Summary

Cams are widely used in engines, machine tools, textile and packaging machines. Their purpose is to convert rotary motion into linear or rocking motion of the cam follower. Within certain limits any desired linear/rocking motion can be obtained by a suitable cam profile.

The purpose of this experiment is to investigate tappet motion for several different cam profiles and the effect of using different followers will be investigate. The apparatus used is the cam and tappet apparatus with roller, domed and flat followers equipped with dial indicator shown in APPENDIX. There are five types of cams used that is convex, tangent, harmonic, circular and constant acceleration cam.

The result of the experiment is tabulated and shown at the Data, Observation and Result section. The graph of displacement against angle for the all types of cam is plotted. The velocity and acceleration value for constant acceleration cam and harmonic cam is calculated and graph is plotted.

Below are the findings of the experiment based on the results and the plotted graph.

1. Different cam profile gives some effects on the throw and so does the follower. All the cams has quite the same graph behaviour that is quadratic. Regardless of the follower and cam used, the displacement will go back to its original position after completing one full revolution of the rotor.

2. The flat follower will give a slower response compared to domed and roller follower. The domed follower is the first showing the output reading (displacement measured).

3. The theoretical and measured values of throw are quite different. The theoretical and measured values of throw shown a small deviation for harmonic, circular and constant acceleration cam and a very large different for tangent and convex cam since error is generated during experiment.

4. The plots of displacement against angle for the constant acceleration, harmonic and circular cams is about the same. However, the displacement at respective angle is greatest for constant acceleration cam, followed by circular cam and harmonic cam. Theoretically, the displacement occurs in one full revolution that is from 0° to 360° for these three cams.

5. The plots of convex and tangent cams is quite same because both profiles has flanks formed by circular arcs. Theoretically, the displacement occurs only about 180° from 90° to 180°.

6. All cams have their maximum throw value at an angle of 180 °.

7. The velocity profile for harmonic cam gives sine curve and for constant acceleration give constant increase and decrease in velocity at alternate 90°.

8. The constant acceleration cam gives constant acceleration and deceleration while the acceleration of harmonic cam is in cosine curve.

9. It has been proven that the constant acceleration cam with domed follower will gave the greatest cam throw and faster response time compared to others.

In conclusion, by doing the cam and tappet experiment, the tappet motion for several different cam profiles have been investigated. The objective of the experiment is achieved since the results of the experiment tends to agree to the theoretical aspects of the experiment.

Purpose / Objective

The purpose of this experiment is to investigate tappet motion for several different cam profiles and to see the effect of different followers.

Procedure

1. The first part of the experiment is performed with domed follower. The two knurled nuts is undo and the two and the two washer is removed so that the cam can be insert into its position.

2. The end of the dial indicator is held and pulled gently away from the rotor or where the cam is to be fitted.

3. The convex cam is then placed onto the two studs with their larger radius at the center of the rotation. This is done so that the incorrect cam orientation will not give much throw and so that the dial instructor can measure the range of travel.

4. The dial indicator stem is then can be gently allowed to touch the cam.

5. The washer is then placed onto the studs and the knurled nuts are added.

6. The dial indicator is set to zero when the rotor is set at 0°.

7. Thereadings of the dial indicator is taken for every 10° on the result sheet.

8. The procedure 1 to 7 is repeated for tangent, simple harmonic, circular and constant acceleration cam.

9. For the second part of the experiment, all the above procedures are repeated using the flat and roller follower. In order to change the follower, the dial indicator unit is removed from the apparatus by removing the two knurled nuts and washer under the base. The follower is unscrewed from the dial indicator stem and one of the other follower is screwed into place. The unit is then placed onto the base with its position adjusted in order for dial indicator to measures the full range of cam throw.

Data, Observation and Result

The data of the cam throw for domed, roller, flat follower and the theoretical value is shown in the tables below.

· Domed follower

Table 1: Convex cam

Apparatus	Theory	x Measured	x Measured	x Theoretical
(degrees)	(degrees)	(* 0.1mm)	(mm)	(mm)
0		0	0	0
10		-1	-0.1	0
20		1	0.1	0
30		1	0.1	0
40		1	0.1	0
50		0.5	0.05	0
60		0	0	0
70		-0.5	-0.05	0
80		-1	-0.1	0
90	0	-1	-0.1	0
100	10	1	0.1	0.1951
110	20	7	0.7	0.7925
120	30	19	1.9	1.8307
130	40	37	3.7	3.3768
140	50	59	5.9	5.5247
150	60	88	8.8	8.3939
160	70	127	12.7	12.1122
170	80	174	17.4	16.7818
180	90	194	19.4	19.85
190	100	184	18.4	16.7818
200	110	142	14.2	12.1122
210	120	98	9.8	8.3939
220	130	65	6.5	5.5247
230	140	39	3.9	3.3768
240	150	21	2.1	1.8307
250	160	17	1.7	0.7925
260	170	0	0	0.1951
270	180	-3	-0.3	0
280		-2.5	-0.25	0
290		-2	-0.2	0
300		-1.5	-0.15	0
310		-1	-0.1	0
320		-0.5	-0.05	0
330		0	0	0
340		0	0	0
350		0	0	0
360		0	0	0

Table 2: Harmonic cam

Apparatus	Theory	x Measured	x Measured	x Theoretical
(degrees)	(degrees)	(* 0.1mm)	(mm)	(mm)
0	0	0	0	0
10	10	1	0.1	0.152
20	20	6	0.6	0.603
30	30	14	1.4	1.339
40	40	22	2.2	2.339
50	50	36	3.6	3.572
60	60	50	5	5
70	70	66	6.6	6.579
80	80	82.5	8.25	8.264
90	90	99.5	9.95	10
100	100	116	11.6	11.736
110	110	131	13.1	13.42
120	120	146	14.6	15
130	130	160	16	16.428
140	140	172	17.2	17.66
150	150	181	18.1	18.66
160	160	188	18.8	19.397
170	170	193	19.3	19.848
180	180	195	19.5	20
190	190	194	19.4	19.848
200	200	190	19	19.397
210	210	183.5	18.35	18.66
220	220	176	17.6	17.66
230	230	165	16.5	16.428
240	240	152	15.2	15
250	250	137.5	13.75	13.42
260	260	121	12.1	11.736
270	270	105	10.5	10
280	280	90	9	8.264
290	290	73	7.3	6.579
300	300	57	5.7	5
310	310	43	4.3	3.572
320	320	30	3	2.339
330	330	19	1.9	1.339
340	340	10	1	0.603
350	350	3	0.3	0.152
360	360	0	0	0


Table 3: Tangent cam

Apparatus	Theory	x Measured	x Measured	x Theoretical
(degrees)	(degrees)	(* 0.1mm)	(mm)	(mm)
0		0	0	0
10		0.5	0.05	0
20		0.5	0.05	0
30		0.5	0.05	0
40		0	0	0
50		0	0	0
60		0	0	0
70		0	0	0
80		0	0	0
90	0	-0.5	-0.05	1.3040
100	10	-0.5	-0.05	0.2971
110	20	-1	-0.1	0.0009
120	30	2	0.2	0.3683
130	40	17	1.7	1.4581
140	50	42	4.2	3.4604
150	60	81	8.1	6.7870
160	70	140	14	12.3224
170	80	181	18.1	22.2020
180	90	196	19.6	43.0031
190	100	188	18.8	22.2020
200	110	155	15.5	12.3224
210	120	92	9.2	6.7870
220	130	43	4.3	3.4604
230	140	17	1.7	1.4581
240	150	1	0.1	0.3683
250	160	-4	-0.4	0.0009
260	170	-3	-0.3	0.2971
270	180	-2.5	-0.25	1.3040
280		-2	-0.2	0
290		-1.5	-0.15	0
300		-1	-0.1	0
310		-0.5	-0.05	0
320		-0.5	-0.05	0
330		0	0	0
340		0.5	0.05	0
350		1	0.1	0
360		1.5	0.15	0


Table 4: Constant accn.		cam

Apparatus	Theory	x Measured	x Measured	x Theoretical
(degrees)	(degrees)	(* 0.1mm)	(mm)	(mm)
0	0	0	0	0
10	10	0.5	0.05	0.1235
20	20	4	0.4	0.4938
30	30	11	1.1	1.1111
40	40	19	1.9	1.9753
50	50	31.5	3.15	3.0864
60	60	44	4.4	4.4444
70	70	62	6.2	6.0494
80	80	82	8.2	7.9012
90	90	102	10.2	10
100	100	124	12.4	12.0988
110	110	143	14.3	13.9506
120	120	159	15.9	15.5556
130	130	172	17.2	16.9136
140	140	183	18.3	18.0247
150	150	192	19.2	18.8889
160	160	198	19.8	19.5062
170	170	202	20.2	19.8765
180	180	203.5	20.35	20
190	190	202.5	20.25	19.8765
200	200	199	19.9	19.5062
210	210	194	19.4	18.8889
220	220	186	18.6	18.0247
230	230	176	17.6	16.9136
240	240	164	16.4	15.5556
250	250	148.5	14.85	13.9506
260	260	130	13	12.0988
270	270	111	11.1	10
280	280	91	9.1	7.9012
290	290	71.5	7.15	6.0494
300	300	52.5	5.25	4.4444
310	310	39	3.9	3.0864
320	320	26	2.6	1.9753
330	330	16	1.6	1.1111
340	340	9	0.9	0.4938
350	350	3	0.3	0.1235
360	360	1	0.1	0


Table 5: Circular cam

Apparatus	Theory	x Measured	x Measured	x Theoretical
(degrees)	(degrees)	(* 0.1mm)	(mm)	(mm)
0	0	0	0	0
10	10	1	0.1	0.2
20	20	4	0.4	0.8
30	30	9	0.9	1.8
40	40	16	1.6	3.1
50	50	21	2.1	4.6
60	60	37.5	3.75	6.3
70	70	50	5	8
80	80	68	6.8	9.8
90	90	84.5	8.45	11.6
100	100	101	10.1	13.2
110	110	119	11.9	14.6
120	120	137	13.7	16
130	130	154	15.4	17.1
140	140	168	16.8	18
150	150	179	17.9	18.7
160	160	189	18.9	19.2
170	170	195	19.5	19.5
180	180	197	19.7	19.7
190	190	196	19.6	19.5
200	200	191	19.1	19.2
210	210	183	18.3	18.7
220	220	171	17.1	18
230	230	159	15.9	17.1
240	240	144	14.4	16
250	250	124	12.4	14.6
260	260	108	10.8	13.2
270	270	90	9	11.6
280	280	73.5	7.35	9.8
290	290	56.5	5.65	8
300	300	43.5	4.35	6.3
310	310	31	3.1	4.6
320	320	21.5	2.15	3.1
330	330	13	1.3	1.8
340	340	7	0.7	0.8
350	350	3	0.3	0.2
360	360	1.5	0.15	0

· Roller follower

Table 6: Convex cam

Apparatus	Theory	x Measured	x Measured	x Theoretical
(degrees)	(degrees)	(* 0.1mm)	(mm)	(mm)
0		0	0	0
10		0	0	0
20		0	0	0
30		-0.5	-0.05	0
40		-0.5	-0.05	0
50		-1	-0.1	0
60		-1.5	-0.15	0
70		-2	-0.2	0
80		-3	-0.3	0
90	0	-3	-0.3	0
100	10	-1	-0.1	0.1951
110	20	5	0.5	0.7925
120	30	16	1.6	1.8307
130	40	31	3.1	3.3768
140	50	53	5.3	5.5247
150	60	81	8.1	8.3939
160	70	118	11.8	12.1122
170	80	168	16.8	16.7818
180	90	193	19.3	19.85
190	100	162	16.2	16.7818
200	110	114	11.4	12.1122
210	120	80	8	8.3939
220	130	52	5.2	5.5247
230	140	30	3	3.3768
240	150	16	1.6	1.8307
250	160	4.5	0.45	0.7925
260	170	-1	-0.1	0.1951
270	180	-2	-0.2	0
280		-2	-0.2	0
290		-1.5	-0.15	0
300		-1	-0.1	0
310		-0.5	-0.05	0
320		0	0	0
330		0	0	0
340		0.5	0.05	0
350		0.5	0.05	0
360		0.5	0.05	0


Table 7: Harmonic cam

Apparatus	Theory	x Measured	x Measured	x Theoretical
(degrees)	(degrees)	(* 0.1mm)	(mm)	(mm)
0	0	0	0	0
10	10	2	0.2	0.152
20	20	7	0.7	0.603
30	30	14.5	1.45	1.339
40	40	24	2.4	2.339
50	50	30	3	3.572
60	60	50	5	5
70	70	61	6.1	6.579
80	80	83	8.3	8.264
90	90	99	9.9	10
100	100	117	11.7	11.736
110	110	133	13.3	13.42
120	120	148	14.8	15
130	130	162	16.2	16.428
140	140	175	17.5	17.66
150	150	184	18.4	18.66
160	160	197	19.7	19.397
170	170	197	19.7	19.848
180	180	198	19.8	20
190	190	194	19.4	19.848
200	200	192	19.2	19.397
210	210	185	18.5	18.66
220	220	175	17.5	17.66
230	230	163	16.3	16.428
240	240	149	14.9	15
250	250	133	13.3	13.42
260	260	117	11.7	11.736
270	270	99	9.9	10
280	280	83	8.3	8.264
290	290	65	6.5	6.579
300	300	51	5.1	5
310	310	38	3.8	3.572
320	320	26	2.6	2.339
330	330	16	1.6	1.339
340	340	8	0.8	0.603
350	350	3	0.3	0.152
360	360	2	0.2	0


Table 8: Tangent cam

Apparatus	Theory	x Measured	x Measured	x Theoretical
(degrees)	(degrees)	(* 0.1mm)	(mm)	(mm)
0		0	0	0
10		0	0	0
20		0	0	0
30		0	0	0
40		-0.5	-0.05	0
50		-1.5	-0.15	0
60		-1.5	-0.15	0
70		-1.5	-0.15	0
80		-2	-0.2	0
90	0	-3	-0.3	1.3040
100	10	-3	-0.3	0.2971
110	20	-3.5	-0.35	0.0009
120	30	1	0.1	0.3683
130	40	12	1.2	1.4581
140	50	32	3.2	3.4604
150	60	62.5	6.25	6.7870
160	70	121	12.1	12.3224
170	80	179	17.9	22.2020
180	90	194	19.4	43.0031
190	100	172	17.2	22.2020
200	110	113	11.3	12.3224
210	120	57	5.7	6.7870
220	130	26	2.6	3.4604
230	140	7	0.7	1.4581
240	150	-2	-0.2	0.3683
250	160	-4	-0.4	0.0009
260	170	-4	-0.4	0.2971
270	180	-3.5	-0.35	1.3040
280		-3	-0.3	0
290		-2.5	-0.25	0
300		-2	-0.2	0
310		-1.5	-0.15	0
320		-1	-0.1	0
330		-1	-0.1	0
340		-0.5	-0.05	0
350		-0.5	-0.05	0
360		0	0	0


Table 9: Constant accn.		cam

Apparatus	Theory	x Measured	x Measured	x Theoretical
(degrees)	(degrees)	(* 0.1mm)	(mm)	(mm)
0	0	0	0	0
10	10	1	0.1	0.1235
20	20	5	0.5	0.4938
30	30	11	1.1	1.1111
40	40	19	1.9	1.9753
50	50	30	3	3.0864
60	60	43	4.3	4.4444
70	70	59	5.9	6.0494
80	80	74	7.4	7.9012
90	90	101	10.1	10
100	100	120	12	12.0988
110	110	140	14	13.9506
120	120	156	15.6	15.5556
130	130	171	17.1	16.9136
140	140	184	18.4	18.0247
150	150	192	19.2	18.8889
160	160	199	19.9	19.5062
170	170	203	20.3	19.8765
180	180	204	20.4	20
190	190	203	20.3	19.8765
200	200	199	19.9	19.5062
210	210	192	19.2	18.8889
220	220	184	18.4	18.0247
230	230	171	17.1	16.9136
240	240	158	15.8	15.5556
250	250	142	14.2	13.9506
260	260	122	12.2	12.0988
270	270	100	10	10
280	280	80	8	7.9012
290	290	61	6.1	6.0494
300	300	45	4.5	4.4444
310	310	32	3.2	3.0864
320	320	20	2	1.9753
330	330	12	1.2	1.1111
340	340	6	0.6	0.4938
350	350	2	0.2	0.1235
360	360	1	0.1	0


Table 10: Circular cam

Apparatus	Theory	x Measured	x Measured	x Theoretical
(degrees)	(degrees)	(* 0.1mm)	(mm)	(mm)
0	0	0	0	0
10	10	1	0.1	0.2
20	20	4	0.4	0.8
30	30	9	0.9	1.8
40	40	16	1.6	3.1
50	50	26	2.6	4.6
60	60	36	3.6	6.3
70	70	49	4.9	8
80	80	64	6.4	9.8
90	90	81	8.1	11.6
100	100	98	9.8	13.2
110	110	116	11.6	14.6
120	120	133	13.3	16
130	130	151	15.1	17.1
140	140	165	16.5	18
150	150	177	17.7	18.7
160	160	187	18.7	19.2
170	170	193	19.3	19.5
180	180	195	19.5	19.7
190	190	193	19.3	19.5
200	200	184	18.4	19.2
210	210	178	17.8	18.7
220	220	166	16.6	18
230	230	160	16	17.1
240	240	135	13.5	16
250	250	117	11.7	14.6
260	260	97	9.7	13.2
270	270	80	8	11.6
280	280	64	6.4	9.8
290	290	49	4.9	8
300	300	37	3.7	6.3
310	310	26	2.6	4.6
320	320	16	1.6	3.1
330	330	10	1	1.8
340	340	5	0.5	0.8
350	350	2	0.2	0.2
360	360	1	0.1	0

· Flat follower

Table 11: Convex cam

Apparatus	Theory	x Measured	x Measured	x Theoretical
(degrees)	(degrees)	(* 0.1mm)	(mm)	(mm)
0		0	0	0
10		-0.1	-0.01	0
20		-1	-0.1	0
30		-1	-0.1	0
40		-1.5	-0.15	0
50		-2	-0.2	0
60		-3	-0.3	0
70		-2.5	-0.25	0
80		-2.5	-0.25	0
90	0	-3	-0.3	0
100	10	2	0.2	0.1951
110	20	15	1.5	0.7925
120	30	34	3.4	1.8307
130	40	56	5.6	3.3768
140	50	86	8.6	5.5247
150	60	120	12	8.3939
160	70	160	16	12.1122
170	80	187	18.7	16.7818
180	90	194.5	19.45	19.85
190	100	191	19.1	16.7818
200	110	178	17.8	12.1122
210	120	143	14.3	8.3939
220	130	106	10.6	5.5247
230	140	72	7.2	3.3768
240	150	44	4.4	1.8307
250	160	22.5	2.25	0.7925
260	170	4.5	0.45	0.1951
270	180	-2	-0.2	0
280		-1.5	-0.15	0
290		-1	-0.1	0
300		-0.5	-0.05	0
310		-0.1	-0.01	0
320		0	0	0
330		0	0	0
340		0.5	0.05	0
350		0.5	0.05	0
360		0	0	0


Table 12: Harmonic cam

Apparatus	Theory	x Measured	x Measured	x Theoretical
(degrees)	(degrees)	(* 0.1mm)	(mm)	(mm)
0	0	0	0	0
10	10	3	0.3	0.152
20	20	11	1.1	0.603
30	30	21.5	2.15	1.339
40	40	34	3.4	2.339
50	50	49	4.9	3.572
60	60	64	6.4	5
70	70	80	8	6.579
80	80	98	9.8	8.264
90	90	114	11.4	10
100	100	128	12.8	11.736
110	110	144	14.4	13.42
120	120	158	15.8	15
130	130	167.5	16.75	16.428
140	140	178	17.8	17.66
150	150	186	18.6	18.66
160	160	192	19.2	19.397
170	170	196	19.6	19.848
180	180	198	19.8	20
190	190	197	19.7	19.848
200	200	193	19.3	19.397
210	210	187	18.7	18.66
220	220	180	18	17.66
230	230	170	17	16.428
240	240	158	15.8	15
250	250	145	14.5	13.42
260	260	130	13	11.736
270	270	114	11.4	10
280	280	98	9.8	8.264
290	290	80	8	6.579
300	300	65	6.5	5
310	310	50	5	3.572
320	320	35	3.5	2.339
330	330	23	2.3	1.339
340	340	12	1.2	0.603
350	350	3	0.3	0.152
360	360	0	0	0


Table 13: Tangent cam

Apparatus	Theory	x Measured	x Measured	x Theoretical
(degrees)	(degrees)	(* 0.1mm)	(mm)	(mm)
0		0	0	0
10		1	0.1	0
20		1.5	0.15	0
30		1.2	0.12	0
40		1	0.1	0
50		1	0.1	0
60		1	0.1	0
70		0.9	0.09	0
80		0.5	0.05	0
90	0	0	0	1.3040
100	10	-0.5	-0.05	0.2971
110	20	0	0	0.0009
120	30	18.5	1.85	0.3683
130	40	44	4.4	1.4581
140	50	81	8.1	3.4604
150	60	132.5	13.25	6.7870
160	70	177.5	17.75	12.3224
170	80	192.5	19.25	22.2020
180	90	197	19.7	43.0031
190	100	192	19.2	22.2020
200	110	179	17.9	12.3224
210	120	147.5	14.75	6.7870
220	130	92	9.2	3.4604
230	140	51.5	5.15	1.4581
240	150	22	2.2	0.3683
250	160	0	0	0.0009
260	170	-2	-0.2	0.2971
270	180	-2	-0.2	1.3040
280		-1.5	-0.15	0
290		-1.5	-0.15	0
300		-1	-0.1	0
310		-1	-0.1	0
320		-1	-0.1	0
330		-0.8	-0.08	0
340		-0.5	-0.05	0
350		0	0	0
360		0	0	0


Table 14: Constant accn.		cam

Apparatus	Theory	x Measured	x Measured	x Theoretical
(degrees)	(degrees)	(* 0.1mm)	(mm)	(mm)
0	0	0	0	0
10	10	2	0.2	0.1235
20	20	8	0.8	0.4938
30	30	17	1.7	1.1111
40	40	29	2.9	1.9753
50	50	44	4.4	3.0864
60	60	61.5	6.15	4.4444
70	70	79	7.9	6.0494
80	80	101.5	10.15	7.9012
90	90	121	12.1	10
100	100	137	13.7	12.0988
110	110	153	15.3	13.9506
120	120	166	16.6	15.5556
130	130	172	17.2	16.9136
140	140	187	18.7	18.0247
150	150	194	19.4	18.8889
160	160	200	20	19.5062
170	170	203.5	20.35	19.8765
180	180	205	20.5	20
190	190	204	20.4	19.8765
200	200	201	20.1	19.5062
210	210	196	19.6	18.8889
220	220	189	18.9	18.0247
230	230	180	18	16.9136
240	240	169	16.9	15.5556
250	250	155	15.5	13.9506
260	260	140	14	12.0988
270	270	124	12.4	10
280	280	105	10.5	7.9012
290	290	84	8.4	6.0494
300	300	65	6.5	4.4444
310	310	48	4.8	3.0864
320	320	33	3.3	1.9753
330	330	20	2	1.1111
340	340	10	1	0.4938
350	350	3	0.3	0.1235
360	360	0.5	0.05	0


Table 15: Circular cam

Apparatus	Theory	x Measured	x Measured	x Theoretical
(degrees)	(degrees)	(* 0.1mm)	(mm)	(mm)
0	0	0	0	0
10	10	2	0.2	0.2
20	20	6.5	0.65	0.8
30	30	14	1.4	1.8
40	40	23.5	2.35	3.1
50	50	35	3.5	4.6
60	60	49	4.9	6.3
70	70	65	6.5	8
80	80	81	8.1	9.8
90	90	98	9.8	11.6
100	100	115	11.5	13.2
110	110	131	13.1	14.6
120	120	147	14.7	16
130	130	160	16	17.1
140	140	173	17.3	18
150	150	183	18.3	18.7
160	160	191	19.1	19.2
170	170	195.5	19.55	19.5
180	180	197	19.7	19.7
190	190	196	19.6	19.5
200	200	191	19.1	19.2
210	210	184	18.4	18.7
220	220	175	17.5	18
230	230	163	16.3	17.1
240	240	149	14.9	16
250	250	134	13.4	14.6
260	260	117	11.7	13.2
270	270	100	10	11.6
280	280	83	8.3	9.8
290	290	66	6.6	8
300	300	51	5.1	6.3
310	310	37	3.7	4.6
320	320	25	2.5	3.1
330	330	15	1.5	1.8
340	340	8	0.8	0.8
350	350	3	0.3	0.2
360	360	1.5	0.15	0

From the data recorded, the graph of measured and theoretical displacement against angle for different types of cam based on the data in the tables above was plotted in one graph, attached in the APPENDIX.

Discussion

With reference to the experimental data tabulated and the plotted graphs, the tappet motion for several different cam profiles and the effect of different followers is obtained. It can be seen that the follower (flat, domed and roller) gives some effects on the throw and so does the profiles of the cam used. All the cams has quite the same graph behaviour that is quadratic. Regardless of the follower and cam used, the displacement will go back to its original position after completing one full revolution of the rotor. In term of time of response, the flat follower will give a slower response compared to domed and roller follower. The domed follower is the first showing the output reading (displacement measured).

For different cam types, the theoretical and measured values of throw are different. The theoretical and measured values of throw shown a small deviation for harmonic, circular and constant acceleration cam and a very large different for tangent and convex cam. This may be caused by the error that occurs while performing the experiment. One possible source of error is due to the incorrect cam orientation during the experiment that give too much flow which unable the measurement of range travel. Moreover, the dial indicator reliability is low since it not precise in giving the results because it has been used in the experiment that is done many times before this. In addition, paralax error occurs during reading of the dial indicator is taken that give fluctuation in positive and negative reading. All this has lead to the loss of accuracy and precision of the experiment results.

The plots of displacement against angle for the constant acceleration, harmonic and circular cams is about the same. However, the displacement at respective angle is greatest for constant acceleration cam, followed by circular cam and harmonic cam. So, it can be said that constant acceleration cam has the greatest cam throw compared to others. Both experimentally and theoretically have shown

that all three cams have their maximum value at an angle of 180 °.

Table 16 below shows the velocity and acceleration value for constant acceleration cam and harmonic cam.

Angle	Harmonic cam		Constant accn. cam
(degrees)	Velocity	Acceleration	Velocity	Acceleration
	(m/s)	(m/s²)	(m/s)	(m/s²)
0	0.0000	0.0100	0.0000	0.5556
10	0.0017	0.0098	0.3704	0.5556
20	0.0034	0.0094	0.7407	0.5556
30	0.0050	0.0087	1.1111	0.5556
40	0.0064	0.0077	1.4815	0.5556
50	0.0077	0.0064	1.8519	0.5556
60	0.0087	0.0050	2.2222	0.5556
70	0.0094	0.0034	2.5926	0.5556
80	0.0098	0.0017	2.9630	0.5556
90	0.0100	0.0000	3.3333	0.5556
100	0.0098	-0.0017	-2.9630	-0.5556
110	0.0094	-0.0034	-2.5926	-0.5556
120	0.0087	-0.0050	-2.2222	-0.5556
130	0.0077	-0.0064	-1.8519	-0.5556
140	0.0064	-0.0077	-1.4815	-0.5556
150	0.0050	-0.0087	-1.1111	-0.5556
160	0.0034	-0.0094	-0.7407	-0.5556
170	0.0017	-0.0098	-0.3704	-0.5556
180	0.0000	-0.0100	0.0000	-0.5556
190	-0.0017	-0.0098	-0.3704	-0.5556
200	-0.0034	-0.0094	-0.7407	-0.5556
210	-0.0050	-0.0087	-1.1111	-0.5556
220	-0.0064	-0.0077	-1.4815	-0.5556
230	-0.0077	-0.0064	-1.8519	-0.5556
240	-0.0087	-0.0050	-2.2222	-0.5556
250	-0.0094	-0.0034	-2.5926	-0.5556
260	-0.0098	-0.0017	-2.9630	-0.5556
270	-0.0100	0.0000	-3.3333	-0.5556
280	-0.0098	0.0017	-2.9630	0.5556
290	-0.0094	0.0034	-2.5926	0.5556
300	-0.0087	0.0050	-2.2222	0.5556
310	-0.0077	0.0064	-1.8519	0.5556
320	-0.0064	0.0077	-1.4815	0.5556
330	-0.0050	0.0087	-1.1111	0.5556
340	-0.0034	0.0094	-0.7407	0.5556
350	-0.0017	0.0098	-0.3704	0.5556
360	0.0000	0.0100	0.0000	0.5556

Table 16

From the data in Table 16 above, the graph of velocity and acceleration against angle for both of the cams is plotted. It is shown in the APPENDIX.

For the graph of velocity for harmonic cam, it is observed that the graph is a sinusoidal shape, of sine curve having a period of 360°. Consequently, for its acceleration, the graph is also in sinusoidal shape of cosine curve, with full 360° period. On the other hand, constant acceleration cam gives constant acceleration from 0° to 90° and the same value but deceleration from 90° to 270°. From 270° to 360°, the graph is back to the constant acceleration value initiaaly. Since acceleration is the second differential of distance, so the velocity graph is almost a linear straight line graph to give the constant acceleration and deceleration value. This is the most important property of the constant acceleration cams.

Conclusion

In conclusion, by doing the cam and tappet experiment, the tappet motion for several different cam profiles have been investigated. The results of the experiment tends to agree to the theoretical aspects of the experiment. Although there is an error occur during performing the experiment, it does not effect the results of the experiment. Therefore, the objective of the experiment is achieved since the results of the experiment has revealed the effect of using different types of follower and cam profiles in the process of converting rotary motion into linear or rocking motion of the cam follower. The throw displacement, velocity and acceleration is very dependent to the types and profiles of the cams and also the followers for the performance of a variety of tasks.

Appendix

A. General equation: Please refer to the formula included in the lab manual.

B. Theoretical Sample of calculation:

Taking q = 10° for all calculation

· Convex cam

Displacement, x = OE – 20

Where OE = 55 sin b / sin (180-q)

b = q - a

sin a = 35 sin (180-q)/55

\x (q = 10°) = 0.1951 mm

· Tangent cam

In the apparatus setup, q = q _{dial indicator} - f

Where f = 19.47°

\ q = - 9.47°

Displacement, x = 21.5 (sec q - 1)

= 21.5 (sec –9.47 - 1)

= 0.2971 mm

· Harmonic cam

Displacement, x = R (1 – cos q) mm

Velocity, v = w (R sin q ) m/s

Acceleration, a = w² R cos q m/s²

Where R = 10 mm and w = 1 rad/s since constant angular velocity

\x = 10 (1 – cos 10°)= 0.152 mm

\v = 1 ( 10x10^-3sin 10°) = 0.0017n m/s

\a = 1² (10x10^-3 cos 10°) = 0.0098 m/s²

· Constant acceleration cam

Displacement, x = [ (q/15)² /3.6 ] = 0.1235 mm

Velocity, v = (2q) / (3.6*15) = 0.3704 m/s

Acceleration, a = 2 / 3.6 = 0.5556 m/s²

· Circular cam : the theoretical value is included in the lab manual.