Golf club heads with variable face thickness

Abstract

A variable face thickness pattern is determined for a golf club head by setting a target value for a first constraint. Parametrization zones are defined and values set for a first parameter and a second parameter for each parametrization zone. Resultant first constraint values are evaluated from simulated impacts against the target first constraint value and the values are changed for the first and second parameters to result in a simulated face thickness pattern. In one aspect, the club head has a maximum coefficient of restitution at a first location of the striking face and a second coefficient of restitution that is no less than 98% of the maximum coefficient of restitution at a second location that is at least 7.5 mm from the first location. In another aspect, the club head has a moment of inertia, Izz, and a mass, mh, satisfying: Izz>mh*9.3 cm.sup.2.

Claims

1. A method of manufacturing a golf club head, the method comprising: (a) forming a golf club head main body by either a forging process or an investment casting process, a golf club head main body including a heel, a toe opposite the heel, a sole, and a top portion opposite the sole; (b) determining, with a computing device, a variable face thickness pattern of a striking face for the golf club head by: (i) setting a target value for a first constraint; (ii) on a computer-simulated striking face having a simulated face center, defining a plurality of parametrization zones including a central zone having the simulated face center; (iii) for each parametrization zone, setting values for a first parameter and a second parameter; (iv) simulating impacts for a plurality of impact locations about the simulated striking face; (v) evaluating resultant first constraint values from the simulated impacts against the target first constraint value; and (vi) changing the values for the first parameter and the second parameter by increasing or decreasing the values, such changes in values resulting in a simulated variable face thickness pattern; (c) forming the striking face such that the striking face includes a variable face thickness pattern corresponding to the simulated variable face thickness pattern; and (d) attaching the striking face to the golf club head main body, wherein the golf club head has blade length less than 80 mm and a moment of inertia, Izz, and a golf club head mass, mh, that satisfies: Izz>mh*9.3 cm.sup.2.

2. The method of claim 1, wherein step (c) further includes: defining a central region, an intermediate region, and at least one of an upper region, a lower region, and a toe region; recessing the central region to have a thickness less than a thickness of the intermediate region; and recessing the at least one of the upper region, the lower region, and the toe region to have a thickness less than that of the central region thickness.

3. The method of claim 2, wherein the central region, the intermediate region, the upper region, the lower region, and the toe region each correspond to one of the plurality of parametrization zones.

4. The method of claim 2, wherein the golf club head has a weighted coefficient of restitution of no less than 0.79.

5. The method of claim 2, wherein the intermediate region has a thickness of at least 2.5 mm and no more than 3.3 mm.

6. The method of claim 2, wherein the recessing steps comprise removing material by machining.

7. The method of claim 1, wherein the first parameter is a parametrization zone width and the second parameter is a parametrization zone thickness.

8. The method of claim 1, wherein the first constraint is a mechanical stress limit of the striking face.

9. The method of claim 1, wherein the golf club head is an iron-type cavity-back golf club head.

10. The method of claim 1, wherein the golf club head has a topline thickness of no more than 6.5 mm.

11. A method of manufacturing a golf club head, the method comprising: (a) forming a golf club head main body by either a forging process or an investment casting process, a golf club head main body including a heel, a toe opposite the heel, a sole, and a top portion opposite the sole; (b) determining, with a computing device, a variable face thickness pattern of a striking face for the golf club head by: (i) setting a target value for a first constraint; (ii) on a computer-simulated striking face having a simulated face center, defining a plurality of parametrization zones including a central zone having the simulated face center; (iii) for each parametrization zone, setting values for a first parameter and a second parameter; (iv) simulating impacts for a plurality of impact locations about the simulated striking face; (v) evaluating resultant first constraint values from the simulated impacts against the target first constraint value; and (vi) changing the values for the first parameter and the second parameter by increasing or decreasing the values, such changes in values resulting in a simulated variable face thickness pattern; (c) forming the striking face such that the striking face includes a variable face thickness pattern corresponding to the simulated variable face thickness pattern; and (d) attaching the striking face to the golf club head main body, wherein the golf club head has a blade length less than 80 mm, a maximum coefficient of restitution at a first location of the striking face, and a second coefficient of restitution that is no less than 98% of the maximum coefficient of restitution at a second location of the striking face that is at least 7.5 mm away from the first location.

12. The method of claim 11, wherein the second coefficient of restitution is no less than 99% of the maximum coefficient of restitution.

13. The method of claim 11, step (c) includes: defining a central region, an intermediate region, and at least one of an upper region, a lower region, and a toe region; recessing the central region to have a thickness less than a thickness of the intermediate region; and recessing the at least one of the upper region, the lower region, and the toe region to have a thickness less than that of central region thickness.

14. The method of claim 13, wherein the central region, the intermediate region, the upper region, the lower region, and the toe region each correspond to one of the plurality of parametrization zones.

15. The method of claim 13, wherein the golf club head has a weighted coefficient of restitution of no less than 0.79.

16. The method of claim 13, wherein the intermediate region has a thickness of at least 2.5 mm and no more than 3.3 mm.

17. The method of claim 13, wherein the recessing steps comprise removing material by machining.

18. The method of claim 11, wherein the first parameter is a parametrization zone width and the second parameter is a parametrization zone thickness.

19. The method of claim 11, wherein the first constraint is a mechanical stress limit of the striking face.

20. The method of claim 11, wherein the golf club head is an iron-type cavity-back golf club head.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The features and advantages of the embodiments of the present disclosure will become more apparent from the detailed description set forth below when taken in conjunction with the drawings. The drawings and the associated descriptions are provided to illustrate embodiments of the disclosure, and not to limit the scope of what is claimed.

(2) FIG. 1 is a front view of an exemplary golf club head according to one or more embodiments.

(3) FIG. 2 is a rear view of an exemplary cavity-back club head according to one or more embodiments.

(4) FIG. 3 is a heel side view of the cavity-back club head of FIG. 2 according to one or more embodiments.

(5) FIG. 4 is a cross-section view of the cavity-back club head of FIG. 2 according to one or more embodiments.

(6) FIG. 5 is a rear view of an exemplary hollow club head according to one or more embodiments.

(7) FIG. 6 is a cross-section view of the hollow club head of FIG. 5 according to one or more embodiments.

(8) FIG. 7 depicts an exemplary rear surface of a striking face of a cavity-back club head according to one or more embodiments.

(9) FIG. 8 depicts an exemplary rear surface of a striking face of a hollow club head according to one or more embodiments.

(10) FIG. 9 depicts an exemplary rear surface of a striking face of a club head including a thickness pattern according to one or more embodiments.

(11) FIG. 10 depicts an exemplary rear surface of a striking face of a club head including a different thickness pattern according to one or more embodiments.

(12) FIG. 11 is a flowchart for an example thickness pattern forming process for a striking face according to one or more embodiments.

(13) FIG. 12 is a flowchart for another example thickness pattern forming process for a striking face according to one or more embodiments.

DETAILED DESCRIPTION

(14) Representative examples of one or more novel and nonobvious aspects and features of the golf club heads and methods of manufacturing such club heads as disclosed below are not intended to be limiting in any manner. Furthermore, the various aspects and features of the present disclosure may be used alone or in a variety of novel and nonobvious combinations and sub-combinations with one another.

(15) FIG. 1 is a front view of exemplary golf club head 100 according to one or more embodiments. As shown in FIG. 1, club head 100 includes toe portion 102, heel portion 104, topline portion 106, and sole portion 111. Club head 100 also includes hosel 110 that extends from heel portion 104. Hosel 110 may include an open end for receiving a golf club shaft (not shown) of a golf club. Hosel axis 20 extends axially through the center of hosel 110, and lies in a virtual vertical hosel plane (e.g., virtual vertical hosel plane 21 shown in FIG. 3). Club head 100, including striking face 109, may be formed, for example, of a steel material.

(16) In FIG. 1, club head 100 is oriented in a reference position with sole portion 111 in contact with virtual ground plane 13, and with central hosel axis 20 in the virtual vertical plane. As used herein, a club head is orientated in the “reference position” when the sole of the club head (e.g., sole portion 111) is in contact with a virtual ground plane (e.g., virtual ground plane 13), its central hosel axis (e.g., central hosel axis 20) is positioned in a vertical plane, and its score-lines (e.g., score-lines 112) are parallel to the ground plane. In the reference position, club head 100 is positioned at a predetermined Loft Angle (LA) (i.e., LA in FIG. 3) and a predetermined lie angle (i.e., α in FIG. 2). Unless otherwise indicated, all parameters of the various embodiments in this disclosure are specified with the club heads orientated in the reference position.

(17) In one or more embodiments, LA ranges from about 18 degrees to about 40 degrees. In other embodiments, the golf club head is a wedge-type golf club head and LA ranges from about 40 degrees to about 64 degrees.

(18) As shown in FIG. 1, club head 100 includes striking face 109 configured to strike a conventional golf ball. In some implementations, striking face 109 may form part of a face insert that is fixedly attached to a main body of club head 100. In other implementations, striking face 109 may be integrally formed as part of the main body of club head 100. Striking face 109 is provided with one or more grooves or score-lines 112, which impart additional spin to the golf ball when struck. In FIG. 1, striking face 109 includes face center 14, which is located on virtual center plane 10 that extends vertically through face center 14 perpendicularly to a face plane defined by striking face 109 (e.g., face plane 22 in FIG. 3). As used herein, a “face center” of a striking face is determined according to the procedure described in the United States Golf Association's (USGA's) “Procedure for Measuring the Flexibility of a Golf Clubhead” (Revision 2.0, Mar. 25, 2005). In the example of FIG. 1, face center 14 denotes a point on striking face 109 that is midway between the heel-to-toe extents of score-lines 112, and midway between the sole-to-topline extents of striking face 109. In other embodiments, score-lines may extend to a toe-side edge of the striking face. In such embodiments, the lateral dimension of the face center is determined as midway between the heel-most extent of the score-lines and a club face apex, such as club face apex 107 in FIG. 1.

(19) In the example of FIG. 1, sweet spot 16 is located on striking face 109 a horizontal distance, CGH, toward heel portion 104 from virtual center plane 10. Sweet spot 16 is located on virtual vertical CG plane 12 such that sweet spot 16 is located on striking face 109 where a virtual line projected normal to a face plane of striking face 109 (e.g., face plane 22 in FIG. 3) passes through a CG of club head 100 (e.g., CG 18 in FIG. 2). As used herein, a club head's “sweet spot” is defined as a location on the club head's striking face from which a virtual line projected normal to a face plane of the striking face passes through the club head's CG location.

(20) As discussed in more detail below, striking face 109 has been formed with a variable thickness in different regions or parameterization zones of striking face 109 to provide improved mass and/or performance properties of club head 100. Such properties can include, for example, greater Coefficients of Restitution (CORs) and/or greater Characteristic Times (CTs) on a larger area and/or more commonly hit area of striking face 109, greater Moments of Inertia (MOIs) about a virtual vertical CG axis (e.g., virtual vertical CG axis 24 in FIG. 4) and/or about a virtual horizontal CG axis (e.g., virtual horizontal CG axis 15 in FIG. 2), and/or an improved CG location for club head 100. The improvement of these mass and performance properties can be accomplished by the selective thinning or thickening of the different regions or parameterization zones and/or the relocation of discretionary mass from the striking face to other portions of the club head. As used herein, a striking face thickness is measured perpendicular to a face plane defined by the striking face (e.g., face plane 22 in FIG. 3 and face plane 42 in FIG. 6).

(21) A total mass of the club head may serve as a target total mass comprised of structural mass and discretionary mass. Structural mass as used herein generally refers to mass necessary to establish a minimum structural integrity for the club head to be operable for its intended use. Discretionary mass, on the other hand, can refer to the remaining mass that, given a target mass, is not needed to establish the minimum structural integrity of the club head, and may therefore be located primarily to adjust mass and/or performance properties of the club head.

(22) For example, the thickness of different regions or parameterization zones of striking face 109 can result in mass being moved from such regions or parameterization zones to other locations in club head 100 to provide higher MOIs of club head 100 and an improved location for the CG of club head 100 (e.g., CG 18 in FIG. 2), while increasing COR values in particular locations on the striking face. For example, mass removed from particular areas of the striking face can improve the COR of the striking face and the removed mass can be relocated in the club head so that the CG of club head 100 can be advantageously located closer to virtual center plane 10, closer to virtual ground plane 13, and farther behind striking face 109. As a result, sweet spot 16 can be advantageously located closer to face center 14 to better correspond to a player's expected sweet spot location and/or a more frequently hit area the striking face, and to provide a more forgiving club head to result in better off-center shots in terms of shot height, straightness, and distance. In this regard, sweet spot 16 in some implementations can be located horizontally no greater than 2.0 mm from face center 14 as a result of the relocation of mass from striking face 109 in accordance with the present disclosure. In other words, the CG of club head 100 (e.g., CG 18 in FIG. 2) in such implementations can be located not more than 2.0 mm from virtual center plane 10. In one or more embodiments, golf club heads having this lateral CG location do not include any high-density materials (e.g., tungsten alloys).

(23) As noted above, the variable thickness pattern of the striking face discussed in more detail below can increase the COR at locations on striking face 109 corresponding to more commonly hit locations or a larger area of striking face to provide better energy transfer for off-center shots or for a statistically greater number of shots. Additionally or alternatively, the disclosed variable thickness patterns for a striking face can increase the area of the striking face that has a relatively high COR. For example, in some implementations, striking face 109 in FIG. 1 may include a maximum COR no less than 0.80 at a first location, and a COR of no less than 98% of the maximum COR at an auxiliary location on the striking face that is no less than 7.5 mm from the first location. In such implementations, the first location corresponding to the maximum COR may be at or near sweet spot 16, such as within 5 mm of sweet spot 16. Some implementations of variable thickness patterns discussed below for improving CORs on the striking face include, for example, a central region of the striking face having a heel-side thickness greater than a toe-side region.

(24) FIG. 2 is a rear view of an exemplary cavity-back club head according to one or more embodiments. In this regard, club head 100 in FIG. 2 includes rear cavity 114 behind at least a portion of striking face 109, and rear muscle 116 near sole portion 111. For the purposes of ease of illustration, FIG. 2 provides a rear view of club head 100 from FIG. 1. However, those of ordinary skill in the art will appreciate with reference to the present disclosure that club head 100 may include a different construction in other implementations, such as the hollow body construction shown in FIG. 6, for example.

(25) As shown in FIG. 2, CG 18 is located on virtual horizontal CG axis 15. A horizontal MOI of golf club head 100, Ixx, is shown about virtual horizontal CG axis 15, which extends through CG 18 and is parallel to striking face 109. As noted above, the reduction of mass achieved by varying the thickness of striking face 109 can allow for an increased Ixx, and thereby improve performance of golf club head 100 for off-center shots in a vertical direction along striking face 109 (e.g., toward topline portion 106 or toward sole portion 111).

(26) Club head 100 in FIG. 2 has a Blade Length (BL) measured between a toe-most extent of club head 100 at virtual vertical toe plane 25 and the intersection of hosel axis 20 and ground plane 13, which also defines lie angle α. In some implementations, club head 100 can have a BL less than 80 mm. This blade length may, for example, correspond to an expected BL for an iron-type club head. In this regard, changes can be made to the thickness of striking face 109 without sacrificing the conventional outer dimensions of club head 100, such as the BL or topline thickness of topline portion 106 (e.g., TL.sub.T in FIG. 3). In addition, the overall or target club head mass of club head 100 (e.g., swing weight) in some implementations may correspond to expected masses for iron-type club heads.

(27) As noted above, the mass for iron-type club heads typically vary based on the Loft Angle (LA). When presented in a set, iron-type club heads can increase in mass with loft. For example, the mass of iron-type club heads may adhere the following equation:
mh=2.1 g/degree*LA+a,  Equation 1
where mh is a club head mass, LA is the loft angle of the club head when orientated in a reference position, and a is between 190 g and 210 g. In some implementations, club head 100 maintains such a head mass, mh, while having an improved face thickness pattern.

(28) FIG. 3 is a heel side view of club head 100 according to one or more embodiments. As shown in FIG. 3, the LA of club head 100 is defined between face plane 22 and virtual vertical hosel plane 21. As noted above, hosel axis 20 extends axially through the center of hosel 110, and lies in virtual vertical hosel plane 21. Face plane 22 is defined such that striking face 109 lies in face plane 22. With reference to Equation 1 above, the club head mass of club head 100 may vary depending on the LA of club head 100 such that higher numbered clubs with larger angles for LA have a greater club head mass.

(29) As shown in FIG. 3, a distance between face plane 22 and rear side plane 26 defines Top Line Thickness (TL.sub.T), which corresponds to a thickness of top line portion 106 shown in FIG. 1. The TL.sub.T of club head 100 is no greater than 6.5 mm. This TL.sub.T may correspond to an expected TL.sub.T for an iron-type club head. In this regard, changes can be made to the thickness pattern of striking face 109 without sacrificing the traditional outer dimensions of club head 100, such as the TL.sub.T of club head 100, which may be preferred by some golfers.

(30) FIG. 4 is a cross-section view of club head 100 taken along cross section line 4 in FIG. 1 according to one or more embodiments. As shown in FIG. 4, a rear surface of striking face 109 facing rear cavity 114 and rear muscle 116 includes upper region groove 118, central region recess 120, and lower region groove 122. In implementations where striking face 109 includes a face insert, a rear surface of the face insert can include upper region groove 118, central region recess 120, and lower region groove 122.

(31) The rear surface of striking face 109 also includes intermediate region 108 at least partially surrounding the central region including central region recess 120. In this regard, intermediate region 108 includes upper intermediate region 108u and lower intermediate region 108L above and below central region recess 120, respectively. Each of the central region, the upper region, and the lower region including central region recess 120, upper region groove 118, and lower region groove 122, respectively, has an average thickness that is less than the average thickness of intermediate region 108, which may have an approximately uniform thickness. Upper region groove 118 and lower region groove 122 may extend in generally a heel to toe direction, as in the examples of upper region grooves 318 and 418 and lower region grooves 322 and 422 in FIGS. 7 and 8, respectively.

(32) In some implementations, at least one of upper region groove 118 and lower region groove 122 can be an elongate groove having a width no less than approximately 2.0 mm. In addition, thickness of central region recess 120 may taper in some embodiments such that a heel-side region of the central recess may be thicker than a toe-side region of the central recess, as in the example of central region recess 320 in FIG. 7. As another example, the central recess can include a heel-side region that has a greater thickness than a toe-side region, as in the example of heel-side region 435 and toe-side region 433 in FIG. 8. In some implementations, the thickness of the central region may decrease stepwise from a heel-side of the central region toward a toe-side of the central region.

(33) In FIG. 4, Izz, is centered about virtual vertical CG axis 24. Discretionary mass removed or saved from striking face 109 to form upper region groove 118, central region recess 120, and lower region groove 122 can be relocated to heel portion 104 and toe portion 102 to increase Izz. In some implementations, Izz may satisfy:
Izz>mh*9.3 cm.sup.2  Equation 2
where mh is the mass of club head 100. As noted above, increasing the MOI about virtual vertical axis 24 extending through CG 18 improves the forgiveness of club head 100 so as to cause less bending of club head 100 about virtual vertical axis 24 during off-center shots in a horizontal direction along striking face 109 (e.g., shots that are more toe-ward or heel-ward of sweet spot 16).

(34) In addition, the variable thickness pattern of striking face 109 can increase the COR at locations on striking face 109 corresponding to more commonly hit locations or a larger area of striking face to provide better energy transfer for off-center shots or for a statistically greater number of shots. The variable thickness pattern of striking face 109 with upper region groove 118, central region recess 120, and lower region groove 122 can increase the area of the striking face that has a relatively high COR.

(35) For example, mass removed from particular areas of striking face 109 can improve the COR of striking face 109, and the removed mass can be relocated in club head 100 so that CG 18 can be advantageously located closer to a lateral center of striking face 109, closer to virtual ground plane 13, and farther behind striking face 109. In such an example, mass removed or saved from striking face 109 to form upper region groove 118, lower region groove 122, and central region recess 120, such as by machining (e.g., grinding, milling) or by a known casting or forging process, can be relocated to rear muscle 116 to lower the location of CG 18 and move CG 18 farther behind striking face 109. As another example, mass removed from striking face 109 can be relocated from a heel-side of striking face 109 to a toe-side of striking face 109 to move CG 18 away from heel portion 104 toward toe portion 102.

(36) Those of ordinary skill in the art will appreciate with reference to the present disclosure that other implementations may vary from the arrangement shown in FIG. 4. For example, other implementations of a cavity-back club head may include a different shape of rear cavity 114 or rear muscle 116. As another example variation, the cross-section shapes of one or more of upper region groove 118, central region recess 120, and lower region groove 122 may differ from what is shown in FIG. 4 in other implementations. As yet another example variation, some implementations may not include central region recess 120, and only include one or more grooves adjacent a periphery of the rear surface of striking face 109, such as upper region groove 118 and/or lower region groove 122.

(37) FIG. 5 is a rear view of exemplary hollow body club head 200 head according to one or more embodiments. Club head 200, including striking face 209, may be formed, for example, of a steel material. As with club head 100 in FIGS. 1 to 4, club head 200 includes a hosel 210, a toe portion 202, and a heel portion 204. However, instead of having a rear cavity such as with rear cavity 114 in FIGS. 2 and 4 for club head 100, club head 200 in FIGS. 5 and 6 includes interior cavity 224 behind at least a portion of striking face 209, as shown in FIG. 6. In some implementations, striking face 209 may form part of a face insert that is fixedly attached to a main body of club head 200. In other implementations, striking face 209 may be integrally formed as part of the main body of club head 200. For the purposes of ease of illustration, FIG. 5 provides a rear view of club head 200 that may have a similar exterior front appearance as club head 100 in FIG. 1. However, those of ordinary skill in the art will appreciate with reference to the present disclosure that club head 200 may include a different construction in other implementations than shown in FIGS. 5 and 6.

(38) As shown in FIG. 5, CG 48 is located on virtual horizontal CG axis 45. A horizontal MOI of club head 200, Ixx, is shown about virtual horizontal CG axis 45, which extends through CG 48 and is parallel to striking face 209, which is shown in FIG. 6. The reduction of mass achieved by varying the thickness of striking face 209 can allow for an increased Ixx by relocating mass to other portions of club head 200, and thereby improve performance of golf club head 200 for off-center shots in a vertical direction along striking face 209 (e.g., toward topline portion 206 or toward sole portion 211).

(39) Club head 200 in FIG. 5 has a Blade Length (BL) measured between a toe-most extent of club head 200 at virtual vertical toe plane 45 and the intersection of hosel axis 40 and ground plane 13, which also defines lie angle α. In some implementations, club head 200 can have a BL less than 80 mm. This blade length may, for example, correspond to an expected BL for an iron-type club head. In this regard, changes can be made to the thickness of striking face 209 without sacrificing the conventional outer dimensions of club head 200, such as the BL or topline thickness of topline portion 206. In addition, in some implementations, the overall or target club head mass of club head 200 (e.g., swing weight) may correspond to expected masses for iron-type club heads.

(40) As noted above, the mass for iron-type club heads typically vary based on the Loft Angle (LA). As shown in FIG. 6, the LA of club head 200 is defined between face plane 42 and virtual vertical hosel plane 41. Virtual vertical hosel plane 41 includes hosel axis 40 that extends axially through the center of hosel 210. Face plane 42 is defined such that striking face 209 lies in face plane 42. The mass of club head 200 can satisfy Equation 1 provided above with respect to the LA, while having an improved face thickness pattern. In addition, club head 200 can have a depth less than that of a typical hybrid-type golf club head. For example, club head 200 may have a depth less than 30 mm, as measured from a leading edge to a trailing edge of sole portion 211 of club head 200. As noted above, the relocation of mass from striking face 209 can ordinarily allow for improved performance and mass properties, such as increased MOIs, better CG location, and increased CORs or CTs, without changing the expected dimensions, footprint, or exterior appearance of a conventional iron-type golf club head.

(41) FIG. 6 is a cross-section view of club head 200 taken along cross-section line 6 in FIG. 5 according to one or more embodiments. As shown in FIG. 6, a rear surface of striking face 209 facing interior cavity 224 and rear muscle 216 includes upper region groove 218, and central region recess 220. In implementations where striking face 209 includes a face insert, a rear surface of the face insert can include upper region groove 218 and central region recess 220.

(42) The rear surface of striking face 209 also includes intermediate region 208 at least partially surrounding the central region including central region recess 220. In this regard, intermediate region 208 includes upper intermediate region 208.sub.U and lower intermediate region 208.sub.L above and below central region recess 220, respectively. Each of the central region including central region recess 220, and the upper region including upper region groove or recess 218 has an average thickness that is less than the average thickness of intermediate region 208. In some implementations, intermediate region 208 may have an approximately uniform thickness. Upper region groove 218 may extend in generally a heel to toe direction, as in the examples of upper region grooves 318 and 418 in FIGS. 7 and 8, respectively.

(43) In some implementations, upper region groove 218 can have an elongate groove having a width no less than approximately 2.0 mm. In addition, a thickness of central region recess 220 may taper in some implementations such that a heel-side region of the central recess may be thicker than a toe-side region of the central recess, as in the example of central region recess 320 in FIG. 7. As another example, the central recess can include a heel-side region that has a greater thickness than a toe-side region, as in the example of heel-side region 435 and toe-side region 433 in FIG. 8.

(44) Such a tapering or variation of the central region thickness or central recess can also ordinarily improve the COR in the central region and/or increase an area of striking face 209 having a greater COR, as discussed below in more detail with reference to FIGS. 7 to 10. In addition, the thickness of different regions or parameterization zones of striking face 209 can result in mass being moved from such regions or parameterization zones to other locations in club head 200 to provide higher MOIs of club head 200 and an improved location for CG 48, while increasing COR values in particular locations on the striking face.

(45) For example, mass removed from particular areas of striking face 209 can improve the COR of striking face 209, and the removed mass can be relocated in club head 200 so that CG 48 can be advantageously located closer to a lateral center of striking face 209, closer to virtual ground plane 13, and farther behind striking face 209. In such an example, mass removed from striking face 209 to form upper region groove 218 and central region recess 220, such as by machining or by a known casting or forging process, can be relocated to rear muscle 216 to lower the location of CG 48 and move CG 48 farther behind striking face 209. In some implementations, striking face 209 can be formed separately and attached to a main body of club head 200 by welding or other known methods. As another example, mass removed from striking face 209 can be relocated from a heel-side of striking face 209 to a toe-side of striking face 209 to move CG 48 away from heel portion 204 toward toe portion 202.

(46) As a result, the sweet spot on striking face 209 (e.g., sweet spot 16 in FIG. 1) can be advantageously located closer to a face center (e.g., face center 14 in FIG. 1) to better correspond to a player's expected sweet spot location or to more frequently hit locations on striking face 209. In this regard, the sweet spot of club head 200 in some implementations can be located horizontally no greater than 2.0 mm from a face center as a result of the relocation of mass from striking face 209.

(47) As noted above, the variable thickness pattern of the striking face can increase the COR at locations on striking face 209 corresponding to more commonly hit locations to provide better energy transfer for a statistically greater number of shots, resulting in an improved weighted COR for the striking face. Additionally or alternatively, the disclosed variable thickness patterns for a striking face can increase the area of the striking face that has a relatively high COR. For example, in some implementations, striking face 209 may include a maximum COR no less than 0.80 at a first location, and a COR of no less than 98% of the maximum COR at an auxiliary location on striking face 209 that is no less than 7.5 mm from the first location. In such implementations, the first location corresponding to the maximum COR may be at or near the sweet spot, such as within 5 mm of the sweet spot. Some implementations of variable thickness patterns discussed below for improving CORs on the striking face include, for example, a central region of the striking face having a heel-side thickness greater than a toe-side region.

(48) In FIG. 6, Izz, is centered about virtual vertical CG axis 44. Discretionary mass removed or saved from striking face 209 to form upper region groove 218 and central region recess 220 can be relocated to heel portion 204 and toe portion 202 to increase Izz. In some implementations, Izz may satisfy Equation 2 provided above. Increasing the MOI about virtual vertical axis 44 extending through CG 48 improves the forgiveness of club head 200 so as to cause less bending of club head 200 about virtual vertical axis 44 during off-center shots in a horizontal direction along striking face 209 (e.g., shots that are more toe-ward or heel-ward of the sweet spot).

(49) Those of ordinary skill in the art will appreciate with reference to the present disclosure that other implementations may vary from the arrangements shown in FIGS. 5 and 6. For example, other implementations of a hollow body club head may include a different shape of interior cavity 214 or rear muscle 216. As another example variation, the cross-section shapes of upper region groove 218 or central region recess 220 may differ from what is shown in FIG. 4 in other implementations. In this regard, other implementations may also include a lower region groove, as in the example of FIG. 4 discussed above. In yet other implementations, central region recess 220 may be omitted, such that the recess or recesses on the rear surface of striking face 209 may only include one or more grooves or channels adjacent a periphery of the rear surface, such as upper region groove 218.

(50) FIG. 7 depicts an exemplary rear surface 328 of striking face 309 of a cavity-back club head, such as cavity-back club head 100 in FIGS. 2 to 4, according to one or more embodiments. As shown in FIG. 7, rear surface 328 includes recesses in an upper region, a central region, a toe region, and a lower region. In more detail, rear surface 328 includes upper region groove or channel 318, toe region groove or channel 326, and lower region groove or channel 322 that are adjacent a periphery of rear surface 328. Central region recess 320 is formed in a central region between upper region groove 318, toe region groove 326, and lower region groove 322. Intermediate region 308 surrounds central region recess 320 and is disposed between central region recess 320 and each of upper region groove 318, toe region groove 326, and lower region groove 322. In addition, intermediate region 308 has an average thickness that is greater than that of each of central region recess 320, upper region groove 318, toe region groove 326, and lower region groove 322.

(51) Preferred dimensions of central region recess 320 have a face thickness of no more than 2.5 mm, that preferably tapers from 2.3 mm on a heel-side of central region recess 320 to 1.9 mm on a toe-side of central region recess 320. Preferred dimensions of upper region groove 318 have a face thickness of no more than 1.5 mm, and a maximum width of no less than 5.0 mm. Preferred dimensions of toe region groove 326 have a face thickness less than upper region groove 318, and a maximum width no less than 2.0 mm. Preferred dimensions of lower region groove 322 have a face thickness of no more than 1.5 mm, that is preferably greater than toe region recess 326, and a width no less than 2.5 mm. As referred to herein, the width of a groove or channel is defined by a maximum perpendicular distance between the longer opposite sides of the groove or channel. A preferred thickness of intermediate region 308 surrounding the recesses of central region recess 320, upper region groove 318, toe region groove 326, and lower region groove 322 has a thickness less than 3 mm and greater than 2.5 mm, and preferably about 2.7 mm.

(52) Some preferred dimensions for the recesses of rear surface 328 in FIG. 7 can include the dimensions in Table 1 below. As used below, the thickness refers to a thickness of striking face 309, the width refers to a distance measured perpendicular to opposing longest sides of the recess, and the radius refers to a radius of curvature between a bottom of the recess that has the face thickness indicated for the recess and an adjacent wall of the recess.

(53) TABLE-US-00001 TABLE 1 Club Central Region Upper Region Toe Region Lower Region Head Recess 320 Groove 318 Groove 326 Groove 322 Club Thickness: 2.3 mm Thickness: 1.5 mm Thickness: 0.9 mm Thickness: 1.2 mm Head (heel-side) tapered to 1.9 Width: 6.5 mm Width: 2.5 mm Width: 3.0 mm 1A mm (toe-side) Radius: 0.4 mm Radius: 0.4 mm Radius: 1.5 mm Radius: 0.4 mm Club Thickness: 2.4 mm Thickness: 1.5 mm Thickness: 0.9 mm Thickness: 1.2 mm Head (heel-side) tapered to 2.0 Width: 6.5 mm Width: 2.5 mm Width: 3.0 mm 2A mm (toe-side) Radius: 0.4 mm Radius: 0.4 mm Radius: 1.5 mm Radius: 0.4 mm Club Thickness: 2.4 mm Thickness: 1.5 mm Thickness: 0.9 mm Thickness: 1.2 mm Head (heel-side) tapered to 2.0 Width: 6.5 mm Width: 2.5 mm Width: 3.0 mm 3A mm (toe-side) Radius: 3.0 mm Radius: 1.25 mm Radius: 1.5 mm Radius: 3.0 mm

(54) The foregoing preferred dimensions for central region recess 320, upper region groove 318, toe region groove 326, and lower region groove 322 improve performance and mass related properties of cavity-back club heads. Such performance and mass related properties include, for example, the CG location for the club head, CORs or CTs at various locations on the striking face, and MOIs about different virtual axes passing through the CG. The recesses on rear surface 328 not only increase the COR of striking face 309 with a reduction of mass in striking face 309 at particular locations, but can also improve the weight distribution of the club head to increase MOIs and/or better locate the CG for performance, as discussed above. The recesses on rear surface 328 may also be determined with maximum face stress as a constraint so that striking face 309 is comparable to prior art club heads when tested for durability, despite the reduced mass of striking face 309.

(55) Those of ordinary skill in the art will appreciate with reference to the present disclosure that other implementations of a rear surface of a striking face for a cavity-back club head may differ from the arrangement shown in the example of FIG. 7. For example, other arrangements may not include one or more of the recesses shown in FIG. 7.

(56) FIG. 8 depicts exemplary rear surface 428 of striking face 409 of a hollow body club head, such as hollow body club head 200 in FIGS. 5 and 6, according to one or more embodiments. As shown in FIG. 8, rear surface 428 includes recesses in an upper region, a central region, a toe region, and a lower region. However, unlike the example of rear surface 328 in FIG. 7, rear surface 428 in FIG. 8 includes a different thickness pattern for central region recess 420. In more detail, middle portion 437 of central region recess 420 is thicker than heel-side portion 435 and toe-side portion 433. Such an arrangement ordinarily further improves COR or CT for a larger area of striking face 409 in the central region.

(57) In addition, rear surface 428 includes upper region groove or channel 418, toe region groove or channel 426, and lower region groove or channel 422 that are adjacent a periphery of rear surface 428. Central region recess 420 is formed in a central region between upper region groove 418, toe region groove 426, and lower region groove 422. Intermediate region 408 surrounds central region recess 420 and is disposed between central region recess 420 and each of upper region groove 418, toe region groove 426, and lower region groove 422. In addition, intermediate region 408 has an average thickness that is greater than that of each of central region recess 420, upper region groove 418, toe region groove 426, and lower region groove 422.

(58) Some preferred thicknesses in striking face 409 for the recesses of rear surface 428 in FIG. 8 include the following thicknesses for Club Heads 1B, 2B, 3B, and 4B in Table 2 below. The central region thicknesses provided for the Comparable Club Head B in Table 2 are measured thicknesses of its striking face at the locations where the central region recesses of FIG. 8 (i.e., heel-side central region recess 435, middle central region recess 437, and toe-side central region recess 433) would otherwise be located. The Comparable Club Head B includes a continuous peripheral groove or channel of uniform width and depth along a majority of the periphery of the rear surface of its striking face. Table 2 also includes preferred widths for upper region groove 418, toe region groove 426, and lower region groove 422, as measured perpendicularly between the two longest opposing sides of the groove.

(59) TABLE-US-00002 TABLE 2 Comparable Club Head Club Head Club Head Club Head Recess Thickness or Width Club Head B 1B 2B 3B 4B Mid. Cent. Reg. Recess 437 2.3 mm 1.8 mm 2.0 mm 2.0 mm 2.0 mm Thickness Heel Cent. Reg. Recess 435 2.3 mm 2.0 mm 2.2 mm 2.2 mm 2.2. mm  Thickness Toe Cent. Reg. Recess 433 2.3 mm 1.6 mm 1.8 mm 1.8 mm 1.8 mm Thickness Upper Reg. Groove 418 1.1 mm 1.1 mm 1.1 mm 1.1 mm 1.1 mm Thickness Toe Reg. Groove 326 1.1 mm 0.9 mm 0.9 mm 0.9 mm 0.9 mm Thickness Lower Reg. Groove 422 1.1 mm 1.3 mm 1.3 mm 1.3 mm 1.4 mm Thickness Upper Reg. Groove 418 3.0 mm 6.5 mm 6.5 mm 6.5 mm 6.5 mm Width Toe Reg. Groove 326 3.0 mm 2.5 mm 2.5 mm 2.5 mm 2.5 mm Width Lower Reg. Groove 422 3.0 mm 4.0 mm 4.0 mm 4.0 mm 4.0 mm Width

(60) The foregoing preferred dimensions for central region recess 420 (i.e., middle central region recess 437, heel-side central region recess 435, and toe-side central region recess 433), upper region groove 418, toe region groove 426, and lower region groove 422 improve performance and mass related properties of hollow club heads. Such performance and mass related properties include, for example, the CG location for the club head, CORs or CTs at various locations on the striking face, and MOIs about different virtual axes passing through the CG. In this regard, Table 4 below provides measured or computer-simulated values for the removal of mass from striking face 409, the COR at face center 54, the COR at an off-center location 58 that is 7.5 mm toe-ward of sweet spot 56, and a weighted COR representing an expected or overall COR for striking face 409 that is calculated by weighting the CORs at different locations on striking face 409 using a probability that a golf ball will be hit at the location.

(61) In some implementations, striking face 409 can include a maximum COR no less than 0.80 at a first location, such as at or within 5 mm of sweet spot 46, and a COR no less than 98% of the maximum COR at a second location 48 that is no less than 7.5 mm from the first location. The thicknesses of the recesses of striking face 409 may also be determined so as to increase a weighted COR. The weighted COR can be determined based on a bin-by-bin or location-by-location impact probability, as discussed in more detail in U.S. Pat. No. 10,456,643, titled “GOLF CLUB HEAD,” and filed on Dec. 28, 2018, the entire contents of which are hereby incorporated by reference. The weighted COR, “expected COR” or “overall COR” may be considered to represent a probability-adjusted measure of club head performance that a typical golfer would actually expect given how impacts are empirically dispersed about striking face 409. Using such information, a golfer may make a more informed decision in selecting a golf club based on its weighted COR. Alternatively or additionally, a golfer may determine which golf clubs may be better suited to the golfer's specific handicap or skill level.

(62) The weighted COR can be determined by superimposing onto striking face 409 a rectangular virtual evaluation region comprising a first pair of horizontal sides having a length of 35 mm, a second pair of vertical sides having a length of 25 mm, and a geometric center that coincides with the face center. The rectangular virtual evaluation region is divided into bins by dividing the rectangular virtual evaluation region into five rows (i.e., m=5) having equal height of 5 mm, and seven columns (i.e., n=9) having equal width of 5 mm, thereby forming a matrix of bins having coordinates i and j. An average COR is determined (e.g., measured or computer-simulated) for each bin represented by its coordinates i, j, and the weighted COR can be determined by Equation 3 below. In other implementations, a COR may be determined for a center position of each bin.
Weighted COR=Σ.sub.i=1.sup.nΣ.sub.j=1.sup.mp.sub.ij*c.sub.ij  Equation 3
where p.sub.ij is an impact probability for the bin at coordinates i, j according to an impact probability matrix, such as Table 3 below.

(63) TABLE-US-00003 TABLE 3 i = 1 i = 2 i = 3 i = 4 i = 5 i = 6 i = 7 j = 1 0.42% 0.43% 0.30% 0.22% 0.11% 0.03% 0.03% j = 2 3.58% 3.64% 2.96% 2.23% 1.20% 0.76% 0.31% j = 3 5.46% 8.29% 8.54% 6.50% 4.42% 2.43% 1.06% j = 4 3.36% 5.97% 6.55% 6.65% 5.01% 2.83% 1.19% j = 5 1.52% 2.43% 3.31% 3.18% 2.49% 1.80% 0.81%

(64) Other impact probability matrices may be used to determine the weighted COR in different implementations. For example, other impact probability matrices for determining a weighted COR or expected COR can include those disclosed in U.S. Pat. No. 10,456,643 incorporated by reference above. As another example variation, the measurement locations for the CORs can correspond to points or a differently shaped boundary than the rectangular bins described above for Table 3. In yet other variations, the COR measurement locations can correspond to areas that are spaced apart form each other that do not abut. As another example variation, the orientation of the bins or COR measurement locations may not form a rectangular matrix, but rather, an irregular arrangement of a different configuration, such as an annulus or sunburst configuration.

(65) The recesses on rear surface 428 not only increase CORs of striking face 409 with a reduction of mass in striking face 409 at particular locations, but can also improve the weight distribution of the club head to increase MOIs and/or better locate the CG for performance, as discussed above. The recesses on rear surface 428 may also be determined with maximum face stress as a constraint so that striking face 409 is comparable to prior art club heads when tested for durability, despite the reduced mass of striking face 409.

(66) With reference to the dimensions in Table 2 above for the recesses of rear surface 428 in FIG. 8, Table 4 below provides computer-simulated or measured mass and performance properties for the corresponding Comparable Club Head B, Club Head 1B, Club Head 2B, Club Head 3B, and Club Head 4B. As shown in Table 4 below, the amount of mass removed or saved from the striking faces decreases from Club Head 1B to Club Head 4B, as the face center COR, off-center COR, and weighted COR decreases from Club Head 1B to Club Head 4B. However, each of Club Head 1B to Club Head 4B provide greater values for the amount of mass removed, face center COR, off-center COR, and weighted COR than for Comparable Club Head B.

(67) TABLE-US-00004 TABLE 4 Comparable Club Head Club Head Club Head Club Head Property Club Head B 1B 2B 3B 4B Mass Savings from Striking NA 7.57 g 5.67 g 5.14 g 4.97 g Face of Comparable Club Head Face Center COR 0.7976 0.8098 0.8053 0.8043 0.8039 Off-Center COR at 7.5 mm 0.7843 0.7997 0.7936 0.7931 0.7926 Toe-Ward of Sweet Spot Weighted COR 0.7837 0.7953 0.7910 0.7902 0.7897

(68) Those of ordinary skill will appreciate with reference to the present disclosure that other arrangements of recesses are possible than those shown in FIG. 8. In this regard, the removal of mass from striking face 309 with the recesses formed in rear surface 328 in FIG. 7 discussed above can also result in a reduction in mass from striking face 309, an increased COR at the face center, an increased COR at an off-center location that is 7.5 mm toe-ward of the sweet spot, and an increased weighted COR. As another example variation, some implementations may not include one or more of upper region groove 418, toe region groove 426, lower region groove 422, or central region recess 420 or portions thereof, such as heel-side central region recess 435, middle central region recess 437, or toe-side central region recess 433.

(69) In this regard, Table 5 below provides preferred striking face thicknesses and widths for recesses in variations of striking face 409 that do not include lower region groove 422, but still include heel-side central region recess 435, middle central region recess 437, toe-side central region 433, upper region groove 418, and toe-side region groove 426. All of the recesses in Table 5 below can have a radius of 0.4 mm between a bottom of the recess having the indicated thickness and an adjoining wall.

(70) TABLE-US-00005 TABLE 5 Club Central Region Upper Region Toe Region Lower Region Head Recess 420 Groove 418 Groove 426 Groove 422 Club Middle Central Region Thickness: 1.75 mm Thickness: 1.75 mm None Head 437 Thickness: 2.15 mm Width: 6.5 mm Width: 6.25 mm 1C Heel-Side Central Region 435 Thickness: 1.95 mm Toe-Side Central Region 433 Thickness: 1.95 mm Club Middle Central Region Thickness: 1.85 mm Thickness: 1.85 mm None Head 437 Thickness: 2.00 mm Width: 6.5 mm Width: 2.5 mm 2C Heel-Side Central Region 435 Thickness: 1.95 mm Toe-Side Central Region 433 Thickness: 1.95 mm

(71) FIG. 9 depicts exemplary rear surface 528 of striking face 509 including an example thickness pattern according to one or more embodiments. The thickness pattern of FIG. 9 includes regions or parameterization zones that have varying thicknesses, as opposed to the grooves discussed above that are surrounded by an intermediate region of greater average thickness. Striking face 509 may be formed, for example, of a steel material.

(72) As shown in FIG. 9, rear surface 528 includes upper region 536, perimeter region 538, lower region 534, and central region 520, which includes toe-side central region portion 533, middle central region portion 537, and heel-side central region portion 535. The determination of thicknesses for these regions may be determined, for example, using an iterative process, such as the thickness pattern forming process of FIG. 11 discussed below. The thicknesses may provide for improved CORs (e.g., greater maximum COR and/or weighted COR), while maintaining a maximum striking face stress limit or range as a constraint so that striking face 509 is comparable to prior art club heads when tested for durability, despite a reduced mass of striking face 509.

(73) In this regard, preferred thicknesses are provided in Table 6 below for the parameterization zones or regions shown in FIG. 9 for Club Head 1D, with resulting values for a stress limit for yielding (i.e., a von Mises stress for the striking face), weighted COR, maximum COR, and striking face mass shown in Table 7 below. Thicknesses for these regions are also provided below for a Comparable Club Head D in Table 6, with the resulting values for the stress limit, weighted COR, maximum COR, and striking face mass provided below in Table 7 for comparison. The thickness and width of perimeter region 538 for both Comparable Club Head D and Club Head 1D can be the same, such as with a thickness of 2.4 mm and a width of 2.5 mm, for example. The thicknesses provided below may vary between the regions, such as by tapering or with a stepwise transition. In some implementations, the thicknesses provided below may represent an average thickness for the region. In other implementations, the thicknesses provided below may represent a thickness at a center of the region.

(74) TABLE-US-00006 TABLE 6 Comparable Club Head Region Thickness Club Head D 1D Middle Central Region 537 2.4 mm 2.8 mm Thickness Heel Central Region 535 2.5 mm 2.4 mm Thickness Toe Central Region 533 2.3 mm 1.8 mm Thickness Upper Region 536 2.2 mm 1.8 mm Thickness Lower Region 534 2.3 mm 1.9 mm Thickness

(75) As shown above, the thicknesses across the striking face of Comparable Club Head D are nearly uniform with a small variation in thickness among the different regions. In contrast, middle central region 537 of Club Head 1D is much thicker than the other regions, and especially thicker than toe central region 535, upper region 536, and lower region 534. As shown in Table 7 below, such variations in the thickness of striking face 509 provide an increased weighted COR and an increased maximum COR, as compared to those of Comparable Club Head D. In addition, the variable thickness pattern of Club Head 1D also reduces the mass of striking face 509 by 6 g, while maintaining a similar or improved stress limit, and thereby providing a similar or greater durability than Comparable Club Head D. The removed or saved 6 g of mass from striking face 509 may be redistributed to other portions of the club head, such as to a rear muscle or toe portion to increase MOIs, and/or to better locate the CG and sweet spot for the club head, as discussed above.

(76) TABLE-US-00007 TABLE 7 Comparable Club Head Property Club Head D 1D von Mises Stress 1405 1472 Weighted COR 0.782 0.788 Maximum COR 0.822 0.825 Striking Face Mass 64 g 58 g

(77) Those of ordinary skill in the art with reference to the present disclosure will appreciate that other implementations can include differently shaped or arranged regions or parameterization zones than those shown in the example of FIG. 9. In this regard, FIG. 10 provides a different thickness pattern with a different arrangement of regions or parameterization zones.

(78) FIG. 10 depicts exemplary rear surface 628 of striking face 609 of a club head including a different thickness pattern according to one or more embodiments. As with the example thickness pattern of FIG. 9, the thickness pattern of FIG. 10 includes regions or parameterization zones that have varying thicknesses, as opposed to the grooves discussed above that are surrounded by an intermediate region of greater average thickness. Striking face 609 may be formed, for example, of a steel material.

(79) As shown in FIG. 10, rear surface 628 includes perimeter region 638, outer region 630, and central region 620, which includes outer central region 644, toe-side inner central region 642, and heel-side inner central region 640. The determination of thicknesses for these regions may be determined, for example, using an iterative process, such as the thickness pattern forming process of FIG. 11 discussed below. The thicknesses may provide for improved CORs (e.g., greater maximum COR and/or weighted COR), while maintaining a striking face stress limit or range as a constraint so that striking face 609 is comparable to prior art club heads when tested for durability, despite a reduced mass of striking face 609.

(80) In this regard, preferred thicknesses are provided in Table 8 below for the parameterization zones or regions shown in FIG. 10 for Club Head 1E and Club Head 2E, with resulting values for a stress limit for yielding (i.e., a von Mises stress for the striking face), weighted COR, maximum COR, and striking face mass shown in Table 9 below. The thickness and width of perimeter region 638 for both club heads can be the same, such as with a thickness of 2.4 mm and a width of 3.5 mm, for example. The thicknesses provided below may vary between the regions, such as by tapering or with a stepwise transition. In some implementations, the thicknesses provided below may represent an average thickness for the region. In other implementations, the thicknesses below may represent the thickness at a center location for the region.

(81) TABLE-US-00008 TABLE 8 Club Head Club Head Region Thickness 1E 2E Outer Region 630 1.7 mm 1.7 mm Thickness Outer Central Region 644 2.2 mm 2.3 mm Thickness Toe-Side Inner Central 2.6 mm 2.5 mm Region 642 Thickness Heel-Side Inner Central 2.6 mm 2.6 mm Region 640 Thickness

(82) As shown above, central region 620 is generally much thicker than outer region 630, with toe-side inner central region 642 and heel-side central region 640 being even thicker than outer central region 644. As shown in Table 7 below, such variations in the thickness of striking face 609 provide an increased weighted COR and an increased maximum COR, as compared to those of Comparable Club Head D discussed above with reference to Table 7. In addition, the variable thickness patterns of Club Heads 1E and 2E also reduce the mass of striking face 609 as compared to Comparable Club Head D by 6 g and 7 g, respectively, while maintaining a similar stress limit, and thereby providing a similar durability as Comparable Head D. The removed or saved 6 g or 7 g of mass from striking face 609 may be redistributed to other portions of the club head, such as to a rear muscle or toe portion to increase MOIs, and/or to better position the CG and sweet spot for the club head, as discussed above.

(83) TABLE-US-00009 TABLE 9 Club Head Club Head Property 1E 2E von Mises Stress 1448 1484 Weighted COR 0.782 0.788 Maximum COR 0.822 0.825 Striking Face Mass 64 g 58 g

(84) FIG. 11 is a flowchart for an example thickness pattern forming process for a striking face according to one or more embodiments. The process of FIG. 11 may be used, for example, with the parameterization zones or regions shown in FIGS. 9 and 10 discussed above. A computing device or other electronic processing device may be used for determining the variable thickness pattern in some implementations.

(85) In block 1102, a plurality of parameterization zones or regions are defined for a striking face of a club head. The club head can be formed with a club head body having a striking face, a heel portion, a toe portion opposite the heel portion, a sole, and a top portion opposite the sole. The club head may be formed, for example, of a steel material, and may include a hollow body type club head or a cavity-back type club head. Each parameterization zone or region may have a variable first parameter and a variable second parameter. In some implementations, the first and second parameters can include a thickness and a width, or other dimension of the parameterization zone or region.

(86) In block 1104, a target value is set for each constraint value for the striking face. In some implementations, a first constraint value can be a striking face mass, a second constraint value can be a mechanical stress limit of the striking face, and a third constraint can be a weighted COR value for the striking face, as described above. The target value for each parameterization zone or region may be set, for example, based on desired improvements for the club head, such as an increased amount of discretionary mass to be redistributed from the striking face, an increased or minimum durability for the striking face, or an increased weighted COR that is balanced against rules for a maximum COR or CT set by a regulatory body.

(87) In block 1106, the parameters of each parameterization zone or region are varied. For example, a maximum width and a thickness may be varied as parameters for each of a central region, upper region, lower region, and toe region of the striking face. In some implementations, the parameters may be iteratively varied to generate sets of values for the one or more constraint values based on the changes to the parameters.

(88) In block 1108, impact with a golf ball is optionally simulated for a plurality of impact locations. In some implementations blocks 1106 and 1108 may be combined. For example, an impact probability matrix as in Table 3 above may be used with Equation 3 above to generate a weighted COR based on variations of first and second parameters for the parameterization zones or regions in block 1106.

(89) In block 1110, constraint values resulting from the variation of parameters in block 1106 are evaluated with respect to the target value for one or more constraint values. For example, a resultant weighted COR value closest to 0.80 may at least in part determine the width and thicknesses of the parameterization zones or regions. As another example, a greatest mass removal or mass savings from the striking face may be another factor considered in determining a size and/or thickness of a parameterization zone or region.

(90) In block 1112, a variable thickness pattern is formed on the striking face based on the evaluation in block 1110. In some cases, a rear surface of the striking face can have material removed using a cutting tool or other machining to form the variable thickness pattern. In other cases, the variable thickness pattern on the striking face may be formed by using a casting or forging process.

(91) Those of ordinary skill in the art will appreciate with reference to the present disclosure that the thickness pattern forming process of FIG. 11 may differ in other implementations. For example, the setting of one or more targets for one or more corresponding constraint values in block 1104 may occur before the definition of parameterization zones or regions in block 1102. As another example variation, varying of parameters for each parameterization zone in block 1106 may be combined with the evaluation of resultant constraint values in block 1110. In some implementations, block 1108 may be omitted.

(92) FIG. 12 is a flowchart for another example thickness pattern forming process for a striking face according to one or more embodiments. The process of FIG. 12 may be used, for example, with the parameterization zones or regions shown in FIGS. 7 and 8 discussed above. A computing device or other electronic processing device may be used for determining the variable thickness pattern in some implementations.

(93) In block 1202, regions of a striking face of a club head are defined including a central region, an intermediate region, and at least one of an upper region, lower region, and toe region. The club head can be formed with a club head body having a striking face, a heel portion, a toe portion opposite the heel portion, a sole, and a top portion opposite the sole. The club head may be formed, for example, of a steel material, and may include a hollow body type club head or a cavity-back type club head. The central region includes a face center of the striking face, and the intermediate region at least partially surrounds the central region. The upper region can be located above the central region, and a lower region can be located below the central region. A toe region can be located toe-ward of the central region. The intermediate region can be disposed between the central region and each of, or at least one of, the upper region, lower region, and toe region.

(94) In block 1204, the central region is recessed such that the central region has a thickness less than the intermediate region. In this regard, the intermediate region may have a uniform or approximately uniform thickness, such as a thickness of at least 2.5 mm and no more than 3.3 mm. The recess of the central region may be made by, for example, tapering the central region from a toe side of the central region to a heel side of the central region. In other implementations, the thickness of the central region may vary with stepwise changes in thickness to form the recess. The recess of the central region may be formed, for example, by machining to remove mass or by forging or casting at least a portion of the club head to save mass from the central region.

(95) In block 1206, at least one of the toe region, upper region, and lower region is recessed, such as with a groove or channel, such that the recessed region has a thickness less than that of the central region. Such a groove may include, for example, an elongate groove having a width no less than about 2.0 mm in at least one of the toe region, upper region, and lower region. The groove may be formed, for example, by machining to remove mass or by forging or casting at least a portion of the club head to save mass from the at least one region. In some implementations, the upper region may include an elongate groove or channel having a width of no less than 6.0 mm.

(96) The recess of the central region formed in block 1204 and the recess of at least one of the toe region, upper region, and lower region in block 1206 result in a striking face that includes a sweet spot corresponding to a first COR, COR1, and an auxiliary location spaced at least 7.5 mm from the sweet spot and corresponding to a second COR, COR.sub.AUX, where COR2≥0.98*COR1. In this regard, the foregoing addition of recesses and corresponding removal of mass or mass savings from the striking face increases an area of the striking face that has a relatively high COR. In some implementations, a maximum COR for the striking face may also be increased or better positioned to correspond to a sweet spot and/or a more frequently hit portion of the striking face, as may be quantified with a weighted COR, as discussed above.

(97) In addition, the removal or saving of mass from the striking face can also allow for redistribution of the mass in the club head, such as to a rear muscle or toe portion of the club head, so as to increase MOIs and/or better position the club head CG and striking face sweet spot. For example, a sweet spot may be located not more than 2.0 mm from a vertical center plane perpendicular to the face plane and extending through the face center. As another example, a CG for the club head may be located not more than 1.0 mm from the vertical center plane so as to better position the sweet spot on the face with an expected location or more frequently hit location.

(98) The foregoing description of the disclosed example embodiments is provided to enable any person of ordinary skill in the art to make or use the embodiments in the present disclosure. Various modifications to these examples will be readily apparent to those of ordinary skill in the art, and the principles disclosed herein may be applied to other examples without departing from the scope of the present disclosure. For example, some alternative embodiments may include different sizes or shapes of regions or parameterization zones of a striking face. Accordingly, the described embodiments are to be considered in all respects only as illustrative and not restrictive, and the scope of the disclosure is, therefore, indicated by the following claims rather than by the foregoing description. All changes which come within the meaning and range of equivalency of the claims are to be embraced within their scope. The described embodiments are to be considered in all respects only as illustrative and not restrictive. In addition, the use of language in the form of “at least one of A and B” in the following claims should be understood to mean “only A, only B, or both A and B.”