臺灣博碩士論文加值系統

滾珠導螺桿、螺帽、鋼珠及回流管構成的系統，其主要功能可將旋轉運動換成線性運動，或將扭矩轉換為軸向反覆的作用力，為現今科技精密定位上不可或缺的元件。螺桿精度等級若屬於研磨級以上，製造商將提供累積導程誤差圖表，以期補償由旋轉換成直線位移在加工上所造成的誤差。然而，對於滾珠導螺桿之螺帽，至今仍無適合檢測其累積導程誤差之測量儀器。
本論文目的即為發展一套自動化檢驗滾珠螺帽累積導程誤差之量測系統。類似於螺桿檢測的方法，旋轉待測螺帽，並將固定在交插滾子滑動台的細長槓桿伸入螺帽內部，槓桿前端為配合螺帽溝槽大小的滾珠探頭並附著於螺帽溝槽內，使探頭在螺帽旋轉下不斷地被拉入內部。透過市售高解析度的旋轉編碼器與自行研發的奈米解析度光學尺系統，可將旋轉角度換算成理想直線位移，並與實際前進的位移進行比對，自動化檢測滾珠導螺桿之螺帽的累積導程誤差。
對於旋轉中的元件，其將經歷軸向之滑移、徑向偏心與角度的傾斜，進而造成量測系統誤差，因此必須先被消除與補償。本研究藉由旋轉主軸誤差數學模型的建立，並透過電容式位移計量測其誤差參數，首先消除了軸向滑移與角度傾斜對系統的影響；另外再透過壓電致動器結合自行設計的撓性絞鍊元件，藉由PID控制方法，將量測探頭保持與螺帽固定位置，相當於是直接補償了旋轉中螺帽徑向上的跳動，消除徑向偏心。
完成之滾珠螺帽動態導程量測儀，將實際對市售之滾珠螺帽進行檢測，並提供滾珠螺帽累積導程誤差之實驗數據與圖表。

Ballscrew is a precision mechanical component serving to convert rotational motion to linear motion in a precision linear stage. The measuring system for the screw’s accumulative lead error can be found on the market. Up to now, however, there is no suitable measuring machine for accumulative lead error measurement of the nut. It is known that this error directly reflects the grade of the nut.
This paper presents a developed automatic accumulative lead error measuring system for ballscrew nuts. Similar to the screw measuring system, the nut is clamped by a rotational stage and the probe ball is in contact with the groove of the nut. The probe is mounted on a cross roller table so that when rotating the nut the probe ball will be pulled by the groove wall and moved axially. A high resolution diffraction interferometer scale will read the linear movement of the probe to nanometer resolution. Combining the angular and linear motions the accumulative lead error can be realized.
In practice, however, the nut will experience axial slip, radial run-out, and tilt during the motion. These spindle-like rotating induced errors have to be compensated in order to guarantee precise measurement results. Based on the derived theoretical model of axial slip, the axial runout could be measured by placing capacitive displacement sensors to acquire the translational displacement of the spindle and the angle of the pitch. Furthermore, a sensor gap measurement system associated with a servo piezoelectric actuator stage has been developed for the purpose of radial runout compensation. A microprocessor based PID controller is established to real-time adjust the probe ball’s vertical position so as to remain contact with the nut groove.
Experimental results will show the applicability of this developed measuring system.

誌謝 i
中文摘要 ii
ABSTRACT iii
目錄 iv
圖目錄 vi
表目錄 x
第一章 緒論 1
1-1. 研究動機與目的 1
1-2. 參考文獻回顧 2
1-2-1. 螺紋輪廓量測 2
1-2-2. 螺紋節圓直徑量測 4
1-2-3. 螺紋節距量測 5
1-3. 研究方法與內容概要 10
第二章 傳動系統設計 11
2-1. 夾持治具 12
2-2. 傳動主軸 19
2-3. 馬達與軸聯結器 23
第三章 位移與角度量測模組設計 25
3-1. 位移量測模組設計 25
3-1-1. 光柵位移轉換原理與相關文獻 25
3-1-2. 位移正交訊號解碼測試 32
3-1-3. 位移量測模組組裝與校正 34
3-2. 角度訊號解析模組設計 37
3-2-1. 旋轉編碼器與細分電路 37
3-2-2. 光遮斷器原點 40
3-3. 量測探頭製作 41
3-4. 小結…… 42
第四章 轉動圓柱數學模型修正軸向與角度誤差 43
4-1. 轉動圓柱各項誤差定義 43
4-2. 轉動圓柱數學模型 45
4-3. 轉動圓柱數學模型應用於量測系統 48
第五章 徑向偏心誤差補償 50
5-1. 徑向偏心補償系統之設計概念 50
5-2. 壓電材料與撓性絞鍊之設計 51
5-2-1. 壓電材料介紹 51
5-2-2. 位移放大撓性絞鍊 54
5-2-3. 撓性絞鍊性能測試 56
5-3. PID控制法實踐徑向偏心補償 60
5-3-1. 偏心動態補償系統建模 63
5-3-2. 古典控制與Ziegler-Nichols整定法 65
5-4. 微處理機周邊電路與程式設計 68
第六章 實驗設計與結果 72
6-1. 轉動圓柱數學模型驗證實驗 72
6-1-1. 四爪夾頭調整偏心與傾角之方法 72
6-1-2. 轉動圓柱誤差模型驗證 73
6-2. 徑向偏心補償實驗 75
6-3. 滾珠導螺桿之螺帽動態導程誤差量測 78
第七章 結論與未來展望 84
7-1. 結果討論 84
7-2. 未來展望 86
參考文獻 88
附錄: 92
A.I 軸向位移公式化簡 92
A.II 偏轉角度代換 93

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