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Figure 15-12
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Fig. 1.33
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effects of the magnitudes of components a1, b1, a2, b2, a3, b3, . . . at each point. Also, large forced vibrations may occur when the period (sec) of one of the terms of the series coincides with (or is a multiple of) the period (sec) of the natural frequency of the system. This is called resonance, which occurs at the critical speed of the respective harmonic number, i.e., when n equals an integer. Furthermore, the magnitude of the response at resonance depends primarily on the magnitude of the components a1, b1, a2, b2, a3, b3, . . . for that harmonic. Vibration is caused by a force, and thus the harmonics of the acceleration curve rather than the displacement curve are responsible for it. For any contour the acceleration and displacement harmonics are proportional. Harmonic analysis of the acceleration forces produced by a given cam design will give an indication of the performance to be expected. As before, the natural frequency wn should be as high as possible so that resonance at a given speed range will occur with a higher harmonic number of consequently smaller amplitude harmonics. Fortunately only a few of the low numbers cause excessive vibratory amplitudes. Some of the higher numbers appear as noise and may be objectionable. Last, the amplitude of the forced oscillation is small if the frequency of the external force is different from the natural frequency and, of course, depends on the proximity to the natural frequency of the system. Also, it should be remembered that a smooth, bumpless acceleration curve generally gives weaker harmonics and thus a smaller response. By smooth is meant few points of in ection, i.e., the DRD acceleration curve has one point of in ection. A re nement would y y be to have all derivatives of the acceleration curve , . . . continuous functions. However, in practice it is impossible to fabricate the cam to the accuracy demands of these higher derivatives and their practical value has never been veri ed. If F(t) (cam curve) is given numerically or graphically because no analytical expression is available, some approximate numerical method for calculating harmonics can be employed to analyze trigonometric series curves. Let us elaborate on the Fourier analysis of cam-follower systems. The solution for Eq. (12.7) may be put into the form:
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Using appropriate load factors, strength load combinations for typical dead and live loads may only be expressed as: ASD LFD LRFD 1.0 DL 1.3 DL 1.0 (LL 2.17 (LL I) I) Resistance safety factor Rn 1.50 DW 1.75 (LL I) Rn
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(14.24)
to obtain an actual array that contains the contents of the list. You can do this by calling ToArray( ). There are several reasons why you might want to convert a collection into an array. Here are two: You may want to obtain faster processing times for certain operations, or you might need to pass an array to a method that is not overloaded to accept a collection. Whatever the reason, converting an ArrayList to an array is a trivial matter, as the following program shows:
EXAMPLE
%MPF100 (CAMCO, B-12345) N5M95 N10G04X.5 /N15(PROGRAM-STOP)M00 N20G60G90S2000 N25G00Z250 N30U0.0V69.8500 N35C205.0000 N40Z235.725 N45M03 N50G01G94F150 /N55M00 N60M26 N65G64G90 N70G04X15.0 N71V69.8500Z235.723C205.2500 N72V69.8500Z235.705C205.5000 N73V69.8500Z235.658C205.7500 N74V69.8500Z235.572C206.0000 N75V69.8500Z235.440C206.2500 **** N860V69.8500Z234.423C222.7500 N861V69.8500Z234.749C223.0000 N862V69.8500Z235.028C223.2500 N863V69.8500Z235.258C223.5000 N864V69.8500Z235.440C223.7500 N865V69.8500Z235.572C224.0000 N866V69.8500Z235.658C224.2500 N867V69.8500Z235.705C224.5000 N868V69.8500Z235.723C224.7500 N869V69.8500Z235.725C225.0000 N874G90G00 N879Z250 N884M05M27 N889G60 N894C360.000 N899@123R0R1K9995 N904@621R0 N909G91B=R2 N914@100K-5 N9995B0 N9999M30
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LAB 1.1
such that Eq. (13.30) as well as the following boundary conditions are satis ed: (13.32) . The boundary conditions Y (3) (t) for t = 0 and 1 ensure that the cam velocities Yc (t) at t = 0 and 1 are continuous. Otherwise, an impact exists at the cam. The boundary conditions Y(4) (t) at t = 0 and 1 ensure continuity of the cam acceleration at time t = 0 and 1. In Part 1 of the reference papers, Chew et al. (1983), the authors also considered four ... . alternate forms of Eq. (13.31). Ffe was replaced with Ffe, Ffc, Ffe and Ff. Equation (13.31) was shown to be the best option. Use of Ff gave an unacceptable .reversal in the follower motion at the start of the rise. Use of Ffe gave a higher value of Ffe at the end of the rise, meaning increased sensitivity to running speed. Use of Ffe did allow continuity of the accel. eration at t = 0 and 1. Additionally, Ffe was shown to be nearly as good as Ffe. Y ( 0) = 0, Y (1) = 1, Y (1) = Y (2 ) = Y (3) = Y (4 ) = 0 for t = 0, 1.
will automatically display the possible LC matches (in L network form) along with the parallel equivalents, the VSWR, and the return loss. Impedance Matching Network Designer by John Wetherell is a free online program that assists in the rapid design of 16 various matching networks; just enter the source s resistance and reactance, with the frequency of interest and the desired circuit Q, and the program will display the values of the appropriate matching topologies. It is available online at http://wwwinst.EECS.Berkeley.EDU/ wetherel/rftoolbox/matcher2.html. Motorola s Impedance Matching Program (MIMP) for power amplifiers permits the load and source impedances to be specified, then lets the user place lumped or distributed elements between this source and load, enabling the viewing of the quality of the resultant match on the program s Smith chart and return loss graph. It is obtainable free on Motorola s Web site. Multfreq, by Cezar A. Carioca et al., is available free (through Applied Microwave and Wireless Magazine Online), and will automatically design a lumped or distributed diode frequency multiplier of the varactor or Schottky type. Since this program will display the distributed filter structures necessary for the multiplier circuits, along with the filter s dimensions and frequency response, a distributed bandpass and low-pass filter can also be designed with this one-of-a-kind program. MixSpur, by The Engineer s Club, is a low-cost program that will graphically, and in tabular format, display the spurious output frequencies and their amplitude as emitted from a mixer and LO stage. A must for receiver and transmitter design to confirm that both in-band and out-of-band mixer-generated spurious signals are below specifications or that more filtering, a new LO frequency, or a different mixer may be required. It is available for sale at http://www.engineers.com/mxrspur.htm. PUFF, a microwave program by Caltech s David Rutledge, Scott W. Wedge, Richard Compton, and Andreas Gerstlauer, is a linear (S-parameter) simulator that permits a designer to simulate lumped and distributed circuits, and then plot gain, return loss, and phase in a fully graphical format. Indeed, if an engineer does not possess a more expensive, high-end wireless software package, such as AWR s Microwave Office, Eagleware s Genesys, or HP s EEsof, for example, then PUFF is indispensable. The full version of PUFF is included with this book on CD ROM. On a system design level, Kirt Blattenberger s low-cost RF Workbench should be purchased, as it will assist the designer to define the specifications of a transmitter or receiver s amplifiers, filters, and mixer stages, and then view the resultant spectrum in the frequency domain. RF Workbench will not only permit you to see if the system s sum frequency or LO feedthrough will be troublesome, but also, if any stage is going into compression, what the system s gain, P1dB, IP3, POUT, and NF values are. This program checks whether any mixer spurs are in or out of band (and what their amplitudes may be), calculates the complete transmitter-to-receiver path, creates a frequency and cascaded amplitude budget plan, and does other functions too numerous to mention. Available on the Web.
Extruding Objects
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