Apparatus for adding a liquid reducing agent to the exhaust gas from an internal combustion engine and motor vehicle

Abstract

The present disclosure relates to an apparatus for adding a liquid reducing agent, preferably an aqueous urea solution, to the exhaust gas from an internal combustion engine. The apparatus according to the present disclosure comprises a dosing device arranged in an exhaust line of the internal combustion engine, which device is designed to generate a reducing agent spray by means of an injector. The apparatus furthermore comprises a swirl generator device, designed as a hollow body, preferably a hollow cylinder, about a longitudinal axis, which has a first end facing the injector and a second end facing away from the injector. The shell surface L of the swirl generator device, designed as a hollow body, furthermore comprises at least one exhaust inlet opening extending substantially in the longitudinal direction and a guide element, attached adjacent to the exhaust inlet opening and covering the exhaust inlet opening in the interior of the swirl generator device, at least in part at a distance, for deflecting an exhaust gas flow. According to the present disclosure, the guide element is closed in the direction of the first end of the swirl generator device, by means of a wall or connection to the shell surface, for example, and open in the direction of the second end of the swirl generator device. The present disclosure furthermore relates to a motor vehicle, preferably a utility vehicle, having a corresponding apparatus.

Claims

1. An apparatus for admixing a liquid reducing agent to the exhaust gas of an internal combustion engine, comprising a) a metering device which is arranged in an exhaust-gas tract of the internal combustion engine and which is configured to generate a reducing agent spray jet by means of an injector, b) a swirl generating device which is in the form of a hollow body about a longitudinal axis and which has a first end facing toward the injector and a second end averted from the injector, wherein the lateral surface of the swirl generating device comprises at least b1) one exhaust-gas inlet opening extending substantially in a longitudinal direction, and b2) one guide element which is fitted adjacent to the exhaust-gas inlet opening and which at least partially covers the exhaust-gas inlet opening in a spaced-apart manner in the interior of the swirl generating device and which serves for diverting an exhaust-gas flow, wherein the guide element is closed in the direction of the first end of the swirl generating device and is open in the direction of the second end of the swirl generating device.

2. The apparatus as claimed in claim 1, wherein the guide element is connected to the lateral surface along a longitudinal edge and a transverse edge, facing toward the first end of the swirl generating device, of the exhaust-gas inlet opening, in order to thus, when the exhaust-gas flow enters the interior of the swirl generating device through the exhaust-gas inlet opening, generate there an exhaust-gas flow which is directed substantially tangentially and/or in the direction of the second end of the swirl generating device.

3. The apparatus as claimed in claim 1, wherein the guide element comprises the following regions: a) a first wall region which at least partially covers the exhaust-gas inlet opening in a spaced-apart manner, and b) a second wall region which connects the first wall region to the lateral surface in the direction of the first end of the swirl generating device and thus closes the guide element in that direction.

4. The apparatus as claimed in claim 3, wherein the second wall region a) has a curvature and/or b) adjoins the first wall region at an angle not equal to 90°.

5. The apparatus as claimed in claim 3, wherein the first wall region a) has a first longitudinal portion facing toward the injector and b) has a second longitudinal portion averted from the injector, wherein the first longitudinal portion has a greater spacing to the longitudinal axis of the swirl generating device in a radial direction.

6. The apparatus as claimed in claim 5, wherein a length, measured in a longitudinal direction, of the first longitudinal portion is shorter than a length, measured in a longitudinal direction, of the second longitudinal portion.

7. The apparatus as claimed in claim 5, wherein the guide element comprises, between the first and second longitudinal portions, a) two or more steps and/or b) further longitudinal portions which have a spacing to the longitudinal axis of the swirl generating device in a radial direction, which spacing differs from the spacing of the first and second longitudinal portions.

8. The apparatus as claimed in claim 3, wherein the first wall region comprises a) a curved first transverse portion, which is connected to the lateral surface, and b) a substantially straight second transverse portion which adjoins the first transverse portion.

9. The apparatus as claimed in claim 8, wherein the curved first transverse portion is integrally formed on an edge region of the exhaust-gas inlet opening.

10. The apparatus as claimed in claim 8, wherein the second transverse portion of the guide element encloses an angle of between −10° and 30° with a tangent to the lateral surface which runs through a point of the exhaust-gas inlet opening belonging to the guide element and a plane perpendicular to the longitudinal direction.

11. The apparatus as claimed in claim 1, wherein a) the guide element covers the exhaust-gas inlet opening in a radial direction such that, from the longitudinal axis of the swirl generating device, there is no direct line of sight outward in a radial direction through the exhaust-gas inlet opening, and/or b) in that a width, measured in a circumferential direction, of the guide element is greater than a width, measured in a circumferential direction, of the associated exhaust-gas inlet opening, such that the guide element projects beyond the exhaust-gas inlet opening in a circumferential direction.

12. The apparatus as claimed in claim 1, further comprising a protective device which is arranged in the region of the injector and which is in the form of a hollow body and which serves for reducing an exhaust-gas flow in the region of the reducing agent spray jet, the lateral surface of which protective device has a perforation formed preferably from circular holes.

13. The apparatus as claimed in claim 12, wherein the hollow body of the protective device is in the form of a frustum.

14. The apparatus as claimed in claim 1, further comprising a) an inner pipe which adjoins the second end of the swirl generating device, b) an outer pipe which surrounds the inner pipe, and c) at least one flow resistance which is arranged between the inner and outer pipes and which serves for regulating the exhaust-gas throughflow in the region between the inner and outer pipes.

15. The apparatus as claimed in claim 14, wherein a) the inner pipe has a circular cross section, and/or b) the outer pipe has a circular cross section.

16. The apparatus as claimed in claim 14, wherein the flow resistance is formed a) by a reduction in size of the line cross section between the inner and outer pipes by a constriction of the outer pipe, and/or b) by an annular multi-hole aperture.

17. The apparatus as claimed in claim 14, wherein a) the outer pipe has a longer extent in an axial direction than the inner pipe, and b) has a constriction in a region in which the outer pipe does not surround the inner pipe.

18. The apparatus as claimed in claim 1, wherein the liquid reducing agent is an aqueous urea solution.

19. A motor vehicle having an internal combustion engine and an apparatus for admixing a liquid reducing agent to an exhaust gas of the internal combustion engine as claimed in claim 1.

20. The motor vehicle of claim 19 wherein a) the motor vehicle is a utility vehicle, and/or b) the internal combustion engine is a diesel internal combustion engine, and/or the liquid reducing agent is an aqueous urea solution.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Here, the above-describe aspects and features of the present disclosure may be combined with one another in any desired manner. Further details and advantages of the present disclosure will be described below with reference to the appended drawings, in which:

(2) FIG. 1: is a schematic illustration of an exhaust-gas tract of an internal combustion engine having an apparatus for admixing a liquid reducing agent to the exhaust gas according to an embodiment of the present disclosure;

(3) FIG. 2: is a 3D illustration of a swirl generating device according to an embodiment of the present disclosure;

(4) FIG. 3: is a 3D sectional illustration of a swirl generating device according to a second embodiment of the present disclosure;

(5) FIG. 4: shows a longitudinal section through the second embodiment of the swirl generating device illustrated in FIG. 3;

(6) FIG. 5: shows in each case one partial cross section through the swirl generating device in a plane perpendicular to the longitudinal axis, according to two embodiments of the present disclosure;

(7) FIG. 6: is a schematic illustration of an exhaust-gas tract of an internal combustion engine having an apparatus for admixing a liquid reducing agent to the exhaust gas according to a further embodiment of the present disclosure;

(8) FIG. 7: is an exploded illustration of the apparatus illustrated in FIG. 6; and

(9) FIG. 8: is a schematic illustration of a motor vehicle according to an embodiment of the present disclosure.

DETAILED DESCRIPTION

(10) FIG. 1 is a schematic illustration of an exhaust-gas tract 2, that is to say exhaust-gas-conducting parts, of an internal combustion engine 1 which is not illustrated in any more detail here, preferably a diesel internal combustion engine. In the present case, the exhaust-gas tract 2 has an SCR catalytic converter 12 and an apparatus 100 according to the present disclosure for admixing a liquid reducing agent to the exhaust gas of the internal combustion engine 1, which apparatus is arranged in the exhaust-gas tract 2 in front, that is to say upstream, of the SCR catalytic converter 12. The liquid reducing agent may in this case be, for example, an aqueous urea solution which is hydrolyzed and converted into ammonia in the exhaust-gas tract, which ammonia is then fed together with the exhaust gas to the SCR catalytic converter 12.

(11) Here, the apparatus 100 comprises a metering device 3 which is configured to generate a reducing agent spray jet by means of an injector 4, for example a single spray nozzle or a multi-aperture nozzle. It is preferable here for a rotationally symmetrical, for example conical spray jet to be generated. Furthermore, the apparatus 100 comprises a swirl generating device 20 which is formed as a hollow cylinder about a longitudinal axis L and which has a first end 20a facing toward the injector 4 and a second end 20b averted from the injector 4. Preferably, the swirl generating device 20 is in this case positioned downstream of the injector 4 such that the longitudinal axis L of the swirl generating device 20 coincides with the axis of rotation of the rotationally symmetrical reducing agent spray jet generated by the injector 4. Furthermore, the injector 4 may also be arranged within the swirl generating device 20, particularly preferably in a region of the first end 20a of the swirl generating device 20.

(12) By means of the present apparatus 100—specifically by means of the embodiment of the swirl generating device 20 described in more detail below—it is possible in the interior of the swirl generating device 20 for a homogeneous exhaust-gas flow to be generated which is directed as far as possible tangentially and/or in the direction of the second end 20b of the swirl generating device 20, which exhaust-gas flow advantageously permits the most homogeneous possible mixing of reducing agent and exhaust gas. For this purpose, the swirl generating device 20 is closed at its first end 20a by means of a wall which has only one opening for the injection of the reducing agent spray jet for the injector 4. At its second end 20b, the swirl generating device 20 opens into a connecting pipe 13 which leads to the SCR catalytic converter 12. Furthermore, the lateral surface of the swirl generating device 20 comprises multiple uniformly circumferentially distributed exhaust-gas inlet openings 22 which extend substantially in a longitudinal direction. The lateral surface—also referred to as shell or shell wall—can in this case be understood to mean the entire region of the hollow body that is situated between the inner and outer surface. Via the exhaust-gas inlet openings 22, an incident flow of exhaust gas from the internal combustion engine 1 can enter the interior of the swirl generating device 20 and flow from there via the connecting pipe 13 to the SCR catalytic converter 12.

(13) In order to generate the abovementioned advantageous flow conditions when the exhaust-gas flow enters the swirl generating device 20, the swirl generating device 20 comprises guide elements 23 which are fitted adjacent to each exhaust-gas inlet opening 22 and which serves for diverting the exhaust-gas flow. Said guide elements 23 are illustrated, together with the entire swirl generating device 20, according to one embodiment of the present disclosure in a 3D illustration in FIG. 2. In the present case, the hollow cylindrical swirl generating device 20 has a number of fourteen uniformly circumferentially distributed rectangular exhaust-gas inlet openings 22 extending substantially in a longitudinal direction, and, adjacent to these, guide elements 23 which are fastened on two sides and which virtually completely cover or roof the exhaust-gas inlet openings 22 in a spaced-apart manner in the interior of the swirl generating device 20. Here, the guide elements 23 are closed by means of a connection to the lateral surface 21 in each case in the direction of the first end 20a of the swirl generating device 20, that is to say in the direction of the injector 4, and along a longitudinal edge of the exhaust-gas inlet openings 22. Along the other longitudinal edge of the exhaust-gas inlet openings 22, and in the direction of the second end 20b of the swirl generating device 20, the guide elements 23 are however open. Here, the expression “open” can be understood to mean that the end sides of the guide plate 23 are not connected to the lateral surface 21 in these directions. Correspondingly, in this context, the guide element 23 can also be referred to as a roof which is fastened on two sides and/or as a hood which is open on two sides. In other words, the guide element may thus be closed in an upstream direction and open in a downstream direction in relation to the exhaust-gas flow direction.

(14) By means of this embodiment according to the disclosure of the guide elements 23, and in interaction with the respective exhaust-gas inlet openings 22, it is thus advantageously the case that, when the exhaust-gas flow enters through the exhaust-gas inlet opening 22 into the interior of the swirl generating device 20, a homogeneous exhaust-gas flow which is directed substantially tangentially and/or in the direction of the second end 20b of the swirl generating device 20 is generated, which is as far as possible uninfluenced by the external incident flow of exhaust gas and/or the operating point of the internal combustion engine 1. This advantageously promotes the mixing of exhaust gas and reducing agent, prevents reducing agent deposits, and furthermore ensures substantially symmetrically acting flow forces on the propagating reducing agent. Here, it is evident to a person skilled in the art that the swirl generating device 20 may self-evidently have more or fewer such functionally interacting units composed of exhaust-gas inlet opening 22 and guide element 23, without departing from the scope of the present disclosure.

(15) FIG. 3 is a 3D sectional illustration of a swirl generating device 20 according to a second embodiment of the present disclosure. Here, too, the swirl generating device 20 is again in the form of a hollow cylinder with uniformly circumferentially distributed rectangular exhaust-gas inlet openings 22 extending substantially in a longitudinal direction. In the present case, by contrast to the variant shown in FIG. 2, the guide elements 23 which cover the exhaust-gas inlet openings 22 in a spaced-apart manner in the interior of the swirl generating device 20 are however stepped. This means that the respective guide elements 23 have in each case one first longitudinal portion 23a.sub.1 facing toward the injector 4 and one second longitudinal portion 23a.sub.2 averted from the injector 4, wherein the first longitudinal portion 23a.sub.1 has in each case a greater spacing to the longitudinal axis L of the swirl generating device 20 in a radial direction than the second longitudinal portion 23a.sub.2. This embodiment will be illustrated once again by the longitudinal section, shown in FIG. 4, of the second embodiment of the swirl generating device 20.

(16) Here, r.sub.1 denotes the radial spacing of the first longitudinal portion 23a.sub.1, and r.sub.2 denotes the radial spacing of the second longitudinal portion 23a.sub.2, to the longitudinal axis L. The advantage of the greater radial spacing r.sub.1 of the first longitudinal portion 23a.sub.1 lies here in the fact that, in this way, in the region of the first end 20a of the swirl generating device 20, and thus in the vicinity of the injector 4, it is possible to avoid high swirl or centrifuging forces on the reducing agent spray jet, and thus the risk of reducing agent deposits can be reduced. Furthermore, FIG. 4 shows that the transition between the first and second longitudinal portions 23a.sub.1, 23a.sub.2—analogously to the transition 23b between the lateral surface 21 and the first longitudinal portion 23a.sub.1—is realized in the form of a rounded step 24, that is to say without sharp-edged corners. In this way, it is advantageously ensured that, even in the transition region between the first and second wall regions 23a.sub.1, 23a.sub.2, there are no flow-stabilized sinks that could promote undesired deposits of reducing agent. Furthermore, FIG. 4 illustrates that a length l.sub.1, measured in a longitudinal direction, of the first longitudinal portion 23a.sub.1 is shorter than a length l.sub.2, measured in a longitudinal direction, of the second longitudinal portion 23a.sub.2. In the present case, the length l.sub.1 amounts to one third of the length l.sub.2, but it is evident to a person skilled in the art that any other length ratios between l.sub.1 and l.sub.2 may be selected without departing from the scope of the present disclosure. In addition, the guide elements 23 may each also comprise yet further steps, which may be of substantially identical or different form in relation to the illustrated step 24, or further longitudinal portions.

(17) FIG. 5 shows, of two embodiments of the present disclosure, in each case a partial cross section of the swirl generating device 20 in a plane perpendicular to the longitudinal axis L. In both cases, the respective guide elements 23—more specifically the first wall region 23a of the respective guide elements 23—comprise a curved first transverse portion 23a.sub.3, which is connected to the lateral surface 21, and a substantially straight second transverse portion 23a.sub.4, which adjoins the first transverse portion 23a.sub.3 and which covers the exhaust-gas inlet opening 22 in a spaced-apart manner. Here, the embodiments illustrated on the left and on the right differ in terms of the inclination and width of the second transverse portions 23a.sub.4.

(18) Whereas, in the left-hand case, the second transverse portion 23a.sub.4 of the respective guide elements 23 is oriented substantially parallel to a transverse portion of the associated exhaust-gas inlet opening 22, in the right-hand case the second transverse portion 23a.sub.4 is inclined into the interior of the swirl generating device 20, that is to say in the direction of the longitudinal axis L. This inclination can also be quantified in terms of a tangent T to the associated exhaust-gas inlet opening 22. For this purpose, the angle β between the second transverse portion 23a.sub.4 of the guide element 23 and a tangent T to the lateral surface 21 which runs through a point P of the exhaust-gas inlet opening 22 belonging to the guide element 23 in the corresponding cross-sectional plane can be determined. In the left-hand exemplary embodiment, owing to the parallelism, there is an angle β of 0°, whereas, in the right-hand exemplary embodiment, an angle β of +13° is illustrated. Here, a positive angle β may denote an inclination of the second transverse portion 23a.sub.4 in the direction of the longitudinal axis L—that is to say center—of the swirl generating device 20, and a negative angle β may denote an inclination in the direction of the associated exhaust-gas inlet opening 22. In order to advantageously be able to reliably set the tangential component of the exhaust-gas flow that forms in the interior when a flow of exhaust gas is incident on the swirl generating device 20, the angle β may preferably amount to between −10° and +30°.

(19) In addition to the different inclination of the second transverse portions 23a.sub.4 of the guide elements 23, the exemplary embodiments illustrated on the left and on the right furthermore also differ in terms of their width b.sub.L measured in a circumferential direction. Whereas, in the left-hand case, the width b.sub.L of the guide element 23 substantially corresponds to the width b.sub.A, measured in a circumferential direction, of the associated exhaust-gas inlet opening 22, in the right-hand exemplary embodiment the guide element 23 has a greater width b.sub.L than the associated exhaust-gas inlet opening 22. Correspondingly, in the right-hand case, the second transverse portion 23a.sub.4 of the guide elements 23 projects beyond the associated exhaust-gas inlet opening 22 with the overlap Δl. In other words, the respective guide elements 23 may thus not only prevent a direct line of sight in a radial direction from the longitudinal axis L of the swirl generating device 20 to the respectively associated exhaust-gas inlet opening 22 (left-hand case), but may furthermore also cover parts of the lateral surface 21 in a radial direction (right-hand case). Thus, the inflow of exhaust gas in a radial direction is advantageously substantially prevented, which, in the interior of the swirl generating device 20, induces the formation of a homogeneous exhaust-gas flow which is directed substantially tangentially and/or in the direction of the second end 20b of the swirl generating device 20.

(20) FIG. 6 is a schematic illustration of an exhaust-gas tract 2 of an internal combustion engine 1 having an apparatus 100 for admixing a liquid reducing agent to the exhaust gas according to a further embodiment of the present disclosure. By contrast to the case illustrated in FIG. 1, the apparatus 100 here comprises a swirl generating device 20 with stepped guide elements 23, as have been described in detail above with reference to FIGS. 3 and 4. Furthermore, the apparatus 100 comprises a protective device 5 which is arranged in the region of the injector 4 and which is in the form of a perforated frustum and which serves for reducing an exhaust-gas flow in the region of the reducing agent spray jet. Aside from the perforation, shown in the present case, in the form of uniformly circumferentially distributed circular apertures, the openings or apertures of the protective device 5 may alternatively also be elongated apertures. Furthermore, additional guide elements, for example webs, may also be attached to the lateral surface of the protective device 5 without departing from the scope of the present disclosure. Preferably, the protective device 5 is furthermore arranged in the interior of the swirl generating device 20, particular preferably in the interior and in a region of the first end 20a of the swirl generating device 20. Here, the protective device 5 may be positioned downstream of the injector 4 and/or arranged such that the injector 4 can spray the reducing agent spray jet into the interior of the protective device 5. By means of the protective device 5, in the vicinity of the injector 4, an excessive centrifuging action on the reducing agent spray jet can advantageously be prevented, and thus the risk of the formation of reducing agent deposits can be reduced.

(21) As a further difference in relation to the embodiment shown in FIG. 1, the apparatus 100 illustrated in FIG. 6 additionally has a bypass by means of which a fraction of the exhaust-gas flow can be conducted past the swirl generating device 20. In this way, it is advantageously possible for the exhaust-gas flow entering the swirl generating device 20 to be regulated, and for the occurrence of intense centrifuging forces in the interior of the swirl generating device 20, which would impair correct functioning, to be avoided. To form the bypass, the apparatus 100 comprises an inner pipe 6, which adjoins the second end 20b of the swirl generating device 20 and which can also be referred to as mixing pipe, and an outer pipe 7, which surrounds the inner pipe 6 and which has a longer extent in an axial direction than the inner pipe 6. In the present case, both the inner pipe 6 and the outer pipe 7 have a circular cross section, wherein the diameter of the outer pipe 7 decreases over the length thereof in the direction of the end averted from the injector 4. Alternatively, it is however also possible for the inner pipe 6 and outer pipe 7 to have an unchanging diameter or cross section. Altogether, it is thus possible for the incident flow of exhaust gas from the internal combustion engine 1 to pass in the direction of the SCR catalytic converter 12 via two paths. On the one hand, exhaust gas may enter via the exhaust-gas inlet openings 22 into the interior of the swirl generating device 20 and flow from there through the inner pipe 6, alternatively the exhaust gas may also flow past the swirl generating device 20 and subsequently through the region between the outer and inner pipes 6, 7.

(22) In order, here, to regulate the fraction of exhaust gas that flows through the swirl generating device 20 and the fraction of exhaust gas that is conducted past the swirl generating device 20, the apparatus 100 furthermore comprises two flow resistances 8 which are arranged between the inner and outer pipes 6, 7. Here, one of the two flow resistances 8 is formed by the narrowing cross section of the outer pipe 8, and the other flow resistance 8 is formed by an annular multi-aperture plate 9, which can be seen more clearly in the exploded illustration of the embodiment shown in FIG. 7. Aside from the regulation of the exhaust-gas flow that forms in the interior of the swirl generating device 20, the exhaust-gas flow that is conducted between the inner and outer pipes 6, 7 furthermore also homogeneously warms the inner pipe 6, which leads to the evaporation of reducing agent that possibly impinges on the inner pipe 6, and thus likewise prevents deposits of reducing agent. Since the evaporating reducing agent would result in an annularly elevated concentration over the pipe cross section, the outer pipe 7, in order to homogenize the reducing agent distribution, has a nozzle-like constriction 11 in an end region which is averted from the injector 4 and in which the outer pipe 7 does not surround the inner pipe 6. In this way, the reducing agent distribution is again concentrated in the pipe center, whereby a more homogeneous distribution of the reducing agent in the downstream exhaust-gas tract, and in particular upstream at the SCR catalytic converter, is advantageously attained.

(23) FIG. 8 shows a motor vehicle 10 having an internal combustion engine 1, preferably a diesel internal combustion engine, and having an apparatus 100 for admixing a liquid reducing agent to the exhaust gas of the internal combustion engine 1 according to an embodiment of the present disclosure. In the present case, the motor vehicle 10 is a utility vehicle in the form of a heavy goods vehicle. The motor vehicle 10 may furthermore also comprise yet further components (not illustrated in any more detail), including an exhaust-gas tract, an SCR catalytic converter 12, a tank for storing the reducing agent, and corresponding supply lines.

(24) Although the present disclosure has been described with reference to particular exemplary embodiments, it is evident to a person skilled in the art that various modifications may be made, and equivalents used as substitutes, without departing from the scope of the present disclosure. It is consequently the intention for the present disclosure not to be limited to the exemplary embodiments disclosed, but to comprise all exemplary embodiments that fall within the scope of the appended patent claims. In particular, the present disclosure also claims protection for the subject matter and the features of the subclaims independently of the claims to which said subclaims refer back.

LIST OF REFERENCE DESIGNATIONS

(25) 1 Internal combustion engine 2 Exhaust-gas tract 3 Metering device 4 Injector 5 Protective device 6 Inner pipe 7 Outer pipe 8 Flow resistance 9 Multi-aperture plate 10 Motor vehicle 11 Constriction 12 SCR catalytic converter 13 Connecting pipe 20 Swirl generating device 20a First end of the swirl generating device 20b Second end of the swirl generating device 21 Lateral surface 22 Exhaust-gas inlet opening 23 Guide element 23a First wall region of the guide element 23a.sub.1 First longitudinal portion 23a.sub.2 Second longitudinal portion 23a.sub.3 First transverse portion 23a.sub.4 Second transverse portion 23b Second wall region of the guide element 24 Step 100 Apparatus for admixing a liquid reducing agent to the exhaust gas of an internal combustion engine b.sub.A Width of the exhaust-gas inlet opening b.sub.L Width of the guide element l.sub.1 Length of the first longitudinal portion l.sub.2 Length of the second longitudinal portion r.sub.1 Spacing of the first longitudinal portion to the longitudinal axis r.sub.2 Spacing of the second longitudinal portion to the longitudinal axis L Longitudinal axis P Point T Tangent β Angle Δl Overlap