Course Number: MEMB 321
Day and Date experiment performed : 2000
Due Date 2000
Lecturer : ****
Statement of
Purpose/ Objective:
The objective of the experiment is to: -
· Investigate tappet motion for several different cam profiles and to see the effect of different followers.
Data, Observation
and Results:
|
q, Apparatus (degrees) |
q, Theory (degrees) |
X, Theoretical mm |
X measured for Follower |
|||||
|
Roller |
%error |
Flat |
%error |
Domed |
%error |
|||
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0.3 |
15 |
|
10 |
10 |
0 |
0.5 |
25 |
1 |
50 |
0.3 |
15 |
|
20 |
20 |
0 |
0 |
0 |
0 |
0 |
0.3 |
15 |
|
30 |
30 |
3.425 |
1 |
70.8 |
0.5 |
85.4 |
2.7 |
21.2 |
|
40 |
40 |
8.115573 |
5 |
38.4 |
4.5 |
44.6 |
6.8 |
16.2 |
|
50 |
50 |
12.16456 |
9.5 |
21.9 |
14 |
15.1 |
11.5 |
5.5 |
|
60 |
60 |
15.448935 |
14 |
9.4 |
20 |
29.5 |
17.9 |
15.9 |
|
70 |
70 |
17.868903 |
20.5 |
14.7 |
22 |
23.1 |
23.8 |
33.2 |
|
80 |
80 |
19.350935 |
27.2 |
40.6 |
30 |
55.0 |
30.6 |
58.1 |
|
90 |
90 |
19.85 |
63.4 |
219.4 |
64 |
222.4 |
61.6 |
210.3 |
|
100 |
100 |
19.350935 |
62.6 |
223.5 |
62 |
220.4 |
46.5 |
140.3 |
|
110 |
110 |
17.868903 |
31.5 |
76.3 |
31 |
73.5 |
18.7 |
4.7 |
|
120 |
120 |
15.448935 |
23 |
48.9 |
24.5 |
58.6 |
16.6 |
7.5 |
|
130 |
130 |
12.16456 |
15.8 |
29.9 |
21.5 |
76.7 |
10.7 |
12.0 |
|
140 |
140 |
8.115573 |
11.4 |
40.5 |
16 |
97.2 |
4.7 |
42.1 |
|
150 |
150 |
3.425 |
7.6 |
121.9 |
5 |
46.0 |
0.2 |
94.2 |
|
160 |
160 |
0 |
2.7 |
35 |
0 |
100 |
0.6 |
30 |
|
170 |
170 |
0 |
0 |
0 |
1 |
50 |
0.4 |
20 |
|
180 |
180 |
0 |
0.5 |
25 |
0 |
0 |
0 |
0 |
|
190 |
190 |
0 |
0.5 |
25 |
0.5 |
25 |
0.2 |
10 |
|
200 |
200 |
0 |
0.5 |
25 |
0 |
0 |
0.7 |
35 |
|
210 |
210 |
0 |
0.2 |
10 |
0.5 |
25 |
0.5 |
25 |
|
220 |
220 |
0 |
0 |
0 |
0 |
0 |
0.4 |
20 |
|
230 |
230 |
0 |
0 |
0 |
0 |
0 |
0.2 |
10 |
|
240 |
240 |
0 |
0 |
0 |
0.5 |
25 |
0.2 |
10 |
|
250 |
250 |
0 |
0.2 |
10 |
0 |
0 |
0.6 |
30 |
|
260 |
260 |
0 |
0.3 |
15 |
0.5 |
25 |
0.4 |
20 |
|
270 |
270 |
0 |
0.3 |
15 |
0 |
0 |
0 |
0 |
|
280 |
280 |
0 |
0.4 |
20 |
0.5 |
25 |
0.2 |
10 |
|
290 |
290 |
0 |
0.5 |
25 |
0.5 |
25 |
0.7 |
35 |
|
300 |
300 |
0 |
0.3 |
15 |
0 |
0 |
0.5 |
25 |
|
310 |
310 |
0 |
0.5 |
25 |
0.5 |
25 |
0.4 |
20 |
|
320 |
320 |
0 |
0 |
0 |
0 |
0 |
0.2 |
10 |
|
330 |
330 |
0 |
0.5 |
25 |
0.5 |
25 |
0.2 |
10 |
|
340 |
340 |
0 |
0 |
0 |
0 |
0 |
0.7 |
35 |
|
350 |
350 |
0 |
0 |
0 |
0 |
0 |
0.5 |
25 |
|
360 |
360 |
0 |
0 |
0 |
0.5 |
25 |
0.4 |
20 |
|
q, Apparatus (degrees) |
q, Theory (degrees) |
X, Theoretical mm |
X measured for Follower |
|||||
|
Roller |
%error |
Flat |
%error |
Domed |
%error |
|||
|
0 |
0 |
0 |
0.5 |
25 |
0 |
25 |
0.7 |
35 |
|
10 |
10 |
0.3316722 |
0 |
100 |
0 |
100 |
0.7 |
111.1 |
|
20 |
20 |
1.3798221 |
0.1 |
92.8 |
0 |
100 |
0.1 |
92.8 |
|
30 |
30 |
3.3260616 |
0 |
100 |
0 |
100 |
0.8 |
75.9 |
|
40 |
40 |
6.5662567 |
14.3 |
117.8 |
1 |
84.8 |
0.4 |
93.9 |
|
50 |
50 |
11.948062 |
1.8 |
84.9 |
0 |
100 |
0.3 |
97.5 |
|
60 |
60 |
21.5 |
20.5 |
4.7 |
19 |
11.6 |
5.8 |
73.0 |
|
70 |
70 |
41.361795 |
34.3 |
17.1 |
26 |
37.1 |
14.9 |
64.0 |
|
80 |
80 |
102.31357 |
45.6 |
55.4 |
37 |
63.8 |
27.8 |
72.8 |
|
90 |
90 |
102.31357 |
58.3 |
43.0 |
50 |
51.1 |
43.5 |
57.5 |
|
100 |
100 |
41.361795 |
47.4 |
14.6 |
38.5 |
6.9 |
41.5 |
0.3 |
|
110 |
110 |
21.5 |
28.7 |
33.5 |
46.5 |
116.3 |
40.2 |
87.0 |
|
120 |
120 |
11.948062 |
18 |
50.7 |
39 |
226.4 |
39.3 |
229 |
|
130 |
130 |
6.5662567 |
8.5 |
29.4 |
28 |
326.4 |
13.6 |
107.1 |
|
140 |
140 |
3.3260616 |
2.5 |
24.8 |
22 |
561.4 |
10.7 |
221.7 |
|
150 |
150 |
1.3798221 |
0.4 |
71.0 |
17 |
1132 |
36.7 |
2560 |
|
160 |
160 |
0.3316722 |
0.57 |
71.9 |
5 |
1407.5 |
39.7 |
11869 |
|
170 |
170 |
0 |
0.13 |
6.5 |
0 |
0 |
0 |
0 |
|
180 |
180 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
190 |
190 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
200 |
200 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
210 |
210 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
220 |
220 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
230 |
230 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
240 |
240 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
250 |
250 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
260 |
260 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
270 |
270 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
280 |
280 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
290 |
290 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
300 |
300 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
310 |
310 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
320 |
320 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
330 |
330 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
340 |
340 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
350 |
350 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
360 |
360 |
|
0 |
|
0 |
|
0 |
|
|
q, Apparatus (degrees) |
q, Theory (degrees) |
X, Theoretical mm |
X measured for Follower |
|||||
|
Roller |
%error |
Flat |
%error |
Domed |
%error |
|||
|
0 |
0 |
0 |
1 |
50 |
1 |
50 |
1.7 |
85 |
|
10 |
10 |
0.1519 |
1.5 |
887 |
3.5 |
2204 |
2.7 |
1677 |
|
20 |
20 |
0.6031 |
3.2 |
431 |
4 |
563 |
4.6 |
663 |
|
30 |
30 |
1.3397 |
3.7 |
176 |
5 |
273 |
7.3 |
445 |
|
40 |
40 |
2.3396 |
6.8 |
191 |
8 |
242 |
8.7 |
272 |
|
50 |
50 |
3.5721 |
6.8 |
90.4 |
8.5 |
138 |
9.5 |
165.95 |
|
60 |
60 |
5 |
9 |
80 |
10 |
100 |
9.5 |
90 |
|
70 |
70 |
6.5798 |
10 |
52 |
10.5 |
60 |
10.9 |
65.7 |
|
80 |
80 |
8.2635 |
12 |
45 |
11 |
33.1 |
11.7 |
41.6 |
|
90 |
90 |
10 |
12 |
20 |
12.5 |
25 |
12.7 |
27 |
|
100 |
100 |
11.7365 |
13 |
10.8 |
13 |
10.8 |
13.4 |
14.2 |
|
110 |
110 |
13.4202 |
14 |
4.3 |
15 |
11.8 |
13.6 |
1.3 |
|
120 |
120 |
15 |
15 |
0 |
15 |
0 |
14.6 |
2.67 |
|
130 |
130 |
16.4279 |
15 |
8.7 |
15 |
8.7 |
15.4 |
6.3 |
|
140 |
140 |
17.6604 |
15.2 |
14 |
15 |
15.1 |
15.7 |
11.1 |
|
150 |
150 |
18.6603 |
16.8 |
9.97 |
16 |
14.3 |
15.9 |
14.8 |
|
160 |
160 |
19.3969 |
17.5 |
9.8 |
16 |
17.5 |
16 |
18 |
|
170 |
170 |
19.8481 |
17.5 |
11.8 |
16 |
19.4 |
16.2 |
18.4 |
|
180 |
180 |
20 |
18.5 |
-7.5 |
17 |
-15 |
27.3 |
36.5 |
|
190 |
190 |
19.8481 |
17.5 |
11.8 |
16 |
19.4 |
18 |
9.3 |
|
200 |
200 |
19.3969 |
16.5 |
14.9 |
16 |
17.5 |
16.5 |
14.9 |
|
210 |
210 |
18.6603 |
16 |
14.3 |
16 |
14.3 |
15.7 |
15.9 |
|
220 |
220 |
17.6604 |
16 |
9.4 |
15 |
15.1 |
14.9 |
15.6 |
|
230 |
230 |
16.4279 |
15 |
8.7 |
14 |
14.8 |
13.7 |
16.6 |
|
240 |
240 |
15 |
14 |
6.67 |
14 |
6.67 |
13.4 |
10.7 |
|
250 |
250 |
13.4202 |
14 |
4.3 |
13 |
3.1 |
12.8 |
4.6 |
|
260 |
260 |
11.7365 |
13 |
10.8 |
12 |
2.2 |
11.8 |
0.5 |
|
270 |
270 |
10 |
12.5 |
25 |
12 |
20 |
11.7 |
17 |
|
280 |
280 |
8.2635 |
11.2 |
35.5 |
11 |
33.1 |
10.3 |
24.6 |
|
290 |
290 |
6.5798 |
10 |
52 |
10 |
52 |
9.1 |
38.3 |
|
300 |
300 |
5 |
8 |
60 |
8 |
60 |
7.2 |
44 |
|
310 |
310 |
3.5721 |
6.8 |
90.3 |
7 |
96 |
5.3 |
48.4 |
|
320 |
320 |
2.3396 |
4.5 |
92.3 |
6 |
156 |
4 |
71 |
|
330 |
330 |
1.3397 |
4 |
199 |
3 |
124 |
3.7 |
176 |
|
340 |
340 |
0.6031 |
3 |
397 |
3 |
397 |
1.9 |
215 |
|
350 |
350 |
0.1519 |
1.5 |
887 |
2 |
1217 |
1.7 |
1019 |
|
360 |
360 |
0 |
1 |
50 |
0.2 |
10 |
2 |
100 |
|
q, Apparatus (degrees) |
q, Theory (degrees) |
X, Theoretical mm |
X measured for Follower |
|||||
|
Roller |
%error |
Flat |
%error |
Domed |
%error |
|||
|
0 |
0 |
0 |
0.5 |
25 |
1.5 |
50 |
1.1 |
85 |
|
10 |
10 |
0.2 |
3 |
1400 |
4 |
2204 |
1.7 |
1677 |
|
20 |
20 |
0.8 |
5 |
525 |
5 |
563 |
1.8 |
663 |
|
30 |
30 |
1.8 |
5 |
178 |
7 |
273 |
3.9 |
445 |
|
40 |
40 |
3.1 |
6.5 |
110 |
7.5 |
242 |
4 |
272 |
|
50 |
50 |
4.6 |
8.5 |
84.8 |
8.5 |
138 |
6 |
166 |
|
60 |
60 |
6.3 |
9 |
42.9 |
9 |
100 |
7.7 |
90 |
|
70 |
70 |
8 |
10 |
25 |
12.5 |
60 |
8.9 |
65.7 |
|
80 |
80 |
9.8 |
11.5 |
17.3 |
13 |
33.11 |
9.4 |
41.6 |
|
90 |
90 |
11.6 |
13 |
12.1 |
13 |
25 |
11.4 |
27 |
|
100 |
100 |
13.2 |
14 |
6.1 |
14 |
10.8 |
12.1 |
14.2 |
|
110 |
110 |
14.6 |
16 |
9.6 |
15 |
11.8 |
13 |
1.3 |
|
120 |
120 |
16 |
16.5 |
3.125 |
15 |
0 |
14.6 |
2.67 |
|
130 |
130 |
17.1 |
17 |
0.58 |
16 |
8.7 |
15.2 |
6.26 |
|
140 |
140 |
18 |
17 |
5.56 |
16 |
15.06 |
15.7 |
11.1 |
|
150 |
150 |
18.7 |
17.5 |
6.41 |
17 |
14.3 |
16.8 |
14.8 |
|
160 |
160 |
19.2 |
18 |
6.25 |
17 |
17.5 |
17.5 |
17.5 |
|
170 |
170 |
19.5 |
19 |
2.56 |
18 |
19.4 |
17.7 |
18.4 |
|
180 |
180 |
19.7 |
17.5 |
11.2 |
17 |
15 |
18.2 |
36.5 |
|
190 |
190 |
19.5 |
17.5 |
10.3 |
17 |
19.4 |
18.1 |
9.3 |
|
200 |
200 |
19.2 |
17 |
11.5 |
17 |
17.5 |
17.9 |
14.9 |
|
210 |
210 |
18.7 |
17 |
9.09 |
15 |
14.3 |
17.9 |
15.9 |
|
220 |
220 |
18 |
16 |
11.1 |
14 |
15.1 |
17.1 |
15.6 |
|
230 |
230 |
17.1 |
15.5 |
9.4 |
14 |
14.8 |
16.5 |
16.6 |
|
240 |
240 |
16 |
13.5 |
15.6 |
13 |
6.67 |
16.1 |
10.7 |
|
250 |
250 |
14.6 |
13 |
11 |
12 |
3.13 |
14.9 |
4.62 |
|
260 |
260 |
13.2 |
12 |
9.1 |
12 |
2.25 |
14.2 |
0.54 |
|
270 |
270 |
11.6 |
10 |
13.8 |
10 |
20 |
12 |
17 |
|
280 |
280 |
9.8 |
9 |
8.2 |
10 |
33.1 |
11.6 |
24.6 |
|
290 |
290 |
8 |
8 |
0 |
8 |
52 |
10 |
38.3 |
|
300 |
300 |
6.3 |
6 |
4.8 |
7 |
60 |
9.4 |
44 |
|
310 |
310 |
4.6 |
5.5 |
19.6 |
5.5 |
96 |
8.1 |
48.4 |
|
320 |
320 |
3.1 |
3.5 |
12.9 |
5 |
156 |
5.5 |
70 |
|
330 |
330 |
1.8 |
3 |
66.7 |
2 |
124 |
5.4 |
176.2 |
|
340 |
340 |
0.8 |
1.5 |
87.5 |
1.5 |
397.4 |
3.8 |
215 |
|
350 |
350 |
0.2 |
1 |
400 |
1 |
1217 |
2.3 |
1019 |
|
360 |
360 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
q, Apparatus (degrees) |
q, Theory (degrees) |
X, Theoretical mm |
X measured for Follower |
|||||
|
Roller |
%error |
Flat |
%error |
Domed |
%error |
|||
|
0 |
0 |
0 |
0.5 |
25 |
2 |
100 |
1.5 |
75 |
|
10 |
10 |
0.1234568 |
4 |
3140 |
3 |
2330 |
4.2 |
3302 |
|
20 |
20 |
0.4938272 |
4.5 |
811.25 |
5 |
912.5 |
4.6 |
831.5 |
|
30 |
30 |
1.1111111 |
5.5 |
395 |
6 |
440 |
6.3 |
467 |
|
40 |
40 |
1.9753086 |
5.5 |
178 |
7 |
254 |
7 |
254 |
|
50 |
50 |
3.0864198 |
8 |
159.2 |
9 |
191.6 |
8 |
159.2 |
|
60 |
60 |
4.4444444 |
9.5 |
113.75 |
9.5 |
113.75 |
8.9 |
100.25 |
|
70 |
70 |
6.0493827 |
10 |
65.3 |
11 |
81.8 |
9.4 |
55.4 |
|
80 |
80 |
7.9012346 |
11 |
39.2 |
12.5 |
58.2 |
9.7 |
22.8 |
|
90 |
90 |
10 |
13 |
30 |
13 |
30 |
11.3 |
13 |
|
100 |
100 |
12.345679 |
14.5 |
17.45 |
15 |
21.5 |
12.3 |
0.37 |
|
110 |
110 |
14.938272 |
15 |
0.41 |
15 |
0.41 |
14.4 |
3.6 |
|
120 |
120 |
17.777778 |
16 |
10 |
15.5 |
12.81 |
16.9 |
4.9 |
|
130 |
130 |
20.864198 |
19.5 |
6.5 |
16.5 |
20.9 |
17.9 |
14.2 |
|
140 |
140 |
24.197531 |
20 |
17.3 |
16.5 |
31.8 |
19 |
21.5 |
|
150 |
150 |
27.777778 |
20 |
28 |
19 |
31.6 |
20.4 |
26.56 |
|
160 |
160 |
31.604938 |
21 |
33.6 |
19.5 |
38.3 |
21.2 |
32.9 |
|
170 |
170 |
35.679012 |
21.5 |
39.7 |
22 |
38.3 |
21.5 |
39.7 |
|
180 |
180 |
40 |
21 |
47.5 |
20 |
50 |
31.7 |
20.75 |
|
190 |
190 |
35.679012 |
20 |
43.9 |
20 |
43.9 |
19.9 |
44.22 |
|
200 |
200 |
31.604938 |
16 |
49.4 |
18.5 |
41.5 |
17.4 |
44.9 |
|
210 |
210 |
27.777778 |
16 |
42.4 |
16.5 |
40.6 |
16.5 |
40.6 |
|
220 |
220 |
24.197531 |
14 |
42.1 |
16.5 |
31.8 |
13.9 |
42.6 |
|
230 |
230 |
20.864198 |
14 |
32.9 |
13 |
37.7 |
12.7 |
39.1 |
|
240 |
240 |
17.777778 |
12 |
32.5 |
12 |
32.5 |
12.6 |
39.125 |
|
250 |
250 |
14.938272 |
11 |
26.4 |
11 |
26.4 |
11.3 |
24.3 |
|
260 |
260 |
12.345679 |
10 |
19 |
10 |
19 |
9.5 |
23.05 |
|
270 |
270 |
10 |
8 |
20 |
9.5 |
5 |
8.3 |
17 |
|
280 |
280 |
7.9012346 |
7 |
11.4 |
7 |
11.4 |
6.8 |
13.9 |
|
290 |
290 |
6.0493827 |
6 |
0.82 |
6.5 |
7.4 |
6.4 |
5.8 |
|
300 |
300 |
4.4444444 |
5 |
12.5 |
6 |
35 |
4 |
10 |
|
310 |
310 |
3.0864198 |
5 |
62 |
3.5 |
13.4 |
3.8 |
23.12 |
|
320 |
320 |
1.9753086 |
3 |
51.875 |
3 |
51.875 |
2.4 |
21.5 |
|
330 |
330 |
1.1111111 |
1 |
10 |
1.5 |
35 |
2.1 |
89 |
|
340 |
340 |
0.4938272 |
1 |
102.5 |
1 |
102.5 |
2 |
305 |
|
350 |
350 |
0.1234568 |
0 |
100 |
0 |
100 |
1 |
710 |
|
360 |
360 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
Sample calculation:
For Constant Acceleration cam:
u=40o
x = (u/15)2/3.6
=(40/15)2/3.6
=1.975mm
For simple harmonic cam:
q =60o
x = R(1-cos u)
=10(1-cos 60o)
=5mm
For tangent cam:
q=30o
x = 21.5(secu-1)
= 21.5(sec30o-1)
= 3.3261mm
For convex cam:
q=200o
x = 32.85 sinu+7-20
= 32.85 sin 200o+7-20
=
-24.24(0mm displacement)
Analysis and
Discussion:
From the data collected, five graphs were plotted each representing all the cams used in the experiment with different types of followers which were the roller, flat and domed. From the graphs, although each of the plotting were quite similar with one another in terms of the followers used but it does exhibit a different effect. It seems that the roller gave a more stable reading or measurement than the other two followers. Apart from that, nothing significant could be observed except for an obvious relative differences with the theoretical plotting.
In terms of error, the roller was found to have the lowest error followed by the flat and domed follower. The error might be contributed by the unstability of the contact point between the follower and the cam which resulted the reading taken a bit off from the theoretical value. Human error also could not be ignored from this consideration and since the experiment was done on analog apparatus, the possibilty of parallax error always exist.
The three plotting of displacement versus angle for the constant acceleration, harmonic and circular show that they have a similar shape but posses an entirely different slopes which exactly show the characteristics of their motion. The constant acceleration plotting has the steepest slope with a uniform increase and decrease from 0 to 360o followed by the circular and harmonic cam. Although the parabolic shaped cam which refers to the circular cam and hamonic cam seems to show no difference except for the slope, they actually different in its motion. The circular cam actually has a higher acceleration than the harmonic cam. The circular cam velocity’s increases and decreases very rapidly and uniformly but the harmonic cam velocity’s increases and decreases slowly but achieve the highest velocity compared to circular cam.
Conclusion:
As a conclusion, it was found that the tappet motion for all the cam used was found to exhibit the similar profiles as presented by the theoretical plotting of each cams. Although there might be relative errors between the theoretical and measured values, it does not affect the overall result of the profiles obtained. It was also found that the roller follower produced the most satisfying result than the flat and domed follower. This was supported by the error analysis that proved the roller has an advantage over the flat and domed follower in this experiment.
The circular, harmonic and constant acceleration cams were found to posses different characteristics. Eventhough the profiles of the circular and harmonic cam did not show any significant differences, but the velocity and acceleration of these profiles suggest otherwise. The circular cam has a rapid velocity changes and much higher acceleration than the harmonic cam which instead exhibits a much slower velocity changes but achieved the highest velocity than the circular cam.
