homework6asol.fall11

homework6asol.fall11 - ME 352 - Machine Design I Fall...

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- 1 - ME 352 - Machine Design I Name of Student ____________________________________ Fall Semester 2011 Lab Section Number ________________________________ Homework No. 6. Cam Design. Chapter 6. Part I (20 points). Due at the end of lab on Wednesday, October 12th, and Thursday, October 13th. Solve Problem 6.28 on pages 328 and 329. Templates to draw the lift curve and the cam profile are provided with the homework. Part II (20 points). Due at the beginning of lecture on Friday, October 14th. For this cam-follower system, at the cam angle , 225 o θ = determine numerical values for: (i) The first, second, and third-order kinematic coefficients of the displacement diagram. (ii) The radius of the curvature of the cam surface. (iii) The unit tangent and normal vectors to the cam at the point of contact with the follower. (iv) The coordinates of the point of contact between the cam and the follower. Express your answers in the moving Cartesian coordinate reference frame attached to the cam. (v) The pressure angle of the cam. Is your answer acceptable for this cam-follower system?
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- 4 - Solution to Homework 6. Part I. 20 Points. (i) 8 Points. The lift curve is plotted in Figure 1. Figure 1. The Lift Curve or the Displacement Diagram.
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- 5 - (ii) 8 Points. The cam profile is plotted in Figure 2. Figure 2. The Cam Profile.
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- 6 - (iii) 4 Points. Comments on the curves and answers to the design issues: (i) The recommended value of the pressure angle for a cam-follower system, see pages 230 to 232 in the text book, is less that 30 . ° The pressure angle defines the steepness of the cam profile and is a measure of the efficiency of the cam. A plot of the pressure angle against the cam position is shown in Figure 3. 0 50 100 150 200 250 300 350 0 5 10 15 20 25 30 35 40 45 50 θ Cam - Cam Angle - [deg] φ - Pressure Angle - [deg] Figure 3. A plot of the pressure angle against the cam position. In this design, the pressure angle is more than the accepted value at the cam angles 16 64 , −° θ 131 180 , °− ° 216 256 , ° and 299 341 ° Therefore, this cam profile is not a good cam design. The high values of the pressure angle may be due to the selection of the segments for the displacement diagram, and/or the dimensions of the cam and the diameter of the follower. (ii) Position discontinuities never occur. Discontinuities in the derivatives will only occur at transitions between dwell segments and lifting/returning segments of motion. Discontinuities in the derivatives are undesirable especially for a high speed cam follower system. There is an acceleration discontinuity at the beginning and end of the simple harmonic motions, both rise and return. There is a jerk discontinuity at the beginning and end of the cycloidal motions, both rise and return. (iii) The radius of curvature of a cam profile should always be negative for a good cam design. A positive radius of curvature means that the cam has a concave surface and there is the possibility that the follower may lose contact with the cam.
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This note was uploaded on 02/13/2012 for the course ME 352 taught by Professor Staff during the Fall '08 term at Purdue.

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homework6asol.fall11 - ME 352 - Machine Design I Fall...

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