Machinery's Handbook, 31st Edition
2370
CAMS AND CAM DESIGN Table 1. Development of Modified Constant Velocity Cam with Parabolic Matching
Follower Displacement y
Rise Angle
φ Degrees
Computation
Explanation
0 0
0
40
. 0500
h
β
= = =
°
=
5
0.016 0.063 0.141 0.250 0.375 0.500 0.625 0.750 0.875 1.000 1.125 1.250 1.375 1.500 1.617 1.719 1.805 1.875 1.930 1.969 1.992
0.000625 × 5 2
. 40 2 0500 0000625 2 . ^ ^ h^ h
h
y
2
φ
10 0.00625 × 10 2 15 0.000625 × 15 2 20 0.000625 × 20 2
φ 1 = 20 °
2
φ
25 30 35 40 45 50 55 60 65 70
φ 2 = 50 °
1.250 in. divided into 10 uniform divisions
75 2.000 − (0.0003125 × 35 2 ) 80 2.000 − (0.0003125 × 30 2 ) 85 2.000 − (0.0003125 × 25 2 ) 90 2.000 − (0.0003125 × 20 2 ) 95 2.000 − (0.0003125 × 15 2 ) 100 2.000 − (0.0003125 × 10 2 ) 105 2.000 − (0.0003125 × 5 2 ) 110 2.000 − (0.0003125 × 0 2 )
80
. 1000
h
β
=
°
=
. 80 2 1000 110 2 0 0003125 110 2 . ° ° ^ ^ h ^ ^ ^ h h
2
2 = − = −
y
φ 3 = 40 °
2 h
°
−
φ
h
−
φ
See footnote a
2.000 a Since the deceleration portion of a parabolic cam is the same shape as the acceleration portion, but inverted, Formula (5) may be used to calculate the y values by substituting 2 y 3 for h and for β and the result subtracted from the total rise ( y 1 + y 2 + y 3 ) to obtain the follower displacement. The cam pitch curve is also the actual profile or working surface when a knife-edged fol lower is used. To get the profile or working surface for a cam with a roller follower, a series of arcs with centers on the pitch curve and radii equal to the radius of the roller are drawn and the inner envelope drawn tangent to these arcs is the cam working surface or profile shown as a solid line in Fig. 10(b). Cam Grinding : The cams used on gas and gasoline motors, for operating the inlet and exhaust valves, are finished to the correct form by grinding. This grinding may be done in a regular cylindrical grinding machine by using a suitable cam grinding attachment. The general method of grinding cams is by so mounting the cam or camshaft that, while rotating, it will be moved toward and from the grinding wheel by a master cam, the movement causing the cam to be ground to the required form or contour. The master cam is in engagement with a roller which transmits motion to the work-holding fixture. It is evident that cam grinding first involves the generation of master cams, since these must be made to suit each different form of cam that is ground. In modern CNC cam grinding machines, downloaded master cam data replaces the “hard” master cam required on older manual machines.
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