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18 pages, 35401 KiB  
Article
Vibration Reduction on Circular Disks with Vibroacoustic Metamaterials
by Sebastian Rieß, Ron Schmidt, William Kaal, Heiko Atzrodt and Sven Herold
Appl. Sci. 2024, 14(11), 4637; https://doi.org/10.3390/app14114637 - 28 May 2024
Cited by 1 | Viewed by 1000
Abstract
Vibroacoustic metamaterials represent an innovative technology developed for broadband vibration reduction. They consist of an array of local resonators and are able to reduce vibrations over a wide frequency range, commonly referred to as a stop band. Vibroacoustic metamaterials may be a promising [...] Read more.
Vibroacoustic metamaterials represent an innovative technology developed for broadband vibration reduction. They consist of an array of local resonators and are able to reduce vibrations over a wide frequency range, commonly referred to as a stop band. Vibroacoustic metamaterials may be a promising strategy to reduce out-of-plane vibrations of thin-walled, disk-shaped structures, such as saw blades. However, their behavior in rotating systems has not yet been fully understood. In this study, a vibroacoustic metamaterial integrated into a circular disk for the reduction of out-of-plane vibrations is experimentally investigated in the rotating and non-rotating state. Derived from the predominant frequency range of noise emitted by saw blades, a vibroacoustic metamaterial with a numerically predicted stop band in the frequency range from 2000 Hz to 3000 Hz, suitable for integration into a circular disk, is designed. The resonators of the metamaterial are realized by cutting slots into the disk using a waterjet cutting machine. To experimentally examine the structural dynamic behavior, the disk is excited by an impulse hammer and observed by a stationary optical velocity sensor on a rotor dynamics test stand. The results of the rotating and the non-rotating state are compared. The measurements are carried out at two different radii and at speeds up to 3000 rpm. A distinct stop band characteristic is shown in the desired frequency range from 2000 Hz to 3000 Hz in the rotating and non-rotating state. No significant shift of the stop band frequency range was observed during rotation. However, adjacent modes were observed to propagate into the stop band frequency range. This work contributes to a better understanding of the behavior of vibroacoustic metamaterials in the rotating state and enables future applications of vibroacoustic metamaterials for vibration reduction in rotating, disk-shaped structures such as saw blades, brake disks or gears. Full article
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Figure 1

Figure 1
<p>(<b>a</b>) Schematic of a VAMM, (<b>b</b>) schematically depicted stop band in the frequency domain. Source: compare [<a href="#B12-applsci-14-04637" class="html-bibr">12</a>].</p>
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<p>Example of a Campbell diagram (<b>a</b>). Solid lines: stationary observer; dashed lines: rotating observer. Mode shapes for circular disks (<b>b</b>). Source: compare [<a href="#B28-applsci-14-04637" class="html-bibr">28</a>].</p>
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<p>Circular disk with diameters <math display="inline"><semantics> <msub> <mi>d</mi> <mi mathvariant="normal">o</mi> </msub> </semantics></math> = 300 <math display="inline"><semantics> <mi>mm</mi> </semantics></math> and <math display="inline"><semantics> <msub> <mi>d</mi> <mi mathvariant="normal">i</mi> </msub> </semantics></math> = 30 <math display="inline"><semantics> <mi>mm</mi> </semantics></math>, and thickness <span class="html-italic">t</span> = 2 <math display="inline"><semantics> <mi>mm</mi> </semantics></math>.</p>
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<p>(<b>a</b>) FE model of the circular disk with driving point (blue) and measurement points (red). (<b>b</b>) Measured and simulated averaged accelerance transfer function.</p>
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<p>Unit cell design. Thickness: <span class="html-italic">t</span> [<a href="#B12-applsci-14-04637" class="html-bibr">12</a>].</p>
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<p>Unit cell in its first natural frequency with Brillouin zone indicated with arrows (<b>left</b>). Dispersion curve of the unit cell along the Brillouin zone (<b>right</b>). The solid lines indicate out-of-plane vibrations, and the dotted lines that intersect the stop band correspond to in-plane vibrations.</p>
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<p>(<b>a</b>) FE model of the circular saw blade with evaluation points (red) and driving point (blue). (<b>b</b>) Comparison of the measured and simulated averaged transfer functions.</p>
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<p>(<b>a</b>) Out-of-plane modes of the circular disk with VAMM at 2448 <math display="inline"><semantics> <mi>Hz</mi> </semantics></math>, (<b>b</b>) at 2690 <math display="inline"><semantics> <mi>Hz</mi> </semantics></math> and (<b>c</b>) at 2790 <math display="inline"><semantics> <mi>Hz</mi> </semantics></math>.</p>
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<p>(<b>a</b>) Unmodified circular disk. (<b>b</b>) Circular disk with integrated VAMM.</p>
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<p>Experimental setup for characterization of the circular disk.</p>
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<p>Measurement points (red) on the circular disk without (<b>a</b>) and with VAMM (<b>b</b>).</p>
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<p>Averaged transfer functions (accelerance) for the outer (<b>top</b>), middle (<b>middle</b>) and inner measurement points (<b>bottom</b>), both for a disk with VAMM and without. Sketch of the disks: Red: Evaluated measurement points. Blue: Excitation point.</p>
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<p>Modes of the circular disk with VAMM at (<b>a</b>) 2452 <math display="inline"><semantics> <mi>Hz</mi> </semantics></math>, (<b>b</b>) 2710 <math display="inline"><semantics> <mi>Hz</mi> </semantics></math> and (<b>c</b>) 2794 <math display="inline"><semantics> <mi>Hz</mi> </semantics></math>.</p>
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<p>Measurement points (MPs, red) on the circular disk without (<b>a</b>) and with VAMM (<b>b</b>).</p>
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<p>Measured admittance of the circular disk without VAMM (<b>a</b>) and with VAMM (<b>b</b>) at measurement point 1.</p>
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<p>Measured admittance of the circular disk without VAMM (<b>a</b>) and with VAMM (<b>b</b>) at measurement point 2.</p>
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<p>Campbell diagram of the circular disk with VAMM at measurement point 1 (<b>a</b>) and measurement point 2 (<b>b</b>).</p>
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<p>Measured admittance of the circular disk without VAMM and with VAMM at measurement point 1 for different rotational speeds.</p>
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<p>Measured admittance of the circular disk without VAMM and with VAMM at measurement point 2 for different rotational speeds.</p>
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19 pages, 6028 KiB  
Article
Study of Machining of Gears with Regular and Modified Outline Using CNC Machine Tools
by Rafał Gołębski and Piotr Boral
Materials 2021, 14(11), 2913; https://doi.org/10.3390/ma14112913 - 28 May 2021
Cited by 16 | Viewed by 4328
Abstract
Classic methods of machining cylindrical gears, such as hobbing or circumferential chiseling, require the use of expensive special machine tools and dedicated tools, which makes production unprofitable, especially in small and medium series. Today, special attention is paid to the technology of making [...] Read more.
Classic methods of machining cylindrical gears, such as hobbing or circumferential chiseling, require the use of expensive special machine tools and dedicated tools, which makes production unprofitable, especially in small and medium series. Today, special attention is paid to the technology of making gears using universal CNC (computer numerical control) machine tools with standard cheap tools. On the basis of the presented mathematical model, a software was developed to generate a code that controls a machine tool for machining cylindrical gears with straight and modified tooth line using the multipass method. Made of steel 16MnCr5, gear wheels with a straight tooth line and with a longitudinally modified convex-convex tooth line were machined on a five-axis CNC milling machine DMG MORI CMX50U, using solid carbide milling cutters (cylindrical and ball end) for processing. The manufactured gears were inspected on a ZEISS coordinate measuring machine, using the software Gear Pro Involute. The conformity of the outline, the tooth line, and the gear pitch were assessed. The side surfaces of the teeth after machining according to the planned strategy were also assessed; the tests were carried out using the optical microscope Alicona Infinite Focus G5 and the contact profilographometer Taylor Hobson, Talysurf 120. The presented method is able to provide a very good quality of machined gears in relation to competing methods. The great advantage of this method is the use of a tool that is not geometrically related to the shape of the machined gear profile, which allows the production of cylindrical gears with a tooth and profile line other than the standard. Full article
(This article belongs to the Collection Machining and Manufacturing of Alloys and Steels)
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Graphical abstract

Graphical abstract
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<p>Tooth outline: left side of the tooth gap.</p>
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<p>Setting the milling cutter during machining.</p>
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<p>Shaping the transitional outline of a tooth.</p>
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<p>Longitudinal tooth line modification: calculation results.</p>
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<p>Scheme for determining the radius of the circle of longitudinal modification of a tooth.</p>
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<p>Scheme for determining the angularity error of the machined surface.</p>
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<p>Software module: data introduction.</p>
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<p>Software module: (<b>a</b>)tooth outline-generating software; (<b>b</b>)tool path-generating software.</p>
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<p>Clamping system in prismatic jaws: machining process.</p>
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<p>Solid carbide milling cutters used in processing: (<b>a</b>) ball end; (<b>b</b>) cylindrical [<a href="#B33-materials-14-02913" class="html-bibr">33</a>].</p>
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<p>Adopted machining strategy: (<b>a</b>) roughing; (<b>b</b>) finishing.</p>
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<p>Machined gears (<b>a</b>) with modification <span class="html-italic">m</span> = 3, and (<b>b</b>) without modification <span class="html-italic">m</span> = 6; (<b>c</b>) tooth samples from modified gear.</p>
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<p>Graphical presentation of measurement results: (<b>a</b>) gear with tooth line modification, module <span class="html-italic">m</span> = 3; (<b>b</b>) gear with straight tooth line, module <span class="html-italic">m</span> = 6.</p>
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<p>Measurement results: surface roughness Ra parameter, measured longitudinal and perpendicular to machining direction.</p>
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<p>Roughness parameter profile Ra measured perpendicular to the machining direction: (<b>a</b>) sample 1, tooth with modification; (<b>b</b>) sample 1, tooth without modification.</p>
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<p>The stereometric distribution of the tooth surface: (<b>a</b>) sample 1, tooth with modification; (<b>b</b>) sample 1, tooth without modification.</p>
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<p>Selected surface roughness parameters (Sa, Vvc, and Vmp): (<b>a</b>) gear with modification; (<b>b</b>) gear without modification.</p>
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22 pages, 5675 KiB  
Article
Gear Shape Measurement Potential of Laser Triangulation and Confocal-Chromatic Distance Sensors
by Marc Pillarz, Axel von Freyberg, Dirk Stöbener and Andreas Fischer
Sensors 2021, 21(3), 937; https://doi.org/10.3390/s21030937 - 30 Jan 2021
Cited by 29 | Viewed by 5090
Abstract
The demand for extensive gear shape measurements with single-digit µm uncertainty is growing. Tactile standard gear tests are precise but limited in speed. Recently, faster optical gear shape measurement systems have been examined. Optical gear shape measurements are challenging due to potential deviation [...] Read more.
The demand for extensive gear shape measurements with single-digit µm uncertainty is growing. Tactile standard gear tests are precise but limited in speed. Recently, faster optical gear shape measurement systems have been examined. Optical gear shape measurements are challenging due to potential deviation sources such as the tilt angles between the surface normal and the sensor axis, the varying surface curvature, and the surface properties. Currently, the full potential of optical gear shape measurement systems is not known. Therefore, laser triangulation and confocal-chromatic gear shape measurements using a lateral scanning position measurement approach are studied. As a result of tooth flank standard measurements, random effects due to surface properties are identified to primarily dominate the achievable gear shape measurement uncertainty. The standard measurement uncertainty with the studied triangulation sensor amounts to >10 µm, which does not meet the requirements. The standard measurement uncertainty with the confocal-chromatic sensor is <6.5 µm. Furthermore, measurements on a spur gear show that multiple reflections do not influence the measurement uncertainty when measuring with the lateral scanning position measurement approach. Although commercial optical sensors are not designed for optical gear shape measurements, standard uncertainties of <10 µm are achievable for example with the applied confocal-chromatic sensor, which indicates the further potential for optical gear shape measurements. Full article
(This article belongs to the Collection Position Sensor)
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Figure 1

Figure 1
<p>Optical position measuring principles for gear shape measurements consisting of (<b>a</b>) an optical distance sensor (<span class="html-italic">x</span><sub>s</sub>, <span class="html-italic">y</span><sub>s</sub>) in combination with a rotary table (<span class="html-italic">x’</span>, <span class="html-italic">y’</span>) which continuously measures the tooth contour of a gear (<span class="html-italic">x</span>, <span class="html-italic">y</span>) as a function of the rotation angle <span class="html-italic">α</span> and (<b>b</b>) an optical sensor mounted on a linear unit to a measuring unit (<span class="html-italic">x</span><sub>s</sub>, <span class="html-italic">y</span><sub>s</sub>) for laterally scanning the tooth contour of a gear (<span class="html-italic">x</span>, <span class="html-italic">y</span>).</p>
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<p>Geometric model of a nonmodified involute gear for calculating the plumb line distance <span class="html-italic">d</span><sub>plu,i</sub> between the measured and the nominal geometry based on a measured actual point <span class="html-italic">P</span><sub>a,i</sub> on tooth <span class="html-italic">Z</span>, the base point <span class="html-italic">P</span><sub>i</sub> of the nominal geometry for the plumb line distance and the position parameters <math display="inline"><semantics> <mrow> <msub> <mi>ξ</mi> <mi mathvariant="normal">i</mi> </msub> <mo>,</mo> <msub> <mi>θ</mi> <mi mathvariant="normal">z</mi> </msub> <mo>,</mo> <msub> <mi>ψ</mi> <mi mathvariant="normal">b</mi> </msub> <mo>,</mo> <mover accent="true"> <mi>T</mi> <mo>→</mo> </mover> <mo>,</mo> <msub> <mi>φ</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>r</mi> <mrow> <mi mathvariant="normal">I</mi> <mo>,</mo> <mi mathvariant="normal">i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi mathvariant="sans-serif">γ</mi> <mi mathvariant="normal">i</mi> </msub> <mo>,</mo> <msub> <mover accent="true"> <mi>n</mi> <mo>→</mo> </mover> <mi mathvariant="normal">i</mi> </msub> </mrow> </semantics></math> in the workpiece coordinate system. The plumb line distance between the measuring point and the nominal geometry of the tooth flank is displayed enlarged. <a href="#sensors-21-00937-f002" class="html-fig">Figure 2</a> is modified according to [<a href="#B20-sensors-21-00937" class="html-bibr">20</a>].</p>
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<p>Procedure for determining and assessing the gear shape standard measurement uncertainty.</p>
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<p>Measuring objects for evaluating the potential of the triangulation sensor and confocal-chromatic sensor for gear shape measurements and for investigating the measurement deviation contributions through the tilt angle between the gear surface normal and the sensor axis, the varying surface curvature, and gear surface properties. (<b>a</b>) shows an involute tooth flank standard with a nominal geometry with a normal module of 10.64117 mm, 20 teeth, and a base circle diameter of 199.99 mm. (<b>b</b>) shows a spur gear with involute profile and a nominal geometry with a normal module of 3.75 mm, 26 teeth and a base circle radius of 91.62 mm. In addition, the measuring spot and multiple reflections of a triangulation measurement are visible on the spur gear.</p>
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<p>Experimental set-up of the optical position measurement approach for the gear shape measurement with a linear unit for laterally scanning the tooth flank of a tooth flank standard and using the confocal-chromatic sensor as an example. An additional linear unit allows the height of the optical sensor to be adjusted. To examine the influence of multiple reflections, the tooth flank standard is exchanged with a spur gear.</p>
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<p>Principle sketch for the theoretical estimation of the distance variation ∆<span class="html-italic">d</span> within the measuring spot with a diameter of <span class="html-italic">w</span><sub>d</sub> of the optical distance sensors resulting from the tilt angle <span class="html-italic">τ</span> between tooth surface normal and sensor axis and the curvature of the tooth flank. (<b>a</b>) shows the influence of the tilt angle simplified on a flat surface. (<b>b</b>) shows the influence of the curvature of the tooth flank for a gear geometry corresponding to the tooth flank standard.</p>
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<p>Results of one gear shape measurement with the triangulation sensor and confocal-chromatic sensor on the involute tooth flank standard, respectively. (<b>a</b>) shows the transformed triangulation measurement points as blue dots in comparison to the reference geometry of the tooth flank as a black line in a common coordinate system. Note that the x- and <span class="html-italic">y</span>-axis are scaled differently. (<b>b</b>) shows the plumb line distances between the reference and the measured geometry of the tooth flank plotted over the x-positions of the laser triangulation measurement points. (<b>c</b>) illustrates the transformed confocal-chromatic measurement points as blue dots compared to the reference geometry of the tooth flank as a black line in a common coordinate system. (<b>d</b>) illustrates the plumb line distances between the reference and measured geometry of the tooth flank depending on the x-positions of the confocal-chromatic measurement points.</p>
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<p>Dependence of the determined plumb line distances of (<b>a</b>) the triangulation gear shape measurements on the tooth flank standard and (<b>b</b>) the confocal-chromatic gear shape measurements on the tooth flank standard on the absolute values of the estimated tilt angles between the gear surface normal and the sensor axis. The crosses represent the tilt angles in the direction of the root (mathematically negative) and the diamonds represent the tilt angles in the direction of the tip (mathematically positive). From the symmetrical behavior of the plumb line distances it can be seen that no separate influence of the curvature can be observed within the scattering and that a significant dependence on the surface tilt can be expected.</p>
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<p>Remaining deviations of the corrected comparison triangulation gear shape measurements as a function of the x-component of the measurement point. The measurements are performed at different heights on the tooth flank standard to study the influence of the local topography of the surface on the measurement deviation.</p>
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<p>Remaining deviations of the corrected comparison measurements of the gear shape using the confocal-chromatic sensor as a function of the x-component of the measurement point. A second <span class="html-italic">x</span>-axis illustrates the dependency of the plumb line distances of the tilt angles. The measurements are performed at different heights on the tooth flank standard to study the influence of the local topography of the surface on the measurement deviation.</p>
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<p>Plumb line distances of the comparison measurements of the gear shape using the triangulation sensor. The blue crosses present the measurement without the coated adjacent tooth. The red crosses are the results of the measurement with the coated adjacent.</p>
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<p>Plumb line distances of the comparison measurements of the gear shape using the triangulation sensor. The blue crosses present the measurement without the coated adjacent tooth. The red crosses are the results of the measurement with the coated adjacent.</p>
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13 pages, 6614 KiB  
Article
Extending the Depth of Field beyond Geometrical Imaging Limitations Using Phase Noise as a Focus Measure in Multiwavelength Digital Holography
by Tobias Seyler, Markus Fratz, Tobias Beckmann, Annelie Schiller, Alexander Bertz and Daniel Carl
Appl. Sci. 2018, 8(7), 1042; https://doi.org/10.3390/app8071042 - 26 Jun 2018
Cited by 22 | Viewed by 4546
Abstract
Digital holography is a well-established technology for optical quality control in industrial applications. Two common challenges in digital holographic measurement tasks are the ambiguity at phase steps and the limited depth of focus. With multiwavelength holography, multiple artificial wavelengths are used to extend [...] Read more.
Digital holography is a well-established technology for optical quality control in industrial applications. Two common challenges in digital holographic measurement tasks are the ambiguity at phase steps and the limited depth of focus. With multiwavelength holography, multiple artificial wavelengths are used to extend the sensor’s measurement range up to several millimeters, allowing measurements on rough surfaces. To further extend the unambiguous range, additional highly stabilized and increasingly expensive laser sources can be used. Besides that, unwrapping algorithms can be used to overcome phase ambiguities—but these require continuous objects. With the unique feature of numerical refocusing, digital holography allows the numerical generation of an all-in-focus unambiguous image. We present a shape-from-focus algorithm that allows the extension of the depth of field beyond geometrical imaging limitations and yields unambiguous height information, even across discontinuities. Phase noise is used as a focus criterion and to generate a focus index map. The algorithm’s performance is demonstrated at a gear flank with steep slopes and a step sample with discontinuities far beyond the system’s geometrical limit. The benefit of this method on axially extended objects is discussed. Full article
(This article belongs to the Special Issue Applications of Digital Holographic Microscopy)
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Figure 1

Figure 1
<p>Experimental setup for temporal phase-shifting multiwavelength digital holography: (<b>a</b>) sensor internals including laser system (1); lens (2); polarizing beam splitter cubes (3)/(7); piezo (4); camera (8); gear test object (5); and imaging lens (6). The interferometric optical path includes reference and object beams, which are superimposed on the imaging device. Lenses (2) and (6) ensure maximal light yield; (<b>b</b>) data acquisition time series using three lasers and three piezo steps for temporal phase shifting. In total, nine camera images are acquired.</p>
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<p>Algorithm principle from phase map input to phase noise output. (<b>a</b>) Simulated phase map with linearly increasing noise from left to right; (<b>b</b>) phase gradient direction for low-noise and high-noise points in a 6 × 6 px<sup>2</sup> area; and (<b>c</b>) sum of gradient direction vectors <math display="inline"><semantics> <mrow> <mo>∑</mo> <mover> <mo>∇</mo> <mo>^</mo> </mover> <mi>φ</mi> </mrow> </semantics></math> for low-noise (top) and high-noise (bottom) points. A long sum vector indicates an area of smooth phase.</p>
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<p>Phase smoothness <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mi>z</mi> </msub> </mrow> </semantics></math> at different reconstruction distances <math display="inline"><semantics> <mrow> <mi>z</mi> </mrow> </semantics></math> for a gear sample. A maximum around 6 mm can be found, corresponding to the in-focus distance.</p>
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<p>Experimental setup including the gear tooth sample and holography sensor.</p>
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<p>Phase <math display="inline"><semantics> <mi>φ</mi> </semantics></math> (left/right) and phase smoothness <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mi>z</mi> </msub> </mrow> </semantics></math> for two propagation distances <math display="inline"><semantics> <mi>z</mi> </semantics></math>. Left: <math display="inline"><semantics> <mrow> <mi>z</mi> </mrow> </semantics></math> = 3 mm, right: <math display="inline"><semantics> <mi>z</mi> </semantics></math> = 6 mm. Sharp stripes can be observed in areas of low phase noise, whereas areas of high phase noise appear as random phase distribution.</p>
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<p>Phase smoothness <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mi>z</mi> </msub> </mrow> </semantics></math> of several points at different propagation distances, <math display="inline"><semantics> <mi>z</mi> </semantics></math>. <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> <mo>,</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> is marked with a <math display="inline"><semantics> <mo>∗</mo> </semantics></math>, whereas <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> <mo>,</mo> <mi>G</mi> <mi>a</mi> <mi>u</mi> <mi>s</mi> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math> can be read at the peak of the Gaussian fit. Two thumbnails at <math display="inline"><semantics> <mi>z</mi> </semantics></math> = 3.50 mm (left) and <math display="inline"><semantics> <mi>z</mi> </semantics></math> = 6.33 mm (right) illustrate the position of the crosses on the sample near the focus or the orange cross (left) and the red cross (right).</p>
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<p>Shape-from-focus output including phase smoothness <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mi>z</mi> </msub> </mrow> </semantics></math> as the quality criterion, high values show a strong result; (<b>a</b>) discrete focus map <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> <mo>,</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> reconstructed by pixel wise shape-from-focus maximum. The <math display="inline"><semantics> <mi>z</mi> </semantics></math> sections at colored crosses are illustrated in <a href="#applsci-08-01042-f006" class="html-fig">Figure 6</a>; (<b>b</b>) optimized values of <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mi>z</mi> </msub> </mrow> </semantics></math> using maximum filter.</p>
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<p>Shape-from-focus output including phase smoothness <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mi>z</mi> </msub> </mrow> </semantics></math> as a quality criterion, high values show a strong result; (<b>a</b>) focus map <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> <mo>,</mo> <mi>G</mi> <mi>a</mi> <mi>u</mi> <mi>s</mi> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math> reconstructed by pixel wise shape-from-focus Gaussian fit. The <math display="inline"><semantics> <mi>z</mi> </semantics></math> sections at colored crosses are illustrated in <a href="#applsci-08-01042-f006" class="html-fig">Figure 6</a>; (<b>b</b>) optimized values of <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mi>z</mi> </msub> </mrow> </semantics></math> using the Gaussian approach.</p>
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<p>(<b>a</b>) All-in-focus phase map <math display="inline"><semantics> <mi>φ</mi> </semantics></math>–the whole measurement shows sharp stripes and minimized phase noise. In the 3072 × 3072 pixels original image, the fringes are clearly resolved; (<b>b</b>) Magnified view of the red area of (<b>a</b>). The fringe spacing is 10 pixels.</p>
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<p>Masked height map <math display="inline"><semantics> <mi>h</mi> </semantics></math> of the combined tooth data using (<b>a</b>) maximum filter: combination errors due to discrete and hence imprecise shape-from-focus data; (<b>b</b>) Gaussian filter: almost no combination errors occur onto the Gaussian fit output.</p>
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<p>(<b>a</b>) Photograph of step sample with discontinuous height steps <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>z</mi> <mo>=</mo> <mn>1.5</mn> <mo> </mo> <mi>mm</mi> </mrow> </semantics></math> beyond the sensor’s unambiguous range; (<b>b</b>) sketch of the sensor setup including the sample step height.</p>
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<p>Focus map <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> <mo>,</mo> <mi>G</mi> <mi>a</mi> <mi>u</mi> <mi>s</mi> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math> reconstructed by pixel wise Gaussian fit to shape-from-focus output stack; (<b>a</b>) discrete focus map <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> <mo>,</mo> <mi>G</mi> <mi>a</mi> <mi>u</mi> <mi>s</mi> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math> reconstructed by pixel wise shape-from-focus Gaussian fit; (<b>b</b>) optimized values of <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mi>z</mi> </msub> </mrow> </semantics></math> using the Gaussian filter. At very steep slopes, strong artefacts can be observed because of the stripes not being sufficiently sampled.</p>
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<p>Height map <math display="inline"><semantics> <mi>h</mi> </semantics></math> of the combined steps sample data using (<b>a</b>) maximum filter: combination errors due to discrete hence imprecise shape-from-focus data; (<b>b</b>) the Gaussian filter: almost no combination errors occur onto the Gaussian fit output.</p>
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Article
Designing a Tool System for Lowering Friction during the Ejection of In-Die Sintered Micro Gears
by Emanuele Cannella, Emil Krabbe Nielsen and Alessandro Stolfi
Micromachines 2017, 8(7), 214; https://doi.org/10.3390/mi8070214 - 6 Jul 2017
Cited by 9 | Viewed by 6212
Abstract
The continuous improvements in micro-forging technologies generally involve process, material, and tool design. The field assisted sintering technique (FAST) is a process that makes possible the manufacture of near-net-shape components in a closed-die setup. However, the final part quality is affected by the [...] Read more.
The continuous improvements in micro-forging technologies generally involve process, material, and tool design. The field assisted sintering technique (FAST) is a process that makes possible the manufacture of near-net-shape components in a closed-die setup. However, the final part quality is affected by the influence of friction during the ejection phase, caused by radial expansion of the compacted and sintered powder. This paper presents the development of a pre-stressed tool system for the manufacture of micro gears made of aluminum. By using the hot isostatic pressing (HIP) sintering process and different combinations of process parameters, the designed tool system was compared to a similar tool system designed without a pre-stressing strategy. The comparison between the two tool systems was based on the ejection force and part fidelity. The ejection force was measured during the tests, while the part fidelity was documented using an optical microscope and computed tomography in order to obtain a multi-scale characterization. The results showed that the use of pre-stress reduced the porosity in the gear by 40% and improved the dimensional fidelity by more than 75% compared to gears produced without pre-stress. Full article
(This article belongs to the Special Issue Micro/Nano Manufacturing)
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Figure 1

Figure 1
<p>Experimental micro-gear design used in this work.</p>
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<p>Tool system design for the shrink-fit application: (<b>a</b>) stress-ring, sleeve and die section; and (<b>b</b>) rendered CAD model of the stress-ring, sleeve and die.</p>
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<p>The diagram shows the estimated hysteresis cycle during the axial compaction of the investigated micro-gear according to the Bockstiegel model [<a href="#B15-micromachines-08-00214" class="html-bibr">15</a>]. The diagram was obtained by assuming an aluminum-steel frictional condition µ = 0.61. Stages: I, elastic loading; II, plastic loading; III, elastic releasing; IV, plastic releasing.</p>
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<p>Experimental setup: (<b>a</b>) details of the overall pre-stressed tool system, die and punches; and (<b>b</b>) detail of the pre-stressed tool configuration during sintering.</p>
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<p>Measuring setup: (<b>a</b>) diagram showing the variation of the main process parameters; (<b>b</b>) data acquisition system, Data-Translation DT-9800 (Data Translation GmbH, Bietigheim-Bissingen, Germany), and temperature control system, Allen-Bradley 900 TC-32 (Rockwell Automation, Milwaukee, WI, USA).</p>
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<p>Examples of sintered samples using different process parameters. A pen tip was used to give an idea of the real size of the micro-gears.</p>
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<p>Diagrams showing the experimental values of ejection force measured during the ejection of the micro-gears with respect to the process parameters. (<b>a</b>) The four level of punch pressure with constant sintering temperature (550 °C) and holding time (20 min); (<b>b</b>) the four level of sintering temperatures with constant punch pressure (150 MPa) and holding time (20 min); and (<b>c</b>) the four level of holding time with constant punch pressure (150 MPa) and sintering temperature (550 °C).</p>
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<p>Diagrams showing the experimental values of ejection force measured during the ejection of the micro-gears with respect to the process parameters. (<b>a</b>) The four level of punch pressure with constant sintering temperature (550 °C) and holding time (20 min); (<b>b</b>) the four level of sintering temperatures with constant punch pressure (150 MPa) and holding time (20 min); and (<b>c</b>) the four level of holding time with constant punch pressure (150 MPa) and sintering temperature (550 °C).</p>
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<p>The pictures showing the lateral surfaces of NPSGs, left side, and PSGs, right side, acquired using an optical microscope. PSGs: (<b>a</b>) T: 550 °C, holding time: 10 min, punch pressure: 150 MPa, percentage force reduction: −66%; (<b>b</b>) T: 550 °C, holding time: 15 min, punch pressure: 150 MPa, percentage force reduction: −64%; and (<b>c</b>) T: 550 °C, holding time: 15 min, punch pressure: 150 MPa, percentage force reduction: −30%. Regardless of the sintering process parameters, NPSGs show on their surfaces the consequences of the larger ejections.</p>
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<p>The pictures showing the lateral surfaces of NPSGs, left side, and PSGs, right side, acquired using an optical microscope. PSGs: (<b>a</b>) T: 550 °C, holding time: 10 min, punch pressure: 150 MPa, percentage force reduction: −66%; (<b>b</b>) T: 550 °C, holding time: 15 min, punch pressure: 150 MPa, percentage force reduction: −64%; and (<b>c</b>) T: 550 °C, holding time: 15 min, punch pressure: 150 MPa, percentage force reduction: −30%. Regardless of the sintering process parameters, NPSGs show on their surfaces the consequences of the larger ejections.</p>
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<p>Volume pore distributions for (<b>a</b>) NPSG and (<b>b</b>) PSG. Deviation range from 0 to 0.00009 mm<sup>3</sup>.</p>
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<p>Actual-to-nominal comparison for (<b>a</b>) NPSG and (<b>b</b>) PSG. Deviation range ±0.03 mm.</p>
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