郭航言，康敏,2，周瑋

慢刀伺服車削刀具補(bǔ)償算法優(yōu)化

郭航言1，康敏1,2，周瑋1

（1.南京農(nóng)業(yè)大學(xué) 工學(xué)院，南京 210031；2.江蘇省智能化農(nóng)業(yè)裝備重點(diǎn)實(shí)驗(yàn)室，南京 210031）

慢刀伺服；刀具路徑；坐標(biāo)變換；幾何補(bǔ)償；表面粗糙度；面型精度

與普通光學(xué)曲面相比，復(fù)雜光學(xué)曲面具有獨(dú)特的光學(xué)性能，如簡化光學(xué)系統(tǒng)、優(yōu)化成像質(zhì)量等，故其應(yīng)用領(lǐng)域廣泛[1-5]。例如，環(huán)曲面是一種典型的非球狀類復(fù)雜光學(xué)曲面，具有較好的光學(xué)特性，可以在2個(gè)相互垂直的方向上形成不同的屈光度[6]。基于這一特性，環(huán)曲面鏡片廣泛應(yīng)用于矯正散光[6-7]。但是，傳統(tǒng)的車削加工工藝難以滿足復(fù)雜光學(xué)曲面（如環(huán)曲面）的質(zhì)量要求。慢刀伺服車削技術(shù)作為新興的超精密加工方法，具有較高的加工效率和較好的加工質(zhì)量，近年來已經(jīng)應(yīng)用于復(fù)雜光學(xué)曲面的車削加工[8-12]。

1 刀具路徑規(guī)劃

以環(huán)曲面為例，對(duì)慢刀伺服車削刀具路徑規(guī)劃流程進(jìn)行說明，如圖1所示。首先，根據(jù)環(huán)曲面的數(shù)學(xué)表達(dá)式建立相應(yīng)的三維模型和數(shù)學(xué)模型，用于面型分析和刀具路徑仿真分析；然后，利用刀觸點(diǎn)生成算法將環(huán)曲面離散為一系列刀觸點(diǎn)，得到相應(yīng)的刀觸點(diǎn)軌跡；最后，利用刀具補(bǔ)償算法求解計(jì)算一系列刀位點(diǎn)坐標(biāo)，得到相應(yīng)的刀位點(diǎn)軌跡，從而獲得可以用于數(shù)控加工的代碼[17,22]。

1.1 刀觸點(diǎn)生成

目前，常用的刀觸點(diǎn)生成方法是等參數(shù)生成方法，包括等角度法和等弧長法2種[16-17,21]。等角度法的優(yōu)點(diǎn)是算法簡單、編程容易實(shí)現(xiàn)；但缺點(diǎn)是對(duì)于直徑較大的工件，工件外圈的刀觸點(diǎn)存在較大的離散誤差，而內(nèi)圈離散誤差較小，導(dǎo)致工件外圈的加工質(zhì)量相對(duì)較差。等弧長法的優(yōu)點(diǎn)是離散誤差受工件直徑的影響較小，基本保持穩(wěn)定；但缺點(diǎn)是算法比較復(fù)雜，且無論工件直徑較大或較小，工件內(nèi)圈都會(huì)存在較大的離散誤差[16-17,21]?；谶@2種方法的優(yōu)缺點(diǎn)，對(duì)于直徑不是很大的工件，多采用等角度法。因此本文提出的算法和開展的試驗(yàn)，均在等角度法的基礎(chǔ)上進(jìn)行。采用等角度法生成的刀觸點(diǎn)軌跡方程可用式(1)表示。

圖1 慢刀伺服車削刀具路徑規(guī)劃流程

1.2 刀具補(bǔ)償

由于車削所用刀具的刀尖帶有圓弧半徑，在車削加工中，刀尖與工件的接觸點(diǎn)（稱為刀觸點(diǎn)）并非固定點(diǎn)，而是刀尖圓弧上一系列變化的點(diǎn)，因此需要尋找一固定點(diǎn)來確定刀具的位置（該固定點(diǎn)稱為刀位點(diǎn)），所以需要進(jìn)行刀具形狀補(bǔ)償[23-24]。

1.2.1 坐標(biāo)變換

圖2 直角坐標(biāo)系下求解存在的問題

圖3 坐標(biāo)系變換圖

1.2.2 幾何補(bǔ)償

圖4 基于坐標(biāo)變換的幾何補(bǔ)償算法原理圖

2 仿真分析

為了檢驗(yàn)本文提出的補(bǔ)償算法的合理性，選擇環(huán)曲面利用Matlab軟件編寫相應(yīng)程序進(jìn)行仿真分析，環(huán)曲面方程可用式(7)表達(dá)[26]。仿真時(shí)，取h=140 mm，=100 mm，離散角Δ=8°，進(jìn)給速度f=1 mm/r，工件半徑w=20 mm，刀尖圓弧半徑t=140 mm，刀具前角=0°，后角=10°。

圖5 不同算法下的結(jié)果對(duì)比

圖6 刀具路徑仿真結(jié)果

3 試驗(yàn)驗(yàn)證

根據(jù)上述刀具補(bǔ)償算法的理論研究和仿真分析，對(duì)仿真結(jié)果進(jìn)行試驗(yàn)驗(yàn)證。首先，針對(duì)上述不同算法，利用Matlab軟件編寫了適用于慢刀伺服車削并能自動(dòng)生成加工代碼的程序。然后，在本實(shí)驗(yàn)室自行研制的實(shí)驗(yàn)裝置上完成了環(huán)曲面的加工，用于驗(yàn)證本文提出的刀具補(bǔ)償算法的可行性。圖7為本實(shí)驗(yàn)室自行研制的高精度慢刀伺服車削平臺(tái)。加工的工件材料為聚甲基丙烯酸甲酯（PMMA），進(jìn)給速度f=0.01 mm/r，切削深度p=0.04 mm，其余參數(shù)參照上述仿真程序。

圖7 高精度慢刀伺服車削平臺(tái)

圖8 在不同刀具補(bǔ)償算法下加工得到的環(huán)曲面工件

圖9 表面粗糙度的測(cè)量方法

為評(píng)價(jià)加工的環(huán)曲面工件的面型精度，使用MQ686三坐標(biāo)測(cè)量機(jī)對(duì)工件表面的面型進(jìn)行測(cè)量。經(jīng)過數(shù)據(jù)處理后，得到面型誤差分布情況，如圖11所示。得到環(huán)曲面的面型誤差后，計(jì)算面型誤差最大值和最小值的差值，就可以得到環(huán)曲面的面型精度，面型精度用（Peak-to-Valley）表示[17]。

圖10 不同刀具補(bǔ)償算法下得到的表面粗糙度測(cè)量結(jié)果

圖11 不同刀具補(bǔ)償算法下得到的面型誤差分布情況

4 結(jié)論

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Optimization of Tool Compensation Algorithm for Slow Tool Servo Turning

1,1,2,1

(1. College of Engineering, Nanjing Agricultural University, Nanjing 210031, China;2. Key Laboratory of Intelligence Agricultural Equipment of Jiangsu Province, Nanjing 210031, China)

In order to improve the surface quality of complex surface in slow tool servo turning, the tool compensation algorithm was optimized.In view of the problems that normal compensation algorithm can easily lead to the decrease of the dynamic performance of-axis and large interpolation error in-direction compensation algorithm, a geometric compensation algorithm based on coordinate transformation was proposed in this paper.Coordinate transformation can improve the accuracy of the solution and simplify the algorithm.By using the geometric transformation relationship, the compensation component of-axis could be concentrated on the-axis, which not only ensured the dynamic performance of-axis, but also reduced the interpolation error.Taking the toric surface as an example, the tool compensation algorithm proposed in this paper was simulated and verified by experiments.The simulation results showed that the velocity of-axis fluctuates greatly under the normal compensation algorithm, while the-axis can keep uniform motion under the algorithm proposed in this paper.In the tool compensation link, compared with the algorithm proposed in this paper, the interpolation error under-direction compensation algorithm was larger, and the maximum interpolation error was more than 0.015 mm.The experimental results showed that the value of surface roughness of the toric surface was the largest under the normal compensation algorithm (=0.112 μm), which was much larger than that under the-direction compensation algorithm and the algorithm proposed in this paper.However,under the-direction compensation algorithm and the algorithm proposed in this paper,the value of surface roughness of the toric surface was similar (=0.066 μm and=0.062 μm respectively), which indicates that the tool compensation algorithm has little effect on the surface roughness on the premise of ensuring the dynamic performance of-axis.The values ofobtained under the normal compensation algorithm, the-direction compensation algorithm and the algorithm proposed in this paper was 16.9 μm, 13.8 μm and 8.8 μm respectively. Compared with normal compensation algorithm and-direction compensation algorithm, the accuracy of toric surface was improved by 92.0% and 56.8% respectively under the algorithm proposed in this paper, which shows that the tool compensation algorithm proposed in this paper can improve the surface machining quality.

slow tool servo; tool path; coordinate transformation; geometric compensation; surface roughness; form error

TG506

A

1001-3660(2022)04-0308-09

10.16490/j.cnki.issn.1001-3660.2022.04.032

2021-05-21；

2021-09-25

2021-05-21；

2021-09-25

2019江蘇省現(xiàn)代農(nóng)機(jī)裝備與技術(shù)示范推廣項(xiàng)目（6026A9）

Supported by the Demonstration and Extension Project of Modern Agricultural Machinery Equipment and Technology in Jiangsu Province in 2019 (6026A9)

郭航言（1998—），男，碩士研究生，主要研究方向?yàn)閿?shù)控加工技術(shù)。

GUO Hang-yan (1998—), Male, Postgraduate, Research focus: numerical control processing technology.

康敏（1965—），男，博士，教授，主要研究方向?yàn)樘胤N加工技術(shù)。

KANG Min (1965—), Male, Doctor, Professor, Research focus: special processing technology.

郭航言, 康敏, 周瑋. 慢刀伺服車削刀具補(bǔ)償算法優(yōu)化[J]. 表面技術(shù), 2022, 51(4): 308-316.

GUO Hang-yan, KANG Min, ZHOU Wei. Optimization of Tool Compensation Algorithm for Slow Tool Servo Turning[J]. Surface Technology, 2022, 51(4): 308-316.

責(zé)任編輯：萬長清