臺灣博碩士論文加值系統

火砲射擊時彈丸和砲管的交互作用會造成砲管側向位移並因而導致彈丸出砲口時側向偏移，同時也造成彈丸外彈道的不良影響，而其結果將導致射擊精度的降低。考慮彈丸在砲管中的運動過程，彈丸/砲管交互作用之動態分析著眼於彈丸出砲口瞬間砲口的位移。因此，真實的預測彈丸對砲管側向運動的影響而對全砲系統進行動態分析是有必要的。
本文以尤拉樑方程式建立均勻砲管側向運動的模型並用彈性支撐來模擬砲管座，支撐端模擬成有側向與扭轉位移，砲管受力來源主要為運動彈丸之重力、慣性力及砲管/彈丸交互作用時彈殼產生之彈簧力。運用Vallier-Heydenreich表解法可計算出膛壓曲線並獲得彈丸位移曲線。以消去法將彈丸/砲管的耦合運動方程式簡化成一微分方程式，藉由電腦程式的建立可計算出彈丸/砲管交互作用的動態行為。經過分析後，我們可以得到以下幾點結論是有利於火砲射擊時振動之抑制：(1)增加彈丸運動速度(2)增加支撐端側向及扭轉彈簧勁度(3)增加砲管厚度(4)降低彈丸(殼)勁度。

While firing a gunshot, the yawing motion of the gun tube made by the projectile/gun tube interaction leads to yaw of the projectile at exit. This results in improper exterior ballistic free fright of the projectile and the resultant inaccuracy of the shot. The most critical point considering the projectile/gun tube dynamic behavior during a projectile’s travel within gun tube occurs at the instant of shot ejection. Therefore, a realistic prediction of the yawing motion of the projectile/gun tube is necessary when doing the gun tube system dynamic analysis.
The Euler beam equation model of a uniform gun tube is solved with elastic supports, which simulated the tube mount. Both transverse and rotational displacements of the supports are permitted. The beam loadings account for the moving projectile’s gravity force, inertial force and the sabot’s stiffness force. The Vallier-Hendereich method is introduced to calculate the chamber pressure curve and the projectile motion curve is obtained afterwards. The equations of motion for the projectile/gun tube system are coupled. The solution to these equations can be obtained by elimination method. A computer program was established to calculate the projectile/gun tube dynamic response. After the analysis, several conclusions, which are good for control the vibrations of the gunfire, were obtained: (1)to increase the velocity of the projectile; (2)to increase the transverse and rotational spring stiffness; (3)to increase thickness of the tube and (4)to decrease the sabot stiffness.

1. 緒論 1
1.1. 研究背景 1
1.2. 研究方法及目的 4
1.3. 文獻回顧 5
1.4. 論文大綱 6
2. 砲管的數學模型及解析方法 8
2.1. 砲管之統御方程式推導 8
2.1.1. 均勻樑運動方程式 9
2.1.2. 砲管自由振動 11
2.1.3. 模態振動的正交性 12
2.1.4. 砲管強制振動 13
2.2. 砲管的邊界條件設定 15
2.3. 模態驗證 17
2.3.1. 特徵方程式 17
2.3.2. 模態函數 18
3. 彈丸模型及內彈道運動方程式 23
3.1. 彈丸模型 23
3.2. 內彈道推導 24
3.2.1. Vallier-Heydenreich表解法 24
3.2.2. 砲管/彈丸彈道曲線 26
4. 運動方程式之建立 32
4.1. 砲管/彈丸統御方程式 32
4.2. 程式驗證 37
4.2.1. 簡支樑動態與靜態撓動比 37
4.2.2. 懸臂樑動態與靜態撓動比 39
5. 動態響應模擬與模型驗證 43
5.1. 砲管受等速運動之外力作用 44
5.2. 砲管受加速運動之外力作用 45
5.3. 砲管受移動重力、慣性力之交互作用 46
5.4. 砲管與脫殼彈交互作用 47
5.5. 結論 47
6. 不同參數的動態響應分析 55
6.1. 不同邊界條件之砲口端/彈丸位移變化 55
6.2. 不同厚度砲管之砲口端/彈丸位移變化 55
6.3. 不同勁度彈丸之砲口端/彈丸位移變化 56
6.4. 結論 57
7. 結論與建議 62
7.1. 結論 62
7.2. 建議 63
參 考 文 獻 65
附錄A. 樑之撓度曲線方程式 67
A.1. 彎曲公式推導 68
A.2. 撓度曲線微分方程式推導 69
附錄B. 砲管頻率方程式的 值 72
自 傳 75

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