Methods and systems for connecting concentrically-nested tubular workpieces

Abstract

In a method for mechanically interconnecting a plurality of concentrically-nested tubular workpieces, a crimping tool applies an increasing radially-inward (or radially-outward) circumferential crimping force to an axial interval of a primary workpiece causing local radial plastic deformation of both the primary workpiece and a secondary workpiece nested within (or surrounding) the primary workpiece, inducing permanent local radial deformation of both workpieces to create an interference fit. The elastic strain limit of the primary workpiece material is less than that of the secondary workpiece material. The crimping tool continuously measures crimping force and crimping deformation at user-selected measurement times. The crimping tool automatically stops and releases the workpieces when the radial deformation reaches a user-selected target deformation occurring subsequent to the initiation of plastic deformation of the secondary workpiece, which the crimping tool automatically detects based on automatically-calculated indicative relationships between the continuously-measured crimping forces and crimping deformations.

Description

[0001] METHODS AND SYSTEMS FOR CONNECTING CONCENTRICALLY-NESTED TUBULAR WORKPIECES FIELD The present disclosure relates to methods and systems for mechanically interconnecting substantially axisymmetric and concentrically-nested tubular workpieces of ductile material, for purposes such as but not limited to the attachment of centralizers to oilfield tubulars for installation in boreholes. BACKGROUND For reasons well known to persons skilled in the art, it is advantageous during the construction of petroleum, natural gas, and other wells comprising tubular strings (such as casing strings) inserted into boreholes, to limit contact between the tubular strings and the borehole walls. Devices called centralizers are commonly used to provide this function by reducing the eccentricity of (i.e., centralizing) tubular strings within their boreholes. These devices are configured to economically meet a variety of drilling and well completion applications. Within the context of petroleum drilling and well completions, wells are typically constructed by drilling the borehole using a first tubular string (i.e., a drill string), then removing the drill string and completing the well by installing a second tubular string (i.e., a casing string), which is subsequently permanently cemented in place by flowing cement slurry into the wellbore annulus between the casing string and the borehole, thus encasing the casing string. The performance design criteria for centralizers used on these two types of tubular strings are significantly different, for reasons discussed below. Drilling operations typically impose the most severe structural demands on centralizers because the centralizers must withstand extended periods of time in rotating contact with the borehole wall. Centralizers suitable for drilling must therefore be rugged and may be reusable. To meet these requirements, drilling centralizers are typically integral with the drill string, and, if made to be reusable, may be relatively expensive. In contrast, centralizers for casing typically are not required to withstand significant rotational contact with borehole walls, as they typically are optimized to improve quality and integrity of cement encasement, and are only used once. Therefore, casing centralizers are commonly mounted to casing using means imparting little or no torsional load transfer capability and only limited axial load transfer capability; being single-use items, they are constructed for lowest cost, not for durability. Recent advancements in drilling technology have enabled boreholes to be drilled and completed with a single casing string (commonly referred to as “casing drilling” or “drilling with casing”), which eliminates the need to “trip” a separate drill string into and out of the borehole to service the drill bit when making the borehole for the casing string. Casing drilling enables cost savings by reducing drilling time and eliminating the expense of providing and maintaining a drill string, plus various technical advantages such as reduced risk of borehole caving prior to casing installation. However, drilling with casing changes the performance requirements of the casing centralizers employed. If conventional casing centralizers (such as those used in conventional methods as described above) are used for casing drilling, they will typically rotate relative to the casing under application of extended rotation required for drilling, causing wear and potentially failure of the centralizer, the casing, or both. These potential problems can be avoided or mitigated by making centralizers for casing drilling integral with the casing (similar to integral centralizers used for drill strings as described above), but this is costly and more complex to implement than simply attaching centralizers to the casing exterior for single-use service. Accordingly, there is a need for casing centralizers that are comparatively inexpensive and easy to attach to a casing string for purposes of casing drilling, while also being rugged enough, and fixed securely enough to the casing string, to maintain sufficient structural integrity and sufficiently secure attachment to the casing string during casing drilling operations to satisfactorily complete at least one borehole. There is also a corresponding need for methods of attaching such casing centralizers to casing string components to meet these operational requirements. As used in this document, the term “crimping” refers to methods for joining or connecting two or more workpieces by plastically deforming at least two of them to permanently mechanically engage the workpieces by creating an “interference fit”, and thus to resist relative movement of the workpieces. A joint or connection formed by crimping may be referred to herein as a “crimp”. U.S. Patent No.7,082,997 (Slack) discloses a pipe centralizer and a method of attachment of a centralizer to a metal pipe by crimping to create an interference fit between the centralizer and the metal pipe. This prior art method comprises the steps of: • “applying an inward, substantially radially-directed force to a plurality of points about an outer circumference of a tubular section of the centralizer causing it to plastically deform radially-inwardly and come into contact with the outer surface of the metal pipe at points corresponding to the plurality of points”; and • “applying such additional inward, substantially radially-directed force as required to force both the centralizer and the outer surface of the metal pipe to displace radially-inwardly an amount at least great enough that when the force is released, an interference fit is created between the centralizer and the metal pipe.” US 7,082,997 further discloses “obtaining sufficient interference in the crimped connection through purely mechanical means . . . by selecting the elastic limit of the centralizer material, in the section to be crimped, to be less than [the elastic limit] of the pipe on which the centralizer is to be installed. In this context, the elastic limit generally refers to the strain at which the metal of the parts yields. Having the material properties thus selected, it will be apparent to one skilled in the art, that when the radial displacement applied during crimping is sufficient to force the hoop strain of the metal pipe to be at least equal to its elastic limit, such that upon release of the load causing the radial displacement, the metal pipe will tend to radially spring back an amount greater than the centralizer, were both parts separated. Since the parts are not separated, the difference in this amount of spring back is manifest as interference and fulfills the desired purpose of creating interference by purely mechanical means.” US 7,082,997 is silent regarding quantification of the magnitude of the interference fit between the centralizer and the pipe. It is also silent regarding the magnitude of the localized permanent inward change in pipe diameter created by this attachment method, particularly when the deformation induced by crimping is substantially greater than the elastic deformation limit of the pipe. In certain situations when attaching a centralizer to a pipe by crimping, it is desirable to create a local change in pipe diameter (a “dimple”) of precise radial magnitude. Persons of ordinary skill in the art will understand that the radial magnitude of a dimple created by crimping is a function of many properties of the pipe, including the pipe’s diameter, wall thickness, and mechanical material properties. Manufacturing specifications for pipe such as well casing may permit substantial variations in diameter, wall thickness, and mechanical material properties, and it is currently impractical to quantify these properties at every crimp location. As an alternative to quantifying these properties, a known iterative method may be used wherein: (i) the crimping tool is configured to perform a first crimp of a selected radial magnitude based on the nominal specified properties of the centralizer and the pipe; (ii) the first crimp is performed; (iii) the local change in radius (“dimple size”) of the centralizer (or the pipe) is measured; (iv) the crimping tool is reconfigured to perform a further crimp based on the difference between (a) the change in centralizer (or pipe) radius achieved by the immediately preceding crimp and (b) the desired change in centralizer (or pipe) radius; and (v) when the measured dimple size is less than the desired dimple size, steps (ii) to (iv) are repeated on the same centralizer and pipe until the measured dimple size corresponds to the desired change in centralizer (or pipe) diameter. (vi) when the measured dimple size is greater than the desired dimple size, steps (ii) to (iv) are performed on a new centralizer and pipe. With this iterative prior art method, the accuracy of the first crimp (i.e., measured dimple size relative to desired dimple size) depends on the variations of the first pipe properties from the nominal specified pipe properties. The accuracy of the crimp on each subsequent pipe depends on the variation of each subsequent pipe properties from the properties of the immediately preceding crimped pipe. If individual pipe properties vary substantially from pipe to pipe , then the change in pipe radius (“dimple size”) produced by crimping will also vary substantially and the accuracy of crimping will be reduced. Because pipe properties are variable, this prior art method is in effect “chasing a moving target”, as the crimping tool is reconfigured after each crimp in an attempt to improve the accuracy of the following crimp. BRIEF SUMMARY In general terms, the present disclosure teaches methods and systems for crimping a plurality of substantially axisymmetric and concentrically-nested tubular workpieces of ductile material that overcome limitations of prior art crimping methods as described above, and produce crimps with more consistent and more accurate dimple sizes. These methods and systems differ from prior art crimping methods and systems at least in that: • they do not require measurement of deviations of workpiece geometry from their nominal dimensions; • they do not rely on measurement of preceding crimps; and • they do not require reconfiguration of the crimping tool between crimps. As used in this disclosure, the term “tubular workpiece” (or simply “workpiece”) is to be understood as meaning a cylindrical tubular workpiece, unless the context in which these terms are used clearly indicates that the workpiece may be of other than cylindrical tubular configuration. In a first aspect, the present disclosure describes embodiments of a method for mechanically interconnecting, by crimping, a plurality of substantially axisymmetric and concentrically-nested ductile tubular workpieces including a primary workpiece and a secondary workpiece. In one non-limiting embodiment, the method comprises the sequential steps of: (a) providing a crimping tool having a plurality of radially-movable jaws configured to apply crimping force to the primary workpiece in a user-selected radial direction; (b) activating the crimping tool to apply an increasing crimping force to the primary workpiece in the user-selected radial direction, and to obtain measurements indicative of the crimping force and indicative of a crimping displacement at user- selected measurement points in time (alternatively, “measurement times”); (c) identifying, as a crimping initiation time, a point in time when a user-defined crimping initiation criterion is satisfied, said crimping initiation criterion being considered indicative of each workpiece of the plurality of workpieces having come into substantial contact with each radially-adjacent workpiece but with no yielding having occurred in the secondary workpiece; (d) for each user-selected measurement time following the crimping initiation time, calculating an indicative relationship between the crimping force and the crimping displacement, said indicative relationship having a slope value; (e) for each user-selected measurement time following the crimping initiation time, determining whether a specified yield criterion of the secondary workpiece has been satisfied; (f) when the specified yield criterion of the secondary workpiece has been satisfied, designating, as a yield time, the point in time when the specified yield criterion of the secondary workpiece was satisfied; (g) calculating a target displacement of the crimping tool jaws as equal to the sum of the crimping displacement at the yield time plus a user-selected target deformation; (h) stopping radial movement of the crimping tool jaws when the crimping displacement reaches the target displacement; and (i) radially retracting the crimping tool jaws to release the plurality of tubular workpieces from the crimping tool (thus permitting elastic rebound of the plurality of tubular workpieces); wherein: (A) the crimping force at any point in time is a circumferentially-distributed radial force applied to the primary workpiece by the crimping tool jaws along a user- selected axial interval; (B) the crimping displacement at any point in time is the radial displacement of the crimping tool jaws relative to a user-selected reference datum; (C) when the user-selected radial direction is radially inward, the primary workpiece is the radially-outermost workpiece and the secondary workpiece is the radially- innermost workpiece; (D) when the user-selected radial direction is radially outward, the primary workpiece is the radially-innermost workpiece and the secondary tubular workpiece is the radially-outermost workpiece; (E) the elastic strain limit of the primary workpiece material is selected to be less than the elastic strain limit of the secondary workpiece material (to achieve a desired degree of interference); (F) the specified yield criterion for the secondary workpiece is that the slope value calculated in step (d) crosses a slope threshold equal to a user-selected ratio of a maximum of all slope values calculated subsequent to the crimping initiation time; and (G) the user-selected target deformation corresponds to a specified net permanent local change of a radius of the secondary workpiece resulting from steps (b) through (i). As used in this document: • The term “crimping force” denotes a radial force that is applied generally uniformly around the circumference of a user-selected one of the outer and inner cylindrical surfaces of the primary workpiece by the jaws of a crimping tool along a user-selected axial interval of the primary workpiece, and directed either inward toward the longitudinal axis or outward away from the longitudinal axis as appropriate for the context of each embodiment. • The term “increasing crimping force” denotes a crimping force having a magnitude that increases monotonically over time, but not necessarily at a constant rate. • The term “crimping displacement” denotes radial displacement of the radially-movable jaws of a crimping tool used to apply a crimping force to the primary workpiece. As noted above, the crimping displacement is measured relative to a user-selected reference datum, and will vary in time during the crimping process. By way of non-limiting example, the user-selected reference datum may be the radial position of the jaws at the time the crimping tool is activated. As alternative non-limiting examples, the user- selected reference datum may be the radially-outermost possible position of the jaws when the user-selected radial direction is radially inward, or the radially-innermost possible position of the jaws when the user-selected radial direction is radially outward. • The term “user-selected target deformation” denotes a user-specified net permanent local change of a radius of the secondary workpiece resulting from crimping the plurality of tubular workpieces together to form an interference fit. Crimping methods and systems in accordance with the present disclosure may be used to attach an outer tubular workpiece (such as a tubular centralizer) to an inner tubular workpiece (such as a metal pipe). In such applications, an increasing crimping force directed inward toward the longitudinal axis (also referred to herein as an “inward crimping force”) is applied around a user-selected axial interval of the outer surface of the outer workpiece (or “primary” workpiece in this case), causing the outer workpiece to plastically deform and contact the outer surface of the inner (or “secondary”) workpiece. Additional inward crimping force is applied as required to induce radially-inward local displacement and plastic deformation of both workpieces so that when the inward crimping force is released, an interference fit is created between the outer and inner workpieces. The elastic strain limit of the material of the outer workpiece (in this embodiment being the primary workpiece, as defined above) must be selected to be less than the elastic strain limit of the material of the inner workpiece (in this embodiment being the secondary workpiece, as defined above). The minimum degree to which the elastic strain limit of the outer (primary) workpiece material is less than the elastic strain limit of the inner (secondary) workpiece material will be a design choice that depends upon the desired degree of interference resulting from the crimping process, which in turn may depend on design criteria and parameters including but not limited to desired axial translation and rotational retention force, the geometry of the workpieces, and the coefficient of friction between the workpieces. Crimping methods and systems in accordance with the present disclosure may also be used to attach an inner tubular workpiece (such as a casing patch) to the inside of an outer tubular workpiece (such as a metal pipe). In such applications, an increasing crimping force directed outward away from the longitudinal axis (also referred to herein as an “outward crimping force”) is applied around a user-selected axial interval of the inner workpiece (or “primary” workpiece in this case), causing the inner workpiece to plastically deform and contact the inner surface of the outer (or “secondary”) workpiece. Additional outward crimping force is applied as required to induce radially-outward local displacement and plastic deformation of both workpieces so that when the outward crimping force is released, an interference fit is created between the inner and outer workpieces. The elastic strain limit of the material of the inner workpiece (in this embodiment being the primary workpiece, as defined above) must be selected to be less than the elastic strain limit of the material of the outer workpiece (in this embodiment being the secondary workpiece, as defined above). Methods and systems in accordance with the present disclosure may be used in applications involving crimping only two substantially axisymmetric and concentrically-nested tubular workpieces (i.e., a primary workpiece and a secondary workpiece). In variant embodiments, however, methods and systems in accordance with the present disclosure may also be used in applications involving crimping of more than two such tubular workpieces, such as (by way of non-limiting example) a plurality of tubular workpieces comprising a tertiary workpiece concentrically nested between a primary workpiece and a secondary workpiece. In such variant embodiments, the elastic strain limit of the primary workpiece material is preferably (but not necessarily) selected to be less than the elastic strain limit of the tertiary workpiece material. The crimping method described above is distinguishable over prior art crimping methods in several ways. This method is both continuous and automatic. It achieves the user-selected target deformation more consistently and more accurately (i.e. with less error) than prior art crimping methods, and automatically adjusts for manufacturing variations in the geometry of the workpieces. The parameters needed for determining the yield time of the secondary workpiece (i.e., when the previously-defined “yield criterion” has been met) are continuously determined, as the crimping force increases, by one or more processors according to automatically-measured time-varying crimping forces and crimping displacements of the crimping tool jaws prior to the yield time. The point in time at which the target displacement has been achieved is automatically determined by one or more processors according to the automatically-measured crimping displacement of the crimping tool jaws subsequent to the yield time. Accordingly, once the crimping tool has been activated, the crimping process continues without any operator input until the required crimp (i.e., the desired degree of interference fit) has been achieved. These practical advantages are made possible by basing the determination of sufficient crimping on: • the yield time of the secondary workpiece (rather than on physical measurements of previously-crimped workpieces); and • an innovative criterion for determining the yield time of the secondary workpiece. In contrast, prior art crimping methods are iterative methods, involving trial-and-error, stop-and-start procedures. A first (or “trial”) crimp is performed on a first plurality of tubular workpieces, the crimping tool is then necessarily deactivated, and the resultant local change in diameter (“dimple size”) of the secondary workpiece is physically measured. • If the measured dimple size is less than the desired change in secondary workpiece radius (representative of the desired degree of interference fit), the crimping tool is physically reconfigured and then reactivated to perform a second and further crimp on the same plurality of workpieces, whereupon the thus-increased dimple size is physically measured and compared against the desired dimple size (and so on until the measured dimple size equals or exceeds the desired dimple size). • If the measured dimple size is considered excessively greater than the desired change in secondary workpiece radius, the crimping tool is physically reconfigured and then activated to crimp a new plurality of tubular workpieces (and the excessively-crimped first plurality of workpieces may be discarded). Such prior art crimping methods are slower than crimping methods in accordance with the present disclosure, and they are less reliable in terms of the accuracy and precision of the crimps they produce, particularly when the user-selected target deformation is small relative to the manufacturing variability of the radius of the secondary workpiece. In some embodiments of methods in accordance with the present disclosure, the user- defined crimping initiation criterion referenced in step (c) of the non-limiting method embodiment described above may be that the crimping force applied to the primary workpiece has crossed a user-defined crimping force threshold. The lower limit of the crimping force threshold may be based on the crimping force required to cause plastic deformation in all workpieces of the plurality of workpieces except for the secondary workpiece. The upper limit of the crimping force threshold may be based on: • the crimping force required to cause plastic deformation in all workpieces of the plurality of workpieces except for the secondary workpiece; plus • the minimum crimping force needed to yield the secondary workpiece based on the nominal specifications and manufacturing tolerances of the secondary workpiece. In other embodiments, the user-defined crimping initiation criterion may be that the crimping displacement has crossed a user-defined crimping displacement threshold. The crimping displacement threshold may be selected based on the maximum total radial gap between the plurality of workpieces permitted by manufacturing tolerances. The lower limit of the crimping displacement threshold may be based on the maximum total of radial gaps between the plurality of workpieces that is possible without exceeding workpiece manufacturing tolerances. The upper limit of the crimping displacement threshold may be based on: • the maximum total of radial gaps between the plurality of workpieces that is possible without exceeding workpiece manufacturing tolerances; plus • the minimum radial elastic deflection of the secondary workpiece based on the nominal specifications and manufacturing tolerances of the secondary workpiece. In some embodiments of methods in accordance with the present disclosure, the indicative relationship between the crimping force and the crimping displacement may be calculated using a least-squares fit of the measurements to a linear equation. In a second aspect, the present disclosure describes embodiments of a system for mechanically interconnecting, by crimping, a plurality of tubular workpieces including a primary workpiece and a secondary workpiece, wherein the plurality of tubular workpieces are substantially axisymmetric and concentrically nested. In one non-limiting embodiment, the system comprises: (a) a crimping tool having a plurality of radially-movable jaws configured to apply an increasing crimping force to the primary workpiece in a user-selected radial direction; (b) a force sensor configured to measure the crimping force applied by the jaws to the primary workpiece in the user-selected radial direction; (c) a displacement sensor configured to measure radial displacement of the jaws relative to a user-selected reference datum; and (d) one or more processors, wherein: (d.1) at least one of the one or more processors is configured to receive force data from the force sensor indicative of the crimping force applied by the jaws to the primary workpiece at user-selected measurement times; (d.2) at least one of the one or more processors is configured to receive displacement data from the displacement sensor indicative of the crimping displacement of the crimping tool jaws at each user-selected measurement time; (d.3) at least one of the one or more processors is configured to identify, as a crimping initiation time, a point in time when a user-defined crimping initiation criterion is satisfied, said crimping initiation criterion being considered indicative of each workpiece of the plurality of workpieces having come into contact with each radially-adjacent workpiece but no yielding having occurred in the secondary workpiece; (d.4) at least one of the one or more processors is configured to calculate an indicative relationship between the crimping force and the crimping displacement at each user-selected measurement time, wherein each said indicative relationship has an associated slope value; (d.5) at least one of the one or more processors is configured to designate as a yield time, a point in time when a specified yield criterion of the secondary workpiece is satisfied; (d.6) at least one of the one or more processors is configured to calculate the target displacement of the crimping tool jaws as equal to the sum of the crimping displacement at the yield time plus a user-selected target deformation; (d.7) at least one of the one or more processors is configured to stop the radial displacement of the crimping tool jaws when the crimping displacement reaches the target displacement; and (d.8) at least one of the one or more processors is configured to radially retract the crimping tool jaws to release the plurality of tubular workpieces from the crimping tool. In an alternative non-limiting embodiment, the system comprises: (a) a crimping tool having: (a.1) a double-acting hydraulic actuator comprising a piston axially movably disposed within a cylinder, said cylinder defining a first variable-volume fluid chamber on a first side of the piston and a second variable-volume fluid chamber on a second side of the piston; and (a.2) a plurality of radially-movable jaws configured to apply an increasing crimping force to the primary workpiece in a user-selected radial direction when the first variable-volume fluid chamber is pressurized; (b) a first pressure sensor in fluid communication with the first variable-volume fluid chamber; (c) a displacement sensor configured to measure radial displacement of the jaws relative to a user-selected reference datum; and (d) one or more processors, wherein: (d.1) at least one of the one or more processors is configured to receive fluid pressure data from the first pressure sensor, and to use said fluid pressure data to calculate an actuator differential pressure indicative of the crimping force at user-selected measurement times; (d.2) at least one of the one or more processors is configured to receive displacement data from the displacement sensor, and to use said displacement data to calculate an actuator axial displacement indicative of the crimping displacement of the crimping tool jaws at each user-selected measurement time; (d.3) at least one of the one or more processors is configured to identify, as a crimping initiation time, a point in time when a user-defined crimping initiation criterion is satisfied, said crimping initiation criterion being considered indicative of each workpiece of the plurality of workpieces having come into contact with each radially-adjacent workpiece but with no yielding having occurred in the secondary workpiece; (d.4) at least one of the one or more processors is configured to receive calculated actuator differential pressures and actuator axial displacements, from the corresponding processor or processors, for each user-selected measurement time; (d.5) at least one of the one or more processors is configured to calculate an indicative relationship between the crimping force and the crimping displacement at each user-selected measurement time, wherein each said indicative relationship has an associated slope value; (d.6) at least one of the one or more processors is configured to designate as a yield time, a point in time when a specified yield criterion of the secondary workpiece is satisfied; (d.7) at least one of the one or more processors is configured to calculate the target displacement of the crimping tool jaws as equal to the sum of the crimping displacement at the yield time plus a user-selected target deformation; (d.8) at least one of the one or more processors is configured to stop the radial displacement of the crimping tool jaws when the crimping displacement reaches the target displacement; and (d.9) at least one of the one or more processors is configured to radially retract the crimping tool jaws to release the plurality of tubular workpieces from the crimping tool (thus permitting elastic rebound of the plurality of tubular workpieces). In a variant embodiment, the first pressure sensor is a differential pressure sensor in fluid communication with both the first variable-volume fluid chamber and the second variable- volume fluid chamber. In another embodiment, the system further comprises a second pressure sensor in fluid communication with the second variable-volume fluid chamber. In each of these system embodiments, any one of the system’s one or more processors may be configured to perform one or more of the corresponding functions described above. BRIEF DESCRIPTION OF THE DRAWINGS Embodiments in accordance with the present disclosure will now be described with reference to the accompanying Figures, in which numerical references denote like parts, and in which: FIGURE 1 is an isometric view of a prior art centralizer generally corresponding to the centralizer shown in Figure 1 in US 7,082,997. FIGURE 2 is an isometric view of the prior art centralizer shown in FIG. 1 mounted on a metal pipe as it would appear before crimping, generally corresponding to the centralizer and pipe shown in Figure 2 in US 7,082,997. FIGURE 3 is a schematic longitudinal section through a prior art centralizer mounted coaxially on a metal pipe and inside a collet-type crimping tool, as it would appear prior to crimping and generally corresponding to the centralizer, pipe, and crimping tool shown in Figure 3 in US 7,082,997. FIGURE 4 is a longitudinal section through the prior art assembly shown in FIG. 3 as it would appear during crimping and generally corresponding the assembly shown in Figure 4 in US 7,082,997. FIGURE 5 is an isometric view of a prior art hydraulically-actuated collet-type crimping tool. FIGURE 6 is an isometric view of the crimping tool in FIG. 5, modified in accordance with the present disclosure to include sensors for measuring differential pressure and displacement of the hydraulic actuator. FIGURE 7 is a longitudinal section through the crimping tool shown in FIG. 6, positioned coaxially around a centralizer and a metal pipe prior to crimping. FIGURE 8 is flow chart showing the general steps of methods in accordance with the present disclosure. FIGURE 9 is a graph showing example measurements of the hydraulic actuator differential pressure of the crimping tool in FIG. 5 during the process of attaching a centralizer to a metal pipe. FIGURE 10 is a graph showing example measurements of the hydraulic actuator displacement of the crimping tool in FIG. 5 during the same process of attaching the centralizer to the metal pipe as in FIG. 9. FIGURE 11 is a graph showing slope values, calculated from the example measurements of FIG. 9 and FIG. 10, representative of the relationship between the hydraulic actuator differential pressure and the hydraulic actuator displacement. FIGURE 12 is a graph showing the crimping force applied by the jaws of the crimping tool in FIG. 5, as calculated from the example hydraulic actuator differential pressure measurements in FIG. 9. FIGURE 13 is a graph showing the crimping displacement of the jaws of the crimping tool in FIG. 5, as calculated from the example hydraulic actuator displacement measurements in FIG. 10. FIGURE 14 is a graph showing slope values, calculated from the example measurements of FIG. 9 and FIG. 10, indicative of the relationship between the crimping force of FIG. 12 and the crimping displacement of FIG. 13. FIGURE 15 is a graph showing the relationship between the crimping force in FIG. 12 and the crimping displacement in FIG. 13. FIGURE 16 is a graph showing an example stress-strain curve for a first ductile material exhibiting an abrupt transition from elastic behavior to plastic behavior. FIGURE 17 is a graph showing an example stress-strain curve for a second ductile material exhibiting a gradual onset of non-linear behavior. FIGURE 18 is a graph showing the relationship between the example hydraulic actuator differential pressure measurements in FIG. 9 and the example hydraulic actuator displacement measurements in FIG. 10. FIGURES 19A to 19D are four graphs showing the relationship between the hydraulic actuator differential pressure measurements and the hydraulic actuator displacement measurements from four different tool-workpiece configurations. FIGURE 20 is a schematic longitudinal section schematic view of two substantially axisymmetric and concentrically-nested tubular workpieces, with a collet-type crimping tool positioned within the innermost tubular workpiece, and prior to crimping. FIGURE 21 is a longitudinal section schematic view of the two tubular workpieces and collet-type crimping tool in FIG. 20 after during crimping. FIGURE 22 is a graph showing an illustrative example of the relationship between the crimping force and the crimping displacement for the crimping configuration in FIGS.20 and 21. FIGURE 23 is a longitudinal section schematic view of three substantially axisymmetric and concentrically-nested tubular workpieces inside a collet-type crimping tool prior to crimping. FIGURE 24 is a longitudinal section schematic view of the three tubular workpieces and collet-type crimping tool in FIG. 23 during crimping. FIGURE 24 is a graph showing an illustrative example of the relationship between the crimping force and the crimping displacement for the crimping configuration in FIGS.23 and 24. DETAILED DESCRIPTION General Discussion: Collet-Type Crimping Tools FIG.1 shows a prior art centralizer 1 having an internal bore 2, a cylindrical end section 3 suitable for crimping, and a centralizing section 4 with ribs 5. Internal bore 2 of centralizer 1 is selected to slidingly fit over a metal pipe 6, shown as a threaded and coupled casing joint in FIG. 2, based on the maximum diameter permitted by the manufacturing tolerances for the outer body surface of pipe 6. This allows centralizer 1 to be readily placed over the threaded end of pipe 6 and located somewhere along the length of pipe 6 prior to crimping. FIG. 3 schematically illustrates a tapered-collet-in-housing architecture of a prior art mechanism for applying an increasing radially-inward force to crimp the cylindrical end 3 of centralizer 1 to pipe 6. The mechanism comprises the externally-tapered jaws 7 of a collet (i.e., segments of an externally-conical sleeve) inside a matching internally-tapered collet housing 8. Application of an axial setting force (denoted by vector F) to housing 8, and a resulting induced reaction force (denoted by vector R) on a face 7a of jaws 7, will urge jaws 7 toward the diametrically-smaller bore of housing 8 along the angle of the conical bore of housing 8. This urges jaws 7 radially inward to engage a primary workpiece to be crimped (in the present case shown as cylindrical end 3 of centralizer 1). Alternatively, the action of the collet may be described in terms of an axial setting displacement of housing 8 relative to jaws 7. In this case, setting force F and reaction force R can be understood as arising correlative with the axial setting displacement. Upon application of sufficient setting force F, jaws 7 are urged radially inward (crimping displacement) to plastically deform the cylindrical end 3 of centralizer 1 and bring it into contact with pipe 6. This amount of crimping displacement removes the annular clearance of the sliding fit initially required for placing and positioning centralizer 1 on pipe 6. Application of additional setting force F then urges both cylindrical end 3 of centralizer 1 and the underlying wall of pipe 6 inward. The crimping force and crimping displacement may be increased until the hoop stress and strain in the pipe wall at the crimp location equals or exceeds the pipe material’s elastic limit. It will be apparent to persons of ordinary skill in the art that increasing the crimping displacement beyond the pipe material elastic limit will cause little increase in residual interference after the workpieces (i.e., centralizer 1 and pipe 6) are released from jaws 7 but will locally reduce the drift diameter of pipe 6. FIG. 4 schematically shows the tapered-collet-in-housing mechanism, centralizer 1, and pipe 6 as they would appear at the point of greatest crimping force and crimping displacement during a crimping process. When the desired crimping displacement has occurred, the axial setting displacement of the mechanism is reversed, thus reducing the crimping force to zero and releasing the mechanism from centralizer 1, allowing the collet to be removed, and leaving centralizer 1 crimped to pipe 6. As a non-limiting example, the setting force F and reaction force R may be applied by a hollow-bore hydraulic actuator. FIG. 5 is an isometric view of a prior art tapered-collet-in- housing crimping tool 10 having a double-acting hydraulic actuator and configured for crimping centralizers onto pipe. FIG. 6 is an isometric view of a crimping tool 100 comprising crimping tool 10 modified with components to measure the differential pressure between the two chambers of the hydraulic actuator, and the displacement between the piston and the cylinder of the hydraulic actuator. FIG. 7 is a longitudinal section through crimping tool 100 positioned coaxially over a centralizer 101 and a metal pipe 106 prior to crimping. Centralizer 101 and metal pipe 106 are generally axisymmetric and concentrically-nested tubular workpieces made of ductile materials (not necessarily being made of the same material), and have a common longitudinal axis A. Crimping tool 100 comprises: • externally-tapered jaws 107; • an internally-tapered housing 108; and • a hollow-bore double-acting hydraulic actuator, having a piston 110 and a cylinder 120. Housing 108 threadingly engages cylinder 120. Piston 110 generates force from fluid pressure in a direction parallel to longitudinal axis A and transfers it to jaws 107. Piston 110 is configured with an internal bore having a diameter greater than the outside diameter of pipe 106. Housing 108 is configured with greater radial strength and stiffness than the combined assembly of centralizer 101 and pipe 106 to be crimped, such that housing 108 will remain elastic and deform relatively little during crimping. A closed-loop hydraulic system is formed between crimping tool 100 and a hydraulic pump (not shown). The pump supplies high-pressure fluid and receives low-pressure fluid via two flow lines (not shown) attached to connections 122 of crimping tool 100. A connection block 123 provides channels for flow of hydraulic fluid into and out of the two chambers of the double-acting hydraulic actuator and ports to connect two pressure sensors 124, one to each chamber of the hydraulic actuator. The pump includes electrically operated hydraulic valves to control the direction of fluid flow to and from the two chambers of the hydraulic actuator of crimping tool 100. In an alternative embodiment, hydraulic valves to control fluid flow are mounted directly to a crimping tool. The crimping force applied by crimping tool 100 to the outer surface of centralizer 101 is a function of the axial setting force F and axial reaction force R generated by the hydraulic actuator and transferred to the housing 108 and jaws 107, respectively. The axial force generated by the hydraulic actuator is substantially proportional to the difference between the hydraulic pressures in the two chambers of the hydraulic actuator (“actuator differential pressure”) and acting on piston 110. Accordingly, the actuator differential pressure, which may be calculated from the measurements of the two pressure sensors 124, is indicative of the crimping force applied by crimping tool 100 to the outer surface of centralizer 101. Persons of ordinary skill in the art will appreciate that this indicative relationship is affected by the friction acting between the various sliding surfaces within crimping tool 100. Crimping tool 100 is preferably configured to have consistent friction (and preferably low friction) acting between jaws 107 and housing 108. The sliding contact surfaces of jaws 107 and housing 108 are lubricated. In an alternative embodiment, the actuator differential pressure is directly measured by a single differential pressure sensor connected to both chambers of a double-acting hydraulic actuator of a crimping tool. In a further alternative embodiment, the actuator differential pressure is calculated from the measurements of a single pressure sensor connected to the chamber of a hydraulic actuator that is supplied with high pressure fluid from a pump to produce a crimping force. The hydraulic system in this further alternative embodiment is configured so that fluid in the other chamber of the hydraulic actuator maintains near-zero pressure so as to not cause a significant error in the calculated actuator differential pressure. Persons of skill in the art will understand that this functionality may be achieved by selecting flow lines with a large flow area relative to the fluid flow rate from the hydraulic pump. The crimping force applied by crimping tool 100 to the outer surface of centralizer 101 will also cause deformation of housing 108, which can be measured, for example, by strain gauges. The deformation of housing 108 preferably will be elastic rather than plastic, such that the magnitude of the deformation of housing 108 will be at least approximately proportional to and indicative of the crimping force. The radial displacement of jaws 107 (or “crimping displacement”) will be substantially proportional to the axial displacement of the jaws 107 relative to housing 108, which will be substantially equal to the axial displacement of piston 110 relative to cylinder 120 (“actuator displacement”). A displacement sensor 125 is mounted to cylinder 120 and measures the position of a plate 126 mounted to piston 110. Accordingly, both the axial displacement of jaws 107 relative to housing 108 and the actuator displacement are indicative of the crimping displacement. Persons of ordinary skill in the art will appreciate that these indicative relationships are affected by the mechanical stiffness (and compliance) of various components of crimping tool 100. Crimping tool 100 is preferably configured with housing 108 having significantly greater radial stiffness than that of the combined assembly of centralizer 101 and pipe 108, such that the outward radial deformation of housing 108 during crimping will be negligible compared to the crimping displacement. The crimping displacement may be more accurately determined from the actuator displacement by also measuring the deformation of housing 108. Persons of ordinary skill in the art will be familiar with pressure sensors suitable for measuring the actuator differential pressure and with displacement sensors suitable for measuring the actuator displacement. The sensors may be connected to signal conditioning and data acquisition equipment and to processors programmed to perform one or more steps of methods in accordance with the present disclosure. General Crimping Methodology In general terms, crimping methods and systems in accordance with the present disclosure mechanically interconnect a primary workpiece and a secondary workpiece, resulting in an interference fit and localized permanent changes of radius of both the primary and secondary workpieces. The accuracy of the crimping methods and systems is defined by the difference between the actual localized change of radius of the secondary workpiece and a user-selected target deformation. Several non-limiting embodiments of crimping methods in accordance with the present disclosure are described below. FIG. 8 is a flow chart showing the general steps of methods in accordance with the present disclosure (as previously described in the Brief Summary) and used in the following embodiments. First Embodiment: User-selected radial direction is radially inward FIG. 7 illustrates a first non-limiting embodiment of an apparatus for implementing crimping methods in accordance with the present disclosure. The user-selected radial direction is radially inward toward longitudinal axis A of two substantially axisymmetric and concentrically-nested tubular workpieces: centralizer 101 (a primary workpiece) and pipe 106 (a secondary workpiece). Crimping tool 100 may be used to mechanically interconnect centralizer 101 and pipe 106 by applying a crimping force to centralizer 101. Pressure sensors 124 are used to determine the actuator differential pressure, and linear displacement sensor 125 measures the actuator displacement. By way of non-limiting example, FIGS. 9 and 10, respectively, show example measurements of the actuator differential pressure and the actuator displacement during the process of attaching centralizer 101 to pipe 106. These measurements are indicative of the crimping force applied by jaws 107 to centralizer 101, and the crimping displacement of jaws 107. The speed of the hydraulic actuator, as indicated by the slope of the actuator displacement measurements (FIG. 10), varies because crimping tool 100 (in this particular illustrated embodiment) is supplied with hydraulic fluid from a multi-stage positive displacement hydraulic pump. The crimping force and the crimping displacement of jaws 107 (shown in FIGS. 12 and 13) are calculated from the hydraulic actuator differential pressure and displacement measurements, based on the mechanics of crimping tool 100 and using fundamental crimping tool operating principles known to persons of ordinary skill in the art. FIG. 15 is a graph of the relationship between the crimping force and the crimping displacement. Thus presented, the characteristic shape and features of this relationship curve depend primarily upon the workpieces being crimped, and may be interpreted as showing: • a point in time 131 at which jaws 107 first substantially contact the outer circumference of centralizer 101; • a point in time 132 at which local yielding of centralizer 101 begins to occur; and • a point in time 133 at which centralizer 101 substantially contacts the outer circumference of pipe 106. FIG. 15 also shows a gradual transition of pipe 106 from linear elastic deformation to plastic deformation. The post-yield mechanical stiffness (i.e. strain hardening behavior) of the pipe material may contribute to this gradual transition from elastic deformation to plastic deformation. However, even when the pipe material exhibits an abrupt change from elastic to a perfectly plastic response, the crimping-force-to-crimping-displacement behavior of the pipe structure will exhibit a gradual transition. This is due to the non-uniform stress and strain distributions that develop in pipe 106 as the crimping force and crimping displacement (deformation) increase during crimping, as follows: • local yielding will begin at an axial location along pipe 106 corresponding to the applied crimping force, and will progressively propagate to the axially-adjacent pipe material; • local yielding will begin at the inner surface of pipe 106 and will progressively propagate to the outer surface; • the axially-adjacent pipe material that has not yielded will remain elastic and contribute positive stiffness resisting deformation; and • there may be variations in the pipe wall thickness causing non-uniform yielding. Various criteria for defining a yield point of ductile materials are known to persons of skill in the art. FIG.16 shows an example stress-strain curve 20 for a first ductile material having an abrupt transition from elastic behavior to plastic behavior. In materials science and engineering, a yield point 21 may be commonly defined as a point on stress-strain curve 20 that indicates the limit of fully elastic behavior and the beginning of plastic behavior (“first material yield criterion”). Before yield point 21, the first ductile material will deform elastically when a stress is applied and will return to its original shape when the applied stress is removed. Once yield point 21 is passed, some fraction of the local deformation will be permanent and non- reversible and is known as plastic deformation. In some ductile materials, there is a gradual onset of non-linear behavior such that a precise yield point may be difficult to identify (as illustrated by an example stress-strain curve 30 in FIG.17 for a second ductile material). For such materials, a yield criterion such as, by way of example, the stress at which 0.2% plastic deformation occurs is commonly used to define a yield point (“second material yield criterion”). Assuming that such materials will elastically rebound when applied stress is removed, a line 32 may be defined that is parallel to the linear elastic portion of stress-strain curve 30 and offset relative to the linear elastic portion of stress- strain curve 30 along the horizontal axis by 0.2% strain. A yield point 33 may be determined from the intersection of line 32 with stress-strain curve 30. Petroleum well casing strings may be manufactured from a variety of steel materials, and these steels may exhibit either an abrupt transition from elastic behavior to plastic behavior or a gradual onset of non-linear behavior. Another commonly used yield criterion (for petroleum well casing steel materials) is the stress at which 0.5% deformation occurs (“third material yield criterion”). This criterion is illustrated by a line 24 in FIG. 16 and a line 34 in FIG. 17, and defines a yield point 25 for stress-strain curve 20 and a yield point 35 for stress-strain curve 30. The above material yield criteria are expressed in terms of stress and strain (terms well understood by persons of ordinary skill in the art), which are proportional in the elastic range, and which are measured using individual material samples designed to have uniform stress and strain along a gauge section. When mechanically interconnecting a primary workpiece and a secondary workpiece by crimping, the workpieces form a multi-component system. The stresses and strains in the components of the system are not uniform, and the structural response of the system is characterized by the relationship between the crimping force and the crimping displacement. The geometry of the components (i.e., diameter, wall thickness, and length) must be known in order to relate, in some way, the crimping force and crimping displacement to the non-uniform stress and strain distributions within the components. Methods according to the present disclosure use a yield criterion for the secondary workpiece that does not require precise knowledge of the geometry and material properties of the secondary workpiece (i.e., deviations of these properties from nominal values do not need to be measured). A point in time is designated as a yield time of pipe 106 (the secondary workpiece) based on a specified yield criterion for a slope value indicative of the relationship between the crimping force and the crimping displacement. The slope value for each user-selected measurement time may be calculated by: • selecting a time interval encompassing the user-selected measurement time; • fitting a linear (or higher order) equation to the crimping force and crimping displacement measurements of the selected time interval; and • calculating the slope of the fitted equation associated with the crimping displacement at the user-selected measurement time. For example, the slope value at 6.0 seconds may be calculated by selecting a time interval of 5.7 to 6.0 seconds, fitting a linear equation to the crimping force and crimping displacement measurements of this time interval, and calculating the slope of the linear equation associated with the crimping displacement at 6.0 seconds. FIG. 14 shows the slope values calculated from the example crimping force and crimping displacement. For each user-selected measurement time, the selected time interval was 0.3 seconds in duration ending at the user-selected measurement time. As is apparent from FIG. 15, the crimping force applied by jaws 107 when pipe 106 (the secondary workpiece) begins to yield is substantially greater than the crimping force applied when centralizer 101 (the primary workpiece) substantially contacts the outer circumference of pipe 106 (at point 133). With some knowledge of the approximate properties of centralizer 101 and pipe 106 (and / or prior crimping experience), a crimping force threshold may be selected that is greater than the crimping force at point 133 and less than the crimping force when pipe 106 begins to yield. Slope values prior to reaching this user-selected crimping force threshold are not prerequisites to the designation of a yield point and do not need to be calculated, thus reducing computational effort. With the example data shown in FIG. 12, a crimping force threshold ^^,^^of 300,000 lb is selected for a user-defined crimping initiation criterion, and is reached at a crimping initiation time ^^^of 6.34 seconds and a crimping displacement ^^,^^of 0.145 inch. Methods in accordance with the present disclosure designate a point in time as a yield time when a specified yield criterion for the secondary workpiece is satisfied. The specified yield criterion for the secondary workpiece is that the slope value crosses a slope threshold equal to a user-selected ratio of the maximum of all slope values subsequent to crossing the user-selected crimping force threshold ^^,^^. FIGS.14 and 15 together show that slope values fluctuate during the interval when pipe 106 is undergoing substantial elastic deformation, before generally trending downward. The user-selected ratio may be chosen as a non-unity value such that the specified yield criterion is satisfied when pipe 106 begins to experience substantial plastic deformation. The user-selected ratio may be chosen based on physical calibration of a crimping process. User-selected ratios chosen in the inclusive range of approximately 0.30 to approximately 0.95 have been successfully used to crimp a variety of combinations of steel centralizers and steel casing used in oil and gas wells. A user-selected ratio of approximately 0.70 has been found to produce reasonably accurate crimps for broad combinations of steel centralizers and steel casing. User-selected ratios may be chosen outside the range of approximately 0.30 to approximately 0.95 in methods in accordance with the present disclosure with certain combinations of workpieces and crimping equipment. User-selected ratios may be chosen greater than approximately 0.95 and less than unity when workpiece properties approach perfect uniformity and measurement noise becomes vanishingly small. User-selected ratios may be chosen greater than zero and less than approximately 0.30 when the pipe structural behaviour produces a transition from elastic deformation to plastic deformation that is less gradual (i.e., more abrupt). The user-selected ratio for this first non-limiting embodiment is approximately 0.70. Referring to FIG. 14, the specified yield criterion for the secondary workpiece (i.e., for pipe 106) is satisfied at a yield time ^^of 10.46 seconds. The maximum slope ^^,^^^subsequent to crossing the user-selected crimping force threshold ^^,^^is 49.0 million lb / inch, and the slope threshold ^^,^^is 34.3 million lb / inch. From FIGS. 12 and 13, the crimping force at the yield time ^^,^is about 905,000 lb and the crimping displacement at the yield time ^^,^is 0.159 inch. A target displacement ^^,^of jaws 7 is calculated as the crimping displacement at the yield time ^^,^plus a user-selected target deformation ^^,^. In this first embodiment, the user- selected target deformation ^^,^is 0.018 inch. The calculated target displacement ^^,^with the example data is 0.177 inch. The movement of jaws 7 is stopped when the crimping displacement equals the target displacement ^^,^, which occurs at a time ^^^of 15.44 seconds. The operation of crimping tool 100 is then reversed to reduce the crimping force to zero and release the crimped centralizer 101 and pipe 106 from crimping tool 100. Second Embodiment: Using indicative measurements directly In a second non-limiting embodiment of a method in accordance with the present disclosure, crimping tool 100 may be configured such that the crimping force applied to the outer surface of centralizer 101 (primary workpiece) is substantially proportional to the actuator differential pressure, and the crimping displacement of jaws 107 is substantially proportional to the actuator displacement. FIG. 18 is a graph of the relationship between the actuator differential pressure measurements and the actuator displacement measurements. The relationship curve depends primarily upon the geometry and material properties of the workpieces being crimped, and therefore has a characteristic shape and features similar to those of the first embodiment, and may be interpreted as showing: • a point in time 141 at which jaws 107 first substantially contact the outer circumference of centralizer 101; • a point in time 142 at which local yielding of centralizer 101 begins to occur; • a point in time 143 at which centralizer 101 substantially contacts the outer circumference of pipe 106; and • a gradual transition of pipe 106 (secondary workpiece) from linear elastic deformation to plastic deformation. In this second embodiment, slope values (as shown in FIG.11) may be calculated directly from the measurements of actuator differential pressure and actuator displacement since the relationship between actuator differential pressure and actuator displacement is indicative of the relationship between the crimping force and crimping displacement of jaws 107. Referring to FIG. 9, a differential pressure threshold ^^^,^^of 1,260 psi (which corresponds to the crimping force threshold ^^,^^of 300,000 lb for the first embodiment) may be selected for a user-defined crimping initiation criterion based on knowledge of the approximate properties of centralizer 101 and pipe 106 (or prior crimping experience). Slope values prior to reaching the user-selected differential pressure threshold ^^^,^^are not prerequisites to the designation of a yield time and do not need to be calculated, reducing computational effort. With the example data, the differential pressure threshold ^^^,^^is reached at a crimping initiation time ^^^of 6.34 seconds (which is the same time as for the first embodiment) and an actuator displacement ^^,^^of 0.965 inch as shown in FIG. 10. Referring to FIG. 11, with a user-selected ratio of approximately 0.70 for the yield criterion, the specified yield criterion for the secondary workpiece (i.e., for pipe 106) is satisfied at a yield time ^^of 10.46 seconds (which is the same as for the first embodiment). The maximum slope ^^,^^^subsequent to crossing the user-selected differential pressure threshold ^^^,^^is 25,300 psi / inch, and the slope threshold ^^,^^is 17,700 psi / inch. The actuator differential pressure at the yield time ^^^,^is 3,340 psi (shown in FIG. 9) and the actuator displacement at the yield time ^^,^is 1.058 inch (shown in FIG. 10). A target displacement of the hydraulic actuator ^^,^is calculated as the actuator displacement at the yield time ^^,^plus an incremental actuator displacement ^^,^corresponding to a user-selected target deformation ^^,^. Based on the geometry and kinematics of crimping tool 100, the user-selected target deformation ^^,^of 0.018 inch (which is the same as for the first embodiment) corresponds to an incremental actuator displacement ^^,^of 0.120 inch. Accordingly, the calculated target displacement of the hydraulic actuator ^^,^is 1.178 inch (corresponding to target displacement ^^,^of jaws 107 in the first embodiment of 0.177 inch). The movement of jaws 107 is stopped when the actuator displacement equals the target displacement of the hydraulic actuator ^^,^, which occurs at a time ^^^of 15.44 seconds (which is the same stop time as for the first embodiment). The operation of crimping tool 100 is then reversedto reduce the crimping force to zero and release the crimped centralizer 101 and pipe 106 from crimping tool 100. FIGS. 19A, 19B, 19C, and 19D illustrate how crimping methods in accordance with the present disclosure can be used across a wide range of tool and workpiece configurations, as outlined in Table 1 below. Crimping tests were conducted on four different crimping tool / workpiece configurations using three different exemplary crimping tool models and three different sizes of steel casing (secondary workpieces) covering a wide range of sizes and wall thickness. Although the secondary workpieces for configurations 2 and 4 were the same size and grade, they did not come from the same manufacturer, and they may have had significant variations in true material strength, wall thickness, and post-yield hardening properties. The industry standard specification for commercial products of these sizes permit the casing outside diameter to vary in a range of -0.5% to +1% of the nominal diameter. Configuration Tool / Workpiece Nominal Nominal Nominal Crimp i i t li A y For all four configurations, the same differential pressure threshold ^^^,^^of 1260 psi and the same user-selected ratio for the yield criterion of 0.70 were used to identify the yield time. The actuator displacement at the yield time ^^,^and the user-selected target deformation ^^,^were different for each configuration. As a result, the target actuator displacement ^^,^was unique to each configuration. Nonetheless, the crimping accuracy (i.e., difference between the user- selected target deformation and the corresponding measured deformation of the secondary workpiece after crimping) was consistent and very low for all tested configurations (i.e., plus or minus a maximum of 0.002 inches). These test result illustrate and prove the previously-noted advantage of methods in accordance with the present disclosure that it achieves accurate crimp depth control that automatically adjusts for the manufacturing variation of individual secondary workpieces. Third Embodiment: User-selected radial direction is radially outward In a third non-limiting embodiment of a method in accordance with the present disclosure, the user-selected radial direction is radially outward from the axis of two substantially axisymmetric and concentrically-nested workpieces. As shown schematically in FIG. 20, a primary workpiece 301 is the innermost workpiece of the plurality of workpieces, and a secondary workpiece 306 is the outermost workpiece of the plurality of workpieces. Workpieces 301 and 306 are made of ductile materials and have a common longitudinal axis A. An example of a crimping tool for applying crimping force to primary workpiece 301 in the user-selected radial direction is schematically illustrated as a mechanism with a tapered- collet-on-mandrel architecture and coaxially aligned with longitudinal axis A. The crimping tool comprises internally-tapered jaws 307 of a collet (i.e., segments of an internally conical sleeve) and a matching externally-tapered mandrel 308. Application of an axial setting force (denoted by vector ^^) to mandrel 308, and a resulting induced axial reaction force (denoted by vector ^^) on axial faces of jaws 307, will urge jaws 307 toward the diametrically-larger axial end of mandrel 308 along the angle of the conical surface of mandrel 308. This causes jaws 307 to move radially outward and engage primary workpiece 301. Alternatively, the action of the crimping tool may be described in terms of an axial setting displacement of mandrel 308 relative to jaws 307. Setting force ^^and reaction force ^^can be understood as arising correlative with the axial setting displacement. As a non-limiting example, setting force ^^and reaction force ^^may be applied by a double-acting hydraulic actuator. FIG. 21 schematically shows the crimping tool, primary workpiece 301, and secondary workpiece 306 as they might appear at the point of greatest crimping force and crimping displacement during a crimping process. When the required crimping displacement has occurred, the setting displacement of the crimping tool is reversed, thus reducing the crimping force to zero and releasing jaws 307 from primary workpiece 301, allowing the crimping tool to be removed, and leaving primary workpiece 301 crimped to secondary workpiece 306. Measurements indicative of the crimping force applied by jaws 307 to primary workpiece 301 and the crimping displacement of jaws 307 are obtained from suitable sensors installed on the crimping tool. FIG.22, which is a graph showing and illustrative example of the relationship between the crimping force and the crimping displacement for this third embodiment, has a characteristic shape and features similar to those of the first embodiment (FIG. 15), and may be interpreted as showing: • a point 331 at which jaws 307 first substantially contact the inner circumference of primary workpiece 301; • a point 332 at which local yielding of primary workpiece 301 begins to occur; • a point 333 at which primary workpiece 301 substantially contacts the inner circumference of secondary workpiece 306; and • a gradual transition of secondary workpiece 306 from linear elastic deformation to plastic deformation. Similar to the first and second embodiments, a crimping force threshold ^^^,^^may be selected for a user-defined crimping initiation criterion that is greater than the crimping force at point 333 (when primary workpiece 306 is plastically deformed and substantially contacts the inner circumference of secondary workpiece 306) and less than the crimping force when secondary workpiece 306 begins to yield. Slope values prior to reaching this crimping force threshold ^^^,^^are not prerequisites to the designation of a yield time and do not need to be calculated, thus reducing computational effort. A point in time may be designated as a yield time when a specified yield criterion for secondary workpiece 306 is satisfied based on a slope value indicative of the relationship between the crimping force and the crimping displacement. The specified yield criterion is that the slope value crosses a slope threshold equal to a user-selected ratio of the maximum of all slope values subsequent to crossing the user-selected crimping force threshold ^^^,^^. The yield time at which the specified yield criterion is satisfied has a corresponding crimping displacement ^^^,^and a corresponding crimping force ^^^,^as indicated in FIG. 22. A target displacement ^^^,^of jaws 307 is calculated as the crimping displacement at the yield time ^^^,^plus a user-selected target deformation ^^^,^. The movement of jaws 307 is stopped when the crimping displacement equals the target displacement ^^^,^. The operation of the crimping tool is then reversedto reduce the crimping force to zero and release the crimped workpieces 301 and 306 from the crimping tool. Fourth Embodiment: Three substantially axisymmetric and concentrically-nested workpieces In a fourth non-limiting embodiment of a method in accordance with the present disclosure, the user-selected radial direction is radially inward toward a common axis of three substantially axisymmetric and concentrically-nested workpieces. As shown schematically in FIG.23, a primary workpiece 401 is the outermost workpiece of the plurality of workpieces, and a secondary workpiece 406 is the innermost workpiece of the plurality of workpieces. A tertiary workpiece 409 is concentrically nested between primary workpiece 401 and secondary workpiece 406. Workpieces 401, 406, and 409 are made of ductile material and have a common longitudinal axis A. A crimping tool for applying crimping force to primary workpiece 401 in the user-selected radial direction is schematically illustrated as a mechanism with a tapered- collet-in-housing architecture and coaxially aligned with longitudinal axis A. The crimping tool comprises the tapered jaws 407 of a collet (i.e., segments of an externally-conical sleeve) and a matching internally-tapered housing 408. Application of an axial setting force (denoted by vector ^^) to housing 408, and a resulting induced reaction force (denoted by vector ^^) on axial faces of jaws 407, will urge jaws 407 toward the diametrically- smaller axial end of housing 408 along the angle of the conical surface of housing 408, causing jaws 407 to move radially inward and engage primary workpiece 401. Alternatively, the action of the crimping tool may be described in terms of an axial setting displacement of housing 408 relative to jaws 407. Setting force ^^and reaction force ^^can be understood as arising correlative with the axial setting displacement. As a non-limiting example, setting force ^^and reaction force ^^may be applied by a double-acting hydraulic actuator. FIG. 24 schematically shows the crimping tool and the plurality of workpieces 401, 406, and 409 as they might appear at the point of greatest crimping force and crimping displacement during a crimping process. When the necessary crimping displacement has occurred, the setting displacement of the crimping tool is reversed, thus reducing the crimping force to zero and releasing jaws 407 from the primary workpiece 401, allowing the crimping tool to be removed, and leaving the plurality of workpieces 401, 406, and 409 mechanically interconnected. Measurements indicative of the crimping force applied by jaws 407 to primary workpiece 401 and the crimping displacement of jaws 407 are obtained from suitable sensors installed on the crimping tool. FIG.25 is a graph showing an illustrative example of the relationship between the crimping force and the crimping displacement for this fourth embodiment, and may be interpreted as indicating: • a point 431 at which jaws 407 first substantially contact the outer circumference of primary workpiece 401; • a point 432 at which local yielding of primary workpiece 401 begins to occur; • a point 433 at which primary workpiece 401 substantially contacts the outer circumference of tertiary workpiece 409; • a point 434 at which local yielding of tertiary workpiece 409 begins to occur; • a point 435 at which tertiary workpiece 409 substantially contacts the outer circumference of secondary workpiece 406; and • a gradual transition of secondary workpiece 406 from linear elastic deformation to plastic deformation. Similar to the previously-described embodiments, a crimping force threshold ^^^,^^may be selected for a user-defined crimping initiation criterion that is greater than the crimping force at point 435 (when primary workpiece 401 and tertiary workpiece 409 are plastically deformed and tertiary workpiece 409 substantially contacts the outer circumference of secondary workpiece 406) and less than the crimping force when secondary workpiece 406 begins to yield. Slope values prior to reaching this crimping force threshold ^^^,^^are not prerequisites to the designation of a yield time and do not need to be calculated, thus reducing computational effort. A point in time may be designated as a yield time when a user-specified yield criterial for secondary workpiece 406 is satisfied based on a slope value indicative of the relationship between the crimping force and the crimping displacement. The specified yield criterion is that the slope value crosses a slope threshold equal to a user-selected ratio of the maximum of all slope values subsequent to crossing user-selected crimping force threshold ^^^,^^. The yield time at which the specified yield criterion is satisfied has a corresponding crimping displacement ^^^,^and a corresponding crimping force ^^^,^as indicated in FIG. 25. A target displacement ^^^,^of jaws 407 is calculated as the crimping displacement at the yield time ^^^,^plus a user-selected target deformation ^^^,^. The movement of jaws 407 is stopped when the crimping displacement equals the target displacement ^^^,^. The operation of the crimping tool is then reversedto reduce the crimping force to zero and release the crimped workpieces 401, 406 and 409 from the crimping tool. It will be readily appreciated by persons of ordinary skill in the art that various modifications to embodiments of methods and systems in accordance with the present disclosure may be devised without departing from the scope of the present teachings, including modifications which may use equivalent structures or materials hereafter conceived or developed, or equivalent mathematical functions, such as (by way of non-limiting example) calculating slope values as a change in crimping displacement for a change in crimping force (instead of calculating slope values as a change in crimping force for a change in crimping displacement) and modifying the specified yield criterion accordingly. It is to be especially understood that the scope of the present disclosure is not intended to be limited to described or illustrated embodiments and example data, and that the substitution of a variant of a described, recited, or illustrated element or feature, without any substantial resultant change in functionality, will not constitute a departure from the scope of the disclosure. In this patent document, any form of the word “comprise” is to be understood in its non-limiting sense to mean that any element or feature mentioned following such word is included, but elements and features not specifically mentioned are not excluded. A reference to an element or feature by the indefinite article "a" does not exclude the possibility that more than one of the element or feature is present, unless the context clearly requires that there be one and only one such element or feature. Any use of any form of the terms "interconnect", "engage", "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 (but not limited to) “equal”, “proportional”, “parallel”, “axisymmetric”, “cylindrical”, “coaxial”, and “concentric” 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 equal” or “substantially cylindrical”) unless the context clearly requires otherwise. In addition, and unless specifically noted otherwise, any reference to an element being “axisymmetric” or “substantially axisymmetric” is intended to denote that the element in question would appear substantially axisymmetric in transverse cross-section, although the cross-sectional configuration of the element might vary along its length. References herein to a point in time at which two concentrically-nested tubular workpieces “substantially contact” each other is to be understood as referring to a point in time at which the radially-adjacent cylindrical surfaces of the two workpieces first come into substantially full but not necessarily uniform circumferential contact with each other. Due to dimensional and surficial irregularities of the workpieces, partial contact between these two cylindrical surfaces could occur before the workpieces “substantially contact” each other. References herein to measurements or data being “indicative of” a crimping force or a crimping displacement are intended to be understood as meaning that crimping force and crimping displacement can be measured or determined by either direct or indirect means. 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.

[0002] LIST OF FEATURES Number / Description Symbol 1 Centralizer 2 Internal bore of centralizer 3 Cylindrical end of centralizer 4 Centralizing section of centralizer 5 Centralizer rib 6 Pipe 7 Collet jaws 7a Face of collet jaw 8 Collet housing 10 Prior art crimping tool 20 Stress-strain curve (abrupt elastic-to-plastic transition) 21 Elastic limit yield point 22 Reference line offset by 0.2% strain from linear elastic portion of stress-strain curve 20 23 Yield point for 0.2% strain offset from linear elastic portion of stress-strain curve 20 24 Reference line at 0.5% strain for stress-strain curve 20 25 Yield point at 0.5% strain for stress-strain curve 20 30 Stress-strain curve (gradual elastic-to-plastic transition) 32 Reference line offset by 0.2% strain from linear elastic portion of stress-strain curve 30 33 Yield point for 0.2% slope offset from linear elastic portion of stress-strain curve 30 34 Reference line at 0.5% strain for stress-strain curve 30 35 Yield point at 0.5% strain for stress-strain curve 30 Number / Description Symbol 100 Modified crimping tool 101 Centralizer 106 Pipe 107 Collet jaws 108 Collet housing 110 Hydraulic actuator piston 120 Hydraulic actuator cylinder 121 Hydraulic actuator directional valve 122 Hydraulic fluid flow line connection 123 Connection block 124 Pressure sensor 125 Displacement sensor 126 Plate 131 Point in time when collet jaws 107 substantially contacts centralizer 101 132 Point in time when local yielding of centralizer 101 begins to occur 133 Point in time when centralizer 101 substantially contacts pipe 106 141 Point in time when collet jaws 107 substantially contacts centralizer 101 142 Point in time when local yielding of centralizer 101 begins to occur 143 Point in time when centralizer 101 substantially contacts pipe 106

[0003] Number / Description Symbol 301 Primary workpiece 306 Secondary workpiece 307 Collet jaws 308 Collet mandrel 331 Point in time when collet jaws 307 substantially contacts primary workpiece 301 332 Point in time when local yielding of primary workpiece 301 begins to occur 333 Point in time when primary workpiece 301 substantially contacts secondary workpiece 306 401 Primary workpiece 406 Secondary workpiece 407 Collet jaws 408 Collet housing 409 Tertiary workpiece 431 Point in time when jaws 407 substantially contacts primary workpiece 401 432 Point in time when local yielding of primary workpiece 401 begins to occur 433 Point in time when primary workpiece 401 substantially contacts tertiary workpiece 409 434 Point in time when local yielding of tertiary workpiece 409 begins to occur 435 Point in time when tertiary 409 workpiece substantially contacts secondary workpiece 406 A Common longitudinal axis of concentrically-nested workpieces F Axial setting force R Reaction force GRAPH LEGEND (re Figures 9-19D, 22, and 25) Symbol Description ^^^Crimping initiation time ^^Yield time ^^^Time when crimping displacement equals target displacement ^^,^^Crimping force threshold for user-defined crimping initiation criterion ^^,^Crimping force at yield time ^^,^^^Maximum slope subsequent to crimping initiation time for embodiment 1^^,^^Slope threshold for embodiment 1 ^^,^^Crimping displacement at crimping initiation time ^^,^Crimping displacement at yield time ^^^,^User-selected target deformation ^^,^Target displacement ^^^,^^Actuator differential pressure threshold indicative of crimping force for user-defined crimping initiation criterion ^^^,^Actuator differential pressure indicative of crimping force at yield time ^^,^^^Maximum slope subsequent to crimping initiation time for embodiment 2 ^^,^^Slope threshold for embodiment 2 ^^,^^Actuator displacement indicative of crimping displacement at crimping initiation time ^^,^Actuator displacement indicative of crimping displacement at yield time^^^,^Actuator displacement indicative of user-selected target deformation ^^,^Actuator displacement indicative of target displacement

Claims

AMENDED CLAIMS received by the International Bureau on 08 May 2025 (08.05.2025)1. A method for mechanically interconnecting, by crimping, a plurality of axisymmetric and concentrically-nested tubular workpieces including a primary workpiece and a secondary workpiece, said method comprising the sequential steps of:(a) providing a crimping tool having a plurality of radially-mov able jaws configured to apply crimping force to the primary workpiece in a user-selected radial direction;(b) activating the crimping tool to apply an increasing crimping force to the primary workpiece in the user-selected radial direction, and to obtain measurements indicative of the crimping force and indicative of a crimping displacement at user-selected measurement times;(c) identifying, as a crimping initiation time, a point in time when a user-defined crimping initiation criterion is satisfied, said crimping initiation criterion being considered indicative of each workpiece of the plurality of workpieces having come into substantial contact with each radially-adjacent workpiece but with no yielding having occurred in the secondary workpiece;(d) for each user-selected measurement time following the crimping initiation time, calculating an indicative relationship between the crimping force and the crimping displacement, said indicative relationship having a slope value;(e) for each user-selected measurement time following the crimping initiation time, determining whether a specified yield criterion of the secondary workpiece has been satisfied;(f) when the specified yield criterion of the secondary workpiece has been satisfied, designating, as a yield time, the point in time when the specified yield criterion of the secondary workpiece was satisfied;(g) calculating a target displacement of the crimping tool jaws as equal to the sum of the crimping displacement at the yield time plus a user-selected target deformation;(h) stopping radial movement of the crimping tool jaws when the crimping displacement reaches the target displacement; and(i) radially retracting the crimping tool jaws to release the plurality of tubular workpieces from the crimping tool; wherein:(A) the crimping force at any point in time is a circumferentially-distributed radial force applied to the primary workpiece by the crimping tool jaws along a user- selected axial interval;(B) the crimping displacement at any point in time is the radial displacement of the crimping tool jaws relative to a user-selected reference datum;(C) when the user-selected radial direction is radially inward, the primary workpiece is the radially-outermost workpiece and the secondary workpiece is the radially- innermost workpiece;(D) when the user-selected radial direction is radially outward, the primary workpiece is the radially-innermost workpiece and the secondary tubular workpiece is the radially-outermost workpiece;(E) the elastic strain limit of the primary workpiece material is selected to be less than the elastic strain limit of the secondary workpiece material;(F) the specified yield criterion for the secondary workpiece is that the slope value calculated in step (d) above crosses a slope threshold equal to a user-selected ratio of a maximum of all slope values calculated subsequent to the crimping initiation time; and(G) the user-selected target deformation corresponds to a specified net permanent local change of a radius of the secondary workpiece resulting from steps (b) through (i) above.

2. The method as in Claim 1 , wherein the plurality of tubular workpieces consists of the primary workpiece and the secondary workpiece.

3. The method as in Claim 1 or Claim 2 wherein the crimping initiation criterion is that the crimping force applied to the primary workpiece has crossed a user-defined crimping force threshold.

4. The method as in Claim 3 wherein the lower limit of the crimping force threshold is based on the crimping force required to cause plastic deformation in all workpieces of the plurality of workpieces except for the secondary workpiece.

5. The method as in Claim 3 or Claim 4 wherein the upper limit of the crimping force threshold is based on the crimping force required to cause plastic deformation in all workpieces of the plurality of workpieces except for the secondary workpiece, plus the minimum crimping force needed to yield the secondary workpiece based on the nominal specifications and manufacturing tolerances of the secondary workpiece.

6. The method as in Claim 1 or Claim 2 wherein the crimping initiation criterion is that the crimping displacement has crossed a user-defined crimping displacement threshold.

7. The method as in Claim 6 wherein the lower limit of the crimping displacement threshold is based on the maximum total of radial gaps between the plurality of workpieces that is possible without exceeding workpiece manufacturing tolerances.

8. The method as in Claim 6 or Claim 7 wherein the upper limit of the crimping displacement threshold is based on the maximum total of radial gaps between the plurality of workpieces that is possible without exceeding workpiece manufacturing tolerances, plus the minimum radial elastic deflection of the secondary workpiece based on the nominal specifications and manufacturing tolerances of the secondary workpiece.

9. The method as in any one of Claims 1-8 wherein the indicative relationship between the crimping force and the crimping displacement is calculated as a least-squares fit of the crimping force and the crimping displacement to a linear equation.

10. The method as in any one of Claims 1-9 wherein:(a) the indicative relationship between the crimping force and the crimping displacement is expressed as a change of the crimping force relative to a change in the crimping displacement; and(b) the user-selected ratio is greater than zero and less than unity.

11. The method as in Claim 10 wherein the user-selected ratio is between approximately 0.30 and approximately 0.95.

12. The method as in Claim 10 wherein the user-selected ratio is approximately 0.70.

13. The method as in any one of Claims 1-12 wherein the elastic strain limit of the primary workpiece material is between approximately 35% and approximately 85% of the elastic strain limit of the secondary workpiece material.

14. The method as in Claim 13 wherein the elastic strain limit of the primary workpiece material is between approximately 50% and approximately 60% of the elastic strain limit of the secondary workpiece material.

15. The method as in any one of Claims 1-14 wherein the user-selected reference datum is the radial position of the jaws at the time the crimping tool is activated.

16. The method as in any one of Claims 1-14 wherein the user-selected radial direction is radially inward, and the user-selected reference datum is the radially-outermost possible position of the jaws.

17. The method as in any one of Claims 1-14 wherein the user-selected radial direction is radially outward, and the user-selected reference datum is the radially-innermost possible position of the jaws.

18. A system for mechanically interconnecting, by crimping, a plurality of axisymmetric and concentrically-nest tubular workpieces including a primary workpiece and a secondary workpiece, said system comprising:(a) a crimping tool having a plurality of radially-movable jaws configured to apply an increasing crimping force to the primary workpiece in a user-selected radial direction;(b) a force sensor configured to measure the crimping force applied by the jaws to the primary workpiece in the user-selected radial direction;(c) a displacement sensor configured to measure radial displacement of the jaws relative to a user-selected reference datum; and(d) one or more processors, wherein:(d.l) at least one of the one or more processors is configured to receive force data from the force sensor indicative of the crimping force applied by the jaws to the primary workpiece at user-selected measurement times;(d.2) at least one of the one or more processors is configured to receive displacement data from the displacement sensor indicative of the crimping displacement of the crimping tool jaws at each user-selected measurement time;(d.3) at least one of the one or more processors is configured to identify, as a crimping initiation time, a point in time when a user-defined crimping initiation criterion is satisfied, said crimping initiation criterion being considered indicative of each workpiece of the plurality of workpieces having come into contact with each radially-adjacent workpiece but no yielding having occurred in the secondary workpiece;(d.4) at least one of the one or more processors is configured to calculate an indicative relationship between the crimping force and the crimping displacement at each user-selected measurement time, wherein each said indicative relationship has an associated slope value;(d.5) at least one of the one or more processors is configured to designate, as a yield time, a point in time when a specified yield criterion of the secondary workpiece is satisfied, said specified yield criterion for the secondary workpiece being that the slope value calculated in accordance with subclause (d.4) above crosses a slope threshold equal to a user- selected ratio of a maximum of all slope values calculated subsequent to the crimping initiation time;(d.6) at least one of the one or more processors is configured to calculate the target displacement of the crimping tool jaws as equal to the sum of the crimping displacement at the yield time plus a user-selected target deformation, said user-selected target deformation corresponding to a specified net permanent local change of a radius of the secondary workpiece from the crimping initiation time to the yield time;(d.7) at least one of the one or more processors is configured to stop the radial displacement of the crimping tool jaws when the crimping displacement reaches the target displacement;(d.8) at least one of the one or more processors is configured to radially retract the crimping tool jaws to release the plurality of tubular workpieces from the crimping tool.

19. The system as in Claim 18 wherein one of the one or more processors is configured to perform two or more functions from the group of functions described in clause (d) in Claim 18.

20. The system as in Claim 18 or Claim 19, wherein:(a) the crimping tool further has a double-acting hydraulic actuator comprising a piston axially movably disposed within a cylinder, said cylinder defining a first variable-volume fluid chamber on a first side of the piston and a second variable-volume fluid chamber on a second side of the piston;(b) the system further comprises a first pressure sensor in fluid communication with the first variable-volume fluid chamber;(c) at least one of the one or more processors is configured to receive fluid pressure data from the first pressure sensor, and to use said fluid pressure data to calculate an actuator differential pressure indicative of the crimping force at each user-selected measurement time; and (d) at least one of the one or more processors is configured to receive calculated actuator differential pressures and actuator axial displacements, from the corresponding processor or processors, for each user-selected measurement time.

21. The system as in Claim 20 wherein the first pressure sensor is a differential pressure sensor in fluid communication with both the first variable-volume fluid chamber and the second variable-volume fluid chamber.

22. The system as in Claim 20 wherein the system further comprises a second pressure sensor in fluid communication with the second variable-volume fluid chamber.

23. The system as in any one of Claims 20-22 wherein at least one of the one or more processors is configured to perform all of the functions described in clauses (c) and (d) in Claim 20.

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