Patent Description:
<CIT> describes a collet closing mechanism utilizing an array of wedge members as the force transmitting elements, to maximize the area for contact with associated bearing surfaces.

Collet-type mechanisms have been used in a wide variety of devices and mechanisms for well over one hundred years. Examples of collet-type mechanisms can be found in many devices, including but not limited to:.

Collet-type mechanisms offer numerous advantages including the following:.

Collet-type mechanisms that grip an external surface of a workpiece are generally known as external collets. Collet-type mechanisms that grip an internal surface of a workpiece are generally known as internal collets.

Conventional collet-type mechanisms typically incorporate two contacting components: a segmented collet assembly (alternatively referred to herein simply as a "segmented collet"), and a collet receiver. The surface of the collet receiver that contacts the segmented collet is configured as a curved lateral surface of a truncated right circular cone. The surfaces of the segmented collet (i.e., surfaces of the collet segments) that contact the collet receiver are also configured as curved lateral surfaces of a truncated right circular cone. The segments of the segmented collet function as wedges acting between the collet receiver and the workpiece.

Application of axial load to the segmented collet in one direction relative to the collet receiver will increase the gripping force acting on the workpiece. Application of axial load to the segmented collet in the opposite direction will urge the collet mechanism to release the workpiece. Axial load may be applied to the segmented collet via the workpiece, as is done with common drilling rig slips (in which case the workpiece is a length of pipe). Alternatively, the axial load may be primarily applied to the segmented collet by means independent of the workpiece, as with common chucks on milling machines.

As used in this disclosure, the term "collet segment" is to be understood as meaning a segment of a segmented collet. The collet segments in a given segmented collet may be physically separate from each other, or may be coupled by some means permitting a selected degree of relative movement between the collet segments in one or more directions or senses. Non-limiting examples of means for permitting relative movement between coupled collet segments include the provision of an integrated metal spring, and forming the collet using two or more materials having different flexural stiffnesses.

When a collet-type mechanism is used to grip a workpiece that dimensionally corresponds to the "nominal" size of the collet-type mechanism (typically corresponding to a "nominal" internal or external diameter), the collet segments will contact the collet receiver and initiate gripping of the workpiece when the segmented collet is located at a "nominal" axial reference position along the length of the collet receiver. At this nominal reference position, the contacting surfaces of the collet segments and the collet receiver will have the same radius at each axial location along the lengths of the components, and the contacting surfaces will thus coincide. As axial force is applied to the segmented collet to increase the gripping force, the contact stress distribution that develops between the collet segments and collet receiver will be nearly uniform. For purposes of this disclosure, this type of contact condition will be referred to as "match contact" (as further discussed later herein with reference to <FIG> and <FIG>).

When a collet-type mechanism holds a workpiece that is not of the nominal size, the collet segments will contact the collet receiver and initiate gripping of the workpiece when the segmented collet is located at an axial position within the collet receiver that is away from the nominal axial reference position. At every axial location, the radii of curvature of the contact surfaces of the collet segments and the collet receiver will be different. As axial force is applied to the segmented collet to increase the gripping force, the contact stress distribution that develops between the collet segments and the collet receiver will be less uniform than for the situation where the workpiece is of the nominal size.

With an internal collet mechanism, if the size of the workpiece is less than the nominal size of the collet, the area of contact of each collet segment with the collet receiver will be reduced toward the longitudinal center of each collet segment. For purposes of this disclosure, this type of contact condition will be referred to as "center contact" (as further discussed later herein with reference to <FIG>).

If the size of the workpiece is greater than the nominal size of the collet, then the area of contact of each collet segment with the collet receiver will be reduced toward the two longitudinal edges of each collet segment. For purposes of this disclosure, this type of contact condition will be referred to as "edge contact" (as further discussed later herein with reference to <FIG> and <FIG>).

With an external collet mechanism, if the size of the workpiece is less than the nominal size of the collet, then edge contact occurs (as in <FIG>). If the size of the workpiece is greater than the nominal size of the collet, then center contact occurs (as in <FIG>).

The reduction of contact area when the workpiece varies from the nominal size of the collet, as described above, leads to an increase in the maximum contact stress for a given gripping force. This increase in maximum contact stress is more pronounced with a given axial positional change from match contact toward an edge contact condition, compared to an axial positional change of the same magnitude toward a center contact condition. Sliding occurs between the contact surfaces as the gripping force increases, or as the workpiece is released, or if the collet mechanism permits relative rotation (such as in tubular running tools described in <CIT>). The risk of the contact surfaces galling or being otherwise damaged increases as the maximum contact stress increases. For this reason, the acceptable size range of workpieces specified for some collet mechanisms may be selected to produce either match contact or center contact, and to avoid edge contact.

If torque is transmitted between the collet receiver and workpiece through the collet mechanism, each collet segment will have a greater tendency to rotate along an axis generally parallel to the longitudinal axis of the collet mechanism when in a center contact condition, as compared to the tendency for such rotation when the collet segment is in a match contact condition or edge contact condition. Such rotation of the collet segments may cause the collet mechanism to jam and impair the collet mechanism's ability to quickly release the workpiece. Therefore, the collet segments are described as having less stability when in a center contact condition than when in a match contact condition or an edge contact condition.

Particular and preferred aspects of the present invention are set out in the claims.

In general terms, the present disclosure teaches embodiments of collet-type mechanisms in which the contact conditions between the collet segments and the collet receiver are less dependent on the size of the workpiece gripped by the mechanism than in prior art collet-type mechanisms that have conical contact surfaces on both the collet segments and the collet receiver. The present disclosure also teaches embodiments of methods for selecting the configuration of the surface of a collet segment that contacts the collet receiver.

More specifically, the present disclosure teaches collet-type mechanisms in which the surface of the collet receiver that contacts the collet segments is configured as a curved lateral surface of a truncated right circular cone, and the surface of each collet segment that contacts the collet receiver (which surface is also referred herein as a "collet segment contact surface") is configured to have curvature which, as viewed in section transversely perpendicular to the longitudinal axis of the mechanism, is invariant along at least part of the axial length of the collet segment. In the most general form, each collet segment contact surface is configured as an arc having a curvature similar to the curvature of the conical collet receiver surface, and projected for at least part of its length along a line parallel to the taper of the conical collet receiver surface.

Embodiments within the scope of the present disclosure include collet segments wherein the surface that contacts the collet receiver is at least partly configured as a curved lateral surface of a circular cylinder, wherein the circular cylinder may be an oblique circular cylinder in some embodiments and a right circular cylinder in other embodiments. As used in this disclosure:.

The skew angle of a circular cylinder is to be understood as meaning the angle between the OCC or RCC axis (as the case may be) and normal vectors extending from the centers of the bases. For a right circular cylinder (RCC), the skew angle is zero. For an oblique circular cylinder (OCC), the skew angle is non-zero.

The term "collet receiver contact surface" is to be understood as meaning the surface of the collet receiver that contacts the collet segments.

For both external and internal collet mechanisms, the angle between the axis of the cylindrical surface of each collet segment and the axis of the conical collet receiver contact surface may be selected to equal the taper angle of the conical collet receiver contact surface.

The radii of the cylindrical surfaces of the collet segments may be selected to optimize the contact stress distribution based on the design objectives for the collet mechanism. For an external collet mechanism, the radius of the cylindrical surface on each collet segment may be selected to be close fitting with the smallest radius of the conical collet receiver contact surface. For an internal collet mechanism, the radius of the cylindrical surface on each collet segment may be selected to be close fitting with the largest radius of the conical collet receiver contact surface.

The skew angle of the circular cylinders defining a portion of the contact surface of each collet segment also may be selected to optimize the contact stress distribution based on the particular design objectives for the collet-type mechanism. In one embodiment in accordance with the present disclosure, the skew angle is selected to equal the taper angle of the conical collet receiver contact surface, and the resulting portion of the contact surface on each collet segment is a part of an oblique cylindrical surface. In another embodiment, the skew angle is selected to be less than the taper angle of the conical collet receiver contact surface -- for example, with the skew angle equal to zero and the resulting portion of the contact surface of each collet segment being part of a right cylindrical surface. In a further embodiment, the skew angle is selected to be greater than the taper angle of the conical collet receiver contact surface.

As further explanation, the contact stress distribution may be optimized by selection of the skew angle and radius of the cylindrical surface on collet segments that contact the collet receiver in accordance with the following principles:.

It will be apparent to persons skilled in the art that when the skew angle of the cylindrical surface of each collet segment is selected to equal the taper angle of the conical contact surface of the collet receiver, match contact will occur at the axial location where the radius of the collet receiver equals the radius selected for the contacting cylindrical surface of the collet segment (for example, at the smallest cone radius for an external collet mechanism, and at the largest cone radius for an internal collet mechanism), independent of the workpiece size.

Using an internal collet as an example for purposes of further explanation, when the skew angle is selected to be less than the taper angle, contact between a collet segment and the collet receiver will tend in the direction toward edge contact. However, unlike the edge contact occurring in prior art internal collets that have conical contact surfaces on the collet segments and on the collet receiver, the degree of bias toward edge contact is independent of the workpiece size, and is controlled by the selection of the skew angle and radius of the cylindrical surface of the collet segment that contacts the collet receiver.

When the skew angle is selected to be greater than the taper angle, contact between a collet segment and the collet receiver will tend toward center contact. However, unlike the center contact occurring in prior art collets that have conical contact surfaces on both the segmented collet and the collet receiver, the degree of bias toward center contact is independent of the workpiece size and is controlled by the selection of the skew angle and radius of the cylindrical surface of the collet segment that contacts the collet receiver.

Collet-type mechanisms in accordance with the present disclosure may thus be designed such that the contact stress distribution between the segmented collet and the collet receiver is less dependent upon variations in workpiece size compared to otherwise-similar prior art collet mechanisms that have conical contact surfaces on the collet segments as well as on the collet receiver. Because the cylindrical surfaces of the collet segments have a constant radius along their length, and the conical collet receiver contact surface has a varying radius along its length, the contact condition varies along the axial length of the collet while also being independent of workpiece size. Thus, the collet segments can be designed to have greater stability when transferring torque between the collet mechanism and the workpiece for workpiece sizes that would otherwise result in a center contact condition with prior art collet mechanisms.

This increased stability results from the provision of a larger contact width in the transverse direction. The same collet segments also can provide lower contact stress for workpiece sizes that would otherwise result in an edge contact condition with prior art collets. This lower contact stress results from the reduction and/or elimination of edge contact and provision of a larger contact area. There is also an associated increase in center contact, which provides gradually converging contact surfaces that can enhance lubrication for collet-type mechanisms that permit relative rotation (such as, for example, in tubular running tools of the type described in <CIT>).

In general terms, therefore, the present disclosure teaches a collet-type mechanism comprising a collet receiver defining a collet receiver contact surface configured as a curved lateral surface of a truncated right circular cone, and a segmented collet assembly comprising a plurality of collet segments. Each collet segment defines:.

In some embodiments, each collet segment contact surface is at least partly configured as a portion of a curved lateral surface of a circular cylinder, which may be either an oblique circular cylinder or a right circular cylinder.

In other embodiments, each collet segment contact surface comprises axially-contiguous first and second surface regions, with the first surface region being at least partly configured as a portion of a curved lateral surface of either an oblique circular cylinder or a right circular cylinder; and with the second surface region being at least partly configured as a portion of a curved lateral surface of a truncated right circular cone.

Collet-type mechanisms in accordance with the present disclosure may be configured as "internal" collet mechanisms for gripping an internal cylindrical surface of a workpiece, or as "external" collet mechanisms for gripping an external cylindrical surface of a workpiece. Accordingly, collet-type mechanisms in accordance with the present disclosure can be incorporated in an internally-gripping tubular running tools such as:.

Embodiments in accordance with this disclosure will now be described with reference to the accompanying Figures, in which numerical references denote like parts, and in which:.

The contact geometry and contact stresses between collet segments and a collet receiver may be theoretically predicted using analytical equations for contact mechanics found in published texts such as:.

Finite element analysis software tools may also be used to predict the contact geometry and contact stresses, and may provide more accurate predictions than analytical equations for some collet-type mechanisms.

<FIG> is a transverse section through an external collet mechanism <NUM> comprising a collet receiver <NUM> having an inside surface <NUM>, and a segmented collet comprising a plurality of collet segments <NUM>, each having an outside surface <NUM>. <FIG> illustrates a match contact condition between the collet receiver <NUM> and one of the collet segments <NUM>. In a match contact condition for an external collet as in <FIG>, the outside surface <NUM> of collet segment <NUM> has the same radius of curvature as the inside surface <NUM> of collet receiver <NUM>.

<FIG> is similar to <FIG> but that it illustrates a center contact condition between collet receiver <NUM> and collet segment <NUM>. In a center contact condition for an external collet as in <FIG>, outside surface <NUM> of collet segment <NUM> has a smaller radius of curvature than inside surface <NUM> of collet receiver <NUM>.

<FIG> is similar to <FIG> but illustrates an edge contact condition between collet receiver <NUM> and collet segment <NUM>. In an edge contact condition for an external collet as in <FIG>, outside surface <NUM> of collet segment <NUM> has a larger radius of curvature than inside surface <NUM> of collet receiver <NUM>.

<FIG> is a transverse section through an internal collet mechanism <NUM> comprising a collet receiver <NUM> having an inside surface <NUM>, and a segmented collet comprising a plurality of collet segments <NUM>, each having an outside surface <NUM>. <FIG> illustrates a match contact condition between the collet receiver <NUM> and one of the collet segments <NUM>. In a match contact condition for an internal collet as in <FIG>, the inside surface <NUM> of collet segment <NUM> has the same radius of curvature as the outside surface <NUM> of collet receiver <NUM>.

<FIG> is similar to <FIG> but illustrates a center contact condition between collet receiver <NUM> and collet segment <NUM>. In a center contact condition for an internal collet as in <FIG>, inside surface <NUM> of collet segment <NUM> has a larger radius of curvature than outside surface <NUM> of collet receiver <NUM>.

<FIG> is similar to <FIG> but illustrates an edge contact condition between collet receiver <NUM> and collet segment <NUM>. In an edge contact condition for an internal collet as in <FIG>, inside surface <NUM> of collet segment <NUM> has a smaller radius of curvature than outside surface <NUM> of collet receiver <NUM>.

<FIG> and <FIG> are longitudinal sections through an embodiment <NUM> of an external collet mechanism in accordance with the present disclosure. External collet <NUM> has a longitudinal axis <NUM>, and comprises a collet receiver <NUM> and a segmented collet comprising a plurality of collet segments <NUM>. Collet receiver <NUM> has a bore defining a collet receiver contact surface <NUM> configured as a curved lateral surface of a truncated right circular cone.

Each collet segment <NUM> has a radially-external collet segment contact surface <NUM> comprising a first surface region <NUM> and a second surface region <NUM>, with second surface region <NUM> being axially contiguous with first surface region <NUM>. First and second surface regions <NUM> and <NUM> are configured for contact with collet receiver contact surface <NUM>, as described in greater detail later herein. Each collet segment <NUM> further has radially-internal workpiece engagement surface <NUM> suitably configured for gripping an outer surface of a tubular workpiece.

In <FIG>, external collet <NUM> is shown with workpiece engagement surfaces <NUM> of collet segments <NUM> in gripping engagement with an external surface <NUM> of a workpiece <NUM> having an external diameter corresponding to the maximum external diameter that collet <NUM> is designed to grip. For purposes of this disclosure, the position in which collet segments <NUM> are shown in <FIG> - i.e., in which the axial length of the contact region between collet segment contact surfaces <NUM> and collet receiver contact surface <NUM> is greatest - is referred to as the retracted position.

<FIG> is an isometric view of external collet <NUM> grippingly engaging workpiece <NUM> as in <FIG>.

In <FIG>, external collet <NUM> is shown with workpiece engagement surfaces <NUM> of collet segments <NUM> in gripping engagement with an external surface <NUM> of a workpiece <NUM> having an external diameter corresponding to the minimum external diameter that collet <NUM> is designed to grip. For purposes of this disclosure, the position in which collet segments <NUM> are shown in <FIG> - i.e., in which the axial length of the contact region between collet segment contact surfaces <NUM> and collet receiver contact surface <NUM> is least - is referred to as the extended position.

<FIG> further illustrate a typical collet segment <NUM> of external collet <NUM>. As previously noted, each collet segment <NUM> has a collet segment contact surface <NUM> comprising first and second surface regions <NUM> and <NUM>. First surface region <NUM> has an axial length LOC and is configured as a portion of a curved lateral surface of an OCC. Second surface region <NUM> has an axial length LC and is configured as a portion of a curved lateral surface of a truncated right circular cone.

Reference numbers 1211A and 1212A in <FIG> indicate surficial lines that are coincident with, and which longitudinally bisect, first and second surface regions <NUM> and <NUM>, respectively. As most clearly seen in <FIG>, surficial lines 1211A and 1212A in the illustrated embodiment are collinear (i.e., all points on lines 1211A and 1212A lie on the same straight line), and are parallel to the taper angle of conical collet receiver contact surface <NUM> radially adjacent to second surficial line 1212A.

The axial length LC and radii RC1 and RC2 of second surface region <NUM> may be selected such that the configuration of second surface region <NUM> matches the configuration of collet receiver contact surface <NUM> when collet segments <NUM> are in their extended position. Thus selected, the taper angle of second surface region <NUM> will be equal to the taper angle of collet receiver contact surface <NUM>.

Radius ROC of first surface region <NUM> may be equal to radius RC1 of second surface region <NUM>. The skew angle of the OCC that is used to define first surface region <NUM> may be selected to be equal to the taper angle of the truncated right circular cone that is used to define collet receiver contact surface <NUM>.

<FIG> and <FIG> are longitudinal sections through an embodiment <NUM> of an internal collet mechanism constructed in accordance with the present disclosure. Internal collet <NUM> has a longitudinal axis <NUM>, and comprises a collet receiver <NUM> and a segmented collet comprising a plurality of collet segments <NUM>. Collet receiver <NUM> has an outer surface defining a collet receiver contact surface <NUM> configured as a curved lateral surface of a truncated right circular cone.

Each collet segment <NUM> has a radially-internal collet segment contact surface <NUM> comprising a first surface region <NUM> and a second surface region <NUM>, with second surface region <NUM> being axially contiguous with first surface region <NUM>. First and second surface regions <NUM> and <NUM> are configured for contact with collet receiver contact surface <NUM>, as described in greater detail later herein. Each collet segment <NUM> further has a radially-external workpiece engagement surface <NUM> suitably configured for gripping an inner surface of a tubular workpiece.

In <FIG>, internal collet <NUM> is shown with workpiece engagement surfaces <NUM> of collet segments <NUM> in gripping engagement with an internal surface <NUM> of a workpiece <NUM> having an internal diameter corresponding to the minimum internal diameter that collet <NUM> is designed to grip. For purposes of this disclosure, the position in which collet segments <NUM> are shown in <FIG> - i.e., in which the axial length of the contact region between collet segment contact surfaces <NUM> and collet receiver contact surface <NUM> is greatest - is referred to as the retracted position.

<FIG> is an isometric view of internal collet <NUM> shown grippingly engaging workpiece <NUM> as in <FIG>.

In <FIG>, internal collet <NUM> is shown with workpiece engagement surfaces <NUM> of collet segments <NUM> in gripping engagement with an internal surface <NUM> of a workpiece <NUM> having the maximum internal diameter that collet <NUM> is designed to grip. For purposes of this disclosure, the position in which collet segments <NUM> are shown in <FIG> - i.e., in which the axial length of the contact region between collet segment contact surfaces <NUM> and collet receiver contact surface <NUM> is least - is referred to as the extended position.

<FIG> is an isometric view of internal collet <NUM> shown grippingly engaging workpiece <NUM>.

<FIG> further illustrate a typical collet segment <NUM> of internal collet <NUM>. As previously noted, each collet segment <NUM> has a collet segment contact surface <NUM> comprising first and second surface regions <NUM> and <NUM>. First surface region <NUM> has an axial length LOC and is configured as a portion of an OCC. Second surface region <NUM> is configured as a portion of a curved lateral surface of a truncated right circular cone.

Reference numbers 2211A and 2212A in <FIG> indicate surficial lines that are coincident with, and which longitudinally bisect, first and second surface regions <NUM> and <NUM>, respectively. As most clearly seen in <FIG>, surficial lines 2211A and 2212A in the illustrated embodiment are collinear (i.e., all points on lines 2211A and 2212A lie on the same straight line), and are parallel to the taper angle of conical collet receiver contact surface <NUM> radially adjacent to second surficial line 2212A.

<FIG> depict an internally-gripping casing running tool (or "CRT") <NUM> similar to the prior art tubular running tool illustrated in <FIG> and <FIG> in <CIT>, but incorporating an internal collet-type mechanism in accordance with the present disclosure to grip a tubular casing workpiece <NUM> having an inner surface <NUM> and an outer surface <NUM>.

CRT <NUM> incorporates a mandrel <NUM> that acts as a collet receiver analogous to collet receiver <NUM> of internal collet mechanism <NUM> herein. The configuration of the outer surface <NUM> of mandrel <NUM> includes a plurality of truncated right circular cones.

CRT <NUM> further incorporates integrated slips <NUM> (alternatively referred to herein as slips elements) acting as collet segments. Integrated slips <NUM> have an outer surface <NUM> suitably configured to grip inner surface <NUM> of casing <NUM>. As shown in <FIG> and <FIG>, integrated slips <NUM> have a plurality of inner surface regions <NUM> that contact outer surface <NUM> of mandrel <NUM>. Inner surface regions <NUM> are configured as OCC surfaces. The skew angle of the OCC surfaces that are used to define inner surface regions <NUM> of integrated slips <NUM> may be selected to equal the taper angle of the truncated right circular cones that are used to define outer surface <NUM> of mandrel <NUM>.

<FIG> depict an externally-gripping CRT <NUM> similar to prior art tubular running tools disclosed in <CIT> and <CIT>, but incorporating an external collet-type mechanism in accordance with the present disclosure to grip a tubular casing workpiece <NUM> having an inner surface <NUM> and an outer surface <NUM>.

CRT <NUM> incorporates a mandrel <NUM> that acts as a collet receiver analogous to collet receiver <NUM> of external collet mechanism <NUM> herein. Mandrel <NUM> has an inner surface <NUM> configured to define a plurality of truncated right circular cones.

CRT <NUM> further incorporates slips assembly <NUM> acting as collet segments, with each slips assembly <NUM> including a jaw <NUM> and a die <NUM>. An inner surface <NUM> on each die <NUM> of slips <NUM> is suitably configured to grip outer surface <NUM> of casing <NUM>. As shown in <FIG> and <FIG>, slips <NUM> have a plurality of outer surface regions <NUM> on jaws <NUM> that contact inner surface <NUM> of mandrel <NUM>. Outer surface regions <NUM> are configured as OCC surfaces. The skew angle of the OCC surfaces that are used to define outer surface regions <NUM> of slips <NUM> may be selected to equal the taper angle of the truncated right circular cones that are used to define inner surface <NUM> of mandrel <NUM>.

It will be readily appreciated by those skilled in the art that various modifications to embodiments in accordance with this disclosure may be devised without departing from the scope of the present teachings, such as but not limited to modifications which may use equivalent materials hereafter conceived or developed, a segmented collet with a different number of collet segments, or collets configured to engage with workpieces of different size or configuration. It is to be especially understood that the scope of this disclosure is not intended to be limited to described or illustrated embodiments, and that the substitution of a variant of a claimed or illustrated element or feature, without any substantial resultant change in functionality, will not constitute a departure from the scope of this disclosure.

The scope of protection of the current invention is defined by the appended claims.

In this patent document, any use of any form of the terms "connect", "engage", "couple", "attach", or any other term describing an interaction between elements is not meant to limit the interaction to direct interaction between the subject elements, and may also include indirect interaction between the elements such as through secondary or intermediary structure.

Relational and conformational terms such as "perpendicular", "parallel", "cylindrical", and "equal" are not intended to denote or require absolute mathematical or geometrical precision. Accordingly, such terms are to be understood as denoting or requiring substantial precision only (e.g., "substantially perpendicular") unless the context clearly requires otherwise. Wherever used in this document, the terms "typical" and "typically" are to be interpreted in the sense of representative of common usage or practice, and are not to be understood as implying essentiality or invariability.

Claim 1:
A collet-type mechanism comprising:
(a) a collet receiver (<NUM>; <NUM>) defining a collet receiver contact surface (<NUM>; <NUM>) configured as a curved lateral surface of a truncated right circular cone, said collet receiver contact surface having a taper angle; and
(b) a segmented collet assembly comprising a plurality of collet segments (<NUM>; <NUM>), each defining:
• a workpiece engagement surface (<NUM>; <NUM>) configured for engagement with a workpiece to be gripped by the collet-type mechanism; and
• a collet segment contact surface (<NUM>; <NUM>) configured for at least partial contacting engagement with the collet receiver contact surface, characterised in that at least part of the collet segment contact surface has a curvature configured as a portion of a curved lateral surface of a circular cylinder, and wherein said curvature, as viewed in section transversely perpendicular to a longitudinal axis of the collet mechanism, is invariant along the axial length of said at least part of the collet segment contact surface.