Iscar is about to change metal cutting… again! - 90 degree carbide insert

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For experiment 3, measured and predicted thickness errors are shown in Fig. 9a,b. The maximum thickness error occurs at the top of the workpiece, where the tool enters the material in the first pass, similar to the cases with Tool 1. The measured maximum thickness error is about 293 \(\upmu \)m. This can be compared with the predicted thickness error at the same position of 222 \(\upmu \)m, which gives a prediction error of about 24%.

In this paper, a modelling framework is proposed for prediction of cutting force induced form errors during flank milling of a thin-walled workpiece. It is shown that the proposed modelling framework is able to predict thickness errors and cutting forces for thin-walled workpieces that are cut on both sides and where material is removed in multiple passes. It is important to highlight that this framework is not restricted to the studied workpiece geometry or a specific fixturing solution. The modelling framework is used to numerically evaluate the effect of different cutting strategies on the resulting thickness errors during machining of thin-walled parts. From the numerical evaluation some conclusions are drawn:

Yuan, H., Wan, M. & Yang, Y. Design of a tunable mass damper for mitigating vibrations in milling of cylindrical parts. Chin. J. Aeronaut. 32(3), 748–758. https://doi.org/10.1016/j.cja.2018.12.002 (2019).

Three cutting experiments are performed to verify the predicted cutting forces and thickness errors. Table 5 shows the considered cutting parameters, cut patterns and tools for these experiments.

Simon also spent time working as a Sales Executive in Harrods’ golf department, even helping supply Sir Nick Faldo with personalized shirts in a last-minute emergency ahead of a flight to a tournament.

All authors contributed to the study conception and design. The numerical work was performed by D.S. and A.A.L. Part of the scripts were programmed by T.A. Preparation of the experiments were performed by A.A.L. The experiments and data collection were mainly performed by A.A.L. and W.W. The first draft of the manuscript was written by A.A.L., D.S. and W.W. All authors read and commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Msaddek, E. B., Bouaziz, Z., Baili, M. & Dessein, G. Influence of interpolation type in high-speed machining (HSM). Int. J. Adv. Manuf. Technol. 72(1), 289–302. https://doi.org/10.1007/s00170-014-5652-7 (2014).

In Fig. 8a,b, predicted and experimentally measured thickness errors are shown for experiment 2. Similar to experiment 1, where the SBS cut pattern was adopted, the maximum thickness error occurs at the top of the workpiece where the tool entries the material in the first pass. From the experimental data, the maximum thickness error is measured to 273 \(\upmu \)m. This can be compared with the predicted thickness error at the same tool position, with a maximum value of 261 \(\upmu \)m, which gives a prediction error of about 4%. Furthermore, Fig. 8c shows a comparison between predicted and experimentally measured thickness errors along the line \(x =\) 54 mm. Here, the overall distribution is well captured but the predicted thickness error is underestimated with about 20–40%. A close agreement between predicted forces and experimentally measured forces is obtained, as shown in Fig. 8d.

The SLE is calculated at each SGP through an iteration algorithm due to the interaction between the in-process radial deflections and the radial cutting forces. To predict the SLE, a reliable cutting force model, as well as structural models of the tool and instantaneous workpiece at each tool position are needed.

This area of the market has really taken off in the last decade as golfers realize the performance benefits of super-stable putters.

Tiger Woods uses a Scotty Cameron Newport 2 GSS Prototype putter, which has been in his bag for most of his career. Check out all the clubs and other equipment Tiger Woods uses here.

In Fig. 10, the predicted thickness errors are shown and Table 6 shows the corresponding standard deviation and average values of the thickness errors. For comparison, Table 6 also shows the maximum thickness error for each simulation. From these results the effect of cut pattern, machining allowance, cutting tools and cutting parameters on the resulting thickness errors can be examined. Simulation 1 and 2 have the same cutting parameters except for the cut pattern. A significantly better machining accuracy (both in maximum value, average value and standard deviation) is predicted for the WL cut pattern. Comparing simulation 2 with simulation 3, it can be seen that Tool 2 (with a tool diameter of 20 mm) gives somewhat smaller thickness errors compared to Tool 1 (with a tool diameter of 12 mm). Furthermore, simulations 3 and 4 shares the same cut pattern and cutting parameters except for the radial width of cut. These results show that when the radial width of cut (or the machining allowance) is increased from 0.6 mm to 1.4 mm the maximum thickness error is decreased from 247 \(\upmu \)m to 207 \(\upmu \)m. The effect of the axial depth of cut on the thickness error can be examined by comparing simulation 4 and 5. This shows that when the axial depth of cut is increased from 8.5 mm to 17 mm, the thickness error is decreased in maximum value, but increased and unchanged in average value and standard deviation. Finally, comparing simulation 5 and 6 shows that a larger feed rate gives larger thickness errors, as expected.

The workpieces are machined using different cut patterns, machining allowance, cutting tools and cutting parameters, i.e. depth of cut, radial width of cut and feed rate, in order to investigate how these changes will affect the SLE on the workpiece.

The wider body offers greater distance consistency on off-center strikes than you get with a blade, which can really help as you’ll be surprised how often you miss the middle of the face, particularly on longer putts.

Despite his youthful looks, Simon has played golf for more than 40 years and plays to a handicap of 10. A lack of club speed means he’s short off the tee, but very handy from 125 yards and in.

A simple but effective way to see how much toe hang a putter has is to balance the shaft on your finger; the angle at which the head points down towards the ground when hanging freely is the amount of toe hang. A putter with no toe hang is often called “face balanced” and the face will be pointing straight to the sky.

Finding 4, which refers to a larger average value of the thickness error over the whole workpiece for larger axial depth of cuts, can be explained by the larger cutting force associated with a large axial depth of cut. Also, the decreased number of cutting levels will effect the average value of the thickness error due to low deviation values between levels, as seen in Fig. 9.

Chen, W., Xue, J., Tang, D., Chen, H. & Qu, S. Deformation prediction and error compensation in multilayer milling processes for thin-walled parts. Int. J. Mach. Tools Manuf. 49(11), 859–864. https://doi.org/10.1016/j.ijmachtools.2009.05.006 (2009).

Rai, J. K. & Xirouchakis, P. Finite element method based machining simulation environment for analyzing part errors induced during milling of thin-walled components. Int. J. Mach. Tools Manuf. 48(6), 629–643. https://doi.org/10.1016/j.ijmachtools.2007.11.004 (2008).

Kang, Y. G. & Wang, Z. Q. Two efficient iterative algorithms for error prediction in peripheral milling of thin-walled workpieces considering the in-cutting chip. Int. J. Mach. Tools Manuf. 73, 55–61. https://doi.org/10.1016/j.ijmachtools.2013.06.001 (2013).

A sightline like this leads the eye all the way to the back of the ball, and I’ve always felt it gives the impression of hitting a nail in with a hammer when putting. The alignment feature doesn’t have to be a line – it can be another design – but explicitly this style of putter doesn’t have a top rail.

Here, \(\zeta _{j,2}\) and \(\zeta _{j,1}\) are the local upper and lower integration boundaries for the current cutter element. These local integration boundaries are determined by first computing the global integration boundaries, \(z_{j,2}\) and \(z_{j,1}\), for the current tool position and immersion angle of the tool, and then comparing these values with the z-coordinates for the element

Simon’s job means he plays regularly around the world, and rates Kingsbarns as his favorite course. He uses a PXG 0311 GEN6 XF driver, TaylorMade Stealth 2 HL (15º), Ping G400 (20.5º), PXG 0317 X Gen2 hybrid, PXG 0311 GEN6 P irons (6–PW), Cleveland CBX2 wedges (52°, 58°), Ping 21 Fetch putter and a TaylorMade Tour Response golf ball.

The mechanistic cutting force model in40 is used to model the cutting force and it is presented here for clarity. In this mechanistic linear-edge force model the differential cutting forces, acting on the j:th flute, in the tangential (t), radial (r) and axial (a) directions, depicted in Fig. 4, are given by

As in21, beam theory is used to model deflections along the tool. The load case is idealized as a cantilever beam with an elastic support in the normal direction of the workpiece, see Fig. 5. The elemental cutting force are equally distributed to the respective end nodes of the cutter element. That is, the elemental radial force of element m is distributed equally on nodes m and \((m+1)\). The tool deflection at node k due to the radial force acting at node m, \(\Delta F_{\mathrm{{m}}}\), is given by39

Wimmer, S. & Zaeh, M. The prediction of surface error characteristics in the peripheral milling of thin-walled structures. J. Manuf. Mater. Process. 2(1), 13. https://doi.org/10.3390/jmmp2010013 (2018).

Machining of thin-walled components is still challenging due to the difficulties (D1–D3) summarized as follows. (D1) Owing to the low stiffness, the deflections of the cutting tool and the workpiece caused by cutting forces results in undercuts as the actual width of cut is smaller than the nominal value. (D2) During material removal, the stiffness of the workpiece becomes even lower which aggravate the in-process deflections. (D3) The forced vibrations and chatter cause poor surface quality and even cutting tool breakages. D1 and D2 are cutting force induced static form errors that affect the machining accuracy as they leave surface location errors (SLE) while D3 is vibration induced errors, i.e. dynamic errors.

where \(N_x\) and \(N_z\) are the number of locations in the x- and y-direction, respectively. The standard deviation is calculated as

The workpieces are thin aluminum plates of 75 mm height and 120 mm length that are clamped along the bottom edge while the remaining three edges are free. The free height of the cantilevered plates is 55 mm. Since the radial width of cut is varied between experiments and the final nominal thickness is to be 3 mm for all samples, the initial thickness is varied accordingly between samples.

The remaining part of this paper is structured as follows. The milling process of the considered thin wall component is described in “Milling process of a thin walled component”. The developed modelling framework and the subsequent model calibration are presented in “Modelling framework” and “Model calibration”, respectively. The experimental series used for model verification and the comparison between experimental results and simulations are given in “Experimental series” and “Comparison of experimental results with simulations”, respectively. “Numerical evaluation of cutting strategies” presents a numerical evaluation of cutting strategies, and in “Results” the results of this evaluation are given. A discussion related to the results is given in “Discussion”, and finally, the conclusions of the present study are given in “Conclusions”.

Zhang, Z., Cai, Y., Xi, X. & Wang, H. Non-uniform machining allowance planning method of thin-walled parts based on the workpiece deformation constraint. Int. J. Adv. Manuf. Technol. 124(7–8), 2185–2198. https://doi.org/10.1007/s00170-022-10480-0 (2022).

At last, finding 5 is explained by the larger cutting forces associated with larger feed rates. In this way both the tool and workpiece deflections is increased which results in larger thickness errors.

Most putters come with different hosel options, which not only affect the look but also the amount of ‘toe hang’ the putter has. Toe hang is measured in degrees and basically dictates how much the putter wants to rotate during your stroke. Generally, golfers with more arc in their putting stroke will benefit from more toe hang, while those with a ‘straight back and through’ stroke will want less.

To address these issues, many approaches have been proposed. (1) Selection of appropriate cutting tools. In order to avoid the interference between the upper portion of wall and the tool shank, a tool with relieved shank was applied1. The helical angle of cutting edges has a significant influence on the cutting stability when using a small width of cut in combination with a low feed rate2. The size of the corner radius affects the cutting force distribution between axial and radial directions and selecting an appropriate corner radius is important to limit the in-process deflections3. In order to suppress vibrations, cutting tools equipped with mass dampers can be used4. (2) Selection of appropriate cutting parameters. As the feed rate strongly affects the cutting forces, feed rate scheduling is a common practical method to control the instantaneous cutting force and thereby also the in-process deflections5. Varying the depth of cut is another effective strategy and in6, a variable depth-of-cut multi-axis machining strategy based on workpiece deflection constraints was developed. Similarly, the radial width of cut in finishing operation is also controlled to limit the in-process deflections7. When the machining allowance left by the roughing operation is removed by a single pass the machining allowance is equal to the width of cut. A large machining allowance gives a higher local stiffness of the workpiece at the cutting point but an increased cutting force, therefore a compromised machining allowance should be selected3,8. Moreover, the spindle speed should be carefully tuned to avoid tooth-passing frequencies that are close to the workpiece natural frequencies9. (3) Choose optimal cut pattern. To reduce the non-cutting time, the side-by-side cut pattern is normally applied to remove the materials on both sides of the workpiece. Regarding thin-walled structures, a higher local stiffness can be achieved by applying the waterline or the jump-to-jump cut pattern3. (4) Tool path compensation. As deflections of the cutting tool and the workpiece cause over/undercut, the toolpath points should be adjusted accordingly so that the desired width of cut is obtained10. (5) Optimization of the cutting sequence. Apart from cut pattern, the material removal sequence can also be planned to improve the local stiffness during cutting. For instance, in11, the material removal volumes are divided into small blocks which are gradually added to the final part model to generate the in-process workpiece. When the cutting force is applied, the in-process deflections can be controlled to be smaller than a given threshold value by adding blocks of material. As a result, the cutting sequencing is obtained by reversing the adding sequencing of blocks. (6) Design of special fixtures. In order to provide extra support, intelligent fixtures are designed to enhance the local stiffness during cutting. For example, wax12 or ice13 are filled in the deep and narrow space to provide extra support as they could easily be removed by the cutting tool. Recent overviews related to fixtures can be found in14,15. Additionally, high-speed machining (HSM) is popularly applied for the machining of aircraft structural components characterized by deep and thin-walled structures. The interpolation type of toolpath generated by CAM software should be tuned with numerical control unit (NCU) and axis performance of machines to achieve surface quality requirement16.

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Having the original headcover in good condition is always desirable and a good sign the putter might well have been cherished by its previous owner. I’d always recommend factoring in the cost of a new grip too just so you get the feel and feedback you want. Our selection of the best putter grips can help you decide which will best suit you.

Ping’s Dr. Paul Wood told me “There’s a real trend of more skilled players wanting fewer alignment features, which sort of makes sense as the better you are at lining up, the less help you need.

Figure 9c, shows a comparison between predicted and experimentally measured thickness errors along \(x =\) 54 mm. As shown, the cutting depth in level 1 is smaller than 17 mm due to the large nose radius/radial depth of cut ratio. Large discrepancies between measured and predicted values are observed. The thickness error in experiment 3 was measured using more measuring points along the z-direction, specifically 20 points instead of the previous 10. This discrepancy is believed to be explained by a re-cutting process that is not modelled in the simulations. For example, during cutting of level 2 with \(a_p\)=17 mm, the fluted part of the tool ranges between the lowest point of level 2 to 9 mm above the top of level 2. Since a thickness error was generated during the cutting of level 1, re-cutting takes place within level 1. Therefore, the measured thickness error in the re-cutting region of height 9 mm shows a valley that is not predicted by the model.

The total cutting forces are computed by integrating the differential cutting forces over the immersed part of flute j

Mallet putters tend to have a bigger footprint than blades, although the blade length from heel to toe is often shorter.

Putters are typically 33″ to 36″ long (discounting arm-lock models, which are longer). The correct length largely depends on your height but also the way you stand when putting; basically, the distance from your wrist to the floor when you address a putt is the length of putter you need.

Li, W., Wang, L. & Yu, G. Force-induced deformation prediction and flexible error compensation strategy in flank milling of thin-walled parts. J. Mater. Process. Technol. 297, 117258. https://doi.org/10.1016/j.jmatprotec.2021.117258 (2021).

Other zero torque putters are available (like the Axis 1 used by Justin Rose) but L.A.B. models are different as they’re designed to resist twisting to the path of your stroke, not your target. So, where Ping founder Karsten Solheim invented the perimeter-weighted Anser to twist less on off-center hits, L.A.B. putters are designed to not twist to the path of your backswing and downswing.

Liu, H. et al. Fixturing technology and system for thin-walled parts machining: A review. Front. Mech. Eng. 17(4), 55. https://doi.org/10.1007/s11465-022-0711-5 (2022).

where \(h_j \left( \phi _j,z \right) \) is the chip thickness as a function of the immersion angle \(\phi _j\) for flute j and the axial coordinate z. The subscripts e and c of, \(K_{\cdot \mathrm e}\) and \(K_{\cdot \mathrm c}\), denote edge force coefficients and cutting force coefficients, respectively. In Fig. 4, D, \(\phi _{\mathrm{{p}}}\) and \(a_{\textrm{e}}\) are the tool diameter, tool pitch angle and the radial width of cut, respectively. The chip thickness varies with the instantaneous immersion angle and can be expressed as

As you’ll see from our selections above, brands including Scotty Cameron, TaylorMade, Odyssey and Ping make what we feel are the best putters in golf.

Quite simply, you’re making the game harder by using a narrow blade putter rather than an MOI Putter, especially on longer putts.

Wang, J., Ibaraki, S. & Matsubara, A. A cutting sequence optimization algorithm to reduce the workpiece deformation in thin-wall machining. Precis. Eng. 50, 506–514. https://doi.org/10.1016/j.precisioneng.2017.07.006 (2017).

Take your time, look at the condition, and get a feeling for how the putter may have been looked after by the previous owner. If the finish is chipped or there are dinks in the top edge it’s highly likely the putter has had a tough life, which could mean it might no longer be at its original spec.

The cylindrical assumption is employed to facilitate the efficient iteration scheme presented in this paper. Taking the nose radius of the tool into account necessitates calculation of cutting forces in multiple distinct regions of the tool and the radial width of the cut would have to be separately addressed in these regions. Consequently, in-process deflection would affect each region differently. Furthermore, the elemental forces in the x-, y-, and z-directions would each require individual computation. This segmentation of tool regions would not align with the Newton-Raphson-inspired iteration scheme we employ.

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The reported work has provided valuable insights on simulation of thin-walled component machining. A detailed literature overview is given in Table 1, in which “\(\times \)” is used to mark that the corresponding variable in “Process Plan” column is fixed in simulations, and “\(\checkmark \)” presents that the corresponding variable varies in simulations. In “Cutting Process” column, “\(\checkmark \)” is used to mark that the deflections of cutting tool/workpiece, and the effect of material removal process on stiffness reduction is considered respectively. If the answer is no, “\(\times \)” is assigned accordingly. Although the effects of the cutting tool and cutting parameters have been studied, studies on the effect of different cut patterns are sparsely reported. In fact, selection of an optimized cut pattern can strongly improve the machining efficiency and quality3,18,19. Therefore, a modelling framework is developed in this work which is capable of varying the cutting tool, fixturing solution, cutting parameters and cut pattern so that the machining process of a thin-walled part can be planned in a comprehensive way. As 40–70% of the machining errors are cutting force-induced errors20, this work focuses on static form error prediction.

While we normally share all the data from our golf club tests, we don’t do that with putters. Whilst we do use a Foresight GC Quad launch monitor in putting mode to measure and gauge the roll, topspin, and skid of every putt hit, over the years we’ve learned that putting data is more player- and day-dependent than any other club in the bag. So, whilst we use this data for analysis, we don’t base big decisions or recommendations on it, as history shows data is very likely to be different on another day’s testing. Essentially, we’re not comfortable making huge claims that one putter rolls better than another, because we know that on another day’s testing, the rolls could be reversed.

Wimmer, S., Hunyadi, P. & Zaeh, M. F. A numerical approach for the prediction of static surface errors in the peripheral milling of thin-walled structures. Prod. Eng. Res. Dev. 13(3–4), 479–488. https://doi.org/10.1007/s11740-019-00901-7 (2019).

There is a clear trend towards wider-bodied blade putters, which sit between a mallet and a blade and offer a bit more forgiveness and reassurance than a very slim blade.

Experimental setup including Haas VF-3SS machining center, cutting tool, force transducer and a mounted workpiece.

Ge, G., Xiao, Y., Feng, X. & Du, Z. An efficient prediction method for the dynamic deformation of thin-walled parts in flank milling. Comput. Aided Des. 152, 103401. https://doi.org/10.1016/j.cad.2022.103401 (2022).

Bolsunovskiy, S., Vermel, V., Gubanov, G., Kacharava, I. & Kudryashov, A. Thin-walled part machining process parameters optimization based on finite-element modeling of workpiece vibrations. Proced. CIRP 8, 276–280. https://doi.org/10.1016/j.procir.2013.06.102 (2013).

As demonstrated above, substantial work has been done to overcome the challenges of thin-walled part machining. The solution space has been explored in either an individual way or in a mixed manner. However, process planners are still struggling to choose appropriate cutting tools, cutting parameters, fixturing solutions and cut patterns to achieve a balance between machining quality and manufacturing cost. The trial-and-error methodology remains the common approach in the industry. Along with the development of computational methods and high-performance PC:s, modelling and simulation have attracted significant attention from both the research community and the industry. Benefiting from simulations, the machining quality in the form of SLE:s of thin-walled structures under different machining conditions can be investigated with limited physical experiments. As a result, both time and cost can be saved. Simulations of thin-walled part machining are usually realized using a hybrid approach. The cutting forces are calculated either analytically or using a meta model17. Finite element models of the thin-walled part are created that reflect the material removal process and its continuous effect on the workpiece stiffness. By applying the cutting force to the finite element model of the in-process workpiece and the cutting tool model, the deflections of the cutting tool and the workpiece can be computed in an iterative manner. Finally, the deflections of the cutting tool and the workpiece are used to predict the generated SLE.

Putters, particularly mallets and MOI models, come with all sorts of different visual aids to help you align putts and strike the ball in the middle of the face more often. A lot comes down to personal preference, so it’s a good idea to pick up as many putters as you can to see what sort of alignment aids suit your eye. Here’s my guide to finding your perfect alignment aid.

Hou, Y., Zhang, D., Zhang, Y. & Wu, B. The variable radial depth of cut in finishing machining of thin-walled blade based on the stable-state deformation field. Int. J. Adv. Manuf. Technol. 113(1–2), 141–158. https://doi.org/10.1007/s00170-020-06472-7 (2021).

Lassila, A.A., Svensson, D., Wang, W. et al. Numerical evaluation of cutting strategies for thin-walled parts. Sci Rep 14, 1459 (2024). https://doi.org/10.1038/s41598-024-51883-1

The reason for the underestimated process forces for experiment 3, and thereby also the underpredicted form errors, are believed to stem from the simplification that the cutting tool is cylindrical. In experiment 3, both the larger tool nose radius and the smaller radial width of cut affect the cutting process such that wider and thinner chips are produced than predicted with a cylindrical tool geometry. This is described and demonstrated in e.g.41. Additionally, since coated carbide inserts were used, the cutting-edge radius can be assumed to be relatively large compared to the thickness of the thinner part of the chip. Consequently, larger friction forces are generated than what this simplified cutting force model predicts.

The cutting forces are measured using an HBM MCS10 multicomponent force transducer. The force signals are amplified and acquired using HBM ClipX measuring amplifiers, a National Instruments USB 6210 data acquisition card together with the data acquisition tool box in MATLAB. Both pre-machining of workpieces and actual experiments are conducted in a vertical machining center of the type Haas VF-3SS. The thickness errors, are measured using a coordinate measuring machine of the type Hexagon DEA Global Advantage 15.20.10 with a resolution of 0.058 \(\upmu \text {m}\). Figure 6 shows the experimental setup, where the workpiece is mounted in the Haas VF-3SS machining center, together with a cutting tool and the force transducer.

Regarding finding 2, this can simply be explained by the difference in bending stiffness for the tools. Due to the larger tool diameter for Tool 2, the bending stiffnes is increased and in that way the tool deflection is decreased.

Ping’s Dr. Paul Wood told me “Research shows a really good match between players who describe a putter matching their eye, and aligning consistently correctly with those models.” So there’s a real link between finding a putter that’s easy to align and putting well with it.

Sm, Liu, Shao, Xd., Xb, Ge. & Wang, D. Simulation of the deformation caused by the machining cutting force on thin-walled deep cavity parts. Int. J. Adv. Manuf. Technol. 92(9–12), 3503–3517. https://doi.org/10.1007/s00170-017-0383-1 (2017).

Chen, Y. P., Gao, J. & Wu, L. F. Review on deflection compensation methods for machining of thin-walled components. Appl. Mech. Mater. 29–32, 1768–1776. https://doi.org/10.4028/www.scientific.net/AMM.29-32.1768 (2010).

Stability putter shafts have grown hugely in popularity over the last decade, as engineers have realized when premium carbon fiber (like with the graphite KBS GPS) is wrapped correctly in the right areas, graphite shafts can resist twisting better than steel.

where \(\left( \varvec{K}_{red}^{tp}\right) ^{-1}\) is the inverse of the reduced stiffness matrix at tool position tp. The vectors \(\varvec{F}_{wp,y}^{tp}(\phi )\) and \(\varvec{w}^{tp}(\phi )\) denote the radial force acting on the workpiece and the normal workpiece deflection at tool position tp. The radial force vector consists of the cutter elemental normal forces acting in the opposite direction and they are distributed on the workpiece nodes by using weight functions.

Wan, M., Zhang, W. H., Dang, J. W. & Yang, Y. A unified stability prediction method for milling process with multiple delays. Int. J. Mach. Tools Manuf. 50(1), 29–41. https://doi.org/10.1016/j.ijmachtools.2009.09.009 (2010).

Agarwal, A. & Desai, K. A. Predictive framework for cutting force induced cylindricity error estimation in end milling of thin-walled components. Precis. Eng. 66, 209–219. https://doi.org/10.1016/j.precisioneng.2020.07.007 (2020).

Choosing the best putter for your game comes down to many factors, including price, the head shape, what alignment aids suit your eye (if any), whether you have a straight or arced putting stroke, whether you prefer a firmer or softer feel, the length that suits your height and setup, and what type of grip feels best in your hands. We’ve discussed every factor in our guide to choosing the best putter for your game.

Izamshah, R., Mo, J. P. T. & Ding, S. Hybrid deflection prediction on machining thin-wall monolithic aerospace components. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 226(4), 592–605. https://doi.org/10.1177/0954405411425443 (2011).

You may have heard about face-balanced, toe-up, and torque-balanced putters before, but L.A.B. Golf’s Zero Torque putters and the new PXG Battle Ready Allan work differently from anything you’ve seen before. The idea came about when Directed Force (the company acquired and relaunched by now L.A.B owner Sam Hahn) built a device called the Revealer, to better understand how putters torque and rotate during the putting stroke. Only by inventing the device, which allows putters to hang freely while being swung, was it possible to spot how putters rotate during the stroke, but also to design a putter that didn’t torque or spin at all.

Experiment 1: measured thickness errors (a), predicted thickness errors (b), predicted and experimentally measured thickness errors along \(x =\) 54 mm (c) and comparison between predicted and measured cutting forces (d).

Ratchev, S., Liu, S., Huang, W. & Becker, A. A. Milling error prediction and compensation in machining of low-rigidity parts. Int. J. Mach. Tools Manuf 44(15), 1629–1641 (2004).

It’s a difficult one to answer, as so much of putting comes down to confidence, which makes it important to choose a putter you love the look and feel of. That said, a high-stability MOI putter will offer greater performance benefits than any other type of putter. If you’re struggling with your putting and have only ever used a traditional blade, it’s well worth seeing how much a forgiving MOI putter could help you.

Liu, H. et al. The influence of ice-based fixture on suppressing machining-induced deformation of cantilever thin-walled parts: A novel and green fixture. Int. J. Adv. Manuf. Technol. 117(1–2), 329–341. https://doi.org/10.1007/s00170-021-07567-5 (2021).

The interaction of the cutting forces and the in-process deflections necessitates an iterative calculation method for the SLE39. Substituting \(a_e\) with \(a_e^f\) in Eq. (7) gives the effective start angle due to tool and workpiece deflections

Pre-loved putters can be a fantastic option as they offer the opportunity to save considerable amounts of cash buying a model somebody else no longer wants. Make sure you’ve tried and tested the putter you want before buying, it’s much less likely you’ll get fitted to any second-hand model.

His favorite ever piece of golf equipment is the Callaway Warbird fairway wood and he considers the biggest technological advancement in the game to have been titanium driver heads.

It means the company insists golfers get fit for each model as it’s vitally important to match the lie angle of the putter to how you putt, to ensure maximum effectiveness. The idea also does away with the fitting of putters to stroke type, so don’t expect to hear toe hang mentioned by L.A.B.

The thin-walled workpiece is modelled using the commercial FE software Abaqus CAE 2017. During the cutting process, the stiffness of the workpiece is continously reduced due to removal of material and therefore the FE-mesh is continously modified. For each tool position, a unique FE-model is created to account for the material that has been removed prior to this position. The generation of FE-models is automated using MATLAB and Python scripts. In this work, the cutting process of each level is divided into 21 tool positions along the feed direction. The number of levels depends on the axial cutting depth and cut pattern.

Xi, X., Cai, Y., Wang, H. & Zhao, D. A prediction model of the cutting force-induced deformation while considering the removed material impact. Int. J. Adv. Manuf. Technol. 119(3–4), 1579–1594. https://doi.org/10.1007/s00170-021-08291-w (2021).

Wan, M., Zhang, W. H., Tan, G. & Qin, G. H. Systematic simulation procedure of peripheral milling process of thin-walled workpiece. J. Mater. Process. Technol. 197(1–3), 122–131. https://doi.org/10.1016/j.jmatprotec.2007.06.005 (2008).

After the experimental verification, the proposed modelling framework is used to investigate the effect of the free parameters, i.e. the cut pattern, machining allowance, cutting tool and cutting parameters, on the resulting thickness error. Six simulations are conducted where the free parameters are varied according to table 6. For comparison, the average value and standard deviation are calculated for the complete thickness error map for each simulation. The thickness errors are arranged in a matrix \(\Delta t_{ij}\) where the rows (i) and the columns (j) corresponds to the location in x- and z-direction, respectively. The average value of the thickness errors is calculated as

Thin-walled components characterized by a large ratio of height to thickness and tight tolerances are typical lightweight designs adopted by the aerospace industry. In the current shift to electro-mobility (E-mobility), they are also widely applied in part design to achieve a balance between structural strength and weight, e.g. the stator housing and the housing of battery packs. Although alternative manufacturing techniques such as additive manufacturing have attracted more attention, peripheral milling/flank milling remains dominant for thin-walled components machining.

Since the final thickness of the workpieces, i.e. the thickness after machining, is the same for all simulations, a higher machining allowance, or radial width of cut, results in a stiffer workpiece during the machining process. This explains the low thickness errors observed for high machining allowances, referred to as finding 3 above. However, numerical evaluations of the SBS cut pattern shows that the effect of decreased thickness errors for larger machining allowances is much less noticeable for the SBS cut pattern compared with WL.

Bao, Y., Wang, B., He, Z., Kang, R. & Guo, J. Recent progress in flexible supporting technology for aerospace thin-walled parts: A review. Chin. J. Aeronaut. 35(3), 10–26. https://doi.org/10.1016/j.cja.2021.01.026 (2022).

Blades are the most traditional-looking putters. They are typically quite slim, with a small profile. Blade putters tend to have quite a lot of toe hang, which means they suit golfers with an arced putting stroke, although some face-balanced blade putters are available for those with a straight back-and-through stroke who want a blade style.

where \(k_c\) is the clamping stiffness for the tool-machine interface, l is the gauge length for the tool, \(z_{\mathrm{{m}}}\) and \(z_{\mathrm{{k}}}\) are the axial coordinates of nodes m and k, respectively, E is the Youngs modulus for the tool material and I is the area moment of inertia of a circular cross-section with diameter \(D_e = sD\). Here, s is a scaling factor that represent the reduced diameter of the tool due to the helical flutes39. The radial deflection at node k due to all nodal forces is then calculated by superposition, i.e.

Away from the course, Simon is a season-ticket holder at Peterborough United Football Club, attending games with his young son. He’s also a keen cyclist and enjoys working (and relaxing) at his allotment.

Yan, Q., Luo, M. & Tang, K. Multi-axis variable depth-of-cut machining of thin-walled workpieces based on the workpiece deflection constraint. Comput. Aided Des. 100, 14–29. https://doi.org/10.1016/j.cad.2018.02.007 (2018).

Atabey, F., Lazoglu, I. & Altintas, Y. Mechanics of boring processes—Part I. Int. J. Mach. Tools Manuf. 43, 463–476. https://doi.org/10.1016/S0890-6955(02)00276-6 (2003).

“This kind of player wants lines to indicate where the outer edges of the ball should be in relation to the putter’s body, like tram lines running straight from the putter’s head out to the edges of the golf ball that’s sat in front of it,” Ping’s Dr. Paul Wood told me. The putter may have a clean top rail, but golfers aren’t using it to align.

Han, Z., Jin, H., Fu, Y. & Fu, H. Cutting deflection control of the blade based on real-time feedrate scheduling in open modular architecture CNC system. Int. J. Adv. Manuf. Technol. 90(9–12), 2567–2579. https://doi.org/10.1007/s00170-016-9444-0 (2016).

Putter faces used to be a simple, flat piece of metal, and although some are still like that, most have an insert or some form of groove pattern designed to help reduce skid and get the ball rolling sooner. Finding the face type or insert that you like the feel of is key to confidence and consistent pace control.

The parameters \(k_{\mathrm{{c}}}\) and s in the tool deflection model described in “Tool deflections” are experimentally measured and calibrated. With the tool mounted in the machine, these measurements are performed by pressing the tool against the force transducer at various points along the tool and for various prescribed tool deflections realized by means of a machine displacement of the tool. A Young’s modulus of E = 620 GPa is assumed for the tool material and the gauge lengths are measured to \(l_{\textrm{1}}\) = 63 mm and \(l_{\textrm{2}}\) =101 mm, where the subscripted indices indicate Tool 1 and Tool 2, respectively. From the measured force-deflection relations, the identified parameters are \(k_c\) = 8.36 kN/mm, \(s_{\textrm{1}}\) = 0.7 and \(s_{\textrm{2}}\) = 0.67.

FE-model of the workpiece for a specific tool position. Red nodes: nodes that are retained. Nodes on the yellow line: surface generation points.

Denkena, B. & Schmidt, C. Experimental investigation and simulation of machining thin-walled workpieces. Prod. Eng. Res. Dev. 1(4), 343–350. https://doi.org/10.1007/s11740-007-0017-9 (2007).

He enjoys excellent relationships with the biggest names in the golf equipment industry, including PXG boss Bob Parsons and TaylorMade’s Tomo Bystedt and Adrian Rietveld.

If you can accept the somewhat unconventional looks of an MOI model, you’re giving yourself maximum benefit. It’s important to love the look of your putter, though, as confidence plays such a huge part on the greens.

For industrial use the proposed modelling framework can be used to optimize the machining process of thin-walled components by combining the modelling framework with an optimization scheme. More clearly, there is a potential to find optimized cutting strategies, including different tools, cutting parameters and cut pattern that minimize the thickness error. Another potential with this modelling framework is that it can be extended with a tool path compensation algorithm. With such an algorithm, an optimized tool path, with respect to a minimized thickness error, can be obtained.

Experiment 3: measured thickness errors (a), predicted thickness errors (b), predicted and experimentally measured thickness errors along \(x =\) 54 mm (c) and comparison between predicted and measured cutting forces (d).

Furthermore, this study shows that the proposed modelling framework is capable to use for investigations of the effect of different cutting strategies on the resulting form error during machining of thin-walled components. Even though the model is capable of quantitatively predict the form error in the complete parameter range, the results in experiment 3 suggests that the validity of the force prediction can become challenging when tools with a large nose radius are used in conjunction with a small radial width of cut. In those conditions, the model generate underpredicted normal and feed forces and, as a consequence, also underpredicted form errors.

From the global stiffness matrix \(\varvec{K}^{tp}\), corresponding to an instantaneous workpiece geometry at tool position tp, the reduced stiffnes matrix \(\varvec{K}_{red}^{tp}\) is calculated. Since only the radial stiffness at potential tool-workpiece contact nodes are retained, the dimension of \(\varvec{K}_{red}^{tp}\) is significantly smaller than the dimension of \(\varvec{K}^{tp}\). The computation of the reduced stiffness matrix is included in the Python script that generates the FE-models and is in that way an automated process using the Abaqus Scripting Interface.

The radial stiffness of the workpiece at each tool position is computed in the form of a reduced stiffness matrix using a substructure step in Abaqus. Figure 3 shows the FE-model of the workpiece for a specific tool position where the reduced stiffness matrix is calculated for the highlighted nodes. Nodes on the yellow line are in the following denoted surface generation points (SGP:s) and at each tool position, finished surface is generated along this line by rotating the tool such that points on the helical flutes intersect with the nodes along the yellow line, see39 for a detailed description. The stiffness at the surface generation points is not significantly influenced by the geometric simplification to a flat contact surface as the displacements are governed by the applied load and global stiffness of the plate. The highlighted nodes represents potential tool-workpiece contact points at this tool position.

Experiment 2: measured thickness errors (a), predicted thickness errors (b), predicted and experimentally measured thickness errors along \(x =\) 54 mm (c) and comparison between predicted and measured cutting forces (d).

The predicted cutting forces and thickness errors are compared with the experimentally measured counterparts.

Two cut patterns are considered; side-by-side (SBS) and waterline (WL) as shown in Fig. 1. For both cut patterns, material is removed from the workpiece in multiple passes. In the SBS cut pattern (Fig. 1a) all passes are completed for one side of the workpiece before proceeding to the other side. In the WL cut pattern (Fig. 1b), the passes for one height level are completed for both sides before proceeding to the next height level. The same axial depth of cut \(a_p\) is used for all passes, except for the lowest pass that is adjusted so that 1 mm height from the fixture is left uncut. The toolpath are generated by Siemens NX version 2206.

The biggest decision when choosing a new putter is whether you want a blade putter, a mallet putter, or a super-stable high MOI putter.

TG Equipment Editor Simon Daddow and Test Pro Neil Wain both putted to a hole 15 feet away and hit at least 20 putts with each model tested. We’re listening for sound, looking for how putts roll across the surface of the green, and gauging the feel and feedback of the putter face. We consider the grip size, shape, and texture, whilst also paying attention to the shaft and the stability on off-center hits.

The SLE at all lateral surface nodes are mapped as \({SLE}^{side}(x,z)\), and the thickness error map is finally calculated as

The workpieces are manufactured from aluminum EN AC-46000 (AlSi9Cu3(Fe)) ingots using water jet cutting. Before each experiment, the workpiece is also pre-machined with conservative cutting parameters in order to align the workpiece with the machine axes. The initial thickness of the workpiece is adapted to the considered radial width of cut, as the final thickness should be 3 mm, i.e. the initial thickness is 2\(a_e\)+3 mm. Before each experiment the initial thickness of the workpiece is carefully measured at multiple locations using a spindle mounted probe and an initial thickness error of less than 50 \(\upmu \text {m}\) is recorded for all workpieces.

Arnaud, L., Gonzalo, O., Seguy, S., Jauregi, H. & Peigné, G. Simulation of low rigidity part machining applied to thin-walled structures. Int. J. Adv. Manuf. Technol. 54(5–8), 479–488. https://doi.org/10.1007/s00170-010-2976-9 (2010).

Xiang, J. & Yi, J. Deformation mechanism in wax supported milling of thin-walled structures based on milling forces stability. CIRP J. Manuf. Sci. Technol. 32, 356–369. https://doi.org/10.1016/j.cirpj.2021.01.020 (2021).

The authors wish to thank the project staff at Volvo GTO for providing the CMM measurements and the project staff from Aurobay for providing the workpiece material and for their help with the milling experiments.

Budak E. Mechanics and dynamics of milling thin walled structures. PhD Dissertation, University of British Columbia (1994).

Typically, this feature is only really found on mallet-style putters, because blades don’t have the body width to create a long sight line. It’s not a hard and fast rule, but it often tends to be less skilled putters who like this style of alignment aid most.

Tlusty, J., Smith, S. & Winfough, W. R. Techniques for the use of long slender end mills in high-speed milling. CIRP Ann. 45(1), 393–396. https://doi.org/10.1016/s0007-8506(07)63088-1 (1996).

where \(z_{j,2}\) and \(z_{j,1}\) represents the upper and lower engagement limits of the immersed part of flute j. As described in39, \(z_{j,2}\) and \(z_{j,1}\) are determined by the start and exit engagement angles of the cut along the tool-workpiece contact zone. In down-milling the exit engagement angle is \(\phi _{\mathrm{{ex}}} =\pi \), always, and the start engagement angle is given by

where \(n_f\) is the number of flutes for the tool. The total cutting force acting on the tool is finally computed by summing the elemental cutting force for each element along the tool

Li, Z. L., Tuysuz, O., Zhu, L. M. & Altintas, Y. Surface form error prediction in five-axis flank milling of thin-walled parts. Int. J. Mach. Tools Manuf. 128, 21–32. https://doi.org/10.1016/j.ijmachtools.2018.01.005 (2018).

Stability putter shafts improve the consistency of off-center hits as the face deflects fractionally less at impact, so the idea has the potential to shave shots from your scorecard and help cut your three-putt percentage.

Golfers who like a golf ball-width feature do so because they like to frame the ball while lining up to putt. There are tons of putters out there that have a feature to frame the ball at address, and while some do it subtly, others are much more explicit.

Golfers who like a clean top rail use the perpendicular line created by the blade sat behind the ball to square up to their target. A lot of putters combine a clean top rail design with other alignment features, but players who like models in this category will often find the extra cosmetic shapes or lines distracting.

Annoni, M., Rebaioli, L. & Semeraro, Q. Thin wall geometrical quality improvement in micromilling. Int. J. Adv. Manuf. Technol. 79(5–8), 881–895. https://doi.org/10.1007/s00170-015-6862-3 (2015).

Finding the best putter for your golf game is hugely important, as it’s the club you use more than any other. There’s nothing more frustrating than hitting a great approach or chip to close range and then missing the putt. Plus, holing a few more putts is a quick way to lower your scores.

The data used and/or analysed during the current study are available from the corresponding author on reasonable request.

Open access funding provided by University of Skövde. This work was supported financially by the Swedish Knowledge Foundation through the project SIMPLE (dnr: 20180168).

Since the methodology is based on a global modelling approach, the purpose of the FE model is to model the force–displacement response of the workpiece. Therefore, the element size was selected by ensuring a converged force–displacement response along the tool/workpiece contact zone at all tool positions. The workpiece is modelled using 15-node quadratic triangular prism elements (C3D15) with an approximate element size of 1.4 mm. The workpiece material is modelled as linear-elastic with a Young’s modulus and Poisson’s ratio of 70 GPa and 0.27, respectively.

Wang, L. & Si, H. Machining deformation prediction of thin-walled workpieces in five-axis flank milling. Int. J. Adv. Manuf. Technol. 97(9–12), 4179–4193. https://doi.org/10.1007/s00170-018-2248-7 (2018).

There’s a growing consensus of not going too large as you can lose feel and distance control. As a very general rule, oversized grips with flat fronts typically will suit straighter stroke players whereas smaller more pistol-shaped grips can be a better fit for golfers with arc and/or release in their putting stroke.

All of the leading manufacturers – including TaylorMade, Odyssey, and Ping – offer a wide range of putters in different shapes, sizes, styles, and types, so how do you know where to start?

Expect a Zero Torque putter to need some bedding in time, they are the hottest trend on tour right now, my best L.A.B. putter page will help you decide if you like the concept and establish which model is for you.

Static form errors due to in-process deflections is a major concern in flank milling of thin-walled parts. To increase both productivity and part geometric accuracy, there is a need to predict and control these form errors. In this work, a modelling framework for prediction of the cutting force-induced form errors, or thickness errors, during flank milling of a thin-walled workpiece is proposed. The modelled workpiece geometry is continuously updated to account for material removal and the reduced stiffness matrix is calculated for nodes in the engagement zone. The proposed modelling framework is able to predict the resulting thickness errors for a thin-walled plate which is cut on both sides. Several cutting strategies and cut patterns using constant z-level finishing are studied. The modelling framework is used to investigate the effect of different cut patterns, machining allowance, cutting tools and cutting parameters on the resulting thickness errors. The framework is experimentally validated for various cutting sequences and cutting parameters. The predicted thickness errors closely correspond to the experimental results. It is shown from numerical evaluations that the selection of an appropriate cut pattern is crucial in order to reduce the thickness error. Furthermore, it is shown that an increased machining allowance gives a decreased thickness error for thin-walled plates.

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A governing assumption for the method presented in this paper is that the quasi-static part of the in-process deflections are substantially larger than the dynamic counterpart. Therefore, the spindle speeds are selected such that the resulting tooth passing frequencies are much lower than the natural frequencies of the vibration modes, therefore the deformation response of the structure is mainly controlled by the stiffness of the structure, i.e. inertial forces that excite vibrations are negligible, resulting in negligible vibrations that are damped fast. Also, the measured force signals also suggest that chatter vibrations are not encountered in experiments.

Predominantly, think of the golfers who gravitate to this style of putter as liking simpler, traditional blade designs with less going on cosmetically and you won’t go far wrong.

Du, Z., Zhang, D., Hou, H. & Liang, S. Y. Peripheral milling force induced error compensation using analytical force model and APDL deformation calculation. Int. J. Adv. Manuf. Technol. 88(9–12), 3405–3417. https://doi.org/10.1007/s00170-016-9052-z (2016).

He joined EMAP Active (now Bauer Media) as Equipment Editor in 2006 and has worked for both Today’s Golfer and Golf World. Working alongside our test pro Neil Wain, Simon has made todays-golfer.com the most reliable source for golf club testing.

A larger axial depth of cut decreases the maximum value of the thickness error but results in a larger average value of the thickness errors over the whole workpiece.

where \(z_{min}^{el}\) and \(z_{max}^{el}\) are the minimum and maximum z-coordinate for the current element, respectively.

He’s a specialist in all things metal having spent a large part of his career as a golf club maker and product development manager, and has worked in the golf industry for more than 30 years. Starting out as trainee professional at Downes Crediton GC where he learned the art of golf club making, he went onto work for Clubhaus Plc and Tony Charles Ltd as a golf club maker, and running Product Development at Benross Golf.

The modelling framework, depicted in Fig. 2, is used to predict the SLE on both sides of the plates and the corresponding thickness error \(\Delta t\). The framework consist of four steps which are denoted Input-step, Generate FE-models-step, Substructure-step and Calculate SLE-step. In the Input-step all input parameters are assigned, which includes the workpiece geometry, cutting tool, cut pattern and cutting parameters. The remaining three steps of the framework are described in the following “Generation of FE-models”–“Prediction of the surface location error”.

The differential cutting forces are transformed into the x (feed), y (normal) and z (axial) directions using the transformation

Finding 1 can be explained by the different material removing sequences for the SBS and WL cut patterns. Compared with the SBS cut pattern, where all material is removed from one side before proceeding to the other side, the WL cut pattern preserves the stiffness of the workpiece in a better way when material is removed by alternating between sides of the workpiece. However, this effect of a preserved stiffness is much more tangible for larger machining allowances, or radial width of cuts.

where \(\phi \) is the reference angle, i.e. \(\phi _1(0)\). The last term in Eq. (3) is the lag angle and represents the angle for which a point on the cutting edge, at axial coordinate z, has lagged behind the end point of the tool. This lag angle, is due to the helix angle \(\beta \) of the tool.

There’s a mountain of putter grip options to choose from, whether you want to explore the size, shape, profile, or material of your putter grip my best putter grip page will help you decide which best suits you.

Don’t forget also if you draw a straight line on your ball, a single line on your putter can be a great accompaniment for that. If you use a triple track golf ball, a putter with three lines can work brilliantly too.

There’s a reason most beginners don’t pick up traditional blades with no sightlines; they’re not so easy to line up. It’s natural, then, for less skilled and less confident golfers to go for wider body, longer sightline models because there’s more insurance. Mallets are more stable and forgiving, but you also get more help lining up, too.

Budak, E. Analytical models for high performance milling. Part I: Cutting forces, structural deformations and tolerance integrity. Int. J. Mach. Tools Manuf. 10(46), 1478–1488. https://doi.org/10.1016/j.ijmachtools.2005.09.009 (2006).

With many of the best putters retailing for over $400, it’s important to decide how much you’re willing to spend. After all, a higher price doesn’t guarantee you’re going to hole more putts. Typically, the leading manufacturers are at the forefront of R&D and use premium materials, which explains the high price, but there’s nothing to say you can’t find a putter for under $200 that works great for you.

Budak, E. & Altintas, Y. Modeling and avoidance of static form errors in peripheral milling of plates. Int. J. Mach. Tools Manuf 35(3), 459–476. https://doi.org/10.1016/0890-6955(94)P2628-S (1995).

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In Table 2 the cutting parameter ranges, cut patterns and cutting tools are specified. Tool 1 and Tool 2 are decribed in “Model calibration”.

The cutter is discretized into n cutter elements and the integrations in Eq. (6) is carried out element wise, in order to compute the elemental cutting force acting on flute j, \(\varvec{F}_{xyz,j}^{el} (\phi )\), according to

Out-on-tour stability putter shafts have their place, but they’re certainly not mainstream, so I’d advise not getting too bogged down in deciding whether or not you need one. Other much more important factors need your full attention. If though at any point you want to go full out and create your ultimate flatstick then absolutely a stability putter shaft should be on your radar.

Simon Daddow is the Equipment Editor for Today’s Golfer. Having tested and played more than 10,000 clubs in his life, what he doesn’t know about golf clubs isn’t worth knowing.

Ge, G., Du, Z. & Yang, J. Rapid prediction and compensation method of cutting force-induced error for thin-walled workpiece. Int. J. Adv. Manuf. Technol. 106(11–12), 5453–5462. https://doi.org/10.1007/s00170-020-05050-1 (2020).

Herranz, S. et al. The milling of airframe components with low rigidity: A general approach to avoid static and dynamic problems. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 219(11), 789–801. https://doi.org/10.1243/095440505x32742 (2005).

From the experimental data, the maximum thickness error occurs at a tool position of \(x =\) 6.9 mm in the feed direction, with a value of 670 \(\upmu \)m. Comparing this with the predicted thickness error of 683 \(\upmu \)m at the same location, gives a prediction error of less than 2%. From Fig. 7a,b it can be seen that the proposed modelling framework successfully predicts the overall distribution of the thickness error. Furthermore, Fig. 7c shows a comparison between the predicted and experimentally measured thickness error along a vertical line at \(x =\) 54 mm, i.e. in the middle of the workpiece. A close agreement is found between the predicted and measured thickness error. In Fig. 7d, the cutting force is plotted against the immersion angle at the instant when the tool is positioned at the top level approximately 6 mm in the feed direction. Again, there is a close agreement between the predicted and measured forces.

In Fig. 7, predicted and experimentally measured results are shown for experiment 1. The experimental and predicted thickness errors are shown in Fig. 7a,b. Here, and in the following thickness error plots, the z-coordinate corresponds to the axial direction of the plate, where \(z =\) 0 and \(z =\) 55 mm corresponds to the fixed and free end of plate, respectively. The maximum thickness error is predicted to occur near the top of the workpiece, where the tool entries the material in the first pass, due to the low workpiece stiffness correlated to this tool position. The thickness error at this tool position is not experimentally measured due to difficulties in measuring the thickness at the corner of the workpiece. Instead, the first measuring point is placed 1 mm from the corner. In the axial direction, the first measuring point is placed 10 mm from the fixed end, due to irregularities that may arise in the interface between machined and unmachined surfaces.

The cutting force coefficients in Eq. (1) are calibrated by fitting average force expressions to experimentally measured average forces through linear regression, following21. The calibration experiments consist of flank milling tests for workpieces made of aluminum EN AC-46000 (AlSi9Cu3(Fe)) using feed per flutes of \(f_{\textrm{z}}\) = [0.050; 0.0875; 0.125; 0.1625; 0.200] mm/flute, which corresponds to feed rates of \(v_{\textrm{f}}\) = [80; 140; 200; 260; 320] mm/min, axial depth of cut \(a_{\textrm{p}}\) = 17 mm, radial width of cut \(a_{\textrm{e}}\) = 1.4 mm and spindle speed n = 800 rpm. The considered tools are carbide end mills of the type Sandvik CoroMill. The tool parameters for Tool 1 (Product code: 2S221-1200-150-NG H10F) and Tool 2 (Product code: 2S221-2000-250-NG H10F) are shown in Table 3 and the corresponding cutting- and edge force coefficients in the tangential, radial and axial directions are calibrated for the considered tools to the values according to Table 4.

Ratchev, S., Govender, E. & Nikov, S. Towards deflection prediction and compensation in machining of low-rigidity parts. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 216(1), 129–134. https://doi.org/10.1243/0954405021519636 (2002).

From the simulation results presented in section 8, some key findings can be stated; (1) the WL cut pattern gives smaller thickness errors compared to the SBS cut pattern; (2) Tool 2, with a tool diameter of 20 mm, gives smaller thickness errors compared to Tool 1, which has a tool diameter of 12 mm; (3) larger machining allowances, or radial widths of cut, give smaller thickness errors ; (4) a larger axial depth of cut decreases the maximum value of the thickness error but results in a larger average value of the thickness errors over the whole workpiece and (5) an increased feedrate gives increased thickness errors.

where \(w(z,\phi )\) denotes the workpiece deflections along the yellow line in Fig. 3. That is, the in-process deflections determine the effective start angle in Eq. (16) and thereby also the upper integration boundary in Eq. (6), which in turn affects the cutting forces and the in-process deflections. Therefore, the iterative solution strategy is required to compute the forces and deflections at the equilibrium state.