1 Uniform velocity This motion is used where the follower is required to rise or fall at a constant speed, and is often referred to as straight-line motion. Part of a uniform-velocity cam graph is shown in Fig. 24.2.
Abrupt changes in velocity with high-speed cams result in large accelerations and cause the followers to jerk or chatter. To reduce the shock on the follower, the cam graph can be modified as indicated in Fig. 24.3 by adding radii to remove the sharp corners. However, this action results in an increase in the average rate of rise or fall of the follower.
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Radius to remove abrupt change in direction
Angular displacement of cam
Radius to remove abrupt change in direction
Angular displacement of cam
2 Uniform acceleration and retardation motion is shown in Fig. 24.4. The graphs for both parts of the motion are parabolic. The construction for the parabola involves dividing the cam-displacement angle into a convenient number of parts, and the follower displacement into the same number of parts. Radial lines are drawn from the start position to each of the follower division lines, and the parabola is obtained by drawing a line through successive intersections. The uniform-retardation parabola is constructed in a similar manner, but in the reverse position.
3 Simple harmonic motion is shown in Fig. 24.5 where the graph is a sine curve. The construction involves drawing a semi-circle and dividing it into the same number of parts as the cam-displacement angle. The diameter of the semi-circle is equal to the rise or fall of the follower. The graph passes through successive intersections as indicated.
The application of the various motions to different combinations of cams and followers is shown by the following practical example.
30 60 90 120 150 180 Angular displacement of cam
30 60 90 120 150 180 Angular displacement of cam
Cam specification:
Plate cam, rotating anticlockwise. Point follower. Least radius of cam, 30 mm. Camshaft diameter, 20 mm.
0-90°, follower rises 20 mm with uniform velocity. 90-150°, follower rises 30 mm with simple harmonic motion.
150-210°, dwell period.
210-270°, follower falls 20 mm with uniform acceleration.
270-360°, follower falls 30 mm with uniform retardation.
50 40 30 20 10
Cam graph
Cam graph
50 40 30 20 10
120 180 240 12 mm represents 30° camshaft angle
120 180 240 12 mm represents 30° camshaft angle
1 Draw the graph as shown. Exact dimensions are used for the Y axis, where the follower lift is plotted. The X axis has been drawn to scale, where 12 mm represents 30° of shaft rotation.
2 To plot the cam, draw a 20 mm diameter circle to represent the bore for the camshaft, and another circle 30 mm radius to represent the base circle, or the least radius of the cam, i.e. the nearest the follower approaches to the centre of rotation.
3 Draw radial lines 30° apart from the cam centre, and number them in the reverse direction to the cam rotation.
4 Plot the Y ordinates from the cam graph along each of the radial lines in turn, measuring from the base circle. Where rapid changes in direction occur, or where there is uncertainty regarding the position of the profile, more points can be plotted at 10° or 15° intervals.
5 Draw the best curve through the points to give the required cam profile.
Note. The user will require to know where the cam program commences, and the zero can be conveniently established on the same centre line as the shaft keyway. Alternatively, a timing hole can be drilled on the plate, or a mark may be engraved on the plate surface. In cases where the cam can be fitted back to front, the direction or rotation should also be clearly marked.
Cam specification:
Plate cam, rotating anticlockwise. Flat follower. Least distance from follower to cam centre, 30 mm. Camshaft diameter, 20 mm.
0-120°, follower rises 30 mm with uniform velocity (modified).
120-210°, dwell period
220-360°, follower falls 30 mm with uniform velocity (modified).
1 Draw the cam graph as shown, and modify the curve to remove the sharp corners. Note that in practice the size of the radius frequently used here varies between one-third and the full lift of the follower for the uniform-velocity part of the graph; the actual value depends on the rate of velocity and the speed of rotation. This type of motion is not desirable for high speeds.
2 Draw the base circle as before. 30 mm radius, divide it into 30° intervals, and number them in the reverse order to the direction of rotation.
3 Plot the Y ordinates from the graph, radially from the base circle along each 30° interval line. Draw a tangent at each of the plotted points, as shown, and draw the best curve to touch the tangents. The tangents represent the face of the flat follower in each position.
4 Check the point of contact between the curve and each tangent and its distance from the radial line. Mark the position of the widest point of contact.
In the illustration given, point P appears to be the greatest distance, and hence the follower will require to be at least R in radius to keep in contact with the cam profile at this point. Note also that a flat follower can be used only where the cam profile is always convex.
Although the axis of the follower and the face are at 90° in this example, other angles are in common use.
Cam specification:
Plate cam, rotating clockwise. 20 mm diameter roller follower.
30 mm diameter camshaft. Least radius of cam, 35
0-180°, rise 64 mm with simple harmonic motion.
180-240°, dwell period.
240-360°, fall 64 mm with uniform velocity.
2 Draw a circle (shown as RAD Q) equal to the least radius of the cam plus the radius of the roller, and divide it into 30° divisions. Mark the camshaft angles in the anticlockwise direction.
3 Along each radial line plot the Y ordinates from the graph, and at each point draw a 20 mm circle to represent the roller.
4 Draw the best profile for the cam so that the cam touches the rollers tangentially, as shown.
Cam specification:
Plate cam, rotating clockwise. 20 mm diameter roller follower set 20 mm to the right of the centre line for the camshaft. Least distance from the roller centre to the camshaft centre line, 50 mm. 25 mm diameter camshaft.
0-120°, follower rises 28 mm with uniform acceleration. 120-210°, follower rises 21 mm with uniform retardation.
210-240°, dwell period.
240-330°, follower falls 49 mm with uniform velocity. 330-360°, dwell period.
1 Draw the cam graph as shown.
2 Draw a 20 mm radius circle, and divide it into 30° divisions as shown.
3 Where the 30° lines touch the circumference of the 20 mm circle, draw tangents at these points.
4 Draw a circle of radius Q, as shown, from the centre of the camshaft to the centre of the roller follower. This circle is the base circle.
5 From the base circle, mark lengths equal to the lengths of the Y ordinates from the graph, and at each position draw a 20 mm diameter circle for the roller follower.
6 Draw the best profile for the cam so that the cam touches the rollers tangentially, as in the last example.
Cam specification:
Face cam, rotating clockwise. 12 mm diameter roller follower. Least radius of cam, 26 mm. Camshaft diameter, 30 mm.
0-180°, follower rises 30 mm with simple harmonic motion.
180-240°, dwell period.
240-360°, follower falls 30 mm with simple harmonic motion.
, Cam graph
Rotation
, Cam graph
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60 120 180 240 300 Shaft angle 12 mm represents 30°
Rotation
60 120 180 240 300 Shaft angle 12 mm represents 30°
Fig. 24.10
1 Draw the cam graph, but note that for the first part of the motion the semi-circle is divided into six parts, and that for the second part it is divided into four parts. 2 Draw a base circle 32 mm radius, and divide into 30° intervals. 3 From each of the base-circle points, plot the lengths of the Y ordinates. Draw a circle at each point for the roller follower. 4 Draw a curve on the inside and the outside, tangentially touching the rollers, for the cam track. The drawing shows the completed cam together with a section through the vertical centre line. Note that the follower runs in a track in this example. In the previous cases, a spring or some resistance is required to keep the follower in contact with the cam profile at all times. Cam specification: Cylindrical cam, rotating anticlockwise, operating a roller follower 14 mm diameter. Cam cylinder, 60 mm diameter. Depth of groove, 7 mm. 0-180°, follower moves 70 mm to the right with simple harmonic motion. 180-360°, follower moves 70 mm to the left with simple harmonic motion. 1 Set out the cylinder blank and the end elevation as shown. Divide the end elevation into 30° divisions. Underneath the front elevation, draw a development of the cylindrical cam surface, and on this surface draw the cam graph. Using the cam graph as the centre line for each position of the roller, draw 14 mm diameter circles as shown. Draw the cam track with the sides tangential to the rollers. Plot the track on the surface of the cylinder by projecting the sides of the track in the plan view up to the front elevation. Note that the projection lines for this operation do not come from the circles in the plan, except at each end of the track. The dotted line in the end elevation indicates the depth of the track. Plot the depth of the track in the front elevation from the end elevation, as shown. Join the plotted points to complete the front elevation. Note that, although the roller shown is parallel, tapered rollers are often used, since points on the outside of the cylinder travel at a greater linear speed than points at the bottom of the groove, and a parallel roller follower tends to skid. |
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