Мещерский 48.2
Материал из Department of Theoretical and Applied Mechanics
Мещерский Задача 48.2
Визуализация 3D-задачи по динамике на JavaScript
Исполнитель: Сызранцев Денис
Группа 23632/2 Кафедра Теоретической механики
Условие задачи[править]
Барабан центрифуги приводится во вращение электродвигателем через двухступенчатый редуктор. Заданы момент инерции J0 электродвигателя, момент инерции J2 барабана, момент инерции J1 промежуточного вала редуктора, передаточные числа i01 и i12 ступеней редуктора. К ротору электродвигателя приложен вращающий момент M0 и момент сил сопротивления M0s, к валу редуктора и к барабану — моменты сил сопротивления M1s и M2s соответственно. Составить дифференциальное уравнение вращения барабана центрифуги.
Решение задачи[править]
Визуализация[править]
Код программы[править]
Текст программы на языке JavaScript:
1 <!DOCTYPE html>
2 <html lang="en">
3 <head>
4 <title>48.2</title>
5 <meta charset="utf-8">
6 <meta name="viewport" content="width=device-width, user-scalable=no, minimum-scale=1.0, maximum-scale=1.0">
7 <style>
8 body {
9 font-family: Monospace;
10 background-color: #f0f0f0;
11 margin: 0px;
12 overflow: hidden;
13 }
14 </style>
15 </head>
16 <body>
17
18 <script src = "http://tm.spbstu.ru/htmlets/Belousova/Statika/three.js">
19 </script>
20 <script src ="http://tm.spbstu.ru/htmlets/Belousova/Statika/stats.min.js">
21 </script>
22 <script src ="http://tm.spbstu.ru/htmlets/Belousova/Statika/OrbitControls.js">
23 </script>
24 <script src ="http://tm.spbstu.ru/htmlets/Belousova/Statika/dat.gui.js">
25 </script>
26
27 <script>
28
29 var container, stats;
30
31 var camera, controls, scene, renderer;
32
33 var start = Date.now();
34
35 var A2 , w0, w1, w2;
36
37
38 var c = new function() {
39 this.i01 = 2;
40 this.i12 = 3;
41 this.J0 = 80;
42 this.J1 = 40;
43 this.J2 = 80;
44 this.M0 = 3;
45 this.M0s = 2;
46 this.M1s = 1.6;
47 this.M2s = 1;
48 this.stop = false;
49 this.restart = function(){
50 start = Date.now()
51 ED.rotation.x = 0;
52 rot.rotation.x = 0;
53 B.rotation.x = 0;
54 }
55
56 this.w2 = 0.0;
57 this.A2 = ((this.M0-this.M0s)*this.i01*this.i12-this.M1s*this.i12-this.M2s)/(this.J0*(this.i01*this.i12)^2+this.J1*this.i12^2+this.J2a)
58 }
59
60
61 var width = window.innerWidth;
62 var height = window.innerHeight;
63 var le1 = 7;
64 var le2 = 3;
65 var re1 = 2;
66 var re2 = 0.3;
67 var lb1 = 9;
68 var rb1 = 3;
69 var rr1 = re1/c.i01;
70 var rb3 = rb1/c.i12;
71 var rr3 = rb1;
72
73 var texture = new THREE.TextureLoader().load( "texture.jpg" );
74 texture.wrapS = THREE.RepeatWrapping;
75 texture.wrapT = THREE.RepeatWrapping;
76 texture.repeat.set( 3, 3 );
77 var material = new THREE.MeshLambertMaterial({color: 0xFFC673,map:texture});
78
79 function physics(t,c) {
80
81 rr1 = re1/c.i01;
82 rb3 = rb1/c.i12;
83
84 ED.position.y = -re1-rr1;
85 B.position.y = rb1+rr3;
86 rot.remove(rot1);
87 rot1 = new THREE.Mesh( new THREE.CylinderGeometry( rr1, rr1, 0.01, 64 ), material );
88 rot1.rotation.z = - Math.PI / 2;
89 rot1.position.x = -le2/2-5;
90 rot1.castShadow = true;
91 rot.add( rot1 );
92 B.remove(B3);
93 B3 = new THREE.Mesh( new THREE.CylinderGeometry( rb3, rb3, 0.01, 64 ), material );
94 B3.rotation.z = - Math.PI / 2;
95 B3.position.x = le2/2-5;
96 B3.castShadow = true;
97 B.add( B3 );
98 B.position.y = rb3+rr3;
99
100 if (c.stop == false){
101 var w1,w0;
102 c.A2 = ((c.M0-c.M0s)*c.i01*c.i12-c.M1s*c.i12-c.M2s)/(c.J0*(c.i01*c.i12)^2+c.J1*c.i12^2+c.J2a);
103 if ((c.A2<0)&&(c.w2 <= 0)){
104 c.A2 = 0;
105 c.w2 = 0;
106 } else {
107 c.w2 = c.A2*t;
108 w1 = c.w2/c.i12;
109 w0 = w1/c.i01;
110
111
112 ED.rotation.x = t * w0*Math.pow(10, -3);
113 rot.rotation.x = - t * w1*Math.pow(10, -3);
114 B.rotation.x = t * c.w2*Math.pow(10, -3);
115 }
116 }
117
118
119
120 }
121
122 function init() {
123
124
125 container = document.createElement( 'div' );
126 document.body.appendChild( container );
127
128 scene = new THREE.Scene();
129 scene.background = new THREE.Color( 0xbfd1e5 );
130
131 camera = new THREE.PerspectiveCamera( 45, width / height, 0.1, 1000 );
132 camera.position.x = -20;
133 camera.position.y = 5;
134 camera.position.z = 20;
135 camera.lookAt(0,0,0)
136
137
138
139
140
141
142
143 var ambient = new THREE.AmbientLight( 0xffffff, 0.3 );
144 scene.add( ambient );
145
146 spotLight = new THREE.SpotLight( 0xffffff, 2 );
147 spotLight.position.set( -30, 45, 35 );
148 spotLight.angle = Math.PI / 3;
149 spotLight.penumbra = 0.05;
150 spotLight.decay = 2;
151 spotLight.distance = 200;
152 spotLight.castShadow = true;
153 spotLight.shadow.mapSize.width = 1024;
154 spotLight.shadow.mapSize.height = 1024;
155 spotLight.shadow.camera.near = 10;
156 spotLight.shadow.camera.far = 200;
157 scene.add( spotLight );
158
159
160 ED = new THREE.Object3D;
161 ED1 = new THREE.Mesh( new THREE.CylinderGeometry( re1, re1, le1, 64 ), material );
162 ED1.rotation.z = - Math.PI / 2;
163 ED1.position.x = -le1/2-3*le2/2-5;
164 ED1.castShadow = true;
165 ED.add(ED1);
166 ED2 = new THREE.Mesh( new THREE.CylinderGeometry( re2, re2, le2, 64 ), material );
167 ED2.rotation.z = - Math.PI / 2;
168 ED2.position.x = -le2-5;
169 ED2.castShadow = true;
170 ED.add(ED2);
171 ED3 = new THREE.Mesh( new THREE.CylinderGeometry( re1, re1, 0.01, 64 ), material );
172 ED3.rotation.z = - Math.PI / 2;
173 ED3.position.x = -le2/2-5;
174 ED3.castShadow = true;
175 ED.add( ED3 );
176 ED.position.y = -re1-rr1;
177 scene.add( ED );
178
179 rot = new THREE.Object3D;
180 rot1 = new THREE.Mesh( new THREE.CylinderGeometry( rr1, rr1, 0.01, 64 ), material );
181 rot1.rotation.z = - Math.PI / 2;
182 rot1.position.x = -le2/2-5;
183 rot1.castShadow = true;
184 rot.add( rot1 );
185 rot2 = new THREE.Mesh( new THREE.CylinderGeometry( re2, re2, le2, 64 ), material );
186 rot2.rotation.z = - Math.PI / 2;
187 rot2.position.x = -5;
188 rot2.castShadow = true;
189 rot.add( rot2 );
190 rot3 = new THREE.Mesh( new THREE.CylinderGeometry( rr3, rr3, 0.01, 64 ), material );
191 rot3.rotation.z = - Math.PI / 2;
192 rot3.position.x = le2/2-5;
193 rot3.castShadow = true;
194 rot.add( rot3 );
195 scene.add( rot );
196
197 B = new THREE.Object3D;
198 B1 = new THREE.Mesh( new THREE.CylinderGeometry( rb1, rb1, lb1, 64 ), material );
199 B1.rotation.z = - Math.PI / 2;
200 B1.position.x = lb1/2+3*le2/2-5;
201 B1.castShadow = true;
202 B.add(B1);
203 B2 = new THREE.Mesh( new THREE.CylinderGeometry( re2, re2, le2, 64 ), material );
204 B2.rotation.z = - Math.PI / 2;
205 B2.position.x = le2-5;
206 B2.castShadow = true;
207 B.add(B2);
208 B3 = new THREE.Mesh( new THREE.CylinderGeometry( rb3, rb3, 0.01, 64 ), material );
209 B3.rotation.z = - Math.PI / 2;
210 B3.position.x = le2/2-5;
211 B3.castShadow = true;
212 B.add( B3 );
213 B.position.y = rb3+rr3;
214 scene.add( B );
215
216 plane = new THREE.Mesh( new THREE.BoxGeometry( 2000, 1, 2000 ), new THREE.MeshPhongMaterial( { color: 0x679ED2, dithering: true } ) );
217 plane.position.y = - 15;
218 plane.receiveShadow = true;
219 scene.add( plane );
220
221 renderer = new THREE.WebGLRenderer();
222 renderer.setSize( width, height );
223 renderer.shadowMap.enabled = true;
224 renderer.shadowMap.type = THREE.PCFSoftShadowMap;
225 container.appendChild( renderer.domElement );
226
227 controls = new THREE.OrbitControls( camera,renderer.domElement );
228
229 var gui = new dat.GUI();
230 gui.add(c, 'i01',1,5);
231 gui.add(c, 'i12',1,5);
232 gui.add(c, 'J0',1,1000);
233 gui.add(c, 'J1',1,1000);
234 gui.add(c, 'J2',1,1000);
235 gui.add(c, 'M0',0,10);
236 gui.add(c, 'M0s',0,10);
237 gui.add(c, 'M1s',0,10);
238 gui.add(c, 'M2s',0,10);
239 gui.add(c, 'stop');
240 gui.add(c, 'restart');
241 gui.add(c, 'w2').listen();
242 gui.add(c, 'A2').listen();
243 }
244
245 function onWindowResize() {
246
247 camera.aspect = window.innerWidth / window.innerHeight;
248 camera.updateProjectionMatrix();
249
250 renderer.setSize( window.innerWidth, window.innerHeight );
251
252
253 }
254
255 //
256
257 function animate() {
258
259 requestAnimationFrame( animate );
260 render();
261 }
262
263 function render() {
264
265 var t = Date.now() - start;
266
267 physics(t,c)
268
269 ED.update;
270 B.update;
271 rot.update;
272
273 controls.update();
274
275 renderer.render( scene, camera );
276
277 }
278
279 init();
280 animate();
281
282
283 </script>
284 </body>
285 </html>
