Abstract: The present disclosure relates to a manufacturing method of an aluminum forging wheel, the manufacturing method being able to homogenize a material, optimize flow ability, prevent picking inside a wheel, and densify the internal structure of an aluminum forging wheel. The manufacturing method of an aluminum forging wheel includes: a billet preparation step S1 of preparing an aluminum billet to manufacture an aluminum forging wheel; a first forming step S2 of manufacturing a primary forming product by performing hot forging on the billet prepared in the billet preparation step S1; a second forming step S3 of manufacturing an aluminum forging wheel that is a secondary forming product by performing hot forging on the primary forming product manufactured in the first forming step S2; and a second machining step S5 of preheating the aluminum forging wheel manufactured in the first forming step S3 and performing F/F.

Abstract: In a method for producing a cooling plate, a workpiece in the form of a flat material blank with uniform material thickness is precisely centered in a tool. A substantially radially extending flat peripheral edge of the workpiece is formed by an outer punch of the tool, as the workpiece is held down by an inner punch of the tool and the outer punch is pressed against the peripheral edge to thereby reduce the material thickness of the peripheral edge. Pins are formed on a coolant-swept effective surface of a base of the workpiece by the inner punch through pressing in cooperation with pin forming openings of the tool as the outer punch is held down, such that the pins protrude approximately perpendicular beyond the base and are surrounded by the peripheral edge.

Abstract: The present disclosure provides an extrusion forming die for a cabin component. The extrusion forming die for a cabin component comprises an upper die assembly, a lower die assembly and a combined concave die. The upper die assembly comprises an extrusion punch (3), and the combined concave die comprises an M-shaped outer concave die (4) having a hollow cavity matched with the extrusion punch (3), and a W-shaped inner concave die (5) having a rotary cavity. The W-shaped inner concave die (5) is arranged in the rotary cavity of the M-shaped outer concave die (4) in a matched manner, and the rotary cavity and the hollow cavity are matched to form a rotary extrusion die cavity (18) with a W-shaped longitudinal section.

Abstract: Disclosed is an impact extrusion can making system that uses induction heating to preheat an extruder punch and an extruder forming die, to increase yield during a cold start. In addition, a highly precise laser measuring device is used to measure dome thickness, so that stroke length and/or position of an extruder and/or extrusion die can be automatically adjusted in a predictive control system. High quality products with high yield are produced using these techniques.

Abstract: A top cap is provided for a bicycle handlebar stem. The top cap includes a cap body, which has a lower portion forming a fitting cylinder of a reduced diameter and a radially expanding circumferential shoulder atop the fitting cylinder. A barrel extends from a bottom of the fitting cylinder. The barrel forms a downward-facing hollow blind hole. The cap body forms a bolt head hole extending therethrough and coaxial with and communicating the blind hole. The barrel forms slits, which define a tightening section.

Abstract: In the metal billet to be used for hot dilation forming, a forward side with respect to the pressing direction has a quadrate section and its diagonal length is not more than an inner diameter of a container. Moreover, a backward side with respect to the pressing direction has a circular section and its diameter is substantially same as the inner diameter of the container. The metal billet is heated to a temperature suitable for press working and is set into a container for press forming. While a center of a workpiece of the metal billet is being bored by a boring punch to be operated by a pressing machine, the metal billet is hot-dilated so that a bottomed container for a cask is formed.

Abstract: Methods for forming a tube that includes a feature extending from an inner surface of the tube are provided. The methods can include using a die and stamper, single impact extrusion, double impact extrusion, and progressive deep draw process.

Abstract: An apparatus for extruding teeth in a blank includes a press that includes a lower die plate for supporting the blank thereon, and upper die plate that moves along an axis relative to the lower die plate. A mandrel, aligned with the axis, moves with the upper die plate along the axis, and includes die teeth which form gear teeth to net shape by back extrusion. An impingement ring, located between the upper die plate and the blank, has an opening that allows the die teeth of the mandrel to contact the blank, and includes a stinger that forces material of the blank toward the axis during the forming cycle.

Abstract: An apparatus for extruding helical teeth in a gear blank includes a press including a die plate and a die base, the die plate being movable along an axis relative to the die base, the die base supporting the gear blank. A mandrel, aligned with the axis and moveable with the die plate along the axis, includes a surface that includes helical die teeth. A servo motor drives the mandrel in rotation about the axis to the required helix angle as the mandrel moves axially relative to the gear blank.

Abstract: An apparatus for extruding teeth in a blank includes a press that includes a lower die plate for supporting the blank thereon, and upper die plate that moves along an axis relative to the lower die plate. A mandrel, aligned with the axis, moves with the upper die plate along the axis, and includes die teeth which form gear teeth to net shape by back extrusion. An impingement ring, located between the upper die plate and the blank, has an opening that allows the die teeth of the mandrel to contact the blank, and includes a stinger that forces material of the blank toward the axis during the forming cycle.

Abstract: A process operating a forging mold for manufacturing a towing bar involves having a softened aluminum material after preheating in a mold; the mold contains a molding cavity; one end of the cavity is provided with a contour of a gooseneck of the towing bar and another end is provided with a contour of a middle section of a shank of the towing bar; the mode is then incorporated with an extension mold containing an extension hole for molding an extended section of the shank of the towing bar; a punch performs forging process on the aluminum material in the cavity externally from the extension hole; and the aluminum material is extruded by the punch to extend for a preset length in the direction towards the extension mold to complete the molding of the towing bar.

Abstract: An aerosol can fabrication process comprises the following steps: formation of slugs from an aluminium-based alloy having the following composition, in weight percentage: Si 0.35-0.45 Mg 0.25-0.40 Mn 0.05-0.15 Fe 0.12-0.20 Total of minor elements ?0.15% Al Balance. thermal treatment of the slugs, forced cooling of the slugs, cold impact extrusion of a slug so as to form a can, applying a lacquer inside the can.

Abstract: The invention relates to a device for correcting a profile bevel error, in particular the tooth alignment error of the gear (V) of a workpiece (W), wherein said device (1) comprises a clamping device (3) for the workpiece (W), a tool (4) and at least one advancing device (7, 7?) generating the relative movement between the workpiece (W) and the tool (4). The inventive device is characterised in that it comprises a guide device (10, 10?) for the tool (4) and/or for the clamping device (3) which enables to carry out the rotating movement of the tool (4) and/or clamping device around the workpiece (W) axis (X) extending in an advance direction, wherein said rotating movement acts as a compensating movement.

Abstract: A method of forming an article such as a helical gear and an apparatus for forming the article are provided. The method includes applying pulsating pressure downward to extruding the work piece and, while the pressure is applied downward, injecting fluid to surround the work piece in fluid. The method eliminates pickling processes and phosphate lube coatings typically required for extrusion and external machining steps subsequently required to remove the coating. Extrusion of a cold net-formed article is thus possible due. An apparatus for carrying out the method is also provided.

Abstract: The invention relates to manufacture of a cup (1) that is designed to serve as a blank in the production of a metal shell (2) by providing a body (3) of a bar material, placing the body (3) in a counterdie (6) in which a first end surface of the body (3), which is substantially perpendicular to the central axis (C) of the body, is placed facing towards the bottom of the counterdie while the inner wall of the counterdie (6) encloses at least a part of the body and preferably the whole body, so that the body (3) is hereby placed in the counterdie (6), applying a mandrel (9) to a second end surface of the body that is substantially perpendicular to the central axis C of the body (3), applying a pressing force to the mandrel (9) so that the body (3) is cold flow pressed through plastic deformation into a cup (1). The invention also relates to an application of a body for manufacture of a blank for a grenade/cartridge shell and a process for manufacture of a grenade/cartridge shell.

Abstract: It is an object of the present invention to provide a novel aluminum tube of an oval cross section that has a wider range of applications and added values. A disk-shaped metal slug (21) is impact-extruded with the use of a die (14) and a punch (13) each having an optimally designed structure to form a metal tube (T) integrally including a mouth, a shoulder and a body of an oval cross section. A hem portion of the oval body of the tube (T) thus formed and hardened by the impact extrusion is once deformed into a circular shape, and then trimmed off by a turning operation.

Abstract: An impact extrusion molded article that is molded while the metal-flow from a bottom of a slug set in a dice toward the side of the molded product article is suppressed; an impact extrusion molding method for manufacturing the impact extrusion molded article, and an impact extrusion molding apparatus used for the impact extrusion molding method, are provided.

Abstract: A method for forging/molding a coarse blank of an oil cylinder, including steps of: placing burn-in softened aluminum material into a preheated mold; using a first punch head to first forge the aluminum material in the mold cavity from outer side of the molding hole so as to form a blank body of the oil cylinder with a first end cap, a second end cap and a shorter cylinder body; moving out the first punch head and connecting an extension mold with the mold; and immediately using a second punch head to secondarily forge the blank body in the mold cavity from outer side of the extension hole and making the end section of the second punch head extend into the mold cavity to a position near the inner end of the mold cavity, whereby the cylinder body of the blank body outward axially extends to the extension mold into a predetermined length so as to form the oil cylinder.

Abstract: Lightweight metal containers are formed from high-strength metal alloys by impact extrusion of a cup-shaped container having a substantially larger diameter than the finished container, drawing and wall ironing the extruded container to reduce its diameter and wall thickness while increasing the height of the container to the appropriate diameter, wall thickness and height.

Abstract: A method of forging a trailer receiver tube by providing a die having an inner surface defining a first portion and a second portion. Providing a hollow tube having an outer surface. Providing a punch having a body and a shaft extending therefrom sized to fit within the hollow tube. Loading the hollow tube within the first portion of the die. Inserting the punch into the hollow tube such that the body abuts an end of the hollow tube and the shaft extends therethrough. Advancing the punch and the hollow tube through the die such that a portion of the hollow tube is extruded into the second portion of the die and the outer surface of the hollow tube conforms to the inner surface of the die to thereby form the trailer receiver tube.

Abstract: A process for shaping a high strength container, particularly an aerosol container and a container obtained through such process. Generally, aerosol containers made of aluminum or tin are obtained by conventional embedding processes from sheet disks and have cylindrical bodies with upper tapering finishing at a curl for fixing a valve cover and are closed by convex and profiled cross section bottoms, for forming a support region for upstanding the container. The bottom of such containers is obtained before tapering by means of a blow or front shock once the cylindrical body having planar circular base is shaped, this impact causing undesirable stresses on the body side wall and material accumulation at the annular region joining with this wall since the bottom thickness is not uniform.

Abstract: A method of producing a glow plug including a glow tube (5) with internal heating coil (4) and optionally regulating coils which are embedded therein using a ceramic filling, whereby a compaction of an area on a combustion chamber side of the glow tube (5) is performed using a recessing-reducing process with a radial feed.

Abstract: A method for attaching an additional object to a resonator body. The method includes the steps of (1) placing the additional object in a recess of a pushing part of an extrusion machine; (2) pressing the pushing part against a bloom of a resonator body; and (3) pulling the pushing part back from the resulting resonator body. The attaching of the additional object occurs in conjunction with the extrusion process.

Abstract: A heat dissipation system and method for extracting heat from an integrated circuit device includes a thermally conductive base having substantially planar upper and lower surfaces, the upper surface is disposed across from the lower surface, and the lower surface is adapted to contact an integrated circuit device. A conductive heat exchange portion including an array of fins extends angularly away from the upper surface of the base. The array has a chamber within to house an air movement device so that the air introduced by the air movement device creates a swirling air movement over the heat exchange portion to increase air movement around the heat exchange portion to enhance the heat extraction from the heat exchange portion.

Abstract: A method for integrally forming and manufacturing an one-piece forged hollow crank of a bicycle includes the following steps: (a) forging and molding a leading edge of a crank; (b) extruding a crank body; (c) forging and possibly sealing a rear end of the crank body; and (d) cutting and piercing the rear end of the crank body so as to form a hollow crank of a bicycle. In such a manner, the hollow crank can be integrally forged and molded quickly by fewer manufacturing steps than that of the conventional method. In addition, the product surface of the hollow crank is finished to have a fine and pretty appearance so that it is not easy to produce a defective product, thereby enhancing the aesthetics and quality and saving the manufacturing cost of hollow crank. Further, better aluminum alloys can be used with this method than can be used with the prior art casting or welding methods.

Abstract: The present invention comprises aluminum solid rivets and methods of manufacturing aluminum solid rivets for aircraft and other demanding applications to provide rivets with high strength and excellent driveabiltity while improving the rivets resistance to fatigue and stress corrosion cracking. In accordance with the method, an aluminum rivet blank approximately the same diameter as the head of the finished rivet is used. This rivet blank is forced into a die to extrude the tapered region and the shank of the finished rivet. The fabrication process provides more uniform cold working at the junction of the shank and the tapered region of the rivet, and better orients the flow lines in this region. The process also can provide a superior surface finish, and may be suitable for use in wet wing fabrication without further processing for improved surface finish. Alternate embodiments are disclosed.

Abstract: A molding tool is designed to make a cooling device and is formed of a lower mold, a lower mold housing, a punching head, and an urging plate. The lower mold is provided with a plurality of through holes. The lower housing is provided with a molding hole and is fixed on the lower mold such that the molding hole is corresponding in location to the through holes of the lower mold. The punching head is fastened with the bottom of the upper mold seat of a punching machine and is provided with a plurality of cavities and ribbed slots. The urging plate is provided with an opening and is disposed under the upper mold seat of the punching machine such that the punching head is put through the opening. The urging plate is further provided with an insertion slot extending along the edge of the opening.

Abstract: A method of manufacturing a hose coupling from an intermediate blank material, the hose coupling having an inner tube or tubular nipple portion, an outer tube or tubular sleeve portion and a head portion, all formed by plastic deformation from an intermediate blank material. The head portion is provided with a bore at an end opposite the end where the nipple portion and the sleeve portion are joined. In addition, the head portion is internally provided with a female thread and a conical seal portion.

Abstract: The invention relates to a filter and a method for manufacturing a filter. The filter comprises a shell construction with a wall construction and a bottom portion, which form at least one section in the shell construction. The filter further comprises at least one resonator within a section of the shell construction. At least the bottom portion of the shell construction and one or more resonators, or at least the part thereof close to the bottom portion of the shell construction, are an integral unit extruded from the same basic block in one piece.

Abstract: A method is provided, which comprises the following steps: Firstly, a profiled material of aluminum is prepared. Then, a profiled piece of predetermined length is produced by cutting the profiled material to length. This profiled piece is then inserted into a press. Finally, the profiled piece is pressed into the desired shape in the press. Further, a shaped part is provided, which consists of cold-worked aluminum.

Abstract: A metalworking method, particularly for obtaining lengths of tube of various sizes and for various uses, made of steel having a carbon content between 0.10% and 0.50% with narrow tolerances. The method entails the provision, as initial material, of a round bar of hot-rolled steel, which is then peeled and cut so as to obtain at least one block, which is drilled and subjected to a chemical treatment. The block is then pressed and optionally subjected to final turning and heat treatment so as to obtain a finished product, such as a hydraulic or oleodynamic cylinder or a casing for high-pressure filters or a tube for high pressures, or a bushing, by using a reduced amount of steel.

Abstract: A handlebar stem fabrication method includes the steps of (a) selecting a metal ingot subject to the cavity of a first forming die and then operating the first forming die to process the selected metal ingot into an embryonic form having a front end section, (b) operating a second forming die to process the embryonic form into an initially processed form having a middle body section integral with the front end section, (c) operating a third forming die to processing the initially processed form into a secondarily processed form having a hollow rear end with a closed bottom wall and a rear end lug raised from the periphery of the hollow rear end, and (d) processing the secondarily processed form a finished handlebar stem by: cutting the closed bottom wall away from the hollow rear end of the secondarily processed form, making a split at the hollow rear end of the secondarily processed form to separate the rear end lug into two separated lugs, and then drilling two vertically spaced mounting holes at the two se

Abstract: A method of forming integrally an axis on a metallic plate at an arbitrary position thereof and perpendicular to a surface thereof. A first surface of the metallic plate is place on a first die having a first diameter opening and a second surface of the metallic plate, opposing the first surface, is pressed with a first punch to form a projection from the first surface via half blanking or forward squeezing. The projection has a tip surface extending into the first diameter opening a first distance from the first surface. The first surface of the metallic plate is then placed on a second die having a depression with the projection extending into the depression. The depression has a second diameter and a depth distance greater than the first distance. The second surface of the metallic plate is then contacted with a second punch causing the tip surface of the projection to contact a bottom surface of the depression and form the axial projection via rear-squeezing.

Abstract: A method of forming a closed-end vessel by backward extrusion comprises providing an extrusion billet having a front surface with an axial recess and a body of an extrudable material positioned in the recess. Backward extrusion results in the formation of a closed-ended vessel, for example a pressurized gas cylinder, composed of the material of the extrusion billet with a weld bonded inner surface lining of the extrudable material.

Abstract: A process and apparatus for cold extruding gear teeth and projections comprises machining an annular ring gear blank with precision inside and outside diameters. The gear blank is mounted on a die ring which is arranged coaxially with respect to the blank. The die ring has internal die teeth. A mandrel having external die teeth is axially aligned with the gear blank. The mandrel or die ring is moved axially to extrude the blank through the internal and external die teeth.

Abstract: An apparatus for forming an extruded cylindrical closed-ended metal tube having a flat end wall and an integrally formed projection on the end wall includes a die having a recess formed therein, the die having a configuration which corresponds to the terminal end portion of the desired tube and including a cavity which corresponds to the desired projection. The apparatus further includes a punch which is receivable in the die, and includes an end wall having a peripheral portion which extends angularly outwardly at an angle of between approximately 10.degree. and 20.degree. relative to a plane which is perpendicular to the longitudinal axis of the die. The apparatus is operative by placing an extrudable metal disc in the recess in the die and advancing the punch into the recess with sufficient force to extrude metal from the disc into the cavity and also between the punch and the die to form the desired tube.

Abstract: An apparatus for forming an extruded cylindrical closed-ended metal tube having a flat end wall and an integrally formed projection on the end wall includes a die having a recess formed therein, the die having a configuration which corresponds to the terminal end portion of the desired tube and including a cavity which corresponds to the desired projection. The apparatus further includes a punch which is receivable in the die, and includes an end wall having a peripheral portion which extends angularly outwardly at an angle of between approximately 10.degree. and 20.degree. relative to a plane which is perpendicular to the longitudinal axis of the die. The apparatus is operative by placing an extrudable metal disc in the recess in the die and advancing the punch into the recess with sufficient force to extrude metal from the disc into the cavity and also between the punch and the die to form the desired tube.

Abstract: A extrusion die assembly for cold extruding internally and/or externally toothed gears and the like, particularly internally toothed ring gears, with the mandrel for forming the internal teeth in the workpiece including axially successive sets of die teeth, with each set including a full complement of annularly arranged and equally spaced die teeth, and the die teeth from the leading set to the trailing set increasing progressively in diameter.In one embodiment, the die teeth from one set to the next on the mandrel extrude the gear teeth in equal radial depth, and in a second embodiment, the die teeth of each succeeding mandrel set extrude the gear teeth by displacing an equal volume of material from one set to the next.

Abstract: A lower die having a first recess corresponding to one of outer shapes of the element, and an upper die having a second recess are provided. The outer diameter of the upper dies is smaller than the inner diameter of the first recess so that a gap is formed between the inside wall of the first recess and the outside wall of the upper die. A workpiece is put between the lower and upper dies, and the upper die is pressed against the lower die to form the element.

Abstract: An enclosed pump motor includes an aluminum housing made by an impact extrusion process. The housing is cylindrical having an integrally-formed closed end with integral fastener bosses for attaching a pump thereto and an integrally-formed thickened cylindrical portion defining a shaft bore for receiving the motor shaft therethrough. At the other end, the cylindrical housing is open for receiving the motor therein. A motor cover is attached to the motor receiving end of the housing by crimping or bending a part of the housing into indents formed in the housing. The motor cover includes a threaded bore adapted to receive a threaded grommet wherein three connector pins are imbedded. The connector pins are connected to electrical power carrying conductors and/or switch conductors leading to a fluid level sensor switch. The conductor-to-pin connections are imbedded within the grommet and are hermetically sealed therein.

Abstract: An aluminum tube manufacturing device is provided that includes a female die having an internal shape identical with an external shape of an upper part of an aluminum tube to be formed thereby, including a mouth portion, a shoulder portion and a portion of a drum part of the tube. A punch having an external shape identical with the internal shape of the upper part of the tube that is to be formed forcibly extrudes the aluminum tube by applying pressure to a ring-shaped element of aluminum material loaded in the female die. A corner portion of the female die which joins the shoulder portion with the drum portion in the internal shape of the female die is formed as a smooth arc, and the punch is formed to have a maximum diameter portion thereof approaching a vertical internal surface of the drum portion below the arc-shaped corner portion of the female die when the punch is being pressed into the female die.

Abstract: A method for forming in a single step metal slugs of tantalum, niobium or a base alloy of one of these metals, by cold pressing. A lubricant film is either an oxide coating on the metal, into which a polytetrafluorethylene of low molecular weight is embedded, or it is a film of chlorotrifluorethylene. A metal slug is shaped by means of a hard-metal punch with a crowned bottom surface on its punch head and a rounded undercut in the area of the transition from the punch head to the punch shank.

Abstract: A process is described for producing forged ring articles from high strength, high temperature materials such as superalloys and titanium alloys. The material to be forged is conditioned and placed into a condition of low strength and high ductility. This starting material is then back extruded to produce a cup. The cup can be sliced into rings in which can thereafter be final forged to a particular contour.

Abstract: An integral manifold for a heat exchanger is formed from a hollow shape having a plurality of individual risers, initially having substantially solid cross-sections and subsequently reshaped by means of a reverse impact extrusion process into hollow risers. The walls of the hollow shape under the hollow risers are perforated, thus forming apertures constituting inlets connecting the cavity of the hollow shape with the individual hollow risers.

Abstract: A waveguide filter (43) comprising a series of resonant cavities (45) separated by walls (47) each formed with an iris opening (49) is assembled from two complementary box-like bodies (25) each having an open side (31) and internal partitions forming portions of the walls (47) between the cavities. Each box-like body is manufactured by impact extrusion using an open-topped box-like die (1) in which a slug of material (5) is placed, and a punch (7) which has smaller dimensions than the die and slots (11) for forming the respective partitions. The punch is driven into the die with a force such that the material of the slug is displaced into the slots in the punch and into the space between the punch and the die.

Abstract: Gears are formed from annular blanks in a gear-forming apparatus including a die block formed with an axial bore and teeth radially projecting into the bore, a cylindrical punch sleeve axially movable toward and away from the bore in the die block, a mandrel movable with the punch sleeve into and out of the bore in the die block, and a backup sleeve axially movable into and out of the bore in the die block in opposite directions to the directions of movement of the sleeve punch and mandrel, wherein gears are formed by preliminarily forcing at least one of the blanks into the bore in the die block until the blank is partially deformed by the teeth of the die block; placing another blank on the preceding blank so that the subsequent blank is received on the preceding blank; causing the mandrel to extend through the respective center holes in the preceding and subsequent blanks; pressing the preceding and subsequent blanks between the end faces of the punch and backup sleeve and forcing the two blanks through th

Abstract: A method of making a male resistance welding electrode includes a forward extrusion step in which the shank portion of the electrode is partially formed by extruding a cut-off billet of dispersion strengthened copper over a pin in a first die. Subsequently, the preform billet produced in the first die is inserted into a second die which defines a tapered shank cavity region around a central pin and a larger cavity region from which the head portion of the electrode is ultimately formed. The shank portion of the electrode is formed and the head portion worked substantially by the application of pressure to the preform billet by a first forming member. Final forming occurs when a second forming member applies pressure to the head of the electrode while the electrode remains in the second die.

Abstract: A piercing mandrel or punch, particularly for backward extrusion, is guided by a member which centers the mandrel or punch in the upper die cavity and is coupled thereto until abutting a centering shoulder in the die cavity; the guiding and centering function continues as the mandrel or punch begins and progresses in the cold flow-working process.

Abstract: An extrusion punch, especially for use in a back extrusion process, wherein a hard wear resistant material is joined on one end to a steel punch body. The hard wear resistant material is joined on at the tip of a steel body so as to prevent wear due to abrasion on the punch caused by the material being extruded in a die means. The hard wear resistant end cap on the tip of the steel body is joined so that it may easily and quickly be replaced when the punch is in position on the machine thereby providing less down time for maintenance on the extrusion press. The method of joining the hard wear resistant end cap to the steel body minimizes the conditions which tend to fracture hard wear resistant material.

Abstract: A thin-walled metal tube includes a tubular nipple section, a shoulder section joined to the nipple section, a tubular barrel section and a border section connecting the shoulder and barrel sections, the barrel section being defined by a wall having a thickness in the range of between about 20 microns and about 70 microns. The border section includes a region which changes in thickness, the wall thickness of the border section being greater than the thickness of the wall defining the barrel section and the thickness changing region having a cross-section having either an arcuate or a tapered region.