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13.8.2 Conclusions and Recommendations on the Use of the Methods Given in this All of the methods presented in this chapter use a single degree-of-freedom dynamic model. Such a model is adequate for almost all well-designed systems because their highest signi cant frequency of excitation at maximum operating speed is usually well below the natural frequency of the model. This is, in turn, well below the second and higher natural frequencies of the real system. Therefore, the dynamic ampli cation by the upper modes is minimal. The models are also all linear, which is accurate for almost all real systems, although the method of Sec. 13.5 does allow optimization using some nonlinear criteria. The sections below present a review of the features of each of the methods discussed in Secs. 13.4 through 13.7 and give recommendations on how best to use them. Guidelines for choosing the best method are given and their limitations are detailed. Cam Synthesis Using Trigonometric Series (Sec. 13.4). This section presents a good general procedure for designing cam pro les to minimize residual vibration. A major advantage of this method is that the optimization can be done over any contiguous range of operating speeds the user desires. This feature is important because many real systems operate over a range of speeds. Even constant speed systems still must vary in speed for startup and shutdown. Also, there is always uncertainty in the design parameters, particularly stiffness and mass. This uncertainty is equivalent to an uncertainty in speed. This section also presents a method to optimize a design for one speed (tuned cam). This is never recommended, however, even for constant-speed systems, because of all the factors noted above. For some cams designed for just one speed, even small variations in speed or parameters can cause large variations in vibration. Therefore, optimization should always be done over a wide enough range of speeds to allow for both the operating speed range and parameter uncertainties. It is not necessary to optimize over the range of speeds well below the maximum speed, since the energy input and primary excitation frequencies will be much lower there. However, including this low-end speed range in the optimization will have little effect on the optimal solution anyway, precisely because of its low effect on vibration. Cam Synthesis Using Optimal Control Theory (Sec. 13.5). There are two signi cant features of this procedure for optimizing cam design. The rst is that a theoretically exact optimal solution is obtained, subject to only a few constraints; it is not restricted to a user-de ned set of basic functions, such as the trigonometric series used in Sec. 13.4. The method constrains the solution by requiring the rst four derivatives of the follower lift to be zero at each end of the lift event and does not allow discontinuities in the acceleration at the follower or the cam. These restrictions unnecessarily constrain the solution, not allowing the acceleration discontinuities at the ends of the lift event that were found to be optimal in Sec. 13.4. The second feature of this procedure is the ability to perform this optimization for nonlinear optimization criteria. This second feature is greatly limited in its usefulness, however, because the nonlinear optimization cannot include cam preload. Preload is important in optimization for stress, for example, due to the highly nonlinear relationship between stress and load.
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From a command prompt, access the /Tools directory on the Password Manager CD and type the following:
Using high-powered motors requires high-powered motor controllers. The motor controllers are commonly called electronic speed controllers (ESCs). In mini sumos, the peak motor current requirements are usually around 1 A. For the international robotic sumo class, peak motor current demands can exceed 100 A. This really depends on the type of motors selected for the sumo bot. Usually, higher-voltage motors require less current. The most cost-effective ESCs are the ones made for the R/C racing car industry. These controllers are designed to handle large amounts of current for short periods of time. They are also easy to integrate into a sumo bot. When looking at electronic speed controllers, make sure that yours has a reversible speed controller. More than half of the electronic speed controllers made today are for forward use only. A sumo bot will be spending about half its time going backward as compared to going forward. The other factor to consider is the current handling capacity when operating in reverse. Of the ESCs that are reversible,
R( f, P) =
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With MAG MSG by over 3 dB even with our approximation methods this transistor will be very stable.
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