平面磨床離散式彈簧阻尼器支撐或具阻尼彈性基礎支撐動載台切削穩定性分析

Dynamics and Cutting Stability Analysis of the Worktable on Discrete Supports with Springs and Dampers or the Winkler Foundation with Damping of a Surface Grinder

查國強(K. C. Cha) ； 王能治(N. Z. Wang) ； 廖建義(J. Y. Liao)

《中華民國振動與噪音工程學會論文集》 2013 (2013/06) Pp. 65-72

摘要

本文探討離散式彈簧阻尼器支撐或具阻尼彈性基礎支撐動載台動態特性與切削穩定性分析。當平面磨床砂輪加工時，工作台是假設依據兩端自由條件的尤拉－伯努利樑理論，由於工作台連續性位置的改變，系統控制方程式變得複雜。利用Lagrange能量法結合自由樑彈性與剛體模態疊加之假設模態展開法，推導多自由度系統動力方程式，建立多組離散式彈簧阻尼器支撐或具阻尼彈性基礎支撐動載台狀態空間模型，以整機結構之動柔度最大負實部的絕對值與極限切削寬度作為性能指標，探討不同型式支撐動載台模型於不同位置時的結構靜、動態特性，並以彈簧阻尼器支撐組數、支撐位置不同、基礎分佈剛度與分佈阻尼等變化，探討這些參數對系統動態性能影響，依據再生型顫振效應與穩定性理論，分析3D穩定性葉瓣曲線圖，並以時域分析模擬佐證，對平面磨床設計與動態性能改善與提升有參考價值。

關鍵字

平面磨床 ； 離散式彈簧阻尼器支撐動載台 ； Winkler基礎 ； 假設模態展開法 ； 穩定性葉瓣曲線

並列摘要

This paper focuses on the dynamic characteristics and the cutting stability for the worktable on discrete supports with springs and dampers or the Winkler foundation with damping of a surface grinder on elastic supports in a surface grinder. When the worktable of the surface grinder is in operation, the dynamics of the worktable is assumed to comply with the Euler-Bernoulli beam theory. The operating worktable is usually dynamically loaded in variable positions, which makes the analysis of dynamics and stability of the worktable complicated. In this study, the assumption of elastic and rigid body modes of a free-free beam is specified for the worktable. By combining the Lagrange energy method with the technique of assumed mode expansion, the system dynamic equations with multiple degrees of freedom are derived and state space models for the dynamically loaded worktable subjected to discrete supports with springs and dampers or foundation are developed. The absolute value of the maximum negative real part of the overall structural dynamic compliance and the limiting chip width are used as the performance indicators to evaluate the structural static and dynamic characteristics of the worktable during simulated machining. The influences of these parameters on the dynamic performance of the system are explored under various positions. The parameters include the number of supports with the springs and dampers, supported position change, the distributed stiffness and damping coefficients of foundation. Furthermore, based on the regenerative chatter and the stability theory for the case studied, the 3D stability lobes diagram is used to provide the maximum depth of cut at the highest available spindle speed. The cutting stability is verified by comparing the results obtained in time-domain analysis with the lobe diagram. The procedure illustrated in this study to improve the dynamics performance of a surface grinder can also be implemented in a similar fashion for many machine tool applications.

並列關鍵字

Surface grinder ； Dynamically loaded worktable with discrete supports ； The Winkler foundation ； Assumed mode expansion ； Stability lobe diagram Grinding