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1、Problem 3-1,Consider the gear reducer shown in Fig.3.1. Let the diameter of the gear on input shaft be equal to d1=2.0 in and width w1=0.5 in. Assume that the gear is made of material steel and that it is a solid frame without any holes. The output gear has the same width and material, and the gear
2、reduction from input to output is N=5, (d2=10.0 in). The length and diameters of the shafts that extend to the sides of the gears are ds1=1.0 in, ds2=1.0 in. and ls1=1.0 in, ls2=1.0 in. Let us consider that there is a net load torque of TL2=50lb/in at the output shaft.(a) Determine the net rotary in
3、ertia reflected on the input shaft due to two gears and two shafts.(b) Determine the necessary torque at the input shaft to balance the load torque.(c) If the input shaft is actuated by a motor that is controlled with 1/10 degree accuracy, what is the angular positioning accuracy that can be provide
4、d at the output shaft?,Regardless of the efficiency:,Consider a translational (linear) position stage driven by a servo motor (Fig.3.3). The travel range of the table is 50cm. The required position accuracy of the stage is 0.1m. Assume that a motor-based rotary incremental encoder is used for positi
5、on sensing. What should be the resolution of the encoder, if the ball-screw pitch is 0.5 rev/mm? If the decoder circuit for the encoder can handle encoder signal frequency up to 1 MHz, what is the implication of this on the motion limits?,Problem 6-2,FIGURE 3.3: Rotary-to-translational motion conver
6、sion mechanism: lead-screw or ball-screw with linear guide bearings,Consider a rotary motion axis and its speed control (i.e. speed control of a spindle of a CNC machine tool or speed control of a precision conveyor). Assume that both high-speed ( wmax = 3600 rpm) and low-speed ( wmin = 1 rpm) speed
7、 controls are required with 0.01 rpm regulation accuracy.(a) Determine specifications for a tachometer to meet the speed control requirements.(b) Select an optical incremental encoder and derive speed information from the position pulses digitally. What is the speed estimation accuracy at minimum sp
8、eed if the sampling period is 1.0 msec? Show how the speed estimation can be improved with a time period measurement technique. What is the maximum pulse frequency of the selected encoder at the maximum speed?,Problem 6-3,(a) The speed-to-voltage gain, Maximum output voltage, Maximum speed， Maximum
9、expected ripple voltage,(c) We select a 10000 lines/rev incremental encoder. So the derived speed is:,N is the pulse count in 1 msec.The speed estimation accuracy:,The time interval for a pulse at 1 rpm speed is:,If we use a time period measurement with 1- sec resolution, the measured time will be 0
10、.006001s or 0.005999 sec, so the speed will be:,Speed estimation can be improved greatly. The maximum pulse frequency at maximum speed is:,Assume a zerolapped four-edge slide valve which has a 20 spool, the radial clearance is 10, the valve open width is full circle. Please calculate the three valve
11、 gains at zero position.（viscous =4010-6m2/s900kg/m3）,Consider a DC motor ( or equivalent ) motion control system. Assume that the DC bus voltage available is Vs = 90 VDC. The back EMF constant of the motor is Ke = 20 V/krpm. The nominal terminal resistance of the motor stator windings is R = 10 Ohm
12、.Determine the maximum no-load speed and the maximum torque capacity at stall (zero speed) of the motor in steady state.,Problem 8-3,Assume a electro-hydraulic position control system for pure inertia loads, in which the hydraulic natural frequency ish=320 1/s, damping ratio is h=0.25, Valves flow g
13、ain is kq=40(cm3/s)/mA, for hydraulic cylinder Ap=20cm2, position feedback gain is kf=0.4V/cm, please determine the valve of Ka if the gain margin is at least 6dB.,Problem 11-1,For 6dB gain margin:,Analyze speed control system as shown in figure. Please draw block diagram of the system and write dow
14、n its open-loop transfer function. If this system is compensated by an integral controller, please determine the integral gain if the gain margin is at least 6dB.,Problem 11-2,Block diagram：Open-loop transfer function：,+,In which:After compensated by an integral controller:For gain margin of 6dB：Hen
15、ce：,Analyze position control system as shown in figure. Please draw block diagram of the system and write down its open-loop transfer function. Draw open-loop Bode plots. Calculate the steady state error for unity step response.,+,Block diagram：Open-loop transfer function：,In which：The steady state
16、error for unity step response:,Bode plot：,Example: select a proportional valve, data of the equipment are as follows: Adjust system pressure:Load pressure at tool feed speed :Load pressure when fast forward:Flow needed at the tool feed speed range Flow needed at the fast forward speed range,Accordin
17、g to flow equations:Then the valve Nominal Flow is:Thus:At tool feed speed:When fast forward:Thus we select the valve with the standard flow of 64L/min.,(4) Example: The speed of 0.02m/s is required in some mechanism system, and the drive force is 200N. DC motor is selected as the driver. Please select the motor.,From Law of Conservation of Energy: then: so: if select: then： Select power： Select DC coreless magnet servo motor, the rated revolution speed is 1050rpm，torque is 60mNm，rated voltage is 2V.Check the velocity:,
