骨螺絲幾何對鎖入力矩影響之數學模型

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姓名

康銘仁(Ming-Jen Kang) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

骨螺絲幾何對鎖入力矩影響之數學模型
(Mathematical Model of Thread Shape and Thread Profile on Insertion Torque of the Bone Screw)

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摘要(中)

骨螺絲在牙科與骨科領域中已成為臨床相當普遍的零件，儘管如此，骨螺絲失效的案例依然層出不窮。當骨螺絲發生斷裂或鬆脫時將導致手術失敗、二次手術與延遲癒合等問題。現今研究認為鎖入力矩與骨螺絲鎖入的初始穩定度相關，足夠的鎖入力矩可以提供較高的穩定度。然而，也有研究指出過高的鎖入力矩可能導致骨螺絲斷裂、骨頭壞死與延遲癒合。影響鎖入力矩的因素有螺絲幾何參數、骨頭強度以及預鑽孔的大小。
本研究目的在於將過去應用於工程自鑽螺絲之數學模型，修改至適用齒科螺絲，並評估不同牙型、螺絲錐度與預鑽孔對鎖入力矩的影響。藉由材料力學觀點來探討螺絲在骨頭中攻牙與摩擦過程的兩種行為。為了驗證理論推導模型的正確性，利用四支齒科螺絲的理論預測與實際測詴結果進行比對，結果顯示牙型有較高的準確性，然而，螺絲錐度在不同預鑽孔的準確性較低。作者認為螺絲錐度與預鑽孔在理論模型中應仔細考慮螺牙表面應力與摩擦係數。
本論文之研究成果在機械力學與材料力學基礎下提供了骨螺絲幾何參數對鎖入力矩之影響的數學模型。給予工程領域的設計人員在研發新型骨螺絲的依據。

摘要(英)

In clinical application, although bone screws became the general parts in the orthodontic and orthopaedic domains, the cases of screw failure were emerged in endlessly. When screw fractured or loosened, it would cause surgery fail, secondary operation, and delayed union. Current researches considered that the initial primary stability during inserted process was correlated to insertion torque; the enough torque can provide higher stability. However, some researches also pointed out the excessive insertion torque might cause fracture of implants, bionecrosis of bone tissue, and delayed union. The influence of factors on insertion torque were geometry of screw、strength of bone and the diameter of pilot hole.
This study improved a mathematical model of the engineering self-tapping screw fastening process in previous research, so that it could be used in dental implants to estimate the influence of difference on thread profile、taper of screw and pilot-hole on insertion torque. The two behaviors of removal and friction in bone was probe by concept of mechanics of materials.To confirm the accuracy of the model, four dental implants were used in this research. Besides, experimental results for torque tester and predictions of the mathematical model were compared. The results appeared high accuracy in thread shape test. However, the results in the taper of screw test showed low accuracy. The author suggested that stress on the surface of thread and coefficient of friction be considered carefully.
The results of this research provided the influence of geometry of bone screws on insertion torque in the fundamental of mechanics and materials, and assist design engineers in developing new bone screws.

關鍵字(中)

★ 鎖入力矩
★ 骨螺絲
★ 失效
★ 數學模型
★ 初始穩定度

關鍵字(英)

★ Mathematical model
★ Bone screw
★ Failure
★ Insertion torque
★ Initial stability

論文目次

摘要 i
Abstract ii
致謝文 iv
目錄 v
圖目錄 vii
表目錄 ix
符號說明 x
第一章緒論 1
1.1 研究背景 1
1.1.1 齒科螺絲 1
1.1.2 創傷螺絲 4
1.1.3 脊椎螺絲 5
1.1.4 骨螺絲常見的破壞模式 6
1.2 研究目的 7
1.3 研究方向 9
1.4 研究架構 10
第二章文獻回顧 12
2.1 齒科螺絲在旋入期間的破壞 12
2.2 鎖入力矩與初始穩定度之關係 13
2.3 工程螺絲旋緊過程之理論模型 14
2.4 延性與脆性材料之破壞準則 17
2.4.1攻牙力矩延性材料受平面應力作用之降伏準則 17
2.4.2脆性材料受平面應力作用之破裂準則 20
2.4.3本研究使用之準則 21
第三章材料與方法 23
3.1 螺絲幾何 23
3.2 鎖入過程理想條件 25
3.3 座標系統 27
3.4 使螺絲前進的軸向力矩 28
3.4.1攻牙力矩 29
3.4.2攻牙力矩推導 30
3.4.3摩擦力矩 39
3.4.4摩擦力矩推導 41
3.5 數學模型之理論預測 49
3.5.1骨螺絲在旋入過程之力學效應 49
3.5.2程式模擬計算 50
3.6 鎖入扭矩實驗 50
3.6.1不同牙形之鎖入力矩比較 52
3.6.2不同預鑽孔與錐度之鎖入力矩比較 52
3.6.3受測螺絲之幾何參數 53
3.6.4受測骨頭之材料參數 55
3.6.5預鑽孔洞程序 56
第四章研究結果 57
4.1 不同牙形之鎖入力矩 57
4.2 不同預鑽孔與錐度之鎖入力矩 60
第五章討論與結論 65
5.1 討論 65
5.2 結論 73
參考文獻 75
附錄一 79
附錄二 81

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指導教授

林上智(Shang-Chih Lin)

審核日期

2010-7-19

推文