In all ore dressing and milling Operations, including flotation, cyanidation, gravity concentration, and amalgamation, the Working Principle is to crush and grind, often with rob mill & ball mills, the ore in order to liberate the minerals. In the chemical and process industries, grinding is an important step in preparing raw materials for subsequent treatment.In present day practice, ore is reduced to a size many times finer than can be obtained with crushers. Over a period of many years various fine grinding machines have been developed and used, but the ball mill has become standard due to its simplicity and low operating cost.
A ball millefficiently operated performs a wide variety of services. In small milling plants, where simplicity is most essential, it is not economical to use more than single stage crushing, because the Steel-Head Ball or Rod Mill will take up to 2 feed and grind it to the desired fineness. In larger plants where several stages of coarse and fine crushing are used, it is customary to crush from 1/2 to as fine as 8 mesh.
Many grinding circuits necessitate regrinding of concentrates or middling products to extremely fine sizes to liberate the closely associated minerals from each other. In these cases, the feed to the ball mill may be from 10 to 100 mesh or even finer.
Where the finished product does not have to be uniform, a ball mill may be operated in open circuit, but where the finished product must be uniform it is essential that the grinding mill be used in closed circuit with a screen, if a coarse product is desired, and with a classifier if a fine product is required. In most cases it is desirable to operate the grinding mill in closed circuit with a screen or classifier as higher efficiency and capacity are obtained. Often a mill using steel rods as the grinding medium is recommended, where the product must have the minimum amount of fines (rods give a more nearly uniform product).
Often a problem requires some study to determine the economic fineness to which a product can or should be ground. In this case the 911Equipment Company offers its complete testing service so that accurate grinding mill size may be determined.
Until recently many operators have believed that one particular type of grinding mill had greater efficiency and resulting capacity than some other type. However, it is now commonly agreed and accepted that the work done by any ballmill depends directly upon the power input; the maximum power input into any ball or rod mill depends upon weight of grinding charge, mill speed, and liner design.
The apparent difference in capacities between grinding mills (listed as being the same size) is due to the fact that there is no uniform method of designating the size of a mill, for example: a 5 x 5 Ball Mill has a working diameter of 5 inside the liners and has 20 per cent more capacity than all other ball mills designated as 5 x 5 where the shell is 5 inside diameter and the working diameter is only 48 with the liners in place.
Ball-Rod Mills, based on 4 liners and capacity varying as 2.6 power of mill diameter, on the 5 size give 20 per cent increased capacity; on the 4 size, 25 per cent; and on the 3 size, 28 per cent. This fact should be carefully kept in mind when determining the capacity of a Steel- Head Ball-Rod Mill, as this unit can carry a greater ball or rod charge and has potentially higher capacity in a given size when the full ball or rod charge is carried.
A mill shorter in length may be used if the grinding problem indicates a definite power input. This allows the alternative of greater capacity at a later date or a considerable saving in first cost with a shorter mill, if reserve capacity is not desired. The capacities of Ball-Rod Mills are considerably higher than many other types because the diameters are measured inside the liners.
The correct grinding mill depends so much upon the particular ore being treated and the product desired, that a mill must have maximum flexibility in length, type of grinding medium, type of discharge, and speed.With the Ball-Rod Mill it is possible to build this unit in exact accordance with your requirements, as illustrated.
To best serve your needs, the Trunnion can be furnished with small (standard), medium, or large diameter opening for each type of discharge. The sketch shows diagrammatic arrangements of the four different types of discharge for each size of trunnion opening, and peripheral discharge is described later.
Ball-Rod Mills of the grate discharge type are made by adding the improved type of grates to a standard Ball-Rod Mill. These grates are bolted to the discharge head in much the same manner as the standard headliners.
The grates are of alloy steel and are cast integral with the lifter bars which are essential to the efficient operation of this type of ball or rod mill. These lifter bars have a similar action to a pump:i. e., in lifting the product so as to discharge quickly through the mill trunnion.
These Discharge Grates also incorporate as an integral part, a liner between the lifters and steel head of the ball mill to prevent wear of the mill head. By combining these parts into a single casting, repairs and maintenance are greatly simplified. The center of the grate discharge end of this mill is open to permit adding of balls or for adding water to the mill through the discharge end.
Instead of being constructed of bars cast into a frame, Grates are cast entire and have cored holes which widen toward the outside of the mill similar to the taper in grizzly bars. The grate type discharge is illustrated.
The peripheral discharge type of Ball-Rod Mill is a modification of the grate type, and is recommended where a free gravity discharge is desired. It is particularly applicable when production of too many fine particles is detrimental and a quick pass through the mill is desired, and for dry grinding.
The drawings show the arrangement of the peripheral discharge. The discharge consists of openings in the shell into which bushings with holes of the desired size are inserted. On the outside of the mill, flanges are used to attach a stationary discharge hopper to prevent pulp splash or too much dust.
The mill may be operated either as a peripheral discharge or a combination or peripheral and trunnion discharge unit, depending on the desired operating conditions. If at any time the peripheral discharge is undesirable, plugs inserted into the bushings will convert the mill to a trunnion discharge type mill.
Unless otherwise specified, a hard iron liner is furnished. This liner is made of the best grade white iron and is most serviceable for the smaller size mills where large balls are not used. Hard iron liners have a much lower first cost.
Electric steel, although more expensive than hard iron, has advantage of minimum breakage and allows final wear to thinner section. Steel liners are recommended when the mills are for export or where the source of liner replacement is at a considerable distance.
Molychrome steel has longer wearing qualities and greater strength than hard iron. Breakage is not so apt to occur during shipment, and any size ball can be charged into a mill equipped with molychrome liners.
Manganese liners for Ball-Rod Mills are the world famous AMSCO Brand, and are the best obtainable. The first cost is the highest, but in most cases the cost per ton of ore ground is the lowest. These liners contain 12 to 14% manganese.
The feed and discharge trunnions are provided with cast iron or white iron throat liners. As these parts are not subjected to impact and must only withstand abrasion, alloys are not commonly used but can be supplied.
Gears for Ball-Rod Mills drives are furnished as standard on the discharge end of the mill where they are out of the way of the classifier return, scoop feeder, or original feed. Due to convertible type construction the mills can be furnished with gears on the feed end. Gear drives are available in two alternative combinations, which are:
All pinions are properly bored, key-seated, and pressed onto the steel countershaft, which is oversize and properly keyseated for the pinion and drive pulleys or sheaves. The countershaft operates on high grade, heavy duty, nickel babbitt bearings.
Any type of drive can be furnished for Ball-Rod Mills in accordance with your requirements. Belt drives are available with pulleys either plain or equipped with friction clutch. Various V- Rope combinations can also be supplied.
The most economical drive to use up to 50 H. P., is a high starting torque motor connected to the pinion shaft by means of a flat or V-Rope drive. For larger size motors the wound rotor (slip ring) is recommended due to its low current requirement in starting up the ball mill.
Should you be operating your own power plant or have D. C. current, please specify so that there will be no confusion as to motor characteristics. If switches are to be supplied, exact voltage to be used should be given.
Even though many ores require fine grinding for maximum recovery, most ores liberate a large percentage of the minerals during the first pass through the grinding unit. Thus, if the free minerals can be immediately removed from the ball mill classifier circuit, there is little chance for overgrinding.
This is actually what has happened wherever Mineral Jigs or Unit Flotation Cells have been installed in the ball mill classifier circuit. With the installation of one or both of these machines between the ball mill and classifier, as high as 70 per cent of the free gold and sulphide minerals can be immediately removed, thus reducing grinding costs and improving over-all recovery. The advantage of this method lies in the fact that heavy and usually valuable minerals, which otherwise would be ground finer because of their faster settling in the classifier and consequent return to the grinding mill, are removed from the circuit as soon as freed. This applies particularly to gold and lead ores.
Ball-Rod Mills have heavy rolled steel plate shells which are arc welded inside and outside to the steel heads or to rolled steel flanges, depending upon the type of mill. The double welding not only gives increased structural strength, but eliminates any possibility of leakage.
Where a single or double flanged shell is used, the faces are accurately machined and drilled to template to insure perfect fit and alignment with the holes in the head. These flanges are machined with male and female joints which take the shearing stresses off the bolts.
The Ball-Rod Mill Heads are oversize in section, heavily ribbed and are cast from electric furnace steel which has a strength of approximately four times that of cast iron. The head and trunnion bearings are designed to support a mill with length double its diameter. This extra strength, besides eliminating the possibility of head breakage or other structural failure (either while in transit or while in service), imparts to Ball-Rod Mills a flexibility heretofore lacking in grinding mills. Also, for instance, if you have a 5 x 5 mill, you can add another 5 shell length and thus get double the original capacity; or any length required up to a maximum of 12 total length.
On Type A mills the steel heads are double welded to the rolled steel shell. On type B and other flanged type mills the heads are machined with male and female joints to match the shell flanges, thus taking the shearing stresses from the heavy machine bolts which connect the shell flanges to the heads.
The manhole cover is protected from wear by heavy liners. An extended lip is provided for loosening the door with a crow-bar, and lifting handles are also provided. The manhole door is furnished with suitable gaskets to prevent leakage.
The mill trunnions are carried on heavy babbitt bearings which provide ample surface to insure low bearing pressure. If at any time the normal length is doubled to obtain increased capacity, these large trunnion bearings will easily support the additional load. Trunnion bearings are of the rigid type, as the perfect alignment of the trunnion surface on Ball-Rod Mills eliminates any need for the more expensive self-aligning type of bearing.
The cap on the upper half of the trunnion bearing is provided with a shroud which extends over the drip flange of the trunnion and effectively prevents the entrance of dirt or grit. The bearing has a large space for wool waste and lubricant and this is easily accessible through a large opening which is covered to prevent dirt from getting into the bearing.Ball and socket bearings can be furnished.
Scoop Feeders for Ball-Rod Mills are made in various radius sizes. Standard scoops are made of cast iron and for the 3 size a 13 or 19 feeder is supplied, for the 4 size a 30 or 36, for the 5 a 36 or 42, and for the 6 a 42 or 48 feeder. Welded steel scoop feeders can, however, be supplied in any radius.
The correct size of feeder depends upon the size of the classifier, and the smallest feeder should be used which will permit gravity flow for closed circuit grinding between classifier and the ball or rod mill. All feeders are built with a removable wearing lip which can be easily replaced and are designed to give minimum scoop wear.
A combination drum and scoop feeder can be supplied if necessary. This feeder is made of heavy steel plate and strongly welded. These drum-scoop feeders are available in the same sizes as the cast iron feeders but can be built in any radius. Scoop liners can be furnished.
The trunnions on Ball-Rod Mills are flanged and carefully machined so that scoops are held in place by large machine bolts and not cap screws or stud bolts. The feed trunnion flange is machined with a shoulder for insuring a proper fit for the feed scoop, and the weight of the scoop is carried on this shoulder so that all strain is removed from the bolts which hold the scoop.
High carbon steel rods are recommended, hot rolled, hot sawed or sheared, to a length of 2 less than actual length of mill taken inside the liners. The initial rod charge is generally a mixture ranging from 1.5 to 3 in diameter. During operation, rod make-up is generally the maximum size. The weights per lineal foot of rods of various diameters are approximately: 1.5 to 6 lbs.; 2-10.7 lbs.; 2.5-16.7 lbs.; and 3-24 lbs.
Forged from the best high carbon manganese steel, they are of the finest quality which can be produced and give long, satisfactory service. Data on ball charges for Ball-Rod Mills are listed in Table 5. Further information regarding grinding balls is included in Table 6.
Rod Mills has a very define and narrow discharge product size range. Feeding a Rod Mill finer rocks will greatly impact its tonnage while not significantly affect its discharge product sizes. The 3.5 diameter rod of a mill, can only grind so fine.
Crushers are well understood by most. Rod and Ball Mills not so much however as their size reduction actions are hidden in the tube (mill). As for Rod Mills, the image above best expresses what is going on inside. As rocks is feed into the mill, they are crushed (pinched) by the weight of its 3.5 x 16 rods at one end while the smaller particles migrate towards the discharge end and get slightly abraded (as in a Ball Mill) on the way there.
We haveSmall Ball Mills for sale coming in at very good prices. These ball mills are relatively small, bearing mounted on a steel frame. All ball mills are sold with motor, gears, steel liners and optional grinding media charge/load.
Ball Mills or Rod Mills in a complete range of sizes up to 10 diameter x20 long, offer features of operation and convertibility to meet your exactneeds. They may be used for pulverizing and either wet or dry grindingsystems. Mills are available in both light-duty and heavy-duty constructionto meet your specific requirements.
All Mills feature electric cast steel heads and heavy rolled steelplate shells. Self-aligning main trunnion bearings on large mills are sealedand internally flood-lubricated. Replaceable mill trunnions. Pinion shaftbearings are self-aligning, roller bearing type, enclosed in dust-tightcarrier. Adjustable, single-unit soleplate under trunnion and drive pinionsfor perfect, permanent gear alignment.
Ball Mills can be supplied with either ceramic or rubber linings for wet or dry grinding, for continuous or batch type operation, in sizes from 15 x 21 to 8 x 12. High density ceramic linings of uniform hardness male possible thinner linings and greater and more effective grinding volume. Mills are shipped with liners installed.
Complete laboratory testing service, mill and air classifier engineering and proven equipment make possible a single source for your complete dry-grinding mill installation. Units available with air swept design and centrifugal classifiers or with elevators and mechanical type air classifiers. All sizes and capacities of units. Laboratory-size air classifier also available.
A special purpose batch mill designed especially for grinding and mixing involving acids and corrosive materials. No corners mean easy cleaning and choice of rubber or ceramic linings make it corrosion resistant. Shape of mill and ball segregation gives preferential grinding action for grinding and mixing of pigments and catalysts. Made in 2, 3 and 4 diameter grinding drums.
Nowadays grinding mills are almost extensively used for comminution of materials ranging from 5 mm to 40 mm (3/161 5/8) down to varying product sizes. They have vast applications within different branches of industry such as for example the ore dressing, cement, lime, porcelain and chemical industries and can be designed for continuous as well as batch grinding.
Ball mills can be used for coarse grinding as described for the rod mill. They will, however, in that application produce more fines and tramp oversize and will in any case necessitate installation of effective classification.If finer grinding is wanted two or three stage grinding is advisable as for instant primary rod mill with 75100 mm (34) rods, secondary ball mill with 2540 mm(11) balls and possibly tertiary ball mill with 20 mm () balls or cylpebs.To obtain a close size distribution in the fine range the specific surface of the grinding media should be as high as possible. Thus as small balls as possible should be used in each stage.
The principal field of rod mill usage is the preparation of products in the 5 mm0.4 mm (4 mesh to 35 mesh) range. It may sometimes be recommended also for finer grinding. Within these limits a rod mill is usually superior to and more efficient than a ball mill. The basic principle for rod grinding is reduction by line contact between rods extending the full length of the mill, resulting in selective grinding carried out on the largest particle sizes. This results in a minimum production of extreme fines or slimes and more effective grinding work as compared with a ball mill. One stage rod mill grinding is therefore suitable for preparation of feed to gravimetric ore dressing methods, certain flotation processes with slime problems and magnetic cobbing. Rod mills are frequently used as primary mills to produce suitable feed to the second grinding stage. Rod mills have usually a length/diameter ratio of at least 1.4.
Tube mills are in principle to be considered as ball mills, the basic difference being that the length/diameter ratio is greater (35). They are commonly used for surface cleaning or scrubbing action and fine grinding in open circuit.
In some cases it is suitable to use screened fractions of the material as grinding media. Such mills are usually called pebble mills, but the working principle is the same as for ball mills. As the power input is approximately directly proportional to the volume weight of the grinding media, the power input for pebble mills is correspondingly smaller than for a ball mill.
A dry process requires usually dry grinding. If the feed is wet and sticky, it is often necessary to lower the moisture content below 1 %. Grinding in front of wet processes can be done wet or dry. In dry grinding the energy consumption is higher, but the wear of linings and charge is less than for wet grinding, especially when treating highly abrasive and corrosive material. When comparing the economy of wet and dry grinding, the different costs for the entire process must be considered.
An increase in the mill speed will give a directly proportional increase in mill power but there seems to be a square proportional increase in the wear. Rod mills generally operate within the range of 6075 % of critical speed in order to avoid excessive wear and tangled rods. Ball and pebble mills are usually operated at 7085 % of critical speed. For dry grinding the speed is usually somewhat lower.
The mill lining can be made of rubber or different types of steel (manganese or Ni-hard) with liner types according to the customers requirements. For special applications we can also supply porcelain, basalt and other linings.
The mill power is approximately directly proportional to the charge volume within the normal range. When calculating a mill 40 % charge volume is generally used. In pebble and ball mills quite often charge volumes close to 50 % are used. In a pebble mill the pebble consumption ranges from 315 % and the charge has to be controlled automatically to maintain uniform power consumption.
In all cases the net energy consumption per ton (kWh/ton) must be known either from previous experience or laboratory tests before mill size can be determined. The required mill net power P kW ( = ton/hX kWh/ton) is obtained from
Trunnions of S.G. iron or steel castings with machined flange and bearing seat incl. device for dismantling the bearings. For smaller mills the heads and trunnions are sometimes made in grey cast iron.
The mills can be used either for dry or wet, rod or ball grinding. By using a separate attachment the discharge end can be changed so that the mills can be used for peripheral instead of overflow discharge.
The motion of the charge, that is the grinding media and the material undergoing grinding, within a mill is of considerable theoretical interest and practical importance, and for these reasons, has been the subject of considerable study by a number of workers, but, even so, no rigid and complete theory, covering all the aspects of the dynamics of the mill charge, has yet been produced. The practical importance of this subject clearly resides in the possibility of the prediction of the grinding behaviour, and other such characteristics, of a mill from the knowledge of the trajectories of the elements of the mill charge. The theoretical interest lies in the study of the dynamics of the system and in the derivation of equations to define the million of the elements of the mill charge in terms of fundamental quantities such as the size and the speed of rotation of the mill. A simple example of the practical importance of this information is in the use of the knowledge of the trajectories followed by the balls in a mill to determine the speed at which the mill must run in order that the descending balls shall fall on the toe of the charge, and not upon the mill liner. The impact of the balls upon the liner plates can lead to unduly rapid wear of the latter, and so to high maintenance costs.
In this chapter the motion of the particles constituting the charge of the mill will be considered; it being assumed that there is no slip between the mill shell and the charge. There exists another type of motion, in which the charge as a whole slips relative to the shell, which gives rise to the phenomenon of surging, but consideration of this type of motion will be deferred until a later chapter.
A study, from first principles, of the behaviour of a mill charge is much simplified if the charge is imagined to be composed of rods, instead of balls, since by this means the complication of any axial motion of the balls is eliminated and the problem is reduced to one in two dimensions. Consider first the motion of a single rod, of diameter d, within a smooth shell of internal diameter D; when the
shell rotates about a horizontal axis with an angulai velocity radians per second. In such a case the rod will lie near the lowest point of the mill, as in Fig. 2.1 and will rotate at such speed that the peripheral speed of the rod is the same as that of the shell. Furthermore, the displacement of the radius vector joining the centre of the mill and that of the rod would be such that the work done by reason of the couple formed by this displacement is equal to the energy dissipated in the distortion of the rod and shell at the line of contact.
If now two rods are placed within the mill, as in Fig. 2.2, themotions of the surfaces of the rods at the point of contact are in opposite senses and free motion inside the shell is eliminated. In this case the angle between the vertical and the radius vector joining the centre of the mill and the centre of gravity of the pair of rods is much greater than that for a single rod. But, again, equality exists between the work done to rotate the shell and that dissipated in friction at the contact points and in distortion of the metal surfaces. A further increase in the number of rods would enhance this effect until relative rotation between the rods is largelyprecluded and, in this respect, the charge behaves almost as a solid body.
The correctness of this view is supported by the work of one of the present authors who, with a co-worker, Rose and Evans has shown that, for all other factors remaining equal, the power to drive a mill increases with the value of the ratio (D/d); that is for increasing numbers of small rods(in the experiments balls were used). This relationship, shown in Fig. 2.3 indicates, at once, that the displacement of the centre of gravity of the charge increases with an increasing number of balls, which is in accordance with the reasoning given above. This figure also shows that the variation in the displacement of the centre of gravity is much less when the coefficient of friction between the surfaces is high, which indicates that, for this condition, the locking of the charge is effective when but a few elements are involved.
If the speed of rotation of the mill is so low that the effects of centripetal acceleration may be neglected, then the displacement of the centre of gravity of the charge will increase until either of two possible limiting conditions is reached; these conditions being:
In fact this is a trivial case, since the effects of centripetal acceleration profoundly affect the motion of the elements of the charge, but for slow speeds of rotation the motion of the charge in a practical mill approximates to that given by case (2) above. In this motion the balls (or rods) will travel on circular arcs, concentric with the shell of the mill, until the point of instability is reached, after which they roll down the surface, which is inclined at about 30 to the horizontal, in a series of parallel layers. This motion is shown on a photograph taken through the transparent end of a model mill in Fig. 2.4. It will be noticed that a small vortex exists towards the middle of the charge. At higher speeds of rotation the balls no longer roll down the surface of the charge but, at a certain point, are projected into space and thereafter describe approximately parabolic paths before again meeting the ball mass; these ball paths being as shown in Fig. 2.5. There appear to be no universally adopted names for these two types of motion of the charge, but the evidence appears to be in favour of cascading for the first type and cataracting for the second type. These names will be adopted for the present work.
As the speed of rotation of the mill is increased the particles are projected with progressively greater velocities until the theoretical trajectory for a particle, which is in fact lying against the mill shell, would fall wholly outside the shell. Clearly, since the particle cannot pass through the shell, it would lie against the shell throughout the cycle and so be carried around continuously with the mill shell. This condition is known as centrifuging and the speed of rotation at which it occurs, for the outermost layer of particles, is known as the critical speed of the mill. This speed, the critical speed, is of considerable importance in mill technology since, for example, other factors being equal, the equal performance of two mills of different sizes demands that the ratio of the actual running speed to the critical speed should be the same for the two mills. An expression for the critical speed of a mill will now be derived.
By reference to Fig. 2.6, it is easily seen that if the trajectory is not to fall inside the shell, the radius of curvature of the path, e, must be greater than R, that is than that of the mill shell. Furthermore, this must be true for from wherever the trajectory might start.
In this treatment is the angular velocity of procession of the mill charge and, because of slip between the mill shell and the charge, this is not necessarily equal to , tin- angular velocity of the mill shell. If, as is often the case, this slip is assumed to be negligible, then = and these equations may be cast into the slightly more convenient practical form
The above formula is based on the assumption that there is no slip between the ball charge and mill shell and, to allow a margin of error, it has been common practice to increase the coefficient in the equation by as much as 20%.
That relative slip between the charge and shell is of importance in this connection is supported by the work of Rose and Evans who report that, using ground steel balls in a small-scale model mill made of solid-drawn brass tube, centrifuging did not occur even at running speeds of 120 % of the critical value. However, when the same mill was fitted with effective lifters centrifuging occurred when the actual speed exceeded the theoretical value by a few per cent. This observation is confirmed by Grunder, who showedthat centrifuging in a mill with porcelain balls and body occurred when the actual speed exceeded the calculated critical value by about 5% to 10%. It is questionable, however, whether with modern liners maintained in reasonable condition the increasing of the value of the inefficient of equation (2.6) by 20% is necessary or desirable.
Attention will now be turned to a more detailed analysis of the motion of the ball charge. In the first place, on the grounds of simplicity, the analysis first developed by Davis will be considered, even though, as shown later, it is, in certain respects, an over-simplification.
Consider a point P, Fig. 2.7, at which the projection of the particle occurs and let this point be at a distance r from the centre of the mill. In this connection, the point of projection may be considered to be the point at which the trajectory of the particle is influenced by gravity and is not wholly controlled by the packing of the surrounding charge.
For projection to occur, it is necessary that the radius of curvature of the path under the influence of gravity should be smaller than the radius of curvature of the initial circular path. An expression for the radius of curvature of the path under gravity is given by equations (2.2) and (2.3) from which
angle OPA is a right angle and from the theorem of geometry that the angle within a circle is also a right angle, it follows that the line from which projection takes place is an arc of a circle of radius g/2; the Davis circle.
The trajectories of the ball paths may, on the assumption that the ball paths are parabolic, be easily plotted. Thus by the integration of equations (2.1) and taking the origin of the co-ordinate system at the point of projection.
From Fig. 2.8, it is clear, from requirements of continuity, that the amount of material entering any annular element p p qq must be equal to the quantity leaving it and so, since the parabolic trajectories cannot cross, a trajectory must terminate in the same annular element as it originates. Thus, the surface bRc is defined by points, such as R, which are obtained by the intersection of the parabolic trajectory with a circle of radius r; where r is the radius at which the trajectory originates. A representative point, such as R, may be obtained by the determination of the values of x and y, taking the point of projection P as the origin, of the point of intersection of the parabola with the circle of radius r through P.
It is clear that, ingeneral, a parabola cuts a circle in four points and, in the present case, three roots of the quartic equationare zero whilst the fourth, given by equation (2.13), is that required.
In Fig. 2.8 let point O be the centre of the mill and let the concentric circle RPQ represent the circular path of tin ball. The arc OPS is the arc, of radius g/2, representing the line at which projection occurs. Project a horizontal through P to cut the circle at Q and with centre Q describe an arc of radius QP, to cut the circle at R. The point R is then a point on the surface in which the flying balls meet the charge. Repeating the construction for a number of circles, of different radii, leads to the required surface bRC.
The curve ab is a circular arc struck from the centre of the mill and represents a surface which does not osculate with the segment of circle OPS, and, in consequence, from which no projection takes place. The radius of this arc is fixed by the magnitude of the mill charge and, denoting the radius by r, Davis gives the expressions
Since K cannot be less than zero, it follows that the mill filling cannot exceed about 0.7 without interference between the particles taking place. Actually Davis states that, in order that interference shall not occur, r should not be less than 0.228/n, where n is the speed in revolutions per second.
If now it is assumed that the motion of the charge may be represented by the motion of the particle at the radius of gyration of the charge, it is necessary to find the angle to corresponding to the radius
Thusit follows that, as a first approximation, 56% of the time is spent in the circular path and also that the area between the mill shell and the curves dPabRC is 56% of the area occupied by the charge when the mill is at rest. It also follows that, on an average, every ball strikes another 1.45 times per revolution of the mill.
The analysis of Davis, just outlined, is open to criticism on a number of grounds. For example, the frictional characteristics of the charge are ignored, the effects of interactions between the elements of the charge in a given trajectory and the interference between adjacent trajectories are neglected, as are the centripetal forces acting on the particles. Furthermore, some of the equations involved appear to include a number of rather wide approximations. Even so this work was the first serious attempt to derive a rational theory of the ball mill and, whilst forming a good basis for mill calculations, it had also paved the way for later studies.
The first important modification to the above treatment was suggested by von Steiger; who pointed out that the hypothesis of free flight of the particle along the ascending branch of the parabolic trajectory is invalid since the continuous projection of material along any trajectory results in contact between the particles. Thus for the ascending branch of the parabola the speed along the arc is constant; not variable as is the case with free flight of particles.
The surface from which the projection of the particles occurs is unaltered by this treatment and is, as before, given by a circle of radius g/2 drawn in the way previously explained. The trajectories themselves are considerably altered, however, since for the same initial conditions, the horizontal velocity of a particle, at the summit, is greater under the assumption of von Steiger, and so the particle travels a greater distance horizontally. Also the height of the summit above the point of projection is different in the two cases. Furthermore, since from continuity considerations, a trajectory on termination must cut the surface of the ball charge at the same radius as that at which it commences, it follows that the equilibrium surface of the ball charge is modified. These differences are clearly brought out by the diagram of Fig. 2.10 in which trajectories starting at the same point are plotted in accordance with the two treatments and the corresponding surfaces of the charge are shown.
In the first placethe equilibrium surface of the mill charge is determined and for this purpose the effective coefficient of friction of the charge (balls plus powder) must be established. A generalized coefficient of friction may be determined by forming a large conical heap of
themill charge on a flat surface, as shown in Fig. 2.11; the heap being formed by shovelling the material on to the apex of the cone and allowing the stable angle of repose to become established. The angle of repose, , is then measured and the coefficient of friction is given by
Also, since R = x + z, it follows that the origin of the spiral (the pole) where R = 0, must be situated at x = 0, y= g/; that is on the vertical axis at a distance g/ above the centre of the mill. (It should be noted that this distance is also the diameter of the circle, the Davis circle, defining the surface at which projection occurs.) The coefficient C is a parameter which is related, but not simply, to the degree of filling of the mill.
The configurations of the surface of the charge with various values of speed, coefficient of friction and mill filling, as calculated on this basis, are shown in Fig. 2.13. Examination of this figure shows that, for a given mill filling and coefficient of friction, the surface configuration of the charge is not greatly altered by variations in (N/Nc) the ratio of the running speed to the critical speed. Similarly, for a given value of the ratio N/Nc and a given
coefficientof friction, the slope of the surface does not alter greatly with the mill filling; furthermore, the line defining the surface is almost straight. In fact the average slope of the surface increases very slightly with decreasing filling.
The variable which has the greatest influence on the configuration of the surface of the charge is clearly the coefficient of friction and, all other variables remaining unaltered, the slope of the surface increases rapidly with increasing coefficient of friction.
It is desirable that the meaning of this surface should be borne clearly in mind. If the derivation of the equation is studied it will be seen that the equation represents the surface upon which a particle is in equilibrium under tin influence of the centripetal force, based on the assumption that the particle is traversing a circular path around the centre of the mill with the same angular velocity as the mill shell, of the weight of the particle and of the frictional force between the particle and the underlying surface. Now, clearly, in a real mill the balls which come up from the body of the ball mass must either be projected or must roll down to the toe of the charge and so, in cascading, this mathematical surface cannot represent the free surface of the ball charge. It is probable, however, that a surface of approximately this form exists a few ball diameter, below the free surface; that is, there exists an equilibrium surface down which the cascading ball charge rolls. Thus, such a free surface cannot exist with cascading motion, although it is probable that one does, over a portion of the charge, in the case of cataracting motion.
It is clear from the previous discussion that, if projection of the balls is to take place, the charge must cross the Davis circle. Now, the equilibrium surface, as defined by tin equiangular spiral, can fall either below or above the Davis circle; as shown in Fig. 2.14. When the equilibrium surface falls below the Davis circle, the particles, as they emerge from the main mass of the ball charge, pile up until the Davis circle is reached; as shown in Fig. 2.15. This is clearly possible since in the mass of balls lying above the main equilibrium surface but below the Davis circle, there exists an infinite number of equilibrium surfaces such as ab.
The inner bounding curve for this mass of balls is a circle concentric with the mill shell and tangent to the equilibrium surface. The position of this circular arc and the equilibrium surface is, of course, fixed by the condition thatthe rolling mass of balls and the flying mass are together equal to J, the static filling of the mill. Since, in this case, the projection takes place from the Davis circle, the construction for the termination of the trajectories, given earlier, is valid. In the second case, in which the equilibrium surface falls above the Davis circle, projection does not occur until the equilibrium surface is reached.
By reasoning very similar to that used previously, it can be shown that the termination of a parabolic trajectory, commencing at a point P above the Davis circle, is obtained when, on Fig. 2.16, distance PQ = QR and the point Q is on the Davis circle. Thus, the construction is similar to the previous except that point Q is on the Davis circle whereas point Q is on the mill circle. So for either case the point of termination of the trajectories may be determined by simple graphical methods.
It is interesting to have a knowledge of the proportion of the charge which is in flight, and of that which is rolling; also to see how these quantities vary with the speed of rotation of the mill and with the coefficient of friction of the charge material. A simple construction for this purpose will now be described; this construction being due to Fobelets.
(a) As in Fig. 2.17, draw the mill shell circle and the Davis circle. (b) With compasses determine position of point R ; the termination of the trajectory originating at P. (Use point Q on mill circle as centre.) (c) From the pole C (on the Davis circle), draw radius vectors at 10 intervals; taking vector CR as datum. (d) From C set out along the successive rays a length Ca = CR.e-(/180), where CR is the length CR
measured from the figure, is the angle, in degrees, from the line CR to the ray under consideration and is the coefficient of friction of the charge. (e) Join the points such as a to give a smooth curve, from the centre of the mill, O, draw an arc of a circle tangential to this curve and to cut the Davis circle at b. (f) Draw a line from P through C to intersect a vertical drawn through point R at point S. (g) Repeat (b) and (f) using mill circles of various radii; and so establish the curve bS. (For most purposes this step may be dispensed with and points bS joined by a straight line. There is then some loss of accuracy but this is not generally of great practical importance.) (h) Determine the area SbaRPCS. This when expressed as a fraction of the area of the mill circle gives J, the static mill filling. (i) Determine the ratio of areas PCSbP and PbaRP; this ratio being the ratio of the flying charge to the rolling charge.
(a) As for Case 1. (b) Assume a position for the point of projection, P, and using the construction of Fig. 2.16, determine point R; the termination of a parabolic trajectory which starts at P. (c) and (d) As for Case 1. (e) Join points such as a and the equiangular spiral should pass reasonably close to P. If it does not, start with a new point P and repeat the construction. (f) to (i); As for Case 1.
Although there is still an element of approximation in this treatment, it appears to be superior to that of Davis in that the effects of frictional characteristics of the charge are included and the computation of the flying charge does not involve reference to some mean radius. On the basis of this treatment it is possible to study the conditions for cataracting or cascading in some detail and this will now be done.
It will be noticed that, so far, no rigid definition of cascading and cataracting has been given. In fact such a definition is probably impossible since it now appears that there are not two types of motion of the charge involved, but a single type of motion in which, in certain cases, some details of the motion are not apparent. For the present purpose it is probably sufficient to name the motion cataracting when an appreciable gap exists between the parabolic trajectory of the innermost particle and the upper surface of the rolling charge. Cascading then corresponds to the motion in which this gap is so small as to give, in general, the appearance of being non-existent.
This difference is clearly shown in Fig. 2.18, which are the trajectories for a mill running with a definite charge at a definite speed but with different fillings. In Fig. 2.18a, with the higher filling, the space is very small and when allowance is made for the finite size of balls the mill would appear to be cascading. In the second illustration there is a definite space which, even allowing for interference between the balls in the different trajectories, would not be obliterated, and hence the mill would be described as cataracting. For the present purpose it will be assumed
that when this gap is less than 0.05 of the diameter of the mill, the charge will appear to be cascading; this gap being chosen because, in view of the finite size of the ball in a real mill, it is improbable that a gap smaller than this figure would be discerned. By the plotting of a number of such figures the conditions for a gap of less than the specified size to occur are soon established. The construction for the determination of the flying and rolling ball charges is then applied to each of these limiting cases when the results given in Table 2.1 are obtained. Since any increase in the mill filling above these values will reduce the size of gap it follows that these values are the maximum static mill filling for which cataracting will be apparent.
Itis seen that a fourfold variation in the coefficient of friction produces, for a given speed of rotation, but a negligible variation in the maximum mill filling which will permit cataracting. Thus, it is probably safe to say that these results, shown graphically in Fig. 2.19, are applicable to any practical mill with an accuracy sufficient for any normal purpose. The general validity of these results has received an amount of indirect support in the following way.
The photographs of the motion of the ball charge, published by Rose and Evans, have been questioned on the grounds that they show no cataracting. A study of the original article shows, however, that the three cases are J = 0.25, J=0.5 and J=0.75, with N/Nc = 0.56 in each case. From Table 2.1, however, it is seen that each of these values of J is above the maximum for which cataracting will be apparent, and so the results shown in the photographs are to be expected.
The introduction of a coefficient of friction of constant value, as in the extended theory, is not completely adequate, however, since a study of Fig. 2.13b suggests that the average angle of slope of the surface of the charge should decrease with increasing filling, whereas the
measurements of Rose and Evans show that the slope increases with mill filling. This difference is easily explained since the charge consists of a limited number of balls of finite size and, in consequence, the energy dissipated in friction in the charge increases with the size of the charge. This has an effect equivalent to an increase in the coefficient of friction of the charge; and so brings about an increase in the slope of the surface of the charge, in the same way as is shown in Fig. 2.13a. Thus, it appears that the introduction of a variable value for the coefficient of friction,would bring about an even better agreement between theory and practice. Unfortunately, the introduction of such a variable quantity very much complicates the mathematical analysis.
(1) Use the previous constructions to determine the configuration of the rolling charge in the mill; shown shaded in Fig. 2.20a. (2) Determine the position of the centre of gravity, G, of this area. (3) Through G plot the radial acceleration rG radially and the gravitational acceleration g vertically. (Note: radial force = MrG and vertical force =Mg, so these vectors are proportional to the forces.) (4) Obtain the resultant of these vectors. (5) Draw a straight line connecting the centre of mill O to the point P, where the resultant cuts the mill shell, and determine the angle . (6) Compare tan with the coefficient of friction . For safety must exceed tan by a reasonable margin.
The last condition is clear from Fig. 2.20b, since the resultant has radial and tangential components as shown. The tangential component tends to give rise to slip at the surface and slip will, in fact, occur if the ratio of the tangential force to the radial force exceeds the coefficient of friction: that is if tan > .
Round bar is exactly as it sounds; a long, cylindrical metal bar. Round bar is available in a variety of metals including hot rolled or cold rolled steel, stainless steel, aluminum, alloy steel, brass and more; and in many different diameters ranging from 1/4 up to 24.
Steel round bars are available in hot rolled or cold rolled. Hot rolled round bar is typically used for applications like construction where finish and precise dimensions arent a priority. Conversely, cold rolled round bar is used for applications where a superior surface finish and exact dimensions are essential. Some common applications of steel round bar include frameworks, supports, braces, shafts, and axles.
Aluminum round bars possess light weight and strong corrosion resistance, while being easy to machine and cut. Common applications of aluminum round bar include supports, trim, shaft, braces, pins, and dowels.
Brass round bars are used when strength, electrical conductivity, corrosion resistance, and spark resistance are important. Brass is easy to machine and has an attractive sheen when polished. Some examples of brass bar applications are marine hardware, instruments, fasteners and fittings.
Drill rods are manufactured from tool steel that has been ground to a tight tolerance diameter. While typically round, drill rods may also be fabricated in square shapes. They are also often tempered prior to machining. This process involves heating the steel to relieve the hardness and to make the steel more workable. The steel is then air cooled before machining begins. Common applications of drill rods include drill bits, taps, dowel pins, shafts, and reamers. They are also used to manufacture hammers, files, and punches.
Water hardened drill rods are not heavily alloyed, allowing the material to be more easily machined than the oil hardened variety. During the water hardening process, the rod is heated until glowing red then plunged into a vat of water to cool. The result is a hard, durable metal which is easily machined. However, it is not suitable for welding. Water hardened drill rods are used in the manufacturing of hammers and files.
Oil hardened drill rods are easily welded and machined and are very tough and durable. During the oil hardening process, the rod is heated until glowing red then plunged into a vat of warm oil. This causes the surface to become extremely hard. Oil hardened drill rods are used for general tool making.
Shafting, also known as Turned Ground and Polished shafting, refers to round bars made with fine precision and high-quality steel. They are polished to ensure flawless and perfectly straight surfaces. The manufacturing process is designed for extremely close tolerances for surface finish, roundness, hardness, and straightness which ensures a long service life with reduced maintenance.
Shafting bars are commonly used often used in applications that require high accuracy, such as weather measuring devices, laboratory tools, high-speed motor shafts, drive shafts, pump shafts, and ball bushings. In these scenarios, the bar is often required to rotate at high speeds. Thus extreme straightness is critical to prevent unwanted vibration and wear on bearings.
Induction hardening is a non-contact heating process which uses electromagnetic induction to produce the required heat. The steel is placed into a strong alternating magnetic field which causes an electric current to flow through the metal, generating heat. During this process the core of the steel remains unaffected and retains its physical properties. The steel is then quenched in water, oil, or a special polymer which causes the surface layer to form a martensitic structure which is extremely hard.
Metal Supermarkets is the worlds largest small-quantity metal supplier with over 85 brick-and-mortar stores across the US, Canada, and United Kingdom. We are metal experts and have been providing quality customer service and products since 1985.
At Metal Supermarkets, we supply a wide range of metals for a variety of applications. Our stock includes: stainless steel, alloy steel, galvanized steel, tool steel, aluminum, brass, bronze and copper.
Seams are longitudinal crevices that are tight or even closed at the surface, but are not welded shut. They are close to radial in orientation and can originate in steelmaking, primary rolling, or on the bar or rod mill.AISI Technical Committee on Rod and Bar Mills, Detection, Classification, and Elimination of Rod and Bar Surface Defects
Seams may be present in the billet due to non-metallic inclusions, cracking, tears, subsurface cracking or porosity. During continuous casting loss of mold level control can promote a host of out of control conditions which can reseal while in the mold but leave a weakened surface. Seam frequency is higher in resulfurized steels compared to non-resulfurized grades. Seams are generally less frequent in fully deoxidized steels.
Seams are the most common bar defects encountered. Using a file until the seam indication disappears and measuring with a micrometer is how to determine the seam depth.(Sketch from my 1986 lab notebook)
Seams can be detected visually by eye, and magnaglo methods; electronic means involving eddy current (mag testing or rotobar) can find seams both visible and not visible to the naked eye. Magnaflux methods are generally reserved for billet and bloom inspection.
Seams are straight and can vary in length- often the length of several bars- due to elongation of the product (and the initiating imperfection!) during rolling. Bending a bar can reveal the presence of surface defects like seams.
These long, straight, tight, linear defects are the result of gasses or bubbles formed when the steel solidified. Rolling causes these to lengthen as the steel is lengthened. Seams are dark, closed, but not welded- my 1986 Junior Metallurgist definition taken from my lab notebook. Weve a bit more sophisticated viewof the causes now.
The frequency of seams appearingcan help to define the cause. Randomly within a rolling, seams arelikely due to incoming billets. A definite pattern to the seams indicates that the seams were likely mill induced- as a result of wrinkling associated withthe section geometry. However a pattern related to repetitious conditioning could also testify to billet and conditioning causation- failure to remove the original defect, or associated with a repetitive grinding injury or artifact during conditioning.
Rejection criteria are subject to negotiation with your supplier, as are detection limits for various inspection methods, but remember that since seams can occur anywhere on a rolled product, stock removal allowance is applied on a per side basis.
Metallurgical note: seams can be a result of propogation of cracks formed when the metal soidifies, changes phase or is hot worked. Billet caused seams generally exhibit more pronounced decarburization.
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Great Question! During hot rolling, there can be repeats impressed into the bar surface if an imperfection or buildup on a roll persists. The strict periodicity of the repetition is a clue to look for a damaged roll. Remember, the bar is moving longitudinally at miles per hour speeds toward the end of the rolling, so any contact with the soft metal by rolling mill guides etc, will cause a longitudinal oriented imperfection because of that speed. I also remember one case where a single divot or notch occurred what seemed to be sporadically throught an order. Eventually we determined that it was caused by the bar strand striking an inline shear blade just above the line- when the shear had been repaired, the millwrights had reassembled it off by one tooth on the gearing. This resulted in it sitting a few inches lower and when the bar slack caused it to rise, it could just nick the shear blade hanging there
If you are seeing a repetitive longitudinal pattern of short lines or small chevrons near the end of a cold drawn bar, those can be pusher marks that were not cropped off or Gripper marks that were not cropped off from the drawbench by the cold finisher. I do not have a photograph, but do have some sketches and will create a post based on your question. THANKS!
Im working as a quality control engineer in EZDK company (Egypt) which produce deformed steel rebars. We use QTB technology for producing rebars. Recently, discontinuous cracks appeared on the Deformed 12 mm rebars surface. Micro structure test showed that the crack depth is about 0.8 mm. I need to know the possible reasons could lead to existence of such cracks.
On non resulfurized bar products, it is 0.001 per sixteenth inch of bar diameter PER SIDE. That would be a stock removal of 0.016 per side (maximum allowable seam depth) or 0.032 off the diameter.
On steels where sulfur is deliberately added to improve machinability (Resulfurized Steels) the allowance is 0.0015 per sixteenth of bar diameter per side so on a one inch bar, that would be 0.024 maximum seam depth and Stock removal , or 0.048 off diameter. This standard was originally AISI.
The ASTM A 108 Standard Table A1.1.8 for level 1 products is 1.6% maximum surface discontinuity depth for carbon and alloy nonresulfurized; 2.0% for Resulfurized to (0.08-0.19^ sulfur; and 2.4% for Resulfurized (0.20-0.35% Sulfur)
The ASTM spec has a wiggle room statement that The information in the chart is the expected maximum surface discoontinuity depth within the limits of good manufacturing practice. Occassional bars in qa shipment may have surface discontinuities that exceed these limits.
Recently I have done a lot of trials to eradicate seams on sizes 25mm and above. It included 1. increasing the Si content in the chemistry 2.Addition of aluminium blocks 3.Increasing the CaSi cored wire
Rasheed, I cant get you to seam free, but for best quality I would hold Copper at 0.020 max. Sulfur limits low as possible, but it is really more about the ratio of Manganese to sulfur. I would want to be high range of Managanese and low range of sulfur to minimize surface irregularities such as seams.
Towards forward integration of the processes, company has set up Wire Rod manufacturing & Wire Drawing facilities (HB Wire) at Raipur for manufacturing high quality Wire Rod of sizes 5.0 mm, 5.5 mm, 6.5 mm, 7 mm, 8 mm & 10 mm and HB wire of sizes 6 gauge to 14 Gauge with best available technology and plant & machinery support.
Since the raw material i.e. Steel Billets /Blooms is manufactured in the Steel Melting Shop at Champa, the company is able to produce high quality Wire Rod & H.B. Wire in an efficient & cost effective manner.
These products are used for various applications including Binding wire, Gl wire, Barbed wire for fencing, Armored sealed wire for heavy electrical cables, Nut bolts, Nails, screws, Alpine. Wire ropes. Wire mesh etc.
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Wire rod is a hot-rolled round produced in coil form that is typically drawn into wire for use in a wide variety of construction and industrial applications. CMC Steel produces wire rod in Jacksonville, Florida.The coil weight is approximately 2,600 pounds.
Wire rod has a number of end uses and applications, including tie wire, mesh, fencing, shelving, shopping carts, wire hangers and nails. In addition, wire drawn from rod can be galvanized, plated and painted.
CMC Steel can produce wire rod to meet our customers needs with technical service support available to match customer requirements with our production process options. Our commitment to quality provides assurance that our customers requirements will be successfully met with the highest quality products and superior customer service.
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Basket Case: any vehicle that was completely disassembledor needs to be completely disassembled for restoration or modification purposes. (Referred to as basket case because the process often involves gathering and collecting small parts in a basket over a long period of time).
Frame-off Restoration:a restoration project in which the entire vehicle is completely disassembled with all parts cleaned or replaced as necessary, so that the restored car meets the original factory specifications as closely as possible.
Frame-Up Restoration:not as detailed as a frame-off restoration,this processinvolves restoring the paint, chrome, interior, and mechanicals to original specifications without complete disassembly of the car.
Matching Numbers:a restored or original vehicle in which all serial numbers (VIN, engine, body, transmission, rear end) can be researched and identified as being 100 percentcorrect for that specific vehicle.Get in Touch with Mechanic