MBD Simulation on a Piston Assembly using SOLIDWORKS

AIM:

Multibody dynamics simulation using Solidworks MBD on a crank-piston assembly.

We have to design all the different parts of the cylinder-piston arrangement separately.

The parts are as follows:

• Piston Head
• Gudgeon Pin (Wrist pin)
• Connecting rod
• End Cap
• Crank

After designing all the parts, we have to complete the assembly.

After giving correct mates, we can check our model by rotating the crankshaft with the help of the mouse, this must show the piston reciprocating.

Then motion analysis is being carried out where rotary motion (motor) is provided to the crank. There are a total of 3 contact pairs between the parts of the crank piston assembly (steel is applied as material) and results are being obtained.

GEOMETRY CREATION:

(Personal comment - only adding those points which make sense in this report, not every little detail which has been told in the video already)

1. All the parts are designed in Solidworks individually which have been shown in the video.
2. Some options should be carefully selected while designing, for e.g.- the curved slot in the piston head and in crank as well, it should be done via the extruded cut option in which the flip side cut option must be chosen. (This is done because the sketch was open, I personally prefer to close the sketch so we don't have to worry about it.)
3. Another important thing is that the fillets should be given to every sharp corner mostly if we take into account stress concentration at sharp corners and the simulation to be more precise.
4. All the mates have been told in the video. I had used width mate where we need the symmetric position of the part e.g. - The wrist pins the piston.

Solidworks motion analysis-

1. After complete assembly, the SolidWorks motion is enabled.
2. Rotary motion is provided to the crank (2000 rpm).
3. Solid-Body contact is done between the bodies that are in contact

There are a total of 3 contact pairs -

• connecting rod and crank.
• connecting rod and piston head
• Piston and Wrist pin

1. Gravity is also enabled in a downward direction w.r.to the assembly.
2. Now the most important point is that we add precise contact and frames per second is increased to 7200 for the purpose that we don't want to miss any peak values of the desired parameters and also so that the simulation is smooth and more accurate.
3. Tried results for more than 5 revolutions of the crank.

Sl. No	Wrist Pin Offset `	Crank Speed (Rpm)
1	"0" mm	2000
2	10 mm Positive	2000
3	10 mm Negative	2000

10 MM POSITIVE OFFSET:

10 MM NEGATIVE OFFSET:

3D CAD MODELS:

PISTON HEAD: A piston is a component of reciprocating engines, reciprocating pumps, gas compressors, and pneumatic cylinders, among other similar mechanisms. It is the moving component that is contained by a cylinder and is made gas-tight by piston rings. In an engine, its purpose is to transfer force from expanding gas in the cylinder to the crankshaft via a piston rod and/or connecting rod.

CONNECTING ROD: A connecting rod is a rigid member that connects a piston to a crank or crankshaft in a reciprocating engine. Together with the crank, it forms a simple mechanism that converts reciprocating motion into rotating motion.

END CAP: The end cap is connected to the end of the connecting rod, which is assembled crank.

GUDGEON (WRIST) PIN: In internal combustion engines, the gudgeon pin connects the piston to the connecting rod and provides a bearing for the connecting rod to pivot upon as the piston moves. In very early engine designs the gudgeon pin is located in a sliding crosshead that connects to the piston via a rod. Gudgeon is a pivot or journal.

CRANK: Is a mechanical part able to convert the reciprocating motion from the piston into rotational motion.

FINAL ASSEMBLY: The piston, connecting rod, wrist pin, end cap, and the crank are assembled as shown below using the assembly mate option. First, the crank is made coincident with the assembly planes so that it can rotate about its axis, and then connecting rod and end cap assembly is made coincident with the crank axis. Then the wrist pin is made coincident with the piston and with its front plane and it is then assembled to the connecting rod. This will result in the required assembly for motion analysis.

OUTPUT PLOTS:

WITHOUT OFFSET (ZERO OFFSET):

PISTON WITH POSITIVE OFFSET 10 MM:

PISTON WITH NEGATIVE OFFSET 10 MM:

SUBMERGED RESULT:

OUTPUT VIDEO:

Click here to watch the simulation video

Parts Made by me:

PISTON_HEAD_VISHALBHARDWAJ

GUDGEON_PIN_VISHALBHARDWAJ

END_CAP_VISHALBHARDWAJ

CRANK_VISHALBHARDWAJ

CONNECTING_ROD_VISHALBHARDWAJ

ASSEMBLY_VISHALBHARDWAJ

OUTPUT EXCEL DATA:

		Piston-1	Piston WITH POSITIVE OFFSET 10 MM-1	Piston WITH NEGATIVE OFFSET 10 MM-1
		Zero offset	Linear Displacement1 (mm)	Linear Displacement1 (mm)
Frame	Time	Ref. Coordinate System:	Ref. Coordinate System:	Ref. Coordinate System:
1	0	295.51	302.31	302.15
2	0	295.64	302.31	302.18
3	0	295.82	302.3	302.25
4	0	295.99	302.29	302.25
5	0	296.46	302.26	302.3
6	0	296.91	302.22	302.3
7	0.001	297.34	302.22	302.3
8	0.001	297.76	302.09	302.25
9	0.001	298.16	301.92	302.25
10	0.001	298.55	301.92	302.14
11	0.001	298.92	301.69	301.99
12	0.001	299.27	301.69	301.78
13	0.001	299.6	301.41	301.52
14	0.002	299.91	301.41	301.21
15	0.002	300.21	301.08	300.84
16	0.002	300.49	300.69	300.43
17	0.002	300.76	300.26	299.97
18	0.002	301	299.78	299.46
19	0.002	301.23	299.25	298.9
20	0.002	301.43	298.67	298.3
21	0.003	301.62	298.04	297.64
22	0.003	301.8	297.36	296.94
23	0.003	301.95	296.64	296.2
24	0.003	302.08	295.87	295.41
25	0.003	302.2	295.06	294.58
26	0.003	302.3	294.2	293.71
27	0.003	302.37	293.3	292.8
28	0.003	302.43	292.36	291.85
29	0.004	302.47	291.38	290.86
30	0.004	302.5	290.36	289.83
31	0.004	302.5	289.3	288.77
32	0.004	302.5	288.21	287.67
33	0.004	302.48	287.08	286.54
34	0.004	302.48	285.92	285.38
35	0.004	302.45	284.72	284.18
36	0.004	302.45	283.5	282.96
37	0.004	302.4	282.24	281.71
38	0.004	302.4	280.96	280.44
39	0.004	302.32	279.65	279.14
40	0.004	302.32	278.32	277.82
41	0.005	302.23	276.96	276.48
42	0.005	302.12	275.58	275.11
43	0.005	302	274.18	273.73
44	0.005	301.85	272.77	272.34
45	0.005	301.68	271.33	270.92
46	0.005	301.5	269.88	269.5
47	0.005	301.3	268.42	268.06
48	0.006	301.08	266.95	266.61
49	0.006	300.84	265.46	265.15
50	0.006	300.58	263.97	263.69
51	0.006	300.31	262.47	262.22
52	0.006	300.02	260.96	260.74
53	0.006	299.71	259.45	260.74
54	0.006	299.38	259.45	259.27
55	0.007	299.04	257.94	259.27
56	0.007	298.67	257.94	257.79
57	0.007	298.29	256.43	257.79
58	0.007	297.9	256.43	256.31
59	0.007	297.49	254.92	256.31
60	0.007	297.06	254.92	254.83
61	0.007	296.61	253.41	254.83
62	0.008	296.15	253.41	253.35
63	0.008	295.67	251.9	253.35
64	0.008	295.18	251.9	251.88
65	0.008	294.67	250.4	250.42
66	0.008	294.15	248.91	248.96
67	0.008	293.61	247.43	248.96
68	0.008	293.06	245.95	247.5
69	0.008	292.49	244.48	246.06
70	0.009	291.91	243.03	244.63
71	0.009	291.31	241.59	243.21
72	0.009	290.7	240.16	241.8
73	0.009	290.08	238.75	241.8
74	0.009	289.45	237.36	240.41
75	0.009	288.8	235.98	239.03
76	0.009	288.14	234.62	237.66
77	0.01	287.46	233.29	236.31
78	0.01	286.78	231.97	234.98
79	0.01	286.08	230.67	233.67
80	0.01	285.37	229.4	232.38
81	0.01	284.65	228.15	231.11
82	0.01	283.92	226.92	229.86
83	0.01	283.18	225.72	228.63
84	0.011	282.43	224.54	227.42
85	0.011	281.67	223.39	226.24
86	0.011	280.9	222.27	225.08
87	0.011	280.12	221.17	223.94
88	0.011	279.34	220.1	222.83
89	0.011	278.54	219.06	221.74
90	0.011	277.74	218.05	220.68
91	0.012	276.92	217.07	219.65
92	0.012	276.1	216.11	218.64
93	0.012	275.28	215.19	217.66
94	0.012	274.44	214.29	216.71
95	0.012	273.61	213.43	215.79
96	0.012	272.76	212.6	214.89
97	0.012	271.91	211.8	214.02
98	0.013	271.05	211.03	213.19
99	0.013	270.19	210.29	212.38
100	0.013	269.32	209.58	211.6
101	0.013	268.45	208.9	210.85
102	0.013	267.58	208.26	210.13
103	0.013	266.7	207.65	209.44
104	0.013	265.82	207.07	208.78
105	0.013	264.93	206.52	208.15
106	0.014	264.05	206.01	207.56
107	0.014	263.16	205.53	206.99
108	0.014	262.27	205.08	206.45
109	0.014	261.37	204.66	205.95
110	0.014	260.48	204.27	205.48
111	0.014	259.58	203.92	205.03
112	0.014	258.69	203.6	204.62
113	0.015	257.79	203.32	204.25
114	0.015	256.89	203.06	203.9
115	0.015	256	202.84	203.58
116	0.015	255.1	202.65	203.3
117	0.015	254.21	202.49	203.05
118	0.015	253.31	202.37	202.83
119	0.015	252.42	202.28	202.64
120	0.016	251.53	202.22	202.49
121	0.016	250.64	202.19	202.37
122	0.016	249.76	202.2	202.28
123	0.016	248.87	202.24	202.22
124	0.016	247.99	202.31	202.19
125	0.016	247.12	202.41	202.2
126	0.016	246.24	202.55	202.24
127	0.017	245.37	202.71	202.31
128	0.017	244.51	202.91	202.42
129	0.017	243.65	203.15	202.55
130	0.017	242.79	203.41	202.72
131	0.017	241.94	203.7	202.92
132	0.017	241.09	204.03	203.16
133	0.017	240.25	204.39	203.42
134	0.018	239.42	204.78	203.72
135	0.018	238.58	205.2	204.06
136	0.018	237.76	205.66	204.42
137	0.018	236.94	206.14	204.82
138	0.018	236.13	206.66	205.25
139	0.018	235.33	207.21	205.71
140	0.018	234.53	207.79	206.21
141	0.018	233.74	208.4	206.73
142	0.019	232.95	209.04	207.29
143	0.019	232.17	209.71	207.89
144	0.019	231.41	210.41	208.51
145	0.019	230.64	211.14	209.17
146	0.019	229.89	211.9	209.85
147	0.019	229.14	212.69	210.57
148	0.019	228.41	213.51	211.33
149	0.02	227.68	214.36	212.11
150	0.02	226.96	215.24	212.92
151	0.02	226.25	216.14	213.77
152	0.02	225.54	217.08	214.64
153	0.02	224.85	218.04	215.55
154	0.02	224.16	219.03	216.48
155	0.02	223.49	220.05	217.45
156	0.021	222.82	221.09	218.44
157	0.021	222.16	222.16	219.47
158	0.021	221.52	223.26	220.52
159	0.021	220.88	224.38	221.6
160	0.021	220.25	225.53	222.71
161	0.021	219.63	226.7	223.84
162	0.021	219.02	227.89	225
163	0.022	218.43	229.11	226.19
164	0.022	217.84	230.35	227.4
165	0.022	217.26	231.6	228.64
166	0.022	216.69	232.88	229.9
167	0.022	216.14	234.18	231.18
168	0.022	215.59	235.5	232.48
169	0.022	215.05	236.84	232.48
170	0.023	214.53	238.2	233.81
171	0.023	214.01	239.57	233.81
172	0.023	213.51	240.95	235.16
173	0.023	213.02	242.35	235.16
174	0.023	212.53	243.76	236.52
175	0.023	212.06	245.19	236.52
176	0.023	211.6	246.63	237.9
177	0.023	211.15	248.07	237.9
178	0.024	210.71	249.53	239.3
179	0.024	210.29	249.53	239.3
180	0.024	209.87	250.99	240.72
181	0.024	209.46	252.46	242.15
182	0.024	209.07	253.93	243.6
183	0.024	208.69	253.93	243.6
184	0.024	208.32	255.41	245.06
185	0.025	207.96	255.41	246.53
186	0.025	207.61	256.89	248.01
187	0.025	207.27	256.89	249.5
188	0.025	206.95	258.37	250.99
189	0.025	206.63	258.37	250.99
190	0.025	206.33	259.85	252.49
191	0.025	206.04	259.85	254
192	0.026	205.76	261.32	255.51
193	0.026	205.49	261.32	257.02
194	0.026	205.23	262.8	258.54
195	0.026	204.98	264.27	260.05
196	0.026	204.75	265.73	261.55
197	0.026	204.53	267.18	263.06
198	0.026	204.32	268.63	264.56
199	0.027	204.12	268.63	266.05
200	0.027	203.93	270.06	267.53
201	0.027	203.75	270.06	269
202	0.027	203.75	271.48	270.45
203	0.027	203.59	272.89	271.9
204	0.027	203.43	274.28	273.32
205	0.027	203.29	275.65	274.73
206	0.027	203.16	277.01	276.12
207	0.028	203.04	278.34	277.5
208	0.028	202.94	279.65	278.84
209	0.028	202.84	280.94	280.17
210	0.028	202.76	282.21	281.47
211	0.028	202.69	283.45	282.74
212	0.028	202.63	284.66	283.98
213	0.028	202.58	285.84	285.2
214	0.028	202.54	286.99	286.38
215	0.028	202.54	288.1	287.53
216	0.029	202.52	289.19	288.64
217	0.029	202.52	290.24	289.72
218	0.029	202.5	291.25	290.77
219	0.029	202.5	292.23	291.77
220	0.029	202.5	293.16	292.73
221	0.029	202.5	294.06	293.66
222	0.029	202.51	294.91	294.54
223	0.029	202.51	295.73	295.38
224	0.029	202.53	296.5	296.18
225	0.029	202.53	297.22	296.93
226	0.029	202.56	297.9	297.63
227	0.029	202.61	298.54	298.29
228	0.03	202.67	299.13	298.9
229	0.03	202.73	299.67	299.46
230	0.03	202.81	300.16	299.97
231	0.03	202.9	300.6	300.44
232	0.03	203.01	300.99	300.85
233	0.03	203.12	301.33	301.21
234	0.03	203.25	301.63	301.52
235	0.031	203.39	301.87	301.78
236	0.031	203.53	302.05	301.99
237	0.031	203.7	302.19	302.15
238	0.031	203.87	302.28	302.25
239	0.031	203.87	302.31	302.3
240	0.031	204.05	302.29	302.3
241	0.031	204.25	302.22	302.25
242	0.031	204.45	302.09	302.14
243	0.032	204.67	301.92	301.99
244	0.032	204.9	301.69	301.78
245	0.032	205.15	301.41	301.52
246	0.032	205.4	301.08	301.21
247	0.032	205.66	300.69	300.84
248	0.032	205.94	300.26	300.43
249	0.032	206.23	299.78	299.97
250	0.033	206.53	299.25	299.46
251	0.033	206.84	298.67	298.9
252	0.033	207.16	298.04	298.3
253	0.033	207.49	297.36	297.64
254	0.033	207.84	296.64	296.94
255	0.033	208.2	295.87	296.2
256	0.033	208.56	295.06	295.41
257	0.033	208.94	294.2	294.58
258	0.034	209.33	293.3	293.71
259	0.034	209.73	292.36	292.8
260	0.034	210.15	291.38	291.85
261	0.034	210.57	290.36	290.86
262	0.034	211	289.3	289.83
263	0.034	211.45	288.21	288.77
264	0.034	211.91	287.08	287.67
265	0.035	212.37	285.92	286.54
266	0.035	212.85	284.72	285.38
267	0.035	213.34	283.5	284.18
268	0.035	213.84	282.24	282.96
269	0.035	214.35	280.96	281.71
270	0.035	214.88	279.65	280.44
271	0.035	215.41	278.32	279.14
272	0.036	215.95	276.96	277.82
273	0.036	216.5	275.58	276.48
274	0.036	217.07	274.18	275.11
275	0.036	217.64	272.77	273.73
276	0.036	218.23	271.33	272.34
277	0.036	218.82	269.88	270.92
278	0.036	219.43	268.42	269.5
279	0.037	220.04	266.95	268.06
280	0.037	220.67	265.46	266.61
281	0.037	221.3	263.97	265.15
282	0.037	221.95	262.47	263.69
283	0.037	222.6	260.96	262.22
284	0.037	223.26	259.45	260.74
285	0.037	223.94	259.45	260.74
286	0.038	224.62	257.94	259.27
287	0.038	225.31	257.94	259.27
288	0.038	226.01	256.43	257.79
289	0.038	226.72	256.43	257.79
290	0.038	227.44	254.92	256.31
291	0.038	228.16	254.92	256.31
292	0.038	228.9	253.41	254.83
293	0.038	229.64	253.41	254.83
294	0.039	230.39	251.9	253.35
295	0.039	231.15	251.9	253.35
296	0.039	231.92	250.4	251.88
297	0.039	232.69	248.91	250.42
298	0.039	233.47	247.43	248.96
299	0.039	234.26	245.95	248.96
300	0.039	235.06	244.48	247.5
301	0.04	235.86	243.03	246.06
302	0.04	236.67	241.59	244.63
303	0.04	237.49	240.16	243.21
304	0.04	238.31	238.75	241.8
305	0.04	239.14	237.36	241.8
306	0.04	239.97	235.98	240.41
307	0.04	240.81	234.62	239.03
308	0.041	241.66	233.29	237.66
309	0.041	242.51	231.97	236.31
310	0.041	243.36	230.67	234.98
311	0.041	244.22	229.4	233.67
312	0.041	245.08	228.15	232.38
313	0.041	245.95	226.92	231.11
314	0.041	246.82	225.72	229.86
315	0.042	247.7	224.54	228.63
316	0.042	248.58	223.39	227.42
317	0.042	249.46	222.27	226.24
318	0.042	250.35	221.17	225.08
319	0.042	251.23	220.1	223.94
320	0.042	252.12	219.06	222.83
321	0.042	253.01	218.05	221.74
322	0.043	253.91	217.07	220.68
323	0.043	254.8	216.11	219.65
324	0.043	255.7	215.19	218.64
325	0.043	256.59	214.29	217.66
326	0.043	257.49	213.43	216.71
327	0.043	258.39	212.6	215.79
328	0.043	259.28	211.8	214.89
329	0.043	260.18	211.03	214.02
330	0.044	261.07	210.29	213.19
331	0.044	261.97	209.58	212.38
332	0.044	262.86	208.9	211.6
333	0.044	263.75	208.26	210.85
334	0.044	264.64	207.65	210.13
335	0.044	265.52	207.07	209.44
336	0.044	266.4	206.52	208.78
337	0.045	267.28	206.01	208.15
338	0.045	268.16	205.53	207.56
339	0.045	269.03	205.08	206.99
340	0.045	269.9	204.66	206.45
341	0.045	270.76	204.27	205.95
342	0.045	271.62	203.92	205.48
343	0.045	272.48	203.6	205.03
344	0.046	273.32	203.32	204.62
345	0.046	274.16	203.06	204.25
346	0.046	275	202.84	203.9
347	0.046	275.83	202.65	203.58
348	0.046	276.65	202.49	203.3
349	0.046	277.46	202.37	203.05
350	0.046	278.27	202.28	202.83
351	0.047	279.07	202.22	202.64
352	0.047	279.86	202.19	202.49
353	0.047	280.64	202.2	202.37
354	0.047	281.41	202.24	202.28
355	0.047	282.18	202.31	202.22
356	0.047	282.93	202.41	202.19
357	0.047	283.68	202.55	202.2
358	0.048	284.41	202.71	202.24
359	0.048	285.13	202.91	202.31
360	0.048	285.84	203.15	202.42
361	0.048	286.55	203.41	202.55
362	0.048	287.23	203.7	202.72
363	0.048	287.91	204.03	202.92
364	0.048	288.58	204.39	203.16
365	0.048	289.23	204.78	203.42
366	0.049	289.87	205.2	203.72
367	0.049	290.5	205.66	204.06
368	0.049	291.11	206.14	204.42
369	0.049	291.71	206.66	204.82
370	0.049	292.3	207.21	205.25
371	0.049	292.87	207.79	205.71
372	0.049	293.43	208.4	206.21
373	0.05	293.97	209.04	206.73
374	0.05	294.5	209.71	207.29
375	0.05	295.01	210.41	207.89
376	0.05	295.51	211.14	208.51
377	0.05	295.99	211.9	209.17
378	0.05	296.46	212.69	209.85
379	0.05	296.91	213.51	210.57
380	0.051	297.34	214.36	211.33
381	0.051	297.76	215.24	212.11
382	0.051	298.16	216.14	212.92
383	0.051	298.55	217.08	213.77
384	0.051	298.92	218.04	214.64
385	0.051	299.27	219.03	215.55
386	0.051	299.6	220.05	216.48
387	0.052	299.91	221.09	217.45
388	0.052	300.21	222.16	218.44
389	0.052	300.49	223.26	219.47
390	0.052	300.76	224.38	220.52
391	0.052	301	225.53	221.6
392	0.052	301.23	226.7	222.71
393	0.052	301.43	227.89	223.84
394	0.053	301.62	229.11	225
395	0.053	301.8	230.35	226.19
396	0.053	301.95	231.6	227.4
397	0.053	302.08	232.88	228.64
398	0.053	302.2	234.18	229.9
399	0.053	302.3	235.5	231.18
400	0.053	302.37	236.84	232.48
401	0.053	302.43	238.2	232.48
402	0.054	302.47	239.57	233.81
403	0.054	302.5	240.95	233.81
404	0.054	302.5	242.35	235.16
405	0.054	302.5	243.76	235.16
406	0.054	302.48	245.19	236.52
407	0.054	302.48	246.63	236.52
408	0.054	302.45	248.07	237.9
409	0.054	302.45	249.53	237.9
410	0.054	302.4	249.53	239.3
411	0.054	302.4	250.99	239.3
412	0.054	302.32	252.46	240.72
413	0.054	302.32	253.93	242.15
414	0.055	302.23	253.93	243.6
415	0.055	302.12	255.41	243.6
416	0.055	302	255.41	245.06
417	0.055	301.85	256.89	246.53
418	0.055	301.68	256.89	248.01
419	0.055	301.5	258.37	249.5
420	0.055	301.3	258.37	250.99
421	0.056	301.08	259.85	250.99
422	0.056	300.84	259.85	252.49
423	0.056	300.58	261.32	254
424	0.056	300.31	261.32	255.51
425	0.056	300.02	262.8	257.02
426	0.056	299.71	264.27	258.54
427	0.056	299.38	265.73	260.05
428	0.057	299.04	267.18	261.55
429	0.057	298.67	268.63	263.06
430	0.057	298.29	268.63	264.56
431	0.057	297.9	270.06	266.05
432	0.057	297.49	270.06	267.53
433	0.057	297.06	271.48	269
434	0.057	296.61	272.89	270.45
435	0.058	296.15	274.28	271.9
436	0.058	295.67	275.65	273.32
437	0.058	295.18	277.01	274.73
438	0.058	294.67	278.34	276.12
439	0.058	294.15	279.65	277.5
440	0.058	293.61	280.94	278.84
441	0.058	293.06	282.21	280.17
442	0.058	292.49	283.45	281.47
443	0.059	291.91	284.66	282.74
444	0.059	291.31	285.84	283.98
445	0.059	290.7	286.99	285.2
446	0.059	290.08	288.1	286.38
447	0.059	289.45	289.19	287.53
448	0.059	288.8	290.24	288.64
449	0.059	288.14	291.25	289.72
450	0.06	287.46	292.23	290.77
451	0.06	286.78	293.16	291.77
452	0.06	286.08	294.06	292.73
453	0.06	285.37	294.91	293.66
454	0.06	284.65	295.73	294.54
455	0.06	283.92	296.5	295.38
456	0.06	283.18	297.22	296.18
457	0.061	282.43	297.9	296.93
458	0.061	281.67	298.54	297.63
459	0.061	280.9	299.13	298.29
460	0.061	280.12	299.67	298.9
461	0.061	279.34	300.16	299.46
462	0.061	278.54	300.6	299.97
463	0.061	277.74	300.99	300.44
464	0.062	276.92	301.33	300.85
465	0.062	276.1	301.63	301.21
466	0.062	275.28	301.87	301.52
467	0.062	274.44	302.05	301.78
468	0.062	273.61	302.19	301.99
469	0.062	272.76	302.28	302.15
470	0.062	271.91	302.31	302.25
471	0.063	271.05	302.29	302.3
472	0.063	270.19	302.22	302.3
473	0.063	269.32	302.09	302.25
474	0.063	268.45	301.92	302.14
475	0.063	267.58	301.69	301.99
476	0.063	266.7	301.41	301.78
477	0.063	265.82	301.08	301.52
478	0.063	264.93	300.69	301.21
479	0.064	264.05	300.26	300.84
480	0.064	263.16	299.78	300.43
481	0.064	262.27	299.25	299.97
482	0.064	261.37	298.67	299.46
483	0.064	260.48	298.04	298.9
484	0.064	259.58	297.36	298.3
485	0.064	258.69	296.64	297.64
486	0.065	257.79	295.87	296.94
487	0.065	256.89	295.06	296.2
488	0.065	256	294.2	295.41
489	0.065	255.1	293.3	294.58
490	0.065	254.21	292.36	293.71
491	0.065	253.31	291.38	292.8
492	0.065	252.42	290.36	291.85
493	0.066	251.53	289.3	290.86
494	0.066	250.64	288.21	289.83
495	0.066	249.76	287.08	288.77
496	0.066	248.87	285.92	287.67
497	0.066	247.99	284.72	286.54
498	0.066	247.12	283.5	285.38
499	0.066	246.24	282.24	284.18
500	0.067	245.37	280.96	282.96
501	0.067	244.51	279.65	281.71
502	0.067	243.65	278.32	280.44
503	0.067	242.79	276.96	279.14
504	0.067	241.94	275.58	277.82
505	0.067	241.09	274.18	276.48
506	0.067	240.25	272.77	275.11
507	0.068	239.42	271.33	273.73
508	0.068	238.58	269.88	272.34
509	0.068	237.76	268.42	270.92
510	0.068	236.94	266.95	269.5
511	0.068	236.13	265.46	268.06
512	0.068	235.33	263.97	266.61
513	0.068	234.53	262.47	265.15
514	0.068	233.74	260.96	263.69
515	0.069	232.95	259.45	262.22
516	0.069	232.17	259.45	260.74
517	0.069	231.41	257.94	260.74
518	0.069	230.64	257.94	259.27
519	0.069	229.89	256.43	259.27
520	0.069	229.14	256.43	257.79
521	0.069	228.41	254.92	257.79
522	0.07	227.68	254.92	256.31
523	0.07	226.96	253.41	256.31
524	0.07	226.25	253.41	254.83
525	0.07	225.54	251.9	254.83
526	0.07	224.85	251.9	253.35
527	0.07	224.16	250.4	253.35
528	0.07	223.49	248.91	251.88
529	0.071	222.82	247.43	250.42
530	0.071	222.16	245.95	248.96
531	0.071	221.52	244.48	248.96
532	0.071	220.88	243.03	247.5
533	0.071	220.25	241.59	246.06
534	0.071	219.63	240.16	244.63
535	0.071	219.02	238.75	243.21
536	0.072	218.43	237.36	241.8
537	0.072	217.84	235.98	241.8
538	0.072	217.26	234.62	240.41
539	0.072	216.69	233.29	239.03
540	0.072	216.14	231.97	237.66
541	0.072	215.59	230.67	236.31
542	0.072	215.05	229.4	234.98
543	0.072	214.53	228.15	233.67
544	0.073	214.01	226.92	232.38
545	0.073	213.51	225.72	231.11
546	0.073	213.02	224.54	229.86
547	0.073	212.53	223.39	228.63
548	0.073	212.06	222.27	227.42
549	0.073	211.6	221.17	226.24
550	0.073	211.15	220.1	225.08
551	0.074	210.71	219.06	223.94
552	0.074	210.29	218.05	222.83
553	0.074	209.87	217.07	221.74
554	0.074	209.46	216.11	220.68
555	0.074	209.07	215.19	219.65
556	0.074	208.69	214.29	218.64
557	0.074	208.32	213.43	217.66
558	0.075	207.96	212.6	216.71
559	0.075	207.61	211.8	215.79
560	0.075	207.27	211.03	214.89
561	0.075	206.95	210.29	214.02
562	0.075	206.63	209.58	213.19
563	0.075	206.33	208.9	212.38
564	0.075	206.04	208.26	211.6
565	0.076	205.76	207.65	210.85
566	0.076	205.49	207.07	210.13
567	0.076	205.23	206.52	209.44
568	0.076	204.98	206.01	208.78
569	0.076	204.75	205.53	208.15
570	0.076	204.53	205.08	207.56
571	0.076	204.32	204.66	206.99
572	0.077	204.12	204.27	206.45
573	0.077	203.93	203.92	205.95
574	0.077	203.75	203.6	205.48
575	0.077	203.75	203.32	205.03
576	0.077	203.59	203.06	204.62
577	0.077	203.43	202.84	204.25
578	0.077	203.29	202.65	203.9
579	0.077	203.16	202.49	203.58
580	0.077	203.04	202.37	203.3
581	0.078	202.94	202.28	203.05
582	0.078	202.84	202.22	202.83
583	0.078	202.76	202.19	202.64
584	0.078	202.69	202.2	202.49
585	0.078	202.63	202.24	202.37
586	0.078	202.58	202.31	202.28
587	0.078	202.54	202.41	202.22
588	0.078	202.54	202.55	202.19
589	0.079	202.52	202.71	202.2
590	0.079	202.52	202.91	202.24
591	0.079	202.5	203.15	202.31
592	0.079	202.5	203.41	202.42
593	0.079	202.5	203.7	202.55
594	0.079	202.5	204.03	202.72
595	0.079	202.51	204.39	202.92
596	0.079	202.51	204.78	203.16
597	0.079	202.53	205.2	203.42
598	0.079	202.53	205.66	203.72
599	0.079	202.56	206.14	204.06
600	0.079	202.61	206.66	204.42
601	0.08	202.67	207.21	204.82
602	0.08	202.73	207.79	205.25
603	0.08	202.81	208.4	205.71
604	0.08	202.9	209.04	206.21
605	0.08	203.01	209.71	206.73
606	0.08	203.12	210.41	207.29
607	0.08	203.25	211.14	207.89
608	0.081	203.39	211.9	208.51
609	0.081	203.53	212.69	209.17
610	0.081	203.7	213.51	209.85
611	0.081	203.87	214.36	210.57
612	0.081	203.87	215.24	211.33
613	0.081	204.05	216.14	212.11
614	0.081	204.25	217.08	212.92
615	0.081	204.45	218.04	213.77
616	0.082	204.67	219.03	214.64
617	0.082	204.9	220.05	215.55
618	0.082	205.15	221.09	216.48
619	0.082	205.4	222.16	217.45
620	0.082	205.66	223.26	218.44
621	0.082	205.94	224.38	219.47
622	0.082	206.23	225.53	220.52
623	0.082	206.53	226.7	221.6
624	0.083	206.84	227.89	222.71
625	0.083	207.16	229.11	223.84
626	0.083	207.49	230.35	225
627	0.083	207.84	231.6	226.19
628	0.083	208.2	232.88	227.4
629	0.083	208.56	234.18	228.64
630	0.083	208.94	235.5	229.9
631	0.084	209.33	236.84	231.18
632	0.084	209.73	238.2	232.48