滾珠螺桿進給系統振動抑制技術之探討;Investigations of Vibration Reduction Techniques for Ball Screw Feed Drive Systems

[[abstract]]本研究的主要目的是探討工具機進給系統在進給時的動態行為與其應用不同馬達扭矩進行振動抑制的效果比較。本文首先簡化滾珠螺桿進給系統，並以彈簧、阻尼與質量塊的組合表示工作台、聯軸器、馬達等元件，以樑表示螺桿，亦即螺桿的軸向與扭轉自由度以假設模態法來表示，接著使用Lagrange能量法推導運動方程式，再由運動方程式可以求得滾珠螺桿進給系統之頻率響應與模態振型，最後以?格-庫塔(Runge Kutta)數值積分法求解其系統各個自由度之動態響應。模擬結果顯示工作台軸向速度受到平台自然振動的影響，會以工作台理想軸向速度為基準產生自由振動，而本研究的後半部探討改變馬達扭矩對於工作台之動態影響；其中藉由使用固定頻寬式濾波器、追蹤頻率式濾波器、S形加減速曲線與輸入修正法等振動抑制的方法，在不需要外掛各種減振系統的狀況下，比較出各種方法之優缺點與適合使用之時機。結果顯示改變加速曲線對於振動抑制的效果最為卓越，但使用此方法在加減速時進給系統與工件需承受較大的加速度，而使用輸入修正法之ZV法(Zero -Vibration)在對於單一頻率之振動抑制時有不錯的效果，但對於多頻率之振動抑制的效果較差；然而使用改良後的ZVDD法(Zero-Vibration and Second Derivatives)對於多頻率的振動抑制的效果雖然比ZV法優異許多，但依然無法使用於頻率範圍太廣之振動抑制。最後則是使用濾波器，使用固定頻寬式濾波器雖有不錯的振動抑制效果，但波範圍太大，容易產生訊號失真的現象。而追蹤頻率式濾波器，主要是以欲濾除頻率為中心展開一濾除頻帶，因此可大幅減少濾波頻寬，進而有效的改善因濾除頻段範圍過廣所造成訊號失真的現象。 The main purpose of this study is to compare the effectiveness in vibration reduction of a ball screw feed drive system with various vibration reduction techniques. A simplified ball screw feed drive system which consists of the work table, coupler, motor and ball screw shaft has been created. The ball screw shaft is modeled as a structural beam, whereas the other components are modeled equivalently as the combination of spring, damper and mass. The Lagrange method is utilized to the equation of motion and the resulting vibration response is then obtain by the Runge Kutta numerical integration scheme. Several methods such as filter of fixed frequency bandwidth, tracking filter, S-shaped input torque and input shaping are respectively adopted to suppress the work table vibration while the work table is driven by a motor speed control command input. Results show that S-shaped input torque is most effective among all the methods in suppressing the worktable vibration. The ZV (Zero-Vibration) technique from the input shaping method has a good performance for suppressing the pure tone vibration, but poor for multi-tone excitations. The ZV technique is further improved by the modified ZVDD (Zero-Vibration and Second Derivatives) technique, but ZVDD is still not satisfactory for broad band excitations. For filtering out the worktable natural frequency out of the input torque, the adaptive filter performs in reducing the work table vibration better than that of filter of fixed bandwidth due to less distortion in the input torque. However, the filtering techniques are more complicated in implement and perform poorly in reducing the work table vibration as compared to input shaping and S-shaped input