Accurate Measurement of High-Bandwidth ... - Science Direct

Procedia Manufacturing Volume 5, 2016, Pages 170–181 44th Proceedings of the North American Manufacturing Research Institution of SME http://www.sme.org/namrc

Accurate Measurement of High-Bandwidth Nanomilling Forces Wei Chen1, Emrullah Korkmaz1, B. Arda Gozen2, and O. Burak Ozdoganlar1* 1 2

Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania, USA.

Mechanical and Materials Engineering, Washington State University, Pullman, Washington, USA.

[email protected], [email protected], [email protected], [email protected]

Abstract This paper presents a novel technique for accurate measurement of high-bandwidth nanomilling forces. Nanomilling has recently emerged as a viable mechanical nanomanufacturing technique for creation of three-dimensional nano-scale features on engineering materials. Accurate measurement of nanomilling forces is paramount to advancing the fundamental understanding of nanomilling and to enhancing the process outcomes. However, to date, no effective approach has been described for obtaining accurate measurement of nanomilling forces that exhibit micro/nano Newton range amplitudes and a broad frequency bandwidth. In this paper, we introduce a new in situ microcantilever-based technique for accurate measurement of nanomilling forces within a 10 kHz bandwidth without compromising its high-stiffness configuration. To this end, a microcantilever is designed and fabricated as a sensing element. The sensor possesses the processing and sensing locations close to its fixed and free ends, respectively to enable high stiffness at the processing location and high sensitivity at the sensing location. The sensor is then integrated into our custommade nanomilling system as a force measurement device (FMD), and its dynamic calibration is achieved through an AFM-probe based dynamic testing approach. The calibration approach relates the measured displacements at the sensing location to the applied forces at the processing location. Subsequently, the accurate in situ nanomilling force measurements are obtained within a broad frequency range using the calibrated force sensor. It is concluded that the presented technique provides an effective means of accurate measurement of nanomilling forces within 0-10 kHz frequency range towards realizing essential advances in nanomilling. Keywords: Nanomilling, High-stiffness, AFM probes, Dynamic Calibration, High Bandwidth Force Measurement. *

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Corresponding author. Selection and peer-review under responsibility of the Scientiﬁc Programme Committee of NAMRI/SME c The Authors. Published by Elsevier B.V.

doi:10.1016/j.promfg.2016.08.016

High-Bandwidth Nanomilling Forces Measurement

Chen, Korkmaz, Gozen, and Ozdoganlar

1 Introduction Having unique material and geometric capabilities, nanomilling has recently emerged as a viable technique for nanomanufacturing (Gozen & Ozdoganlar, 2010). In nanomilling, the cutting tool is moved along an orbital path by a three-axis piezoelectric actuator, while the workpiece is fed along the machining path. As such, it is a rotating-tip-based mechanical nanomanufacturing method providing the capability to create three-dimensional (3D) nano-scale features on a myriad of materials from metals to polymers (Gozen & Ozdoganlar, 2012). Furthermore, nanomilling offers attractive advantages, such as high-dimensional accuracy and repeatability as well as high material removal rate and low cutting tool wear through controlled high-frequency motions and its high-stiffness nanotool configuration (Gozen & Ozdoganlar, 2010; Gozen & Ozdoganlar, 2012; Gozen & Ozdoganlar, 2014). As the demand for nanomilling process increases, it is vital to gain a fundamental understanding of nanomilling. Accurate measurement of nanomilling forces is central to gaining this understanding since those forces embody and manifest critical information on mechanics, dynamics, stability, and health of nanomilling process and equipment. Therefore, capability of measuring forces acting on the nanotool during nanomilling process is essential for advancing the fundamental understanding of nanomilling and enhancing the process outcomes, including output quality and productivity (Gozen & Ozdoganlar, 2014). However, since the nanomilling forces are dynamic due to the rotating nature of the cutting tool and its magnitudes are in the micro/nano Newton range, it is challenging to obtain accurate high-bandwidth nanomilling force measurements without hampering its high-stiffness configuration. The state-of-the-art in dynamic micro/nano Newton level force measurement is the commercial atomic force microscope (AFM) based techniques (Ahmad et al., 2008; Beard et al., 2013; Butt et al., 2005; Cerreta et al., 2012). In these techniques, an AFM probe pre-calibrated using the thermal noise method (Butt & Jaschke, 1995) for determining its static stiffness value is used. Briefly, the AFM probe with a natural frequency of ωn behaves like a simple stiffness element at relatively lower frequencies (< 0.1×ωn). This enables the measurement of the force imposed on the AFM probe up to 0.1×ωn through its calibrated static stiffness value and measured deflection of the probe at its free-end (Butt et al., 2005). However, this technique cannot be adopted for nanomilling force measurement due to low stiffness of the AFM probes, which leads to high deflections at the nanomilling processing location, thereby impeding the process performance in accuracy and reproducibility. As such, a comprehensive technique for accurate measurement of high-bandwidth and small-amplitude nanomilling forces is still needed. In this paper, we present a novel microcantilever-based dynamic force-sensing approach for accurate measurement of nanomilling forces within a 10 kHz bandwidth. To this end, a microcantilever, referred as a force measurement device (FMD), with prescribed sensing and processing locations close to its free and fixed ends, respectively, is designed and fabricated. As such, the FMD enables high stiffness at the nanomilling processing location and high sensitivity at the sensing location where the displacement is measured using a non-contact displacement sensor, thereby obviating the drawbacks of the AFM probe-based dynamic force measurement techniques. Subsequently, the FMD is integrated into our tailor-made nanomilling system, and a two-step AFM probe based stepped-sine testing method is used to determine its frequency response function (FRF) between the input force at the processing location and output displacement at the sensing location within 0-10 kHz frequency range. The obtained FRF enables dynamic calibration of the FMD, and accordingly accurate in situ measurement of the nanomilling forces by conducting nanomilling at the processing location while acquiring the displacement at the sensing location. Thus, the presented approach provides the capability to accurately measure dynamic micro/nano newton level forces in applications where high-stiffness is required, such as nanomilling. This paper is organized as follows: the experimental methods, including design and fabrication of the FMD, experimental facility and procedures are first described. Next, the presented technique is

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used to calibrate the microcantilever based FMD within a 10 kHz bandwidth. The designed, fabricated and calibrated FMD are then used to obtain accurate in situ nanomilling force measurements within a broad range of frequencies towards advancing the fundamental understanding of nanomilling.

2 Experimental Methods The overall approach followed for high-bandwidth nanomilling force measurement is illustrated in Figure 1. The technique involves three distinct steps: (1) design and fabrication of the FMD; (2) integration of the FMD into the nanomilling system and its dynamic characterization; and (3) accurate measurement of nanomilling forces using the FMD. First, the FMD is designed through a finite element analysis (FEA), and then fabricated using a mechanical micromachining technique, micromilling on a miniature machine tool (MMT). Subsequently, a two-step AFM probe based dynamic testing is conducted to characterize the fabricated FMD after its integration into the nanomilling system. The dynamic characterization results in a frequency response function (FRF) between the measured displacement at the sensing location of the FMD and the applied force at the processing (nanomilling) location of the FMD. Nanomilling forces are then accurately measured by using the FRF and the acquired displacement at the sensing location while performing nanomilling at the processing location.

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Figure 1: The overall approach for accurate measurement of high-bandwidth small amplitude nanomilling forces.

2.1 Design and Fabrication of the FMD Theory of elasticity and vibrations manifests three fundamental information on mechanics and dynamics of a cantilever: (1) the magnitude of deflection of a cantilever under an external force depends on the location of the applied force on the cantilever; (2) the measured deflection at the free end of a cantilever is relatively large when the force is applied at any location of the cantilever regardless of the force frequency (and thus, regardless of the excited mode shapes); and (3) the force application at the closest possible distance to the fixed end of a cantilever beam results in the smallest magnitude of deflection, while the deflection at the free end is magnified many folds. The only exception is when the dynamic forces at a particular natural frequency of a cantilever are applied at one of the corresponding node locations (where the displacement is zero) in the resonant modes of the cantilever. However, this is not a plausible approach for dynamic force measurement within a broad

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frequency range (Timoshenko & Goodier, 1951; Meirovitch, 2001). Based on this knowledge, we designed a microcantilever-based FMD, depicted in Figure 2, to realize high stiffness at the processing location and high sensitivity at the sensing location. Hence, the processing (nanomilling or force application) location (x) was chosen to be close to the fixed end of the FMD and the sensing location (L), where the deflection is amplified and measured, was selected to be close to the free end of the FMD. This FMD design enables high stiffness and in turn, minimized deflection Z(x) at the processing location and high sensitivity and in turn magnified deflection Z(L) at the sensing location. As such, this FMD design could enable accurate measurement of nanomilling forces without hampering the performance of the nanomilling process.

Figure 2: Design of the force measurement device.

Based on the aforementioned design requirements, the microcantilever-based FMD was designed using a finite element analysis software (ANSYS 14). Considering the space limitations and nanotool dimensions within our custom-made nanomilling system, the processing location (x) was chosen to be 200 µm away from the fixed end of the FMD while the sensing location was prescribed to be the free end of the FMD. The length, width, and thickness of the FMD was chosen to be 6 mm, 100 µm, and 115 µm respectively to allow nanomilling process at the processing location and displacement measurement at the free end of the FMD with required sensitivity for nanomilling force measurement. To further increase the sensitivity at the sensing location, instead of commonly used silicon microcantilevers, a Poly (methyl methacrylate) (PMMA) microcantilever was used since the elastic modulus of polymers is generally much lower than silicon, thereby further improving the sensitivity of the FMD at its free end (Ansari & Cho, 2009). Subsequently, the FMD was accurately created from PMMA with prescribed dimensions using the mechanical micromilling technique, and then sputter-coated with gold to allow the reflections for the lasers of a non-contact displacement sensor.

2.2 Dynamic Characterization of the FMD This section presents the experimental facility and procedures used for dynamic characterization of the FMD. Specifically, a two-step AFM probe-based stepped-sine testing method is introduced to obtain frequency response function (FRF) of the FMD between the input force at the processing location and the output displacement at the sensing location of the FMD within a broad range of frequency. The obtained FRF enables the calibration of the FMD and in turn, accurate measurement of high-bandwidth nanomilling forces.

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2.2.1 Experimental Setup The experimental testbed used for dynamic characterization, and in turn, calibration of the FMD was constructed to be compatible with our custom-made nanomilling system (see Figure 3) (Gozen & Ozdoganlar, 2012). As shown in Figure 3, the FMD was attached to the nanocube (nanopositioning stage) of our nanomilling system and the AFM probe instead of the nanotool was mounted onto the piezoactuator to enable dynamic characterization of the FMD through controlled generation of dynamic input forces within a broad range of frequencies---the maximum frequency is less than 10% of the first natural frequency of the AFM probe. Prior to dynamic characterization, a precise surfacecontact detection between the AFM probe and the FMD was deployed similar to the surface-contact detection between the nanotool and the workpiece previously described in (Gozen & Ozdoganlar, 2012) for our tailor-made nanomilling system. To this end, first, a manual stage was used to enable coarse positioning of the AFM probe. Next, the FMD was gradually (with 4 nm steps) approached to the FMD using the nanocube while measuring the vibrations at the free end of the AFM probe using a laser Doppler vibrometer (LDV) system with pico-meter level resolution. The fine surface-contact between the AFM probe and FMD was detected by the abrupt increase of vibration amplitude at the tip of the AFM probe. During these experiments, the LDV based micro system analyzer (MSA) was used as a non-contact displacement sensor for both contact detection and nanomilling force measurement.

Figure 3: The custom-made nanomilling system and integration of the FMD and AFM probe into this system for dynamic characterization and in turn, calibration of the FMD.

2.2.2 The AFM Probe-Based Dynamic Testing Method After integration of the FMD and the AFM probe into the nanomilling system, prior to the twostep AFM probe-based stepped-sine testing for dynamic characterization of the FMD, the static stiffness ks of the AFM probe was determined by following the well-established thermal noise method described in (Ohler, 2007). Briefly, the AFM probe is assumed to behave as a simple harmonic oscillator. The kinetic energy of this probe under thermal noise is accurately calculated using

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equipartition theorem (Ohler, 2007). The kinetic energy of this probe under thermal noise is also correlated with its static stiffness and its amplitude at its fundamental frequency. Having the kinetic energy of the AFM probe calculated using equipartition theorem and the vibration amplitude of the AFM probe at its fundamental frequency measured, it is possible to determine the only unknown value, the static stiffness ks of the AFM probe (Ohler, 2007).

Figure 4: AFM probe-based stepped-sine testing for dynamic characterization of the FMD.

Subsequently, the two stepped-sine tests (see Figure 4) were performed for dynamic characterization of the FMD. To this end, first, the precise surface-contact detection of the AFM probe with the FMD at the processing location of the FMD was deployed as explained above, and then certain amount of preload was exerted by pushing the FMD against the AFM probe using the nanocube to establish a stable contact. Next, the first step-sine test was conducted to obtain a FRF, G1(jω) between the applied dynamic force F at the processing location of the FMD and the input voltage u to the piezoactuator. To this end, the AFM probe attached to the piezoactuator was excited using a sinusoid voltage u by stepping the sine frequency through the frequency range of interest-from 0 to 10 kHz with a 20 Hz resolution. It is worth nothing that since the AFM probe with a natural frequency of ωn (prescribed natural frequency of the AFM probe is150 kHz) behaves like a simple stiffness element at relatively lower frequencies (< 0.1×ω n,