699 C CA2274699 C CA 2274699C CA 002274699 A CA002274699 A CA 002274699A CA 2274699 A CA2274699 A CA 2274699A CA 2274699 C CA2274699 C CA 2274699C
- Authority
- CA
- Canada
- Prior art keywords
- hopper
- section
- theta
- wall
- inclination
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
Classifications
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B65—CONVEYING; PACKING; STORING; HANDLING THIN OR FILAMENTARY MATERIAL
- B65D—CONTAINERS FOR STORAGE OR TRANSPORT OF ARTICLES OR MATERIALS, e.g. BAGS, BARRELS, BOTTLES, BOXES, CANS, CARTONS, CRATES, DRUMS, JARS, TANKS, HOPPERS, FORWARDING CONTAINERS; ACCESSORIES, CLOSURES, OR FITTINGS THEREFOR; PACKAGING ELEMENTS; PACKAGES
- B65D88/00—Large containers
- B65D88/26—Hoppers, i.e. containers having funnel-shaped discharge sections
- B65D88/28—Construction or shape of discharge section
Abstract
A hopper that greatly reduces the tendency of the particulate material to fo rm bridges within the hopper is shaped so that its walls slope downward more steeply at the bottom of the hopper and slope less steeply with increasing heights above the outlet. In one embodiment the slope decreases continuously with increasing height above the oulet. In another embodiment the hopper is formed of successive sections, each joined around its circumference to the next-lower section, the wall of each section being less steeply inclined tha n the wall of the adjoining next-lower section. Exact relationships are given, relating the slopes of successive sections, and if the hopper is built in conformity with theses relationships, arching of the particulate material is eliminated.
Description
ARCHBREAKING HOPPER FOR BULK SOLIDS
BACKGROUND OF THE INVENTION
One of the most common problems with bulk solids such as coal, sugar, flour and other various chemicals is arching or bridging at the outlet of a converging hopper. The usual solutions for eliminating bridges include enlarging the outlet beyond the critical size for bridging, and using physical agitation such as air blasters, vibrators, air lances and poke bars to dislodge the solids. While physical agitation works to some extent when arching occurs only after time at rest, the only effective way presently to handle a bulk solid that arches instantly when placed in a hopper is to enlarge the outlet size. This increases the size and cost of the feed device required below the outlet.
BRIEF SLTMMARY OF THE INVENTION
An objective of the present invention is to provide a hopper that geatly reduces the tendency of the particulate material to form bridges within the hopper.
In accordance with the present invention this is accomplished by shaping the hopper so that its walls slope downward more steeply at the bottom of the hopper and slope less steeply the higher they are above the outlet.
In a first preferred embodiment the slope decreases continuously with increasing height above the outlet, whereby the profile of the wall is a smooth curve, and the wall of the hopper flares upward from the outlet, like an upwardly directed trumpet. 'In a second preferred embodiment, which reflects contemporary construction techniques, the hopper is formed of successive sections, each joined around its circumference to the next-lower section, the wall of each section being less steeply inclined than the wall of the adjoining next-lower section. .
The present inventor has developed exact relationships between the slopes of successive sections. If the hopper is built in conformity with these relationships, arching of the particulate material is eliminated.
The present inventor has found that when the hopper is shaped consistent with the above scheme, the cross section of the hopper in a horizontal plane may have any of the commonly used shapes, such as circular, rectangular, and race track shaped. Examples of these are shown in the drawings.
The novel features which are believed to be characteristic of the invention, both as to organization and method of operation, together with further objects and advantages thereof, will be better understood from the following description considered in connection with the accompanying drawings in which several preferred embodiments of the invention are illustrated by way of example. It is to be expressly understood, however, that the drawings are for the purpose of illustration and description only and are not intended as a definition of the limits of the invention.
BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING
Figure 1 is a diagram showing a side elevational view of a converging hopper having similar cross sections at all heights and defining some of the symbols used in the description;
Figure 2 is a diagram illustrating the concept of a self supporting arch;
Figure 3 is a diagram showing the relation between certain variables used in the description;
Figure 4 is a diagram showing a right conical hopper in accordance with a preferred embodiment of the present invention;
Figure 5 is a diagram showing a wedge-shaped long slot hopper in accordance with the present invention;
Figure 6 is a diagram showing a one dimensional converging hopper in accordance with the present invention;
Figure 7 is a diagram showing a type of chisel-shaped hopper in accordance with the present invention;
Figure 8 is a diagram showing a combined chisel and one dimensional convergence hopper in accordance with the present invention;
Figure 9 is a diagram showing an offset conical hopper in accordance with the present invention;
Figure 10 is a diagram showing an offset one dimensional convergence hopper in accordance with the present invention; and, Figure 11 is a diagram showing an offset wedge-shaped hopper in accordance with the present invention.
BACKGROUND OF THE INVENTION
One of the most common problems with bulk solids such as coal, sugar, flour and other various chemicals is arching or bridging at the outlet of a converging hopper. The usual solutions for eliminating bridges include enlarging the outlet beyond the critical size for bridging, and using physical agitation such as air blasters, vibrators, air lances and poke bars to dislodge the solids. While physical agitation works to some extent when arching occurs only after time at rest, the only effective way presently to handle a bulk solid that arches instantly when placed in a hopper is to enlarge the outlet size. This increases the size and cost of the feed device required below the outlet.
BRIEF SLTMMARY OF THE INVENTION
An objective of the present invention is to provide a hopper that geatly reduces the tendency of the particulate material to form bridges within the hopper.
In accordance with the present invention this is accomplished by shaping the hopper so that its walls slope downward more steeply at the bottom of the hopper and slope less steeply the higher they are above the outlet.
In a first preferred embodiment the slope decreases continuously with increasing height above the outlet, whereby the profile of the wall is a smooth curve, and the wall of the hopper flares upward from the outlet, like an upwardly directed trumpet. 'In a second preferred embodiment, which reflects contemporary construction techniques, the hopper is formed of successive sections, each joined around its circumference to the next-lower section, the wall of each section being less steeply inclined than the wall of the adjoining next-lower section. .
The present inventor has developed exact relationships between the slopes of successive sections. If the hopper is built in conformity with these relationships, arching of the particulate material is eliminated.
The present inventor has found that when the hopper is shaped consistent with the above scheme, the cross section of the hopper in a horizontal plane may have any of the commonly used shapes, such as circular, rectangular, and race track shaped. Examples of these are shown in the drawings.
The novel features which are believed to be characteristic of the invention, both as to organization and method of operation, together with further objects and advantages thereof, will be better understood from the following description considered in connection with the accompanying drawings in which several preferred embodiments of the invention are illustrated by way of example. It is to be expressly understood, however, that the drawings are for the purpose of illustration and description only and are not intended as a definition of the limits of the invention.
BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING
Figure 1 is a diagram showing a side elevational view of a converging hopper having similar cross sections at all heights and defining some of the symbols used in the description;
Figure 2 is a diagram illustrating the concept of a self supporting arch;
Figure 3 is a diagram showing the relation between certain variables used in the description;
Figure 4 is a diagram showing a right conical hopper in accordance with a preferred embodiment of the present invention;
Figure 5 is a diagram showing a wedge-shaped long slot hopper in accordance with the present invention;
Figure 6 is a diagram showing a one dimensional converging hopper in accordance with the present invention;
Figure 7 is a diagram showing a type of chisel-shaped hopper in accordance with the present invention;
Figure 8 is a diagram showing a combined chisel and one dimensional convergence hopper in accordance with the present invention;
Figure 9 is a diagram showing an offset conical hopper in accordance with the present invention;
Figure 10 is a diagram showing an offset one dimensional convergence hopper in accordance with the present invention; and, Figure 11 is a diagram showing an offset wedge-shaped hopper in accordance with the present invention.
In its simplest form the invention is a converging hopper with a similar cross section throughout and with a variable slope angle starting with a steep angle at the outlet and progressing to a flatter angle toward the top (as shown in Figure 1 ). The steeper angle at the bottom decreases the arching potential of the hopper when the cross section is the smallest. At a higher level of the hopper, the cross section has increased, so the hopper slope can decrease and have the same or better anti-bridging capability as the outlet. For the walls to be effective in reducing bridging they must be smooth and slick enough to cause flow at them. The slick and smooth requirement varies somewhat with the geometry of the hopper and the height of solids in the vertical section. There is a relation between wall slope, wall friction coefficient and distance from the vertical walls that determines the hopper slopes to maintain flow at the walls and thus ensure the anti-bridging effects of the hopper walls. If the wall flow criterion is met, then the anti-bridging potential of a hopper outlet is determined by the support from the hopper of a self supporting arch of thickness h (see Figure 2). The weight W in the arch is supported by the vertical component of force for stress on perpendicular to the hopper walls and shear stress T acting opposite to flow at the hopper wall.
T'~Qn where ~ = coefficient of friction between the wall and the bulk solid.
In general, the hopper angle 8 may vary about the periphery of the hopper.
T'~Qn where ~ = coefficient of friction between the wall and the bulk solid.
In general, the hopper angle 8 may vary about the periphery of the hopper.
i The cross sectional area will depend on the hopper geometry and Qp may change depending on the hopper geometry.
In its most general form, the arch equilibrium is expressed by o~ (Tan 9 + ~c)dP = ~ YdA
(1) where y is the bulls specific weight of the solid. The integral on the right is the downward force integrated over the cross sectional area, and the integral on the left is the upward force integated around the periphery of the hopper.
If y, 8 , and Qo are constant the integration produces Q~ (Tank+u) P/A=Y
Where P is the circumference of the hopper and A is the cross sectional area at a particular level of the hopper. Rearranging gives Q~ _ (YA/P)/(Tan ~ + ~) For arch failure to occur, the maximum major principal stress at the arch must exceed the unconfined yi d stress f~ of the solid in the arch. From Mohr circle geometry (see Figure 3), - Q~ = fcl(E.c2 + 1 ) Tan 8 = Y(~P)(~z + ~)ff~ - ~ (~) For a conical hopper .A/P = B/4 where B is the diameter of the cross section.
For a long slot hopper A/P = B/2 where B is the width of the cross section above which the failed arch was formed.
When the slot length exceeds three times the width, the end effect becomes negligible and the slot can be considered long.
In a theoretical sense one could use the above formula to generate a continuous optimum hopper shape; however, in a practical sense, the hopper is more likely to be constructed of segments, as in Fig. 4. The angle for each segment can be calculated as follows assuming that the lowest segment is designed for the critical arching of the'bulk solid using the appropriate fc and that this f~ is essentially constant for the remaining segments.
Tan ~2 = (B~/B~)Cfan ~ ~ + ~c) - ~c where 81 is the deviation of the hopper wall from vertical for the lowest segment I 2, B1 is the diameter of the discharge opening I4 of the lowest segment, 82 is the deviation of the hopper wall from vertical for the next higher segment 16 and BZ is the diameter of the discharge opening 18 of segment 16, 93 is the deviation of the hopper wall from vertical for the third segment 20, and B3 is the diameter of the discharge opening 22 of segment 20, and so on for any additional segments the hopper may, in general, include.
Equation (4) applies only to the right conical hopper of Fig. 4, to the wedge-shaped long slot hopper of Fig. 5, and to the chisel-shaped hopper of Fig. 7.
A more exact method for these hoppers is to use Equation 3 with the appropriate value of f~
used. In the most general sense an and 8 vary around the periphery and the Mohr circle relation applies only to the maximum an . Subsequent hopper slopes can then be calculated using Equation ( 1 ) with the prescribed variation of an and with Equation (2) used to define the maximum Qn The basic invention of a variable hopper slope angle used to reduce the arching in a converging hopper of similar cross section works equally well with the one-dimensional convergence hopper shown in Figure 6 (see US Patents 4,958,741 and 5,361,945), so called because it converges downwardly only in the left-to-right direction but does not converge in the front-to-back direction as viewed in Fig. 6. It may even diverge downwardly in the front-to-back direction. This hopper has a race track shaped cross section and its perimeter consists of two semicircular ends alternating with two straight line segments. The lengths of the straight line segments measured at the top of each of the successively higher hopper segments 24, 26 and 28 are denoted by Ll, LZ, and L3. The diameter of the semicircular ends measured at the lower end of each segment are denoted respectively by Wl, W2, and W3. The angles of deviation from vertical of the hopper wall of each hopper segment measured at the left and right ends of each segment, where the deviation is greatest, are denoted respectively by 8, , 62 , and 63 . In the case where the flat side walls are slightly diverging, the flat side walls have a vn roughly 0.05 times the .. T _ I
a~ acting in the direction ofthe curved converging walls. Equation ( 1 ) can be approximated by rrw O~m,~ (~342 Tan 9 +,425~c) + 0.1 ~cL Q" m.~c = Y(n W /4 + WL) combining with Equation (2) Tan 8 = (Y(rnvl4 + L) (u2 + 1 )/(rrf~ - .1 ~cL(rtw) - .425~c)1.342 (6) This equation can be used, as Equation (4) was used, to define subsequent slope angles. Assuming f~ and w are constant and f~ is determined by the lowest hopper angle 6,, then the following relation exists between L/'W and 6 for each segment of the hopper:
Llw = .342 rr (Tan9, - Tan 9)/(1.368 Tan ~, + 1.8~c) (~) This equation can be used along with the relation Oh=~L~(2Tan9) which is evident from Fig. 6, to determine a continuous curve that optimizes the hopper shape and minimizes the hopper height while preventing arching.
For the chisel-shaped hopper of Figure 7, the equivalent of Equation (6) is B=2 (f~Y)((~683 + UB) Tan 9 + (.711 + Lfg)I~)l(~Z +1)(n/4 + Llg)) for each segment of the hopper, where B is the width of the opening at the bottom'of a section, L is the length of the opening at the bottom of that section, 8 is the inclination of the flat portion of the section from the vertical, p is the coefficient of friction between the wall and the bulk solid, f~ is the unconfined yield stress of the material, y is the bulk specific weight of the material.
Just as Equation (7) was used to optimize the shape of the one-dimensional convergence hopper of Figure 6, so also Equation (8) can be used to optimize the shape of the chisel-shaped hopper of Figure 7. In Figure 7 the successively higher segments 30, 32, 34 have a race-track shape, but unlike the hopper of Fig. 6, the diameters Bl, B2, B3 of the segments 30, 32 and 34 increase from the bottom to the top of the hopper.
Therefore, the flat portions 36, 38, 40 are inclined from the vertical by the angles 6,, 62, 63 . The longest dimension of each of the segments 30, 32 and 34, measured at the bottom of each segment, are denoted by Ll, LZ, and L3, respectively.
The inventor has found that the slopes used in constructed hoppers can differ from the angles calculated by the above equations by as much as plus or minus 5 degrees without adversely affecting the performance of the hopper.
Typical applications of the invention include:
a) The conical hopper (Figure 4) where the similar cross sections are circular and arranged symmetrically around a common vertical centerline.
b) The wedge-shaped hopper (Figure 5) where the similar cross sections are rectangular and arranged symmetrically about a vertical centerline.
l0 c) The one-dimensional convergence hopper, reference U.S. Patent No.
4,958,741 (Figure 6) with similar cross sections composed of a rectangle with semi-circular ends, with the diameter of the semi-circular ends equal or decreasing slightly in the upward direction and the entire cross section arranged symmetrically about a vertical centerline.
d) The chisel-shaped hopper, reference U.S. Patent No. 4,958,741 (Figure 7) composed of similar cross sections composed of a rectangular central portion and semi-circular ends, with the semi-circular ends arranged so that their outer extremities lie in a vertical line or a line slightly diverging downward.
e) The combination of c) and d), reference U.S. Patent No. 4,958,741.
f) The conical chisel and one-dimensional convergence hopper shown in Figure 8.
g) The offset conical hopper (Figure 9) in which the similar circular cross sections are not symmetric about a vertical axis. In Fig. 9, the walls of the hopper segments 42, 44 and 46 are inclined from the vertical by angles that range from 81,,,ma to 6",,~"~ for the lowest segment 42, from 62~,,m,, to 62,,,~ for the next highest segment 44, and from 63,,,m,, to 63 ~ for the upper segment 46.
h) The offset one-dimensional convergence hopper (Figure 10) in which the essentially vertical parallel side walls 48 and 50 are arranged above each other but the semi-circular end walls are not symmetrically arranged about a vertical axis.
i) The offset wedge-shaped hopper (Figure 11 ) in which the end walls 52 and 54 are still vertical but the sides 56 and 58 are not symmetric about a vertical axis.
In its most general form, the arch equilibrium is expressed by o~ (Tan 9 + ~c)dP = ~ YdA
(1) where y is the bulls specific weight of the solid. The integral on the right is the downward force integrated over the cross sectional area, and the integral on the left is the upward force integated around the periphery of the hopper.
If y, 8 , and Qo are constant the integration produces Q~ (Tank+u) P/A=Y
Where P is the circumference of the hopper and A is the cross sectional area at a particular level of the hopper. Rearranging gives Q~ _ (YA/P)/(Tan ~ + ~) For arch failure to occur, the maximum major principal stress at the arch must exceed the unconfined yi d stress f~ of the solid in the arch. From Mohr circle geometry (see Figure 3), - Q~ = fcl(E.c2 + 1 ) Tan 8 = Y(~P)(~z + ~)ff~ - ~ (~) For a conical hopper .A/P = B/4 where B is the diameter of the cross section.
For a long slot hopper A/P = B/2 where B is the width of the cross section above which the failed arch was formed.
When the slot length exceeds three times the width, the end effect becomes negligible and the slot can be considered long.
In a theoretical sense one could use the above formula to generate a continuous optimum hopper shape; however, in a practical sense, the hopper is more likely to be constructed of segments, as in Fig. 4. The angle for each segment can be calculated as follows assuming that the lowest segment is designed for the critical arching of the'bulk solid using the appropriate fc and that this f~ is essentially constant for the remaining segments.
Tan ~2 = (B~/B~)Cfan ~ ~ + ~c) - ~c where 81 is the deviation of the hopper wall from vertical for the lowest segment I 2, B1 is the diameter of the discharge opening I4 of the lowest segment, 82 is the deviation of the hopper wall from vertical for the next higher segment 16 and BZ is the diameter of the discharge opening 18 of segment 16, 93 is the deviation of the hopper wall from vertical for the third segment 20, and B3 is the diameter of the discharge opening 22 of segment 20, and so on for any additional segments the hopper may, in general, include.
Equation (4) applies only to the right conical hopper of Fig. 4, to the wedge-shaped long slot hopper of Fig. 5, and to the chisel-shaped hopper of Fig. 7.
A more exact method for these hoppers is to use Equation 3 with the appropriate value of f~
used. In the most general sense an and 8 vary around the periphery and the Mohr circle relation applies only to the maximum an . Subsequent hopper slopes can then be calculated using Equation ( 1 ) with the prescribed variation of an and with Equation (2) used to define the maximum Qn The basic invention of a variable hopper slope angle used to reduce the arching in a converging hopper of similar cross section works equally well with the one-dimensional convergence hopper shown in Figure 6 (see US Patents 4,958,741 and 5,361,945), so called because it converges downwardly only in the left-to-right direction but does not converge in the front-to-back direction as viewed in Fig. 6. It may even diverge downwardly in the front-to-back direction. This hopper has a race track shaped cross section and its perimeter consists of two semicircular ends alternating with two straight line segments. The lengths of the straight line segments measured at the top of each of the successively higher hopper segments 24, 26 and 28 are denoted by Ll, LZ, and L3. The diameter of the semicircular ends measured at the lower end of each segment are denoted respectively by Wl, W2, and W3. The angles of deviation from vertical of the hopper wall of each hopper segment measured at the left and right ends of each segment, where the deviation is greatest, are denoted respectively by 8, , 62 , and 63 . In the case where the flat side walls are slightly diverging, the flat side walls have a vn roughly 0.05 times the .. T _ I
a~ acting in the direction ofthe curved converging walls. Equation ( 1 ) can be approximated by rrw O~m,~ (~342 Tan 9 +,425~c) + 0.1 ~cL Q" m.~c = Y(n W /4 + WL) combining with Equation (2) Tan 8 = (Y(rnvl4 + L) (u2 + 1 )/(rrf~ - .1 ~cL(rtw) - .425~c)1.342 (6) This equation can be used, as Equation (4) was used, to define subsequent slope angles. Assuming f~ and w are constant and f~ is determined by the lowest hopper angle 6,, then the following relation exists between L/'W and 6 for each segment of the hopper:
Llw = .342 rr (Tan9, - Tan 9)/(1.368 Tan ~, + 1.8~c) (~) This equation can be used along with the relation Oh=~L~(2Tan9) which is evident from Fig. 6, to determine a continuous curve that optimizes the hopper shape and minimizes the hopper height while preventing arching.
For the chisel-shaped hopper of Figure 7, the equivalent of Equation (6) is B=2 (f~Y)((~683 + UB) Tan 9 + (.711 + Lfg)I~)l(~Z +1)(n/4 + Llg)) for each segment of the hopper, where B is the width of the opening at the bottom'of a section, L is the length of the opening at the bottom of that section, 8 is the inclination of the flat portion of the section from the vertical, p is the coefficient of friction between the wall and the bulk solid, f~ is the unconfined yield stress of the material, y is the bulk specific weight of the material.
Just as Equation (7) was used to optimize the shape of the one-dimensional convergence hopper of Figure 6, so also Equation (8) can be used to optimize the shape of the chisel-shaped hopper of Figure 7. In Figure 7 the successively higher segments 30, 32, 34 have a race-track shape, but unlike the hopper of Fig. 6, the diameters Bl, B2, B3 of the segments 30, 32 and 34 increase from the bottom to the top of the hopper.
Therefore, the flat portions 36, 38, 40 are inclined from the vertical by the angles 6,, 62, 63 . The longest dimension of each of the segments 30, 32 and 34, measured at the bottom of each segment, are denoted by Ll, LZ, and L3, respectively.
The inventor has found that the slopes used in constructed hoppers can differ from the angles calculated by the above equations by as much as plus or minus 5 degrees without adversely affecting the performance of the hopper.
Typical applications of the invention include:
a) The conical hopper (Figure 4) where the similar cross sections are circular and arranged symmetrically around a common vertical centerline.
b) The wedge-shaped hopper (Figure 5) where the similar cross sections are rectangular and arranged symmetrically about a vertical centerline.
l0 c) The one-dimensional convergence hopper, reference U.S. Patent No.
4,958,741 (Figure 6) with similar cross sections composed of a rectangle with semi-circular ends, with the diameter of the semi-circular ends equal or decreasing slightly in the upward direction and the entire cross section arranged symmetrically about a vertical centerline.
d) The chisel-shaped hopper, reference U.S. Patent No. 4,958,741 (Figure 7) composed of similar cross sections composed of a rectangular central portion and semi-circular ends, with the semi-circular ends arranged so that their outer extremities lie in a vertical line or a line slightly diverging downward.
e) The combination of c) and d), reference U.S. Patent No. 4,958,741.
f) The conical chisel and one-dimensional convergence hopper shown in Figure 8.
g) The offset conical hopper (Figure 9) in which the similar circular cross sections are not symmetric about a vertical axis. In Fig. 9, the walls of the hopper segments 42, 44 and 46 are inclined from the vertical by angles that range from 81,,,ma to 6",,~"~ for the lowest segment 42, from 62~,,m,, to 62,,,~ for the next highest segment 44, and from 63,,,m,, to 63 ~ for the upper segment 46.
h) The offset one-dimensional convergence hopper (Figure 10) in which the essentially vertical parallel side walls 48 and 50 are arranged above each other but the semi-circular end walls are not symmetrically arranged about a vertical axis.
i) The offset wedge-shaped hopper (Figure 11 ) in which the end walls 52 and 54 are still vertical but the sides 56 and 58 are not symmetric about a vertical axis.
Claims (6)
1. A hopper that eliminates bridging of a particulate material it contains, comprising:
an outlet;
a wall extending upward from said outlet and including a plurality of sections, each section being joined to the next-lower section and being inclined at a less steep angle of inclination with respect to horizontal than the adjoining next-lower section, wherein the angles of inclination of said plurality of sections are such as to satisfy the equations ~.sigma.n(Tan.theta.+µ)dp=~A
where .sigma.n is stress perpendicular to the wall of the hopper, .theta. is the inclination of the hopper wall with respect to vertical, µ is coefficient of friction between the wall and the particulate material, and .gamma. is the bulk specific weight of the particulate material, and .sigma.n=f c/(µ2+1) where f c is the unconfined yield stress of the particulate material, and µ is the coefficient of friction between the wall and the particulate material.
an outlet;
a wall extending upward from said outlet and including a plurality of sections, each section being joined to the next-lower section and being inclined at a less steep angle of inclination with respect to horizontal than the adjoining next-lower section, wherein the angles of inclination of said plurality of sections are such as to satisfy the equations ~.sigma.n(Tan.theta.+µ)dp=~A
where .sigma.n is stress perpendicular to the wall of the hopper, .theta. is the inclination of the hopper wall with respect to vertical, µ is coefficient of friction between the wall and the particulate material, and .gamma. is the bulk specific weight of the particulate material, and .sigma.n=f c/(µ2+1) where f c is the unconfined yield stress of the particulate material, and µ is the coefficient of friction between the wall and the particulate material.
2. The hopper of claim 1, wherein said hopper is a one-dimensional convergence hopper, and wherein the angles of inclination of said plurality of sections satisfy the following equation L/w=0.342.pi.(Tan .theta.1 -Tan .theta.)/(1.368 Tan .theta.1 +1.6µ) where, for each section, L is the length of the straight portion at the top of the section, W is the width of the outlet of the section, .theta.1 is the inclination of the hopper wall with respect to vertical for the section, .theta. is the inclination of the hopper wall with respect to vertical for the next-higher section, and µ is the coefficient of friction between the wall and the particulate material.
3. The hopper of claim 1 wherein the hopper is a one-dimensional convergence hopper and wherein, for each section, the angle of inclination .theta. of the hopper wall with respect to the vertical is given by the following equation Tan .theta.=(.gamma.(.pi.w/4+L)(µ2+1)/(.pi.f c)-0.1 µL(.pi.w) -0.425µ)/0.342 where, for each section, .gamma. is the bulk specific weight of the particulate material, W is the width of the outlet of the section, L is the length of the straight portion at the top of the section, µ is the coefficient of friction between the wall and the particulate material, and f c is the unconfined yield stress of the particulate material.
4. The hopper of claim 1, wherein said hopper includes an upper chisel portion and a lower one-dimensional convergence portion, and wherein the angles of inclination of said plurality of sections in said upper chisel portion satisfy the following equation Tan .theta.2=(B2/B1)(Tan .theta.1+µ)-µ
where, for each section, .theta. is the inclination of the hopper wall with respect to vertical for the section, B1 is the outlet size for the section, .theta.2 is the inclination of the hopper wall with respect to vertical for the next-higher section, B2 is the outlet size for the bottom of the next-higher section, and µ is the coefficient of friction between the wall and the particulate material, and wherein the angles of inclination of said plurality of sections in the lower one-dimensional convergence portion satisfy the following equation L/w=0.342.pi.(Tan .theta.1 -Tan .theta.)/(1.368 Tan .theta.1+1.6µ) where, for each section, L is the length of the outlet of the straight portion at the top of the section, W is the width of the outlet of the section, .theta.1 is the inclination of the hopper wall with respect to vertical for the section, .theta.2 is the inclination of the hopper wall with respect to vertical for the next-higher section, and µ is the coefficient of friction between the wall and the particulate material.
where, for each section, .theta. is the inclination of the hopper wall with respect to vertical for the section, B1 is the outlet size for the section, .theta.2 is the inclination of the hopper wall with respect to vertical for the next-higher section, B2 is the outlet size for the bottom of the next-higher section, and µ is the coefficient of friction between the wall and the particulate material, and wherein the angles of inclination of said plurality of sections in the lower one-dimensional convergence portion satisfy the following equation L/w=0.342.pi.(Tan .theta.1 -Tan .theta.)/(1.368 Tan .theta.1+1.6µ) where, for each section, L is the length of the outlet of the straight portion at the top of the section, W is the width of the outlet of the section, .theta.1 is the inclination of the hopper wall with respect to vertical for the section, .theta.2 is the inclination of the hopper wall with respect to vertical for the next-higher section, and µ is the coefficient of friction between the wall and the particulate material.
5. The hopper of claim 1, wherein said hopper includes an upper chisel portion, and a lower one-dimensional convergence portion, and wherein, for each section of said upper chisel portion, the angle of inclination .theta. of the hopper wall with respect to the vertical is given by the following equation Tan .theta.=.gamma.(A/P)(µ2+1)/f c-µ
where, for each section, .gamma. is the bulk specific weight of the particulate material, A is the area of the outlet of the section, P is the periphery of the outlet of the section, µ is the coefficient of friction between the wall and the particulate material, and f c is the unconfined yield stress of the particulate material, and wherein, for each section of said lower one-dimensional convergence portion, the angle of inclination .theta. of the hopper wall with respect to the vertical is given by the following equation Tan .theta.=(.gamma.(.pi.w/4+L)(µ2+1)/(.pi.f c)-0.1 µL(.pi.w) -0.425µ)/0.342 where, for each section, .gamma. is the bulk specific weight of the particulate material, W is the width of the outlet of the section, L is the length of the straight portion at the top of the section, µ is the coefficient of friction between the wall and the particulate material, and f c is the unconfined yield stress of the particulate material.
where, for each section, .gamma. is the bulk specific weight of the particulate material, A is the area of the outlet of the section, P is the periphery of the outlet of the section, µ is the coefficient of friction between the wall and the particulate material, and f c is the unconfined yield stress of the particulate material, and wherein, for each section of said lower one-dimensional convergence portion, the angle of inclination .theta. of the hopper wall with respect to the vertical is given by the following equation Tan .theta.=(.gamma.(.pi.w/4+L)(µ2+1)/(.pi.f c)-0.1 µL(.pi.w) -0.425µ)/0.342 where, for each section, .gamma. is the bulk specific weight of the particulate material, W is the width of the outlet of the section, L is the length of the straight portion at the top of the section, µ is the coefficient of friction between the wall and the particulate material, and f c is the unconfined yield stress of the particulate material.
6. The hopper of claim 1, wherein said hopper is an offset one-dimensional hopper, and wherein each of said plurality of sections includes a maximum angle of inclination and a minimum angle of inclination, which, when averaged, define an average angle of inclination for each section, and wherein the average angles of inclination of said plurality of sections satisfy the following equation L/w=0.342.pi.(Tan .theta.1 -Tan .theta.)/(1.368 Tan .theta.1 +1.6µ) where, for each section, L is the length of the straight portion at the top of the section, W is the width of the outlet of the section, .theta.1 is the average inclination of the hopper wall with respect to vertical for the section, .theta. is the average inclination of the hopper wall with respect to vertical for the next-higher section, and µ is the coefficient of friction between the wall and the particulate material.
Applications Claiming Priority (5)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US3032196P | 1996-11-04 | 1996-11-04 | |
| US60/030,321 | 1996-11-04 | ||
| US08/963,528 | 1997-11-03 | ||
| US08/963,528 US6055781A (en) | 1996-11-04 | 1997-11-03 | Archbreaking hopper for bulk solids |
| PCT/US1997/020042 WO1998019957A1 (en) | 1996-11-04 | 1997-11-03 | Archbreaking hopper for bulk solids |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CA2274699A1 CA2274699A1 (en) | 1998-05-14 |
| CA2274699C true CA2274699C (en) | 2002-09-03 |
Family
ID=21853673
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA002274699A Expired - Fee Related CA2274699C (en) | 1996-11-04 | 1997-11-03 | Archbreaking hopper for bulk solids |
Country Status (5)
| Country | Link |
|---|---|
| US (1) | US6055781A (en) |
| EP (1) | EP0937010A4 (en) |
| AU (1) | AU727887C (en) |
| CA (1) | CA2274699C (en) |
| WO (1) | WO1998019957A1 (en) |
Families Citing this family (37)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| SE9803443D0 (en) * | 1998-10-09 | 1998-10-09 | Kvaerner Pulping Tech | Chip bin |
| SE511519C2 (en) * | 1998-12-15 | 1999-10-11 | Kvaerner Pulping Tech | Containers for storage and dispensing of particulate material, preferably pulp chips |
| US6450754B1 (en) * | 2000-06-21 | 2002-09-17 | Cp Motion Products, Inc. | Bulk bag discharger for dry flowable materials |
| EP1264784B1 (en) | 2001-05-31 | 2004-04-07 | HYLSA S.A. de C.V. | Vessel for enabling a uniform gravity driven flow of particulate bulk material therethrough, and direct reduction reactor incorporating same |
| US6871457B2 (en) * | 2001-05-31 | 2005-03-29 | Hylsa, S.A. De C.V. | Vessel for enabling a uniform gravity driven flow of particulate bulk material therethrough, and direct reduction reactor incorporating same |
| GB0121353D0 (en) * | 2001-09-04 | 2001-10-24 | Rig Technology Ltd | Improvements in or relating to transport of waste materials |
| GB0121469D0 (en) * | 2001-09-05 | 2001-10-24 | Ishida Europ Mfg Ltd | Material handling system |
| US6845890B2 (en) * | 2001-10-16 | 2005-01-25 | Universal Aggregates, Llc | Bulk granular solids gravity flow curing vessel |
| WO2004024571A2 (en) * | 2002-09-13 | 2004-03-25 | South, Phillip, Barry | Mass flow hopper and method of manufacture |
| US7493969B2 (en) * | 2003-03-19 | 2009-02-24 | Varco I/P, Inc. | Drill cuttings conveyance systems and methods |
| CA2505628C (en) * | 2003-03-19 | 2007-12-18 | Varco I/P, Inc. | Apparatus and method for moving drilled cuttings |
| US6936092B2 (en) * | 2003-03-19 | 2005-08-30 | Varco I/P, Inc. | Positive pressure drilled cuttings movement systems and methods |
| US6997600B2 (en) * | 2003-10-10 | 2006-02-14 | Process Control Corporation | Intermittent agitation of particular matter |
| DE10351335A1 (en) * | 2003-10-31 | 2005-06-02 | Putzmeister Mörtelmaschinen GmbH | Material feed container for flowable and / or pumpable material |
| US6997346B2 (en) * | 2003-12-08 | 2006-02-14 | Process Control Corporation | Apparatus and method for reducing buildup of particulate matter in particulate-matter-delivery systems |
| US7763341B2 (en) | 2004-01-23 | 2010-07-27 | Century-Board Usa, Llc | Filled polymer composite and synthetic building material compositions |
| AU2005267399A1 (en) | 2004-06-24 | 2006-02-02 | Century-Board Usa, Llc | Continuous forming apparatus for three-dimensional foamed products |
| US7794224B2 (en) | 2004-09-28 | 2010-09-14 | Woodbridge Corporation | Apparatus for the continuous production of plastic composites |
| US7316333B2 (en) * | 2004-11-17 | 2008-01-08 | Mixer Systems, Inc. | Modular volume storage bin |
| US20070222105A1 (en) | 2006-03-24 | 2007-09-27 | Century-Board Usa, Llc | Extrusion of polyurethane composite materials |
| GB2450047A (en) * | 2006-04-05 | 2008-12-10 | Baker Hughes Inc | Drill cuttings transfer system and related methods |
| US20080307603A1 (en) * | 2007-06-14 | 2008-12-18 | Heinz Schneider | Infeed Device for Dedusting Apparatus |
| DE102007039949B3 (en) * | 2007-08-23 | 2008-12-04 | Flooring Technologies Ltd. | Device for applying a suspension to a carrier plate |
| US8846776B2 (en) | 2009-08-14 | 2014-09-30 | Boral Ip Holdings Llc | Filled polyurethane composites and methods of making same |
| US9481759B2 (en) | 2009-08-14 | 2016-11-01 | Boral Ip Holdings Llc | Polyurethanes derived from highly reactive reactants and coal ash |
| CN102390631A (en) * | 2011-07-26 | 2012-03-28 | 中国神华能源股份有限公司 | Discharging hopper of silo and silo |
| AU2012318528A1 (en) | 2011-10-07 | 2014-05-22 | Boral Ip Holdings (Australia) Pty Limited | Inorganic polymer/organic polymer composites and methods of making same |
| WO2014142724A1 (en) * | 2013-03-15 | 2014-09-18 | Valmet Ab | Bin for collecting and discharging smaller ligno-cellulosic material |
| CN103274132B (en) * | 2013-03-22 | 2015-11-18 | 江苏鼎盛重工有限公司 | Transfer flat-bottomed boat hopper in a kind of sea |
| WO2014168633A1 (en) | 2013-04-12 | 2014-10-16 | Boral Ip Holdings (Australia) Pty Limited | Composites formed from an absorptive filler and a polyurethane |
| FR3020800B1 (en) * | 2014-05-09 | 2017-08-25 | Pierre Fabre Dermo-Cosmetique | DEVICE AND METHOD FOR ASEPTIC FILLING |
| US10138341B2 (en) | 2014-07-28 | 2018-11-27 | Boral Ip Holdings (Australia) Pty Limited | Use of evaporative coolants to manufacture filled polyurethane composites |
| US9752015B2 (en) | 2014-08-05 | 2017-09-05 | Boral Ip Holdings (Australia) Pty Limited | Filled polymeric composites including short length fibers |
| WO2016118141A1 (en) | 2015-01-22 | 2016-07-28 | Boral Ip Holdings (Australia) Pty Limited | Highly filled polyurethane composites |
| WO2016195717A1 (en) | 2015-06-05 | 2016-12-08 | Boral Ip Holdings (Australia) Pty Limited | Filled polyurethane composites with lightweight fillers |
| US20170267585A1 (en) | 2015-11-12 | 2017-09-21 | Amitabha Kumar | Filled polyurethane composites with size-graded fillers |
| US11325776B1 (en) * | 2021-05-26 | 2022-05-10 | The Young Industries, Inc. | Mass-flow hopper |
Family Cites Families (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US2943752A (en) * | 1959-06-30 | 1960-07-05 | Farmers Cooperative Exchange | Bulk feed bin |
| US3071297A (en) * | 1961-09-14 | 1963-01-01 | Lee Yee | Hyperbolic hopper outlet means |
| FR1582818A (en) * | 1968-02-26 | 1969-10-10 | ||
| AT304361B (en) * | 1970-03-12 | 1973-01-10 | Waagner Biro Ag | Silo container held by a supporting structure |
| US3797707A (en) * | 1971-04-20 | 1974-03-19 | Jenike And Johanson Inc | Bins for storage and flow of bulk solids |
| US4286883A (en) * | 1979-08-20 | 1981-09-01 | Jenike & Johanson, Inc. | Blending apparatus for bulk solids |
| US4702364A (en) * | 1986-05-09 | 1987-10-27 | Johanneck Richard G | Silo chute hopper attachment |
| US4886097A (en) * | 1987-09-14 | 1989-12-12 | Hylsu S.A. de C.V. | Apparatus for handling and storage of particulate solids |
| US4958741A (en) * | 1989-06-14 | 1990-09-25 | Jr Johanson, Inc. | Modular mass-flow bin |
| US5114040A (en) * | 1991-01-07 | 1992-05-19 | Michael Brenish | Hopper for dispensing cement or mortar |
| US5361945A (en) * | 1993-04-29 | 1994-11-08 | J R Johanson, Inc. | Combination hopper |
-
1997
- 1997-11-03 CA CA002274699A patent/CA2274699C/en not_active Expired - Fee Related
- 1997-11-03 US US08/963,528 patent/US6055781A/en not_active Expired - Fee Related
- 1997-11-03 WO PCT/US1997/020042 patent/WO1998019957A1/en not_active Application Discontinuation
- 1997-11-03 AU AU51655/98A patent/AU727887C/en not_active Ceased
- 1997-11-03 EP EP97946499A patent/EP0937010A4/en not_active Withdrawn
Also Published As
| Publication number | Publication date |
|---|---|
| WO1998019957A1 (en) | 1998-05-14 |
| AU727887C (en) | 2001-08-23 |
| AU727887B2 (en) | 2001-01-04 |
| EP0937010A4 (en) | 2006-10-25 |
| US6055781A (en) | 2000-05-02 |
| EP0937010A1 (en) | 1999-08-25 |
| CA2274699A1 (en) | 1998-05-14 |
| AU5165598A (en) | 1998-05-29 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CA2274699C (en) | Archbreaking hopper for bulk solids | |
| US4958741A (en) | Modular mass-flow bin | |
| EP0695273B1 (en) | Combination hopper | |
| US5769281A (en) | Bulk storage hoppers | |
| US5910243A (en) | Displacement device | |
| US6609638B1 (en) | Flow promoter for hoppers | |
| US6139241A (en) | Multi-faceted modular silo for bulk solids | |
| US5651479A (en) | Mass flow generator | |
| KR860004297A (en) | Heat exchanger between gas and fine particulate matter | |
| EP1127019B1 (en) | Chip bin | |
| US6098851A (en) | Handling system for agglomerable materials | |
| CN208603353U (en) | A kind of Pneumatic conveyer and transportation system of material | |
| CN207346429U (en) | A kind of hyperbolic configuration unloads hod device | |
| RU2213038C2 (en) | Loose material feeder | |
| CN212607079U (en) | Anti-blocking raw coal bunker | |
| JPS6152069B2 (en) | ||
| JPH01117107A (en) | Silo | |
| WO1983001937A1 (en) | Conveyor belt with angled entraining bars | |
| CA1167424A (en) | Multiple discharge chute | |
| GB2070576A (en) | Construction of chutes and bunkers for material handling | |
| WO2020214032A1 (en) | Hopper for a silo, silo and silo assembly | |
| UA151157U (en) | Method of loading grain into sile | |
| CN111746951A (en) | Anti-blocking raw coal bunker | |
| JPS643771B2 (en) | ||
| EP1167237A1 (en) | Handling system for agglomerable materials |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| EEER | Examination request | ||
| MKLA | Lapsed |