US3587598A

US3587598A - Sink roll for supporting an elongate material without direct contact

Info

Publication number: US3587598A
Application number: US790921A
Authority: US
Inventors: Yasunori Miyamatsu; Yuji Hashimoto; Shoji Enari
Original assignee: Toyo Kohan Co Ltd
Current assignee: Toyo Kohan Co Ltd
Priority date: 1968-01-30
Filing date: 1969-01-14
Publication date: 1971-06-28
Anticipated expiration: 1988-06-28
Also published as: GB1237794A; DE1903659A1; FR2000952A1

Abstract

A SINK ROLL FOR GUIDING AN ELONGATE STRIP TO BE PROCESSED IN A TREATING LIQUID TANK IN A MANNER SUCH THAT SAID STRIP IN MAINTAINED OUT OF CONTACT WITH THE OUTER SURFACE OF SAID SINK ROLL, COMPRISING A SEMICIRCULAR CYLINDRICAL GUIDE WALL PORTION PROVIDED WITH AT LEAST ONE RECESS OF SUBSTANTIALLY RECTANGULAR SHAPE, FLAT GUIDE WALL PORTIONS EXTENDING FROM THE DIAMETRICALLY OPPOSITE EDGES OF SAID SEMICIRCULAR CYLINDRICAL GUIDE WALL PORTION TANGENTIALLY THERETO, AND AT LEAST ONE CHANNEL OPENING IN THE RECESS AND COMMUNICATING WITH A PUMP TO SUPPLY THE PRESSURIZED TREATING LIQUID BETWEEN THE SURFACE OF THE SEMICIRCULAR CYLINDRICAL GUIDE WALL PORTION AND THE STRIP.

Description

United States Patent 43/5148 and 43/82573 SINK ROLL FOR SUPPORTING AN ELONGATE MATERIAL WITHOUT DIRECT CONTACT 4 Claims, 18 Drawing Figs.

U.S. Cl 134/122, 226/97 Int. Cl B08b 3/04 Field of Search 134/15, 64, 122; 68/62; 226/97 Primary ExaminerDaniel Blum Att0rney Hall, Pollock and Vande Sande ABSTRACT: A sink roll for guiding an elongate strip to be processed in a treating liquid tank in a manner such that said strip is maintained out of contact with the outer surface of said sink roll, comprising a semicircular cylindrical guide wall portion provided with at least one recess of substantially rectangular shape, flat guide wall portions extending from the diametrically opposite edges of said semicircular cylindrical guide wall portion tangentially thereto, and at least one channel opening in the recess and communicating with a pump to supply the pressurized treating liquid between the surface of the semicircular cylindrical guide wall portion and the strip.

PATENTEUJUNZ H 3,587,598

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ATTOR NEYS' PATENTED JUN28 12m SHEET 5 [IF 7 0 0,. 0 M w. m 0 0 w m m w m ,m a m w H M M. m w 0 F/G l3 INVENTOR; Q$u.nan' I'll 11.01 Yuji #C,I'M.+ sh gnaw] BY 7/414, @1404 2 ATTORNEYS SINK ROLL FOR SUPPORTING AN ELONGATE MATERIAL WITHOUT DIRECT CONTACT This invention relates to a roll mounted in a treating liquid tank, the so-called sink roll which is used for guiding an elongate material or strip to be processed in said tank, utilizing static pressure of pressurized treating liquid generated between the outer surface of the roll and the strip to thereby maintain the strip out of direct contact with said roll.

Hitherto, when an elongate strip is treated chemically in a vertical type tank, the elongate strip is guided to turn its travelling direction by a roll disposed in the tank rotatably with the elongate strip. However, in the case of such a roll, some defects do not allow to produce an elongate strip of good quality: first, when the travelling speed of the elongate strip is accelerated or decelerated, it is difficult to equalize the velocity of the roll surface with that of the travelling strip. Therefore, relative slippage occurs between the surface of the sink roll and that of the elongate strip. Moreover, when the elongate strip travels at high speed, the treating liquid is forced into the part where the surface of the sink roll contacts the elongate strip with the result that the wedge action due to the treating liquid is applied to said part. According to this wedge action, the elongate strip departs partially from the surface of the sink roll causing relative slippage between the surface of the sink roll and that of the elongate strip. This slippage causes many scratches on the surface of the elongate strip. Especially when a weak coat exists at the surface of the elongate strip, the damage by scratching is very heavy. Furthermore, perfect sealing between the rotating shaft of the sink roll and the wall of the tank is very difficult, so maintenance of the sealing must often be attended to.

On the other hand, as a prior art, the device of the type described in British Pat. No. 1016703, entitled Improvements relating to Fluid Pressure Support Bearings, was proposed, However, the roll of this type has some disadvantages; first, it is difficult to obtain a uniform distribution of clearance between the surface of the sink roll and that of the elongate strip, which will also affect the efficiency of pump power. Moreover, when high tension is exerted on the strip, the condition in which no contact will occur between the surface of the roll and the elongate strip can not be obtained, that is, the elongate strip comes partially into contact with the surface of the roll.

An object of this invention is to provide a sink roll by which an elongate material or strip can be guided without causing direct contact between the surface of the sink roll and the elongate strip by the agency of static pressure of pressurized liquid generated therebetween.

Another object of this invention is to provide a sink roll which prevents the surface of the elongate strip from being damaged by relative slippage between the surface of the sink roll and that of the elongate strip.

A further object of this invention is to provide a sink roll which has characteristics superior to those of the prior art described in British Pat. No. 1,106,703. A detailed comparison with the roll of this type will be made later.

According to the present invention there is provided a sink roll fixedly disposed in a treating liquid tank to guide an elongate strip passing around the periphery of said roll without causing direct contact with the outer surface of said roll comprising a substantially semicircular cylindrical wall portion for guiding the elongate strip around said wall surface, flat guide wall'portions extending from the diametrically opposite edges of said semicircular cylindrical guide wall portion tangentially to said wall surface, at least one channel opening in the outer surface of said semicircular cylindrical guide wall portion and communication with a pressure source to supply pressurized liquid between the surface of said semicircular cylindrical guide wall portion and the surface of said strip facing said wall portion, and at least one recess provided in the outer surface of said semicircular cylindrical guide wall portion and surrounding the opening of said channel.

In a preferred form,.the recess according to the present invention has a substantially rectangular shape and is provided with a branched fin-shaped portion extending outwardly in the lateral direction at each corner of the recess.

In another preferred form, each of the flat guide wall portions according to the present invention has, at the end thereof remote from the associated edge of said semicircular cylindrical guide wall, a beveled wall portion having the outer surface slanted inwardly towards the terminal thereof.

Other and more specific objects, features and advantages of the present invention will be apparent from the description given below, in conjunction with the accompanying drawings illustrating preferred embodiments of this invention.

Briefly stated, the present invention utilizes continuous guiding without direct contact of an elongate strip in a treating liquid tank, more reliably compared with the prior art, by using the sink roll of the invention.

By different combinations of the semicircular cylindrical guide wall portion, recess portion, flat guide wall portions and beveled wall portions, which have specific functions respectively as explained later, various kinds of sink rolls can be obtained. The present invention will be better understood from the following description in conjunction with the accompanying drawings in which:

FIG. 1 is a schematic illustration of a treating liquid tank containing a sink roll accordingto this invention and a circulation system of pressurized treating liquid;

FIG. 2 is a front view of a preferred embodiment of the sink roll according to the present invention;

FIG. 3 is a cross section of the sink roll shown in FIG. 2 when taken along the line III-III thereof;

FIG. 4 is a front view of another embodiment of the sink roll according to the present invention;

FIG. 5 is a cross section of the sink roll shown in FIG. 4

when taken along the line V-V thereof;

FIG. 6 is a front view of a third embodiment of the sink roll according to the present invention;

FIG. 7 is a cross section of the sink roll shown in FIG. 6 when taken along the line VII-VII;

FIG. 8 is a graph of the clearance distribution of the present invention;

FIG. 9 is a front view of a fourth embodiment of the sink roll according to the present invention;

FIG. 10 is a cross section of the sink roll shown in FIG. '9 when taken along the line X-X;

FIG. 11 shows the relationship between the mean clearance and the length of the flat guide wall portion;

FIG. 12 shows the relationship between the minimum clearance and the length of the flat guide wall portion;

FIG. 13 is a front view of a fifth embodiment of the sink roll according to the present invention;

FIG. 14 is a cross section of the sink roll shown in FIG. 13 when taken along the line XIVXIV;

FIG. 15 is another graph of the clearance distribution of the present invention; 1

FIG. 16 is a graph of the clearance distribution of the sink roll of the prior art;

FIG. 17 shows another relationship between the mean clearance and the length of the flat guide wall portion; and

FIG. 18 shows another relationship between the minimum clearance and the length of the flat guide wall portion.

Referring now to FIG. I, there is shown a treating liquid tank 2 comprising a sink roll 3 along which an elongate material or strip 1 is guided and maintained out of contact, and a circulation system for a treating liquid consisting of, for example, a pump 4, a valve 5, a supply line 6 through which pressurized operating liquid, namely, treating liquid, is supplied to a pressure chamber 11 and a return line 7 through which the liquid from the tank is returned to the pump.

In the first embodiment of the sink roll of the present inven tion shown in FIGS. 2 and 3, the body 3 thereof must have enough strength to bear static pressure generated at the surface of the sink roll, so the body 3 of the sink roll is usually made of steel. In case the treating liquid (L) is acid, the body 3 must be coated by corrosion resistance material such as, for

instance, vinyl chloride. The shape of the body 3 is hollow and cylindrical as shown in FIGS. 2 and 3 and the supply line 6 is connected to the body 3 at both ends thereof. The supply line 6 leads to a channel or a pressure chamber 11 provided inside the body 3 of the sink roll to deliver the pressurized treating liquid thereto. The sink roll 3 may be supported by supply line 6 in the treating liquid tank, or the body 3 of the sink roll may be fixed to the wall of the treating liquid tank 2 directly. The lower half of the body 3 forms a semicircular cylindrical guide wall 9 along which strip 1 is guided, while the upper half of the body 3 acts only as a boundary wall of the pressure chamber 11, so different shapes may be adopted for the upper half of the body 3. At the diametrically opposite edges of the semicircular cylindrical guide wall portion 9 and tangentially thereto, flat guide wall portions are provided to fonn an extension. A part of the semicircular cylindrical guide wall portion 9 is formed with a recess portion 8 of substantially rectangular shape. In the recess portion 8, openings or supply holes 12 are provided, which communicate with the pressure chamber 11.

In the arrangement as shown in FIG. 1, the strip 1 enters treating liquid (L) and is guided along the flat guide wall portion 10 on one side of the roll, the semicircular cylindrical guide wall 9, and the flat guide wall portion 10 on the opposite side of the roll. Thus, the strip is turned by 180, and then leaves the sink roll 3 upward. The strip 1 is loaded with tension (T) to maintain its proper position while it is travelling.

The treating liquid (L) in the treating liquid tank 2 returns to the pump 4 through the return line 7, and is pressurized by the pump 4. The flow rate of the treating liquid is adjusted by the valve 5. Then the pressurized treating liquid is supplied to the pressure chamber 1 l passing through the supply line 6 and entrance holes 1.6 to the pressure chamber 11. The supplied treating liquid is sent to the recess portion 8 through the openings 12 and is momentarily accumulated there. Static pressure of the treating liquid, enough to support the loaded tension (T), is generated in the recess portion 8. Thereby, the strip 1 is lifted from the surface of the sink roll and maintained out of contact. One part of the treating liquid in the recess portion 8 flows out in the axial direction of the cylinder 3, passing through the clearance formed between the strip 1 and the semicircular cylindrical guide wall portion 9 and the other part of the treating liquidflows out to the treating liquid tank 2 in the circumferential direction, passing through the clearance formed between the strip 1 and the flat guide wall portion 10. Static pressure in the recess portion 8 is maintained by fluid resistance in the clearance between the strip 1 and the surface of the sink roll and supports the loaded tension. In order to obtain the condition in which no contact will occur, the balance between the fluid resistance of the axial flow and that of the circumferential flow, is very important. If these two fluid resistances are out of balance, the condition in which no contact and efficient clearance distribution will occur can not be obtained. The fluid resistance of the circumferential flow is adjusted by the length (C) of the flat guide wall portion 10 whose effect is very remarkable as will be explained later.

The recess portion 8 has a substantially rectangular shape and is provided with a branched small rectangular recess portion 13 extending axially of the roll at each corner of the main recess 8 nearthe flat guide wall portions. Here, we call this portion 13 the fin portion." The provision of the fin portions serves to improve the clearance distribution in the corners of the main recess 8. I

In the embodiment shown in FIGS. 2 and 3, the body 3 has a cylindrical shape, and its diameter (G) is 200 mm. and its length (F) is 500 mm. On the lower half of the body of the roll which defines the semicircular cylindrical guide wall portion 9, the recess portion 8 is provided with a lateral length (E) of 300 mm., and a depth (H) of 3 mm. The circumferential length of the recess portion 8 is limited so that the opposite edges thereof in the circumferential direction terminate short of the ends of the semicircular cylindrical guide wall by the distance (B) of 3 mm. The fin portion 13 is rectangular in shape, and has a length (l) of 40 mm. and a circumferential length (J) is 20 mm. Four supply holes 12 whose diameters (D) are 50 mm. respectively, are provided at an angle (A) of 30 in each recess portion 8. The length (C) of the flat guide wall portion 10 is 20 mm. By using the sink roll of this type, it is possible to guide strips about 400 mm. to 600 mm. in width, under the condition that no contact will occur, at a speed of 500 m/min.

Another embodiment of the sink roll of the present invention is shown in FIGS. 4 and 5. In the case of the sink roll shown in FIGS. 2 and 3, the distribution of clearance along the semicircular cylindrical guide wall portion 9 is not always uniform over the entire guide wall surface, though the lack of uniformity of the clearance distribution in this case is not so remarkable as to prevent the proper travel of the strip. In order to obtain a more uniform distribution of clearance along the semicircular cylindrical guide wall portion 9 and a more improved clearance distribution at the flat guide wall portion 10 and improve the efficiency of the flow rate of the treating liquid, in the embodiment shown in FIGS. 4 and 5 the recess portion is divided into two recess portions 14 with an axially extending portion 15 interposed therebetween at the central portion of the semicircular cylindrical guide wall surface. In each recess portion 14, two openings or supply holes 12 are provided respectively.

The length (E) in the axial direction of the recess portion 14 is 300 mm. and the depth 0-!) ofthe recess portion 14 is 3 mm. The circumferential length of the recess portion 14 is limited in similar manner as mentioned above by the length (B) of 3 mm. and an angle (K) of 60". At the corners of the recess portion 14 near. the flat guide wall portion 10, fin portions 13 whose length (I) is 40 mm. and width (J) is 20 mm., are provided. The other dimensions of the sink roll of this type are the same as those shown in FIGS. 2 and 3.. When the sink roll of this type is used, the maximum clearance is reduced and the clearance distribution along the semicircular cylindrical guide wall portion 9 is improved to be more uniform.

Another embodiment of the sink roll of the invention is shown in FIGS. 6 and 7. The feature of the sink roll in this embodiment is that each of the flat guide wall portions 10 is formed with a beveled wall portion 17 having the outer surface slanted inwardly towards the terminal thereof. The surface of the beveled wall portion 17 is inclined with a gradient of 1:20 to the surface of the flat guide wall portion 10. In this embodiment, the surface of the beveled wall portion 17 is flat. However, it is not necessary that the surface of the portion 17 be flat, and a curved surface which is slightly bent inwardly towards the terminal thereof may be used. In the case of the sink roll shown in FIGS. 2, 3, 4 and 5, a self-excited vibration of the strip 1 occurs often at the flat guide wall portion 10 due to unstable flow thereat. The object of providing the beveled wall portion 17 is to obtain a stable flow along the flat guide wall portion 10 and the beveled wall portion 17. By providing the beveled wall portion 17, the clearance distribution thereat isimproved, namely, the clearance distribution along the flat guide wall portion 10 and the beveled wall portion 17 is not affected by the change of tension as shown in the graph of FIG. 8. More specifically, the graph was drawn up based on the results of experiments when a strip of 450 mm. in width is used in the embodiment shown in FIGS. 2 and 3, and shows the clearance distribution, that is, the relationship between the clearance h and the angle x. According to FIG. 8, it is understood that a perfect condition in which no contact will occur is obtained throughout the total area of the semicircular cylindrical guide wall portion, the flat guide wall portion and the beveled wall portion which are indicated in the graph as W,, W and W respectively. With an increase of tension ap-. plied to the strip, the clearance between the strip and these portions is reduced, and asa result of the static pressure of the liquid in the recessed portion is increased due to the increased fluid resistance in this clearance, thereby the tension of the strip is balanced with the static pressure of the liquid. It is noted that the clearance distribution along the flat guide wall portion and the beveled wall portion does not remarkably change upon variation of the tension of the strip. This characteristic of the sink roll of the present invention is very important in view of the fact that it is most difficult to assure the floating of the strip'at the point at which angle (X) is about 90. The length (M) of the beveled wall portion 17 is 20 mm. The other dimensions of the sink roll shown in FIGS. 6 and 7 are the same as those in FIGS. 2 and 3, respectively. p

In order to obtain more uniform distribution of clearance, it is possible also in the embodiment of FIGS. 6 and 7 to provide a sink roll in which the recess portion is divided into two parts as shown in FIGS. 4 and 5.

It is clear that the width of the strip must be wider than that of the recess portion to obtain enough static pressure in the recess portion. However, when the width of the strip becomes very much wider than that of the recess portion, the balance of the'axial flow and the circumferential flow is broken and the effect of the fin portion is also reduced. As a result, it becomes difficult to assure that no contact will occur. In order to assure that definitely no contact will occur for strips of various widths, it is ideal to change the width of the recess portion in response to the change in width of the strip. But in that case the mechanism becomes very complicated. In order to obtain a similar effect in a simpler structure, the present invention provides a sink roll in which the recess portion is divided into a main recess portion and subrecess portions which are juxtaposed laterally in rows in spaced relation as shown in FIGS. 9, l0, l3 and 14. In response to the width of the strip, the recess portions to be operated are selected and the supply holes of other recess portions are closed to save pump power. Various methods of closing the supply holes can be considered, for example, the use of simple valves, solenoid valves and valves controlled by fluid.

An embodiment of the sink roll of this type is shown in FIGS. 9 and 10. In this embodiment, the recess portion is divided into a main recess portion 8 and four subrecess portions l8, 19. Four main supply holes 12 are provided in the main recess portion 8 and two small supply holes 20, 21 are provided in the subrecess portions l8, 19 respectively. The pressure chamber also is divided into a main pressure chamber 11 and four

subpressure chambers

22, 23. These pressure chambers have entrance holes 27, 28, 29 and

supply lines

24, 25, 26 are connected with the entrance holes 27, 28, 29 respectively. The width (S) of the main recess portion 8 is 200 mm., the width (V) of each subrecess portion I8, 19 is 25 mm. and the spacing (U) between these recess portions is 25 mm. The other dimensions of the sink roll shown in FIGS. 9 and I are the same as those in FIGS. 2 and 3.

In this case where many recess portions are provided, the fin portions which are used in the aforementioned embodiments to improve floating of the strip at the corners of the recess, are not necessary because

subrecess portions

18, 19 take the place of those fin portions.

When the strip 30 is used, the

valves

25, 26 are closed and only the valve 24 is opened. When the strip 31 is used, the valve 26 is closed and the

valves

24, 25 are opened. When the strip 32 is used, all the

valves

24, 25, 26 are opened. By operating these valves, the flow rate of pressurized treating liquid is controlled.

FIGS. 11 and 12 are the results of experiments when a strip of width 450 mm. is used. FIG. 11 shows the relationship between the mean value of clearance along the semicircular cylindrical guide wall portion and the length (C) of the flat guide wall portion 10. FIG. 12 shows the relationship between the minimum value of clearance distribution along the surface of the sink roll and the length (C) of the flat guide wall portion. According to these figures, it is clear that the length (C) of the flat guide wall portion 10 has a significant meaning and must be selected between mm. and 30 mm. The optimum length (C) lies within a range from mm. to 20 mm. If a shorter or longer length (C) is adopted, the desirable condition in which no contact will occur will not be obtained.

Another embodiment of a sink roll in which the recess portion is divided, is shown in-FIGS. I3 and 14. In this embodiment, the sink roll has beveled wall portions 17 besides flat guide wall portions shown in FIGS. 9 and 10. The object of providing the beveled wall portions is the same as that in the case of the embodiment shown in FIGS. 6 and 7. The length (M) ofthe beveled wall portion 17 is 20 mm. The other shapes and dimensions are the same as those of the sink roll in FIGS. 9 and 10.

FIG. 15 is a graph drawn up based on the results of experiments when a strip 32 of 450 mm. in width is used in the embodiment shown in FIGS. 13 and 14, and shows the clearance distribution, that is, the relationship between the clearance h and the angle X. According to FIG. 15, it is understood that a perfect condition in which no contact will occur is obtained by using the sink roll of this invention. With an increase of tension applied to the strip, the clearance distribution along the semicircular cylindrical guide wall of from X=0 to is reduced, thereby static pressure in the recess portion is increased to keep the balance with tension, while the clearance distribution along the flat guide wall portion and the beveled wall portion does not change so remarkably, and this is, as mentioned with reference to F IG. 8, a very important characteristic of the sink roll of this invention.

FIG. 16 shows the result of experiments on the sink roll of the type having many small orifices on its surface as described in British Pat. No. 1,016,703. With an increase of tension, local contact between the strip and the surface of the sink roll occurs. Such a local contact can be avoided by using the sink roll of this invention.

FIG. 17 shows the relationship between the mean clearance along the semicircular cylindrical guide wall portion and the length (C) of the flat guide wall portion. The maximum value of the mean clearance exists at a length (C) of about 20 mm.

FIG. I8 shows the relationship between the minimum clearance along the semicircular cylindrical guide wall portion and the length (C) of the flat guide wall portion. This distribution has also its maximum value at a length (C) of about 20 mm., as in FIG 17, and this peak is pretty sharp. So, if the length (C) is not determined correctly, namely, within a range of from 10 mm. to 30 mm., the condition in which no contact will occur will not be obtained. The key to obtain good clearance distribution depends on the length (C) of the flat guide wall portion.

In order to obtain a perfect condition in which no contact will occur with the sink roll in which static pressure is applied, reliable floating at the leading and trailing part relative to the strip flow is most difficult, so therefore the balance between the flow in the circumferential direction and that in the axial direction must be taken into account. In this invention the balance is adjusted by the length of the flat guide wall portion, the beveled wall portion and the length of the semicircular cylindrical guide wall portion in the axial direction. This idea has not been adopted in the sink roll which has been developed for the same object as that of this invention. I

While a few embodiments of the invention have been illustrated and described in detail, it is clearly understood that the invention is not limited thereto or thereby.

We claim:

1. A sink roll fixedly disposed in a treating liquid tank to guide an elongate strip passing around the periphery of said roll without causing direct contact with the outer surface of said roll, said sink roll comprising a substantially semicircular cylindrical wall portion for guiding said elongate strip around said roll, flat guide wall portions at the opposing edges of said semicircular guide wall portion for guiding said strip toward and away from said semicircular wall portion, at least one channel opening into the outer surface of said semicircular cylindrical guide wall portion and communicating with a pressure source to supply pressurized liquid to the region between the outer surface of said semicircular cylindrical guide wall portion and the surface of said strip facing said semicircular wall portion, and a recess provided in the outer surface of said semicircular cylindrical guide wall portion and' surrounding the opening of said channel, said recess having corners and being formed with a branched fin-shaped portion extending outwardly therefrom in the lateral direction at each comer of said recess.

2. A sink roll as claimed in claim I, wherein each of said flat guide wall portions includes, at the end thereof remote from the associated edge of said semicircular cylindrical guide wall portion, a beveled wall portion having an outer surface slanted inwardly towards the terminal thereof.

3. A sink roll fixedly disposed in a treating liquid tank to guide an elongate strip passing around the periphery of said roll without causing direct contact with the outer surface of said roll, said sink roll comprising a substantially semicircular cylindrical wall portion for guiding the elongate strip around said roll, flat guide wall portions extending from the opposing edges of said semicircular guide wall portion for guiding said strip toward and away from said semicircular cylindrical wall portion, at least one main recess laterally disposed substantially at the center of said semicircular cylindrical guide wall portion, a plurality of further recesses located on the opposite lateral sides of said main recess in juxtaposed spaced relation, and a plurality of channels in said roll communicating with a pressure source, each said channel respectively defining a pressure chamber for an associated recess and having at least one opening communicating with said associated recess.

4. A sink roll as claimed in claim 3 wherein each of flat guide wall portions has, at the end thereof remote from the associated edge of said semicircular cylindrical guide wall portion, a beveled wall portion having an outer surface slanted inwardly towards the terminal thereof.