Influence of Gear Rim Deflections on Planetary Gear Set Behavior

In this study, results of an experimental and theoretical study on the influence of rim thickness of the ring gear on rim deflections and stresses, and planet load sharing of a planetary gear set are presented. Experimental study consists of measurement of ring gear deflections and strains for gear sets having various numbers of planets, different ring gear rim thicknesses as well as various carrier pin hole position errors. Root and hoop strain gauges and displacement probes are placed at various locations so that the variations due to external splines of the stationary ring gear can also be quantified. A family of quasi-static deformable-body models of the test gear planetary gear sets is developed to simulate the experiments. The predictions and the measurements are compared to assess the accuracy of the models within wide ranges of parameters. Influence of rim thickness on ring gear stresses and deflections and planet load sharing are quantified together with the interactions between the rim flexibility and the spline conditions. The results from this study confirm that the ring gear deflections and the ring gear support conditions must be included in the design process as one of the major factors.

Multi-Layer Means of Guiding a Large Displacement Microelectromechanical System

Large-displacment MEMS are susceptible to motion in off-axis directions, or motion deviating from the desired path of the device. The multi-layer means of guiding large displacement devices prevents the shuttle from moving away from the substrate, and effectively constrains the transverse motion; the guiding device does not inhibit the motion necessary for proper function of the device. The novelty of the device lies in the placement of the guide; positioning the guide inside of the the shuttle constrains the device without increasing the footprint size.

Material Property Characterization of Costal Cartilage Using AFM Indentation

Costal cartilage is one of the load bearing tissues of the rib cage. Literature on the material characterization of the costal cartilage is limited. Atomic force microscopy has been extremely successful in characterizing the elastic properties of articular cartilage, but no studies have been published on costal cartilage. In this study AFM indentations on human costal cartilage were performed and compared with macro scale indentation data. Spherical beaded tips of three sizes were used for the AFM indentations. The Hertz contact model for spherical indenter was used to analyze the data and obtain the Young’s modulus. The costal cartilage was found to be almost linearly elastic till 600 nm of indentation depth. It was also found that the modulus values decreased with the distance from the junction. The modulus values from macro indentations were found to be 2-fold larger than the AFM indentation modulus.

The Wolfrom Gear Train: A Case of Highest-Complexity Related Modifications of the Tooth Meshing

The Wolfrom gear is suitable for high speed ratios with an efficiency which is not optimal, but still acceptable. The version with single-rim satellites has significant design and technological advantages. However, the determination of the most appropriate modification coefficients poses a technical problem as the modifications are now related instead of being chosen independently. The geometrical calculations of the single-rim satellites version are performed in the paper. Speed ratio, number of teeth of the satellites, pressure angles and modification coefficients are determined. Advisable values for these parameters are given. As an example a specific design problem for the replacement of a three-stage planetary reducer (consisting of 15 gears) with a Wolfrom gear train (6 gears) the following calculations were performed.

Approximate Closed-Form Solutions for the Shift Mechanics of Rubber Belt Variators

The mechanical behavior of V-belt variators during the speed ratio shift is different from the steady operation as a gross radial motion of the belt is superimposed to the circumferential motion. The theoretical analysis involves equilibrium equations similar to the steady case, but requires a re-formulation of the mass conservation condition making use of the Reynolds transport theorem. The mathematical model of the belt-pulley coupling implies the repeated numerical solution of a strongly non-linear differential system. Nevertheless, an attentive observation of the numerical diagrams suggests simple and useful closed-form approximations for the four possible working modes of any pulley, opening/closing, driver/driven, whose validity ranges over most practical cases. The present analysis focuses on the development of such simplified solutions, succeeding in an excellent matching with the numerical plots, and on the comparison of the theory with some experimental tests on a motorcycle variator, revealing a very good agreement.

The Static and Dynamic Behavior of MEMS Arches Under Electrostatic Actuation

In this paper, we investigate theoretically and experimentally the static and dynamic behaviors of electrostatically actuated clamped-clamped micromachined arches when excited by a DC load superimposed to an AC harmonic load. A Galerkin based reduced-order model is used to discretize the distributed-parameter model of the considered shallow arch. The natural frequencies of the arch are calculated for various values of DC voltages and initial rises of the arch. The forced vibration response of the arch to a combined DC and AC harmonic load is determined when excited near its fundamental natural frequency. For small DC and AC loads, a perturbation technique (the method of multiple scales) is also used. For large DC and AC, the reduced-order model equations are integrated numerically with time to get the arch dynamic response. The results show various nonlinear scenarios of transitions to snap-through and dynamic pull-in. The effect of rise is shown to have significant effect on the dynamical behavior of the MEMS arch. Experimental work is conducted to test polysilicon curved microbeam when excited by DC and AC loads. Experimental results on primary resonance and dynamic pull-in are shown and compared with the theoretical results.

Highly Integrated PiezoMEMS Enabled Millimeter-Scale Robotics

This report provides an overview of ongoing research at the U.S. Army Research Laboratory regarding the development of piezoelectric MEMS-enabled millimeter-scale robotics. Research topics include the development of enabling technologies for terrestrial locomotion, insect-inspired micro-flight, gecko-inspired reversible adhesives, and piezoelectric energy harvesting. The development of complementary lead zirconate titanate thin film MEMS devices, applicable to highly integrated millimeter-scale robotics, is also reviewed.

Stress Analysis of Spherical Gear Sets

The spherical gear is a new type of gear proposed by Mitome et al. [1]. Different from that of the conventional spur or helical gear sets, the spherical gear set can allow variable shaft angles and large axial misalignments without gear interference during the gear drive meshing [1, 2]. Geometrically, the spherical gear has two types of gear tooth profiles, the concave tooth and convex tooth. In practical transmission applications, the contact situation of a spherical gear set is very complex. To obtain a more realistic simulation result, the loaded tooth contact analysis (LTCA) has been performed by employing the finite element method (FEM). According to the derived mathematical model of spherical gear tooth surfaces, an automatic meshes generation program for three-dimensional spherical gears has been developed. Beside, tooth contact analysis (TCA) of spherical gears has been performed to simulate the contact points of the spherical gear set. Furthermore, the contact stress contours of spherical gear tooth surfaces and bending stress of tooth roots have been investigated by giving the design parameters, material properties, loadings and boundary conditions of spherical gears.

Measurements of Piezoelectric Constant D33 of Lead Zirconate Titanate (PZT) Through Use of a Mini Impact Hammer

Lead Zirconate Titanate Oxide (PbZrxTi1−xO3 or PZT) is a piezoelectric material widely used as sensors and actuators. For microactuators, PZT often appears in the form of thin films to maintain proper aspect ratios. This paper is to present a simple and low-cost method to measure piezoelectric constant d33 of PZT thin films, which is a major challenge encountered in the actuator development. We use an impact hammer with a sharp tip to generate an impulsive force that acts on the PZT film. The impulsive force and the responding voltage are then measured to calculate the piezoelectric constant d33. The impulsive force has large enough amplitude so that a good signal-to-noise ratio can be maintained. Furthermore, the impulsive force has extremely short duration, so the discharge effect (i.e., the time constant effect) of the PZT circuit can be ignored. Preliminary testing on bulk PZT through this new method leads to two conclusions. Firstly, boundary conditions of the specimen are critical. In particular, the specimen must be securely fastened. Since the impulsive load only acts on a tiny area, loose boundary conditions can introduce spurious results from other piezoelectric constant d31. Secondly, size of the specimen is critical. Specimen of smaller size leads to more accurate measurements of the piezoelectric constant d33.

Design of Semiactive Vehicle Suspension Controls in Frequency Domain

Through the simulation study of a semiactive quarter car suspension, this paper is to expatiate on the control algorithm documented in the United States Patent 6,873,890 [1]. That patent presents a new method to design semiactive suspension controls in the frequency domain. As is well known, suspension related dynamics has two dominant modes in the working frequency range up to 25Hz. As such, the suspension dynamic system has three distinguishable frequency sections. In order to achieve better performance, different controls have to be applied to each frequency section, respectively. The significant core part of the patented algorithm is to provide an approach to identify the excited frequencies in real time that are transmitted through the vehicle suspension. Then different controls of such as skyhook, groundhook and other damping strategies are combined accordingly to accomplish the best performance overall. Thus through the suspension control the vehicle dynamics (such as ride and handling) is expected to be improved in the broad frequency range in comparison to passive suspensions with a trade-off design.