橢圓形端板的算法比較/ Comparison of algorithms for elliptical end plates

橢圓形端板的算法比較/ Comparison of algorithms for elliptical end plates

1. 端板設計參數說明

  • P : 設計內壓, MPa
  • D : 端板內徑, mm
  • h : 橢圓形端板內部短徑的一半, mm
  • S : 端板材料在設計溫度下的容許應力, N/mm2
  • E : 端板之焊接係數
  • R : 碟形端板內球面或頂冠的半徑, mm
  • r0 : 端板彎折處的半徑, mm ； r0 >= 0.06*(D+2t) , r0 >= 3t (JIS B 8265, E.3)
  • t : 端板成形後最小需要的厚度, mm

Figure 1: 橢圓形端板示意圖

Figure 2: 碟形端板示意圖

1.1. Maxima 原始碼

/* 端板參數 */

P:1.0;
D:1230.0;
h:307.5;
S:138.0;
E:0.85;

/* 2:1 近似半橢圓形端板*/
R: D * 0.9045;
r0: D* 0.1727;

2. 橢圓形端板公式

使用 JIS B 8265 E.3.4，內徑基準

2.1. Maxima 原始碼

/* 橢圓形端板內壓計算, JIS B 8265 E.3.4, 內徑基準*/

thickness_elliptical(P,D,h,S,E) := block([K:1/6*(2+(D/(2*h))^2)],
  (P*D*K)/(2*S*E-0.2*P));


thickness[elliptical]:thickness_elliptical(P,D,h,S,E);

printf(true,"~&2:1 半橢圓形端板計算厚度 ~,3f mm~%",thickness[elliptical]);

3. 碟形端板公式

使用 JIS B 8265 E.3.3, 內徑基準

3.1. Maxima 原始碼

/*碟形端板(Torispherical Heads), JIS B 8265 E.3.3, 內徑基準 */

thickness_torispherical(P,R,r0,S,E) := block([M: 1/4 *(3+sqrt(R/r0))],
  (P*R*M)/(2*S*E-0.2*P));

thickness[torispherical]:thickness_torispherical(P,R,r0,S,E);

printf(true,"~&2:1 近似半橢圓形端板計算厚度 ~,3f mm~%",thickness[torispherical]);

4. 2:1 橢圓形端板與近似半橢圓形端板的計算結果

2:1 半橢圓形端板計算厚度 5.247 mm
2:1 近似半橢圓形端板計算厚度 6.275 mm

Figure 3: 將二個端板外形放在一起比較

5. 授權條款/ License

Copyright (C) 2024 Each Application Mechanical Design Studio

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

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