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Vortex drop shafts are used in urban drainage systems to connect two sewers located at considerably different elevations. After their introduction in 1947, these were studied with particular reference to subcritical approach flow. Vortex shafts for supercritical approach flow can also be used, but the intake structure may have relatively high cost due to the complex geometry. The present study includes experimental results of a specific investigation on the changes to be made in the supercritical approach channel if a subcritical vortex intake is used. The experimental investigation analyzes the effect of a hydraulic jump on the performance of vortex intake structure to define appropriate technical solutions, essentially consisting in a negative step to be located along the supercritical approach channel. Design criteria are finally presented for the evaluation of the step height and its distance from the vortex intake structure. DOI: 10.1061/(ASCE)HY.1943-7900.0000249 CE Database subject headings: Energy dissipation; Hydraulic jump; Sewers; Shafts; Drop structure; Critical flow; Intake structures. Author keywords: Energy dissipation; Hydraulic jump; Sewer hydraulics; Vortex shaft; Drop structure.

With reference to the machining of an involute spur or helical gear by the hobbing process, the paper suggests a new criterion for Selecting the position of the hob axis relative to the gear axis. By adhering to the proposed criterion, the hob axis is set at the minimum distance from the gear axis, thus maximizing the depth of the tooth spaces of the gear The new criterion is operatively implemented by solving a univariate equation, which stems from a new, synthetic analysis of the meshing of crossed-axis involute gears. A numerical example shows application of the suggested procedure to a case study and compares the optimal hob setting to the customary one. [DOI: 10.1115/1.2839012] Keywords: gear, hob, gear machining, gear cutting, skew-axis gearing

An algorithm for synthesis of spiral bevel gear transmissions with a small shaft angle is presented. The algorithm of synthesis provides machine-tool settings with account of design limits for majority of gear generating machines. The proposed algorithm makes it possible to decrease the dimensions of machines that are used for gear and pinion tooth generation. The computer program of synthesis is developed that is based on described algorithm. Recommendations on selection of proper synthesis parameters are presented. An example of synthesis and analysis of a transmission is considered. [DOI: 10.1115/1.2748448] Keywords: spiral bevel gears, design, machine-tool settings, small shaft angle

The objective of this study is to identify the best indexed position of two rotating groups within a tandem axial-piston pump for attenuating the torque ripple amplitude that is exerted on the shaft. By attenuating the torque ripple characteristics of the pump, other vibration aspects of the machine are also expected to be reduced. In particular, the objectives of this paper are aimed at reducing the noise that is generated by the pump. This paper begins by considering the theoretical torque ripple that is created by the discrete pumping elements of a single rotating group within an axial piston machine. From this analysis, an equation is produced that describes a single pulse for the torque ripple as a function of the average torque and the total number of pistons that are used within the rotating group. By superposing another rotating group on top of the first, and by indexing the angular position of one rotating group relative to the other, a second equation is produced for describing the theoretical torque ripple of a tandem pump design. This equation is also a function of the average shaft torque and the total number of pistons that are used within a single rotating group; however, an additional parameter known as the index angle also appears in this result. This index angle is shown to amplify or attenuate the amplitude of the torque ripple depending upon its value. From these results, it is shown that a proper selection of the index angle can reduce the torque ripple amplitude by as much as 75%. [DOI: 10.1115/1.2719785]

The objective of this paper is to formulate the equations of motion and to analyze the vibrations of an atomic force microscope (AFM), which contains a piezoelectric rod coupling with a cantilever beam, and the tip mass interacting with samples. The governing equations of the AFM system are formulated completely by Hamilton's principle. The piezoelectric rod is treated as an actuator to excite the cantilever beam via an external voltage. The repulsive forces between the tip and samples are modeled by the Hertzian, the Derjaguin-Muller-Toporov, and Johnson-Kendall-Roberts models in the contact region. Finally, numerical results are provided to illustrate the coupling effects between the piezoelectric actuator and the cantilever beam and the interaction effects between the tip and samples on the dynamic responses. [DOI: 10.1115/1.2101851]

Structures composed of a rotary disk and a shaft, which are fastened with bolts and nuts having tapered bearing surfaces, are loaded with a rotating-bending force. Upon investigation, two rotating mechanisms of the nut were derived. In one mechanism a high-pressure contact area is formed at the nearest loading point on threads and bearing surfaces. This leads to a difference in the curvature radii between the bearing surface of the disk and that of the nut. During the revolution of the disk, two friction torques occur in opposite directions on the bearing surface and the threads, respectively. The relative rotating direction of the nut is dominated by the greater torque. The other mechanism is due to the eccentricities caused by dimensional errors of the bolt, nut, and disk. By combining the two mechanisms, the rotations of the nuts either cause a loosening or tightening after many revolutions of the disk.

In this research, the diameter of the shaft within an axial-piston swash-plate type hydrostatic pump is considered from a stress point of view. To analyze the loading of the shaft, the components within the pump are studied using a force and torque diagram and it is shown that the loads are applied differently for three main sections of the shaft. From the force and torque diagram, the actual shaft loads are determined based upon the geometry of the pump and the working pressure of the hydraulic system. Using well-accepted machine design practices, governing equations for the shaft diameter are produced for the various regions of loading along the shaft. These equations consider both bending and torsional stresses on the outer surface of the shaft. Results for the required shaft diameter are then computed for a typical pump design and compared to the geometry of an actual shaft. It is noted that stress concentrations can significantly alter these results and that the required shaft diameter can be reduced by applying the proper heat treatments and increasing the shaft strength. Finally, the designer is cautioned regarding the deflection difficulties that can arise when the shaft diameter is reduced too much. [S1050-0472(00)01704-9]