PRECISION LOCATING OF ADDITIVELY MANUFACTURED PARTS USING EMBEDDED KINEMATIC COUPLINGS

Transcription

1 PRECISION LOCATING OF ADDITIVELY MANUFACTURED PARTS USING EMBEDDED KINEMATIC COUPLINGS Ryan Wade Penny and A. John Hart Department of Mechanical Engineering Massachusetts Institute of Technology Cambridge, Massachusetts, USA INTRODUCTION The application of Additive Manufacturing (AM) to precision engineering requires the derivation of design principles for precision locating. This is essential to accurate assembly of components made by AM, as well as locating AM components for precision machining and finishing operations that are often necessary for final use. Moreover, the immense flexibility of AM is challenged by limitations to surface finish and overall part accuracy, making it important to derive processspecific guidelines for the incorporation and use of traditional locating features in AM, as well as for derivation of potentially new designs [1]. As an initial step toward this goal, here we study the fabrication and performance of ball-groove kinematic couplings (KCs), which are widely used due to their high repeatability arising from nearideal contact at six points (Fig 1a). Critical to KC performance is understanding of the geometric accuracy, friction, and elastic-plastic deformation necessary to create couplings that mate repeatably and have adequate stiffness for their intended use [2][3]. Specifically, we evaluate Fused Deposition Modeling (FDM) with ABS (Acrylonitrile Butadiene Styrene) plastic as a means of fabricating KCs, and quantify the stiffness and repeatability achieved. Design of kinematic features for this AM process is particularly challenging for two reasons. First, FDM is a layerwise process in which a part is sliced into a plurality of 2D layers, each with a thickness of mm for this material [4]. This quantization process reduces curved or out of plane features to a stair-step like approximation. Second, the low stiffness, low strength, and anisotropy of FDM ABS ensures that the contacts will plastically deform under most practical loads. SINGLE PAIR TESTS First, we measure the elastic-plastic behavior of single sphere-groove interfaces to provide a basis for interpreting the results of repeatability experiments on full couplings. These tests are performed using a universal testing machine to record force-displacement curves as a single sphere-groove combination is cyclically loaded to a prescribed peak force. Spherical components were designed around a 25.4 mm nominal diameter, with truncated vee components sized to match (Fig. 1b). Initial tests used a single AM sphere or vee, indented using a hardened steel counterpart. These trials both provide insight to the performance of AM parts in a workholding application and enable more intuitive analysis of deformation mechanics. Results from indentation tests on AM on AM parts are also presented, which are more relevant to rapid prototyping and short run manufacturing of precision assemblies. A typical cyclic force-displacement curve is presented Fig. 2; these data were recorded as an AM sphere was loaded to 100 N with a steel vee. The normal stiffness of the coupling pair is simply determined by the slope of the loading curves, which are plotted in red in Fig. 3. The measured stiffness of 1363 N/µm is very close to the value of 1370 N/µm obtained using Hertzian contact mechanics [5]. Moreover, the predicted contact stress ratio is greater than unity, implying that plastic deformation of the coupling will occur. Subsequent cycles show that stiffness approaches 2400 N/µm as the surface deforms and the contact area enlarges. Next, the energy dissipated in a given cycle is represented by the area between the curves generated as the specimen is loaded and unloaded. The unrecovered energy, quantified for this trial in Fig. 4 (red dots), is expended by plastic deformation the specimen, friction, and viscoelastic dissipation arising from short range molecular motion [6]. Dissipation is higher for the first several cycles as the surface texture of the AM part is deformed, then approaches a constant asymptote representative of frictional and viscoelastic losses. Viscoelastic behavior is the largest driver

2 of hysteresis in the coupling, which has been identified as key factor in repeatability [7]. The deformation sustained over 10 cycles is shown in Fig. 1d, which is faintly visible even with the aid of a microscope. Figures 3 and 4 also provide results for specimens that have been printed in an orientation out of plane by +90 about either the +X or +Y direction. The spheres proved stiffest printed upright, and lower stiffness is correlated with increased hysteresis. These trends repeat for specimens loaded to higher peak forces, as listed in Table 1. A stiffness of 2950 N/µm is predicted for the first cycle of a specimen loaded to 1000 N, again in excellent agreement with the experimental result of 2884 N/µm for an AM upright sphere. Once broken in, the coupling s stiffness is greater than 5000 N/µm at the cost of substantial deformation from the original spherical profile, as captured in Fig. 1e. Stiffness of AM vee-steel sphere coupling pairs have also been included in Table 1, again for forces of 100 N and 1000 N. Interestingly, this combination substantially underperformed both as compared to the theoretical stiffness of the coupling and their AM sphere counterparts. This difference is unexpected; Hertzian contact theory for conventional surfaces does not differentiate which material forms the sphere or plane [8]. Heavily loaded specimens show crazing in locations well removed from the contact patch, suggesting that this discrepancy results from the geometry surrounding the contact planes. Specifically, stress concentrations in the corners of the truncated vee are evident, arising from undesirable deformation in these regions. A final point of contrast from the AM sphere results is that vees printed +90 out of plane about the +X direction proved stiffer than the other orientations tested. Last, we measured coupling stiffnesses in which both components have been additively manufactured by FDM. Components were printed in their stiffest orientations as identified above and cyclically loaded to either 100 N or 1000 N. As seen in Table 1, the coupling stiffness is less than the AM vee/steel sphere trials, which serve as an upper bound for the expected stiffness of the coupling. The reduced rigidity is simply explained by the complex interaction of surfaces with large amplitude, structured surface texture. Figure 1f is an image of the deformation sustained from the 1000 N trial, showing a clear imprint from the counterpart, rather than the more uniform deformations seen in the other trials. This checkered texture implies many small regions of high contact pressure, thereby reducing the rigidity of the coupling. FULL COUPLING REPEATABILITY Guided by our coupling stiffness measurements, we performed an experiment to assess the repeatablility of AM KCs. Central to these tests was defining a procedure to break-in the couplings. In any practical application, a coupling would be preloaded upon installation, then subject to additional dynamic loading under use. It is then necessary to break-in the coupling at forces greater than the anticipated worst-case loading, such that plastic deformation is minimized over the coupling s service life. To simulate such a real-world application, we assembled and loaded couplings three times to a force 133% larger than the test load. Break-in was always preformed against the mate used to assess repeatability; a test of AM spheres against AM grooves would have these parts broken-in against each other, for example. After break-in, repeatability was measured using a Wenzel LH108 Coordinate Measuring Machine (CMM). The bottom half of the coupling was rigidly secured to the CMM, and a series of datum features were identified. Then the top half of the coupling was installed, tightened with a torque wrench to place the test load across each spherevee pair, measured with respect to the datum features on the bottom part, and finally disassembled. Three such measurements were taken for each trial configuration. The standard deviation of the X, Y, and Z displacements were then added in quadrature to determine the net repeatability of the fixture. Repeatability measurements, presented in Table 2, show that repeatability of 35 µm or better is readily attainable using deformed couplings. Existing literature suggests that coupling repeatability should be roughly equal to the magnitude of surface roughness present on the contact surfaces [9] [10]. Clearly, the deformed surfaces yield better performance than their original 170 µm surface texture would suggest. Moreover, the more lightly loaded specimens, which feature greater residual surface roughness, show superior repeatability. One may then conclude that lower friction, viscoelastic loss, and smaller

3 TABLE 1. AM KC pair stiffness for a number of test cases. Spheres Vees AM Build Orientation Test Load Cycle 1 Stiffness Cycle 10 Stiffness AM ABS Steel Def ault 100 N 1363 N/mm 2384 N/mm AM ABS Steel +X 100 N 1190 N/mm 1927 N/mm AM ABS Steel +Y 100 N 1030 N/mm 1559 N/mm AM ABS Steel Def ault 1000 N 2884 N/mm 5416 N/mm AM ABS Steel +X 1000 N 2282 N/mm 4732 N/mm AM ABS Steel +Y 1000 N 2103 N/mm 4990 N/mm Steel AM ABS Def ault 100 N 915 N/mm 1316 N/mm Steel AM ABS +X 100 N 835 N/mm 1478 N/mm Steel AM ABS +Y 100 N 836 N/mm 1080 N/mm Steel AM ABS Def ault 1000 N 2367 N/mm 3067 N/mm Steel AM ABS +X 1000 N 2468 N/mm 4273 N/mm Steel AM ABS +Y 1000 N 2366 N/mm 3317 N/mm AM ABS AM ABS Def ault, +X 100 N 537 N/mm 963 N/mm AM ABS AM ABS Def ault, +X 1000 N 1687 N/mm 2612 N/mm contact area are more important factors than the greater surface averaging achieved through higher force. Finally, fully AM couplings feature repeatability on par with mating AM parts against steel counterparts. This result is somewhat counterintuitive, because the AM parts are much more compliant than plastic-steel couplings and would be expected to benefit from deformation against an ideal counterpart. Also of note, a load of 1000 N per coupling pair between AM vees and steel spheres proved sufficient to crack the AM specimen. This clearly had a disastrous effect on the repeatability of the coupling. Failure was not expected on the basis of the indentation tests, in which no specimens showed evidence of catastrophic cracking. However, this does serve as a confirmation of the prior observation that the spherical geometry better handles the stresses developed in the material surrounding the locating features. PRECISION LOCATION OF OPTICAL ELE- MENTS Finally, we illustrate the utility of AM kinematic features in the precision location of optical elements. We present a Keplerian refracting telescope, consisting of a fully 3D printed assembly that positions a pair of replaceable glass lenses. As each lens is constrained by a removable lens mount, one may change the magnification ratio of instrument by changing the combination of lenses installed. Fabrication of the lens mounts is particularly well suited to AM, as each must be customized to match a specific outer diameter and focal length. Likewise, AM permits integration of locating features, magnetic preloading, and light seals into a monolithic central fixture. This optical topology requires that any two lenses installed must be separated by the sum of their focal lengths; furthermore, optical quality improves as this sum is increased for a given magnification ratio [11]. These considerations suggest an optomechanical design in which lenses are separated from their alignment and attachment features to the greatest degree possible, thereby maximizing the optical length of the instrument. KCs are an ideal way to locate the displaced lenses, as the small angular deviations possible about a pinned interface would manifest as large displacements of the lenses, thereby negating the benefit of a long optical path. Our instrument, shown in Fig. 5a, features a 50 mm diameter, 250 mm focal length objective that may be paired with eyepiece lenses to achieve 10 and 25 magnification. This telescope features a comparatively low f-number (f/5) for instruments of its class; achieving this level of performance requires mechanically locating the lenses to within 250 µm for acceptable image quality. As inferred from the blurring of the serifs in Fig. 5c, we have achieved such a level of precision despite having the lenses separated by 275 mm and two KC interfaces (Fig. 5b). This demonstration highlights the potential of AM for building functional precision assemblies with embedded kinematic couplings. ACKNOWLEDGMENTS

4 TABLE 2. AM KC repeatability for a number of test cases. Spheres Vees AM Build Orientation Test Load per Pair Repeatability AM ABS Steel Def ault 1000 N 18 µm Steel AM ABS +X 1000 N 182 µm AM ABS AM ABS Default, +X 1000 N 24 µm AM ABS Steel Def ault 100 N 22 µm Steel AM ABS +X 100 N 9 µm AM ABS AM ABS Default, +X 100 N 6 µm AM ABS Steel +X 1000 N 12 µm Steel AM ABS Def ault 1000 N 15 µm AM ABS AM ABS +X, Default 1000 N 35 µm We thank Chris and Christian Joest, and the staff of Imperial Machine Tool in Columbia, New Jersey for their assistance and use of the CMM for the repeatability tests. Financial support was provided by the National Science Foundation EAGER / Cybermanufacturing program (CMMI ). REFERENCES [1] Turner BN, Gold SA. A review of melt extrusion additive manufacturing processes: II. Materials, dimensional accuracy, and surface roughness. Rapid Prototyping Journal. 2015;21(3): [2] Hale LC, Slocum AH. Optimal design techniques for kinematic couplings. Precision Engineering. 2000;25: [3] Slocum AH. Kinematic couplings for precision fixturing Part I: Formulation of design parameters. Precision Engineering. 1988;10: [7] Design of a kinematic coupling for precision applications. Precision Engineering. 1997;20(1):46. [8] Johnson KL. One hundred years of Hertz contact. Proceedings - Institution of Mechanical Engineers. 1982;196: [9] Zelenika S, Flechsig S. Kinematic Couplings for Synchrotron Radiation Instrumentation. In: 2nd International Workshop on Mechanical Engineering Design of Synchrotron Radiation Equipment and Instrumentation; p [10] Slocum AH, Donmez A. Kinematic couplings for precision fixturing Part 2: Experimental determination of repeatability and stiffness. Precision Engineering. 1988;10: [11] Kasunic KJ. Optical Systems Engineering. New York: McGraw-Hill; [4] Stratasys. ABSplus-P430;. Accessed: Available from: "http: //usglobalimages.stratasys.com/ Main/Files/Material_Spec_Sheets/ MSS_FDM_ABSplusP430.pdf". [5] Slocum AH. Kinematic Coupling 3 Groove Design [Spreadsheet]; Available from: edu/kinematiccouplings/files/ kinematic_coupling_design/excel/ Kinematic_Coupling_3Groove_ Design_ _V1.XLS. [6] Ferry J. Viscoelastic properties of polymers. New York, Wiley [1970]; 1970.

5 (a) Full coupling set. FIGURE 2. Cyclic force-displacement curves for an AM sphere loaded with a steel vee to 100 N. Curves asymptotically approach equilibrium as plastic deformation slows. (b) Indentation test specimens. (c) Undeformed AM sphere showing typical surface texture. (d) AM sphere showing surface deformation after being loaded to 100 N with a steel sphere. Six layers show evidence of deformation. (e) AM sphere showing surface deformation after being loaded to 1000 N with a steel sphere. Fourteen layers have been deformed. Note the relative size of the layers as compared to (b). (f) AM vee showing surface deformation after being loaded to 1000 N with an AM sphere. Note the vertical bands in the contact patch, corresponding to the surface texture of the spherical specimen. FIGURE 1. AM indentation test specimens. FIGURE 3. Measured stiffness of an an AM sphere cyclically loaded with a steel vee to 100 N.

6 FIGURE 4. Energy dissipated by an AM sphere cyclically loaded with a steel vee to 100 N. (a) Fully assembled telescope with 25 eyepiece installed. 10 eyepiece is also pictured. (b) Telescope kinematic couplings. Magnets provide preload across the coupling. (c) Image taken through the telescope at 10 magnification. Inverted images are characteristic of Kepler s design. FIGURE 5. plings. AM telescope with kinematic cou1