Multi-channel switching valve

Abstract

Multi-channel switching valve (10), comprising: a stator (20) having an end face (21), a dynamic surface (22), and a plurality of passages (26) extending through the stator (20) to fluidly connect the end face (21) and the dynamic surface (22), wherein the plurality of passages (26) include first passages (26a) extending between respective first openings (24a) in the dynamic surface (22) and first ports (28a) in the end face (21), second passages (26b) extending between respective second openings (24b) in the dynamic surface (22) and second ports (28b) in the end face (21), an inlet passage (26c) extending between an inlet opening (25) in the dynamic surface (22) and an inlet port (28c) in the end face (21), and an outlet passage (26d) extending between an outlet opening (29) in the dynamic surface (22) and an outlet port (28d) in the end face (21); and a rotor (30) rotatable with respect to the stator (20) about a rotational axis (31) and having a rotor surface (32) configured to sealingly engage the dynamic surface (22) of the stator (20), wherein the rotor surface (32) comprises a first fluid flow path (34a) for fluidically coupling the inlet opening (25) to selected ones of the first openings (24a) and a second fluid flow path (34b) for fluidically coupling the outlet opening (29) to selected ones of the second openings (24b), wherein the second fluid flow path (34b) has a transfer section (36) and a relief section (38), wherein the transfer section (36) has a proximal end (37b) that merges into the relief section (38) and a distal end (37a),wherein the transmission section (36) is widened from the distal end (37a) to the proximal end (37b) by between approximately 10-75° and the relief section (38) is arranged annularly around the rotation axis (31) by at least 30°.

Description

Field of the invention

[0001] The present invention relates to fluid valves in general and, more particularly, to multi-channel valves used in fluidics and analysis, including liquid chromatography. State of the art

[0002] Selector valves are widely used in various fluidics applications to selectively direct fluid between multiple flow paths. One example is multi-column liquid chromatography, where fluid flow can be selectively directed to and between multiple separation columns to achieve the desired overall chromatographic separation.

[0003] DE 11 2013 004 605 B4 discloses a flow system comprising: a first pressurized reservoir containing a first flow material therein, a second pressurized reservoir containing a second flow material therein, and a rotatable selector valve fluidly connected to the first and second pressurized reservoirs, wherein the rotatable selector valve comprises a valve body comprising a rotor and a stator, wherein the stator comprises a first port for a flow of a first flow material and a second port for a flow of a second flow material, wherein the rotor comprises a radially extending rotor groove for a flow of at least the first flow material and the second flow material, and wherein the rotor comprises a C-shaped drain groove arranged between the first port and the second port,wherein the discharge groove is formed for discharging at least a portion of at least the first flow material and the second flow material to an outside of the valve body.,

[0004] US 2013 / 0 276 520 A1 discloses a valve comprising a stator with fluid openings in a sealing surface and a rotor with a sealing surface in contact with the sealing surface of the stator. The rotor has through-holes extending from the sealing surface to a rear side and establishing fluid communication with a conduit arranged adjacent to the rear side of the rotor. Furthermore, a chromatography device and a method for performing chromatography are disclosed.

[0005] US 2010 / 0 269 936 A1 discloses a channel switching valve. In a preferred embodiment, the channel switching valve comprises a stator having a connecting surface and a body portion having a connecting surface, and the stator and the body portion are detachably fastened to each other at their connecting surfaces by bolts. A protruding / recessed pattern is formed on each of the connecting surfaces, and the protruding / recessed patterns are designed to fit each other. By rotating the stator and the body portion relative to each other, the stroke of a spring is changed between a position in which the stator and the body portion are fastened to each other in a state in which their protruding / recessed patterns fit each other and a position in which the stator and the body portion are fastened to each other in a state in which their protruding / recessed patterns do not fit each other.The spring is held in its compressed state in the body section to push the rotor toward the stator. The pressure force for pressing the rotor against the stator is adjusted by varying the spring stroke.

[0006] An example of a selector valve that can be used in chromatographic applications is described in U.S. Patent No. 9,739,383 B2, assigned to the present assignee and incorporated herein by reference in its entirety. While the valve described in U.S. Patent No. 9,739,383 B2 has been proven effective, in certain applications involving high flow rates (e.g., 200 ml / min), backpressure is generated when using the valve, which can cause problems with instruments and fittings elsewhere in the system.

[0007] It is therefore an object of the present invention to provide a multi-channel switching valve capable of accommodating operating conditions with high fluid flow rates, such as in preparative scale liquid chromatography, while maintaining backpressure values ​​below target thresholds. In some embodiments, the target backpressure threshold is 5 bar (72.5 psi) at a fluid flow rate of 200 ml / min. Brief description of the invention

[0008] With the present invention, fluid flow backpressure values ​​can also be managed under operating conditions with relatively high fluid flow rates through multi-channel breakaway valves. The multi-channel switching valve creates unique flow paths that reduce flow restriction.

[0009] In one embodiment, a multi-channel switching valve comprises a stator having an end face, a dynamic surface, and a plurality of passages extending through the stator to fluidly connect the end face and the dynamic surface. The plurality of passages include first passages extending between respective openings in the dynamic surface and first ports in the end face, second passages extending between respective second openings in the dynamic surface and second ports in the end face, an inlet passage extending between an inlet opening in the dynamic surface and an inlet port in the end face, and an outlet passage extending between an outlet opening in the dynamic surface and an outlet port in the end face.The selector valve further includes a rotor rotatable with respect to the stator about a rotational axis and having a rotor surface configured to sealingly engage the dynamic surface of the stator. The rotor surface includes a first fluid flow path for fluidly coupling the inlet port to selected ones of the first ports and a second fluid flow path for fluidly coupling the outlet port to selected ones of the second ports. The second fluid flow path includes a transfer portion and a relief portion, the transfer portion having a proximal end that transitions into the relief portion and a distal end. The transfer portion is flared from the distal end to the proximal end by between about 10-75°. The relief portion is annularly disposed about the rotational axis by at least 30°.

[0010] In another embodiment, the multi-port selector valve of the present invention comprises a stator having an end face, a central axis, and a substantially opposite dynamic surface including a plurality of first openings arranged in a first circumferential pattern about the central axis and a plurality of second openings arranged in a second circumferential pattern about the central axis. The selector valve further comprises a rotor rotatable with respect to the stator about an axis of rotation coincident with the central axis and having a rotor surface configured to sealingly engage the dynamic surface of the stator. The rotor surface includes a first fluid flow path and a second fluid flow path.The first fluid flow path extends from a center of rotation of the rotor surface to a first end to establish selective fluidic communication with one of the first openings. The second fluid flow path includes a transfer section and a relief section, with the transfer section expanding by between approximately 10-75° from a distal end in fluid communication with one of the second openings to a proximal end. The relief section of the second fluid flow path is arranged annularly around the axis of rotation by at least 30°. A brief description of the drawings Fig. 1 is a perspective view of a multi-port selector valve of the present invention. Fig. 2A is a front exploded perspective view of a multi-port selector valve of the present invention. Fig.Figure 2B is a rear exploded perspective view of a multi-port selector valve of the present invention. Fig. 3 is an illustration of a stator section with a rotor section transparently superimposed over it. Fig. 4 is a cross-sectional view of a stator portion of a multi-port selector valve of the present invention. Fig. 5 is a front view of a stator portion of a multi-port selector valve of the present invention. Fig. 6 is a view of a rotor portion of a multi-port selector valve of the present invention. Fig. Figure 7A is an illustration of a rotor portion of a multi-port selector valve of the present invention. Fig. 7B is a perspective view of a rotor portion of a multi-port selector valve of the present invention. Fig.Figure 8A is a cross-sectional view of a rotor-stator interface of a prior art multi-port selector valve. Fig. Figure 8B is a cross-sectional view of a rotor-stator interface of a multi-port selector valve of the present invention. Fig. 9 is an enlarged cross-sectional view of a stator portion of a multi-port selector valve of the present invention. Fig. Figure 10A is a graph showing the back pressure drop at 200 ml / min at the inlet port. Fig. Figure 10B is a graph showing the back pressure drop at 200 ml / min at the outlet port. Fig. Figure 10C is a graph showing the back pressure drop at 150 ml / min at the inlet port. Fig. Figure 10D is a graph showing the back pressure drop at 150 ml / min at the outlet port. Fig.Figure 10E is a graph showing the back pressure drop at 100 ml / min at the inlet port. Fig. Figure 10F is a graph showing the back pressure drop at 100 ml / min at the outlet port. Fig. Figure 10G is a graph showing the back pressure drop at 50 ml / min at the inlet port. Fig. Figure 10H is a graph showing the back pressure drop at 50 ml / min at the outlet port. Detailed description of the preferred embodiments

[0011] An embodiment of a multi-channel selector valve 10 of the present invention is shown in Fig.1. In an example application, a fluid stream may be directed through the valve 10 to one or more selected output channels, such as one or more chromatographic columns, and then returned to the valve 10 for downstream analysis by, for example, a detector.

[0012] The selector valve 10 comprises a stator 20 which is fixedly secured to the valve body 16 by fastening elements 14. In the perspective exploded view of Fig.2, it can be seen that the rotor 30 in the valve 10 is arranged for rotation by means of the valve shaft extending through the valve body 16 in conjunction with a motor assembly relative to the stator 20. The interrelationships and general functionality of the component parts of the selector valve 10 correspond to those described in U.S. Patent No. 9,739,383. A significant difference in the selector valve 10 of the present invention from the valve described in U.S. Patent No. 9,739,383 is the structure of the dynamic surface 32 of the rotor 30 and its relationship to the dynamic surface 22 of the stator.

[0013] Fig. Figure 3 is a representation of the dynamic surface 22 of the stator with a rotor 30 transparently superimposed thereon. The dashed lines represent features of the rotor 30, which is otherwise Fig. 3 is not further shown. The dynamic surface 22 of the stator comprises first openings 24a to first passages 26a (in Fig. 4) and second openings 24b to second passages 26b (in Fig. 4). First openings 24a may be fluidly connected to a central opening 25 through a first groove 34a in the rotor dynamic surface 32 when the rotor 30 is engaged with the stator 20 in the valve 10. In this embodiment, the rotor 30 is arranged to rotate about a longitudinal axis to provide a selection of one of six flow paths through corresponding ports. The stator dynamic surface 22 and the rotor dynamic surface 32 are the respective surfaces of the stator 20 and the rotor 30 at the stator-rotor interface.

[0014] First openings 24a and second openings 24b on the dynamic surface 22 of the stator may be arranged in concentric rings, as in the illustrated embodiment. However, it is conceivable that other arrangements for the first and second openings 24a, 24b may be incorporated into the selector valve 10 of the present invention.

[0015] In the illustrated embodiment, six first and second openings 24a, 24b are shown, which could therefore serve up to six different chromatographic columns or other treatment equipment.

[0016] As in the Fig. 4 and Fig.5, the stator 20 includes first and second openings 28a, 28b on the stator end face 21. First ports 28a open to the respective first passages 26a, such that the first ports 28a are fluidly connected to the respective first openings 24a via the respective first passages 26a. Likewise, second openings 28b on the end face 21 open into second passages 26b, such that second ports 28b and respective openings 24b are fluidly connected by respective second passages 26b. In the illustrated embodiment, an inlet port 28c opens into an inlet passage 26c to fluidly connect the inlet port 28c to the central opening 25. An outlet port 28d opens into an outlet passage 26d to fluidly connect the outlet port 28d to an outlet opening 29 on the dynamic surface 22 of the stator.In preferred embodiments, the outlet opening 29 may be at least partially contained in a collecting groove 40 in the dynamic surface 22 of the stator.

[0017] When operative rotation of rotor 30 positions first groove 34a to overlie both central opening 25 and a respective one of the first openings 24a on stator dynamic surface 22, fluid flow is enabled via first groove 34a in rotor dynamic surface 32 between central opening 25 and that respective first opening 24a of stator 20. When rotor 30 is rotated to a position where first groove 34a does not overlie one of the first openings 24a, central opening 25 is fluidly decoupled from one of the first openings 24a, thereby ceasing fluid flow.

[0018] Similarly, the second groove 34b of the rotor 30 can be used to fluidly couple the collection groove 40 and the second openings 24b of the stator 20. In some embodiments, the collection groove 40 can be an annular groove formed into the dynamic surface 22 of the stator circumferentially about the axis between the first openings 24a and the second openings 24b. When the rotor 30 is operatively rotated such that the second groove 34b overlies at least one of the second openings 24b, fluid communication is established between this second opening 24b, the collection groove 40, and the outlet opening 29 in the collection groove 40. By rotating the rotor 30 relative to the stator 20 so that the second groove 34b does not overlap one of the second openings 24b, the collecting groove 40 is fluidically decoupled from the second openings 24b and the fluid flow is adjusted.

[0019] An exemplary fluid flow path through the selector valve 10 includes fluid from a sample injector through the inlet port 28c in the stator face 21. The fluid then flows through the inlet passage 26c in the stator 20 to the central opening 25 and into the first groove 34a of the rotor 30. When the rotor 30 is rotated to overlie a first opening 24a, as in Fig. 3, the fluid then flows through the first groove 34a and into such a fluidically coupled first opening 24a in the stator 20. From such a first opening 24a, the fluid flows through the respective first passage 26a and the first port 28a into the selected treatment device 50, such as a chromatographic column. The fluid flow direction is in Fig.3 by arrows, although the fluid flow direction may also be reversed from that described herein. In the illustrated case, the fluid then flows from the treatment device 50 into a second port 28b on the stator face 21 and into a corresponding second passage 26b. The fluid flow continues through a respective second opening 24b of such second passage 26b and into the second groove 34b of the rotor 30. The fluid flow flows through at least a portion of the second groove 34b and, in some embodiments, into the collection groove 40. The fluid flow is expelled from the stator / rotor interface in the exemplary fluid flow direction through the outlet opening 29, the outlet passage 26d, and the outlet port 28d of the stator 20.

[0020] To accommodate relatively high flow operating conditions, such as 200 ml / min or more, without causing a back pressure exceeding a threshold, such as 5 bar (72.5 psi), the applicant has discovered an arrangement for the second groove 34b. As shown in the Fig.6-7B, the second groove 34b may include a transfer portion 36 and a relief portion 38 formed in the dynamic surface 32 of the rotor. In some embodiments, the transfer portion 36 and the relief portion 38 form a continuous groove / recess in the dynamic surface 32 of the rotor such that the transfer portion 36 and the relief portion 38 are fluidly connected at all times. In other embodiments, the transfer portion 36 may be fluidly separated from the relief portion 38 in the dynamic surface 32 of the rotor such that fluid communication between the transfer portion 36 and the relief portion 38 is achieved only through the cooperation of a channel, groove, or other formation in the dynamic surface 22 of the stator. An example of such a formation may be the collection groove 40.

[0021] In the illustrated embodiment, the transfer portion 36 of the second groove 34b extends from a narrowed distal end 37a to a widened proximal end 37b. In some embodiments, the proximal end 37b is the point at which the transfer portion 36 merges into the relief portion 38 to form a continuous second groove 34b. In some embodiments, the transfer portion 36 may have an expansion angle α from the narrowed portion 37a to the widened portion 37b of between about 10-75°, and more preferably between about 15-50°, and most preferably between about 20-40°. The transfer section 36 may, in some embodiments, have a depth into the dynamic surface 32 of the rotor of about 0.005-0.05 inches (0.13-1.3 mm), and preferably about 0.01-0.03 inches (0.25-0.75 mm). As shown in Fig.3, the transfer portion 36 of the second groove 34b on the rotor dynamic surface 32 can be arranged to selectively overlie at least one of the second openings 24b in the stator dynamic surface 22. The transfer portion 36 of the second groove 34b is preferably configured to direct fluid flow between selected second openings 24b and the collection groove 40 in the stator dynamic surface 22. However, in embodiments of the selector valve 10 without a collection groove 40, the transfer portion 36 can be configured to fluidly communicate only with the relief portion 38 to permit fluid flow between the outlet opening 29 and one or more selected ones of the second openings 24b in the stator dynamic surface 22.The illustrated arrangement of the transfer section 36 with a widened proximal end 37b allows for smooth fluid transfer between the transfer section 36 and one or more of the relief section 38 and the collection groove 40 and also reduces frictional resistance to fluid flow between the selected opening 24b and one or more of the relief section 38 and the collection groove 40.

[0022] The relief portion 38 of the second groove 34b may, in some embodiments, be configured and arranged to operatively overlie at least a portion of the collection groove 40. Such overlay increases the effective volume of the fluid passage between the outlet port 29 and the selected one or more of the second ports 24b. The increased volume of the fluid passage correspondingly reduces fluid backpressure, which is particularly noticeable during operating conditions with relatively high fluid flow rates. A comparative schematic diagram illustrating the modification of the fluid flow path embodied in the present invention is shown in FIGS. Fig. 8A and Fig. 8B. The Fig.The embodiment of U.S. Patent No. 9,739,383 illustrated in Figure 8A includes a collection ring 118 in the stator 110 in opposed relationship with the rotor 120. In contrast, some embodiments of the selector valve 10 of the present invention include a relief portion 38 of the second groove 34b in the rotor 30 that operatively overlies the collection groove 40 in the stator 20. The total volume available for fluid flow in a channel defined by the combination of the collection groove 40 and the relief portion 38 is substantially greater than that provided by the prior art design. This substantially increased volume contributes to a reduction in fluid flow backpressure through the selector valve 10.

[0023] In the illustrated embodiment, the relief portion 38 of the second groove 34b forms an annular path at least partially around a rotational axis 31 of the rotor 30 in the rotor surface 32. The relief portion 38 may include closed ends 39a, 39b that extend annularly by at least 30° around the rotational axis 31, preferably by at least 60° around the rotational axis 31, and more preferably by at least 180° or 270° around the rotational axis 31. However, it is contemplated that the relief portion 38 of the second groove 34b may form an endless path that may operatively overlie at least a portion of the collection groove 40. It is also contemplated that the second groove 34b, including the described transfer portion 36 and the relief portion 38, may be employed in a selector valve 10 in which the dynamic surface 22 of the stator does not include a collection groove 40.In such an embodiment, fluid communication between the outlet opening 29 and a selected one or more of the second passages 26b may be established solely through the second groove 34b.

[0024] Another aspect of the present invention is the provision of connecting passages 26a-26d as shown in Fig. 4 and in Fig.9. The schematic passageway 26 includes a first portion 26x having a first diameter "x" that is greater than a second diameter "y" of the second portion 26y of the passageway 26. Additionally, the second portion 26y of the passageway 26 may preferably be aligned along a central axis 27 that is substantially perpendicular to the stator dynamic surface 22. Applicant has determined that such alignment, at least for the second portion 26y of the passageway 26 with respect to the stator dynamic surface 22, reduces fluid flow resistance and improves overall fluid flow dynamics at a respective opening 24 of the stator 20. In some embodiments, the second diameter "y" may be between about 20% and 90% of the first diameter "x," and preferably between about 30% and 70% of the first diameter "x."In a particular exemplary embodiment, the first diameter “x” is about 0.037 inches (0.94 mm) and the second diameter “y” is about 0.020 inches (0.51 mm). Experimental

[0025] A comparative fluid flow backpressure study was conducted comparing an embodiment of the valve described in U.S. Patent No. 9,739,383 with a multi-channel switching valve of the present invention. The following table lists the fluid channel dimensions of each valve tested in the study: State-of-the-art valve Existing valve Stator passages (inches) 0.020 (uniform, linear) 0.037 - 0.020 (connection) Collecting groove Maximum depth (inches) 0,014 0,016 Superimposed circumferential second groove (inch) no 0,014

[0026] The valves were tested for back pressure at various flow rates (50 ml / min, 100 ml / min, 150 ml / min, 200 ml / min). Fig.The graphs shown in Figures 10A-10H demonstrate a significant reduction in fluid flow backpressure by the selector valve 10 of the present invention. By maintaining the backpressure below a certain threshold, such as below 5 bar (72.5 psi), users can operate the system at higher flow rates without fear of damaging the components in the analytical system.

Claims

[1] Multi-channel switching valve (10), comprising: a stator (20) having an end face (21), a dynamic surface (22), and a plurality of passages (26) extending through the stator (20) to fluidly connect the end face (21) and the dynamic surface (22), wherein the plurality of passages (26) include first passages (26a) extending between respective first openings (24a) in the dynamic surface (22) and first ports (28a) in the end face (21), second passages (26b) extending between respective second openings (24b) in the dynamic surface (22) and second ports (28b) in the end face (21), an inlet passage (26c) extending between an inlet opening (25) in the dynamic surface (22) and an inlet port (28c) in the end face (21), and an outlet passage (26d) extending between an outlet opening (29) in the dynamic surface (22) and an outlet connection (28d) in the end surface (21); and a rotor (30) rotatable with respect to the stator (20) about a rotational axis (31) and having a rotor surface (32) configured to sealingly engage the dynamic surface (22) of the stator (20), wherein the rotor surface (32) comprises a first fluid flow path (34a) for fluidically coupling the inlet opening (25) to selected ones of the first openings (24a) and a second fluid flow path (34b) for fluidically coupling the outlet opening (29) to selected ones of the second openings (24b), wherein the second fluid flow path (34b) has a transfer section (36) and a relief section (38), wherein the transfer section (36) has a proximal end (37b) that merges into the relief section (38) and a distal end (37a),wherein the transmission section (36) is widened from the distal end (37a) to the proximal end (37b) by between about 10-75° and the relief section (38) is arranged annularly around the rotation axis (31) by at least 30°. [2] A multi-channel switching valve (10) according to claim 1, wherein the first and second fluid flow paths (34a, 34b) comprise grooves in the rotor surface (32). [3] Multi-channel switching valve (10) according to claim 1, wherein the first openings (24a) are arranged circumferentially along an inner ring around the axis and the second openings (24b) are arranged circumferentially along an outer ring around the axis. [4] Multi-channel switching valve (10) according to claim 3, comprising an annular collecting groove (40) in the dynamic surface (22) of the stator (20), the annular collecting groove (40) intersecting with the outlet opening (29). [5] Multi-channel switching valve (10) according to claim 4, wherein the annular collecting groove (40) is located radially between the inner ring and the outer ring. [6] A multi-channel switching valve (10) according to claim 5, wherein the relief portion (38) of the second fluid flow path (34b) is in operative alignment with the annular collecting groove (40). [7] Multi-channel switching valve (10) according to claim 6, wherein the relief section (38) annularly mirrors the collecting groove (40). [8] The multi-channel switching valve (10) of claim 4, wherein the second fluid flow path (34b) fluidly connects the annular collecting groove (40) with selected ones of the second openings (24b). [9] Multi-channel switching valve (10) according to claim 1, wherein the inlet opening (35) lies along the axis of rotation (31). [10] Multi-channel switching valve (10), comprising: a stator (20) having an end face (21), a central axis, and a substantially opposite dynamic surface (22) comprising a plurality of first openings (24a) arranged in a first circumferential pattern around the central axis, and a plurality of second openings (24b) arranged in a second circumferential pattern around the central axis; and a rotor (30) rotatable with respect to the stator (20) about a rotational axis (31) coinciding with the central axis and having a rotor surface (32) configured to sealingly engage the dynamic surface (22) of the stator (20), the rotor surface (32) comprising a first fluid flow path (34a) and a second fluid flow path (34b), the first fluid flow path (34a) extending from the rotational center of the rotor surface (32) to a first end to selectively establish fluidic communication with any one of the first openings (24a), and the second fluid flow path (34b) having a transfer section (36) and a relief section (38),wherein the transmission section (36) is widened from a distal end (37a) in fluid communication with any of the second openings (24b) to a proximal end (37b) by between about 10-75° and the relief section (38) is arranged annularly around the rotation axis (31) by at least 30°. [11] Multi-channel switching valve (10) according to claim 10, wherein the relief section (38) is arranged annularly around the axis of rotation (31) by at least approximately 270°. [12] The multi-channel switching valve (10) of claim 10, wherein the second fluid flow path (34b) fluidly couples any one of the second openings (24b) to an outlet opening (29) in the dynamic surface (22) of the stator (20). [13] A multi-channel switching valve (10) according to claim 10, comprising an annular collecting groove (40) in the dynamic surface (22) of the stator (20) radially between the first axis-circumferential pattern and the second axis-circumferential pattern. [14] Multi-channel switching valve (10) according to claim 13, wherein the annular collecting groove (40) intersects with an outlet opening (29) of the dynamic surface (22) of the stator (20). [15] The multi-channel switching valve (10) of claim 14, wherein the second fluid flow path (34b) fluidly couples any one of the second openings (24b) to the annular collecting groove (40). [16] A multi-channel switching valve (10) according to claim 15, wherein the relief portion (38) of the second fluid flow path (34b) is in operative alignment with the annular collecting groove (40). [17] A multi-channel switching valve (10) according to claim 10, including an inlet opening (25) in the dynamic surface (22) of the stator (20) in operative alignment with the center of rotation of the rotor surface (32).

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