【正文】 t , but the displacement of the tool with respect to the workpiece. In the vertical machining center under investigation , the thermal errors are the bination of the expansion of spindle , the distortion of the spindle housing , the expansion of three axes and the distortion of the column. Due to the dimensional elongation of leadscrew and bending of the column , the thermal errors are not only timevariant in the time span but also spatialvariant over the entire machine working space. In order to measure the thermal errors quickly , a simple protable gauge , i. e. , 1D ball array , is utilized. 1D ball array is a rigid bar with a series of balls fixed on it with equal space. The balls have the same diameter and small sphericity errors. The ball array is used as a reference for thermal error measurement . A lot of preexperiment s show that the thermal errors in zaxis are far larger than those in xaxis and yaxis , therefore major attention is drawn on the thermal errors in zaxis. Thermal errors in the other two axes can be obtained in the same way. The measuring process is shown in . A probe is mounted on the spindle housing and 1D ball array is mounted on the working table. Initially , the coordinates of the balls are measured under cold condition. Then the spindle is run at a testing condition over a period of time to change the machine thermal status. The coordinates of the balls are measured periodically. The thermal drift s of the tool are obtained by subt racting the ball coordinates under the new thermal status f rom the reference coordinates under initial condition. Because it takes only about 1 min to finish one measurement , the thermal drifts of the machine under different z coordinates can be evaluated quickly and easily. According to the rate of change , the thermal errors and the rotation speed are sampled by every 10 min. Since only the drift s of coordinates deviated from the cold condition but not the absolute dimensions of the gauge are concerned , accuracy and precise inst rument such as a laser interferometer is not required. There are only four measurement point s z 1 ,z 2 , z 3 , z 4 to cover the zaxis working range whose coordinates are 50 , 150 , 250 , 350 respectively. Thermal errors at other coordinates can be obtained by an interpolating function. Previous experiment s show that the thermally induced displacement between the spindle housing and the working table is the same with that between the spindle and table. So the thermal errorsΔ z measured reflect those in real cutting condition with negligible error. In order to obtain a thorough impression of the thermal behavior of the machine tool and identify the error model accurately , a measurement strategy is developed. Various loads of the spindle speed are applied. They are divided into three categories as the following : (1) The constant speed 。首先，對(duì)機(jī)床的多個(gè)點(diǎn)進(jìn)行熱量誤差和溫度的測(cè)量是不可取的。大量的之前試驗(yàn)數(shù)據(jù)表明在光軸上的熱量誤差遠(yuǎn)遠(yuǎn)高于在橫軸和縱軸。他們被分為如下三類： 1，常規(guī)轉(zhuǎn)速， 2，轉(zhuǎn)速范圍， 3，真正切割狀態(tài)下的同步轉(zhuǎn)速。外部熱源對(duì)機(jī)床精確度的影響能夠通過環(huán)境溫度來控制。如圖 6所示，用表面磨碎的深度不同來評(píng)估在 z方向的熱量誤差結(jié)果補(bǔ)償。 誤差補(bǔ)償?shù)挠行允怯稍S多切割試驗(yàn)來證實(shí)的。另外，在眾多的實(shí)用中，利用以 經(jīng)驗(yàn)為基礎(chǔ)的誤差模型進(jìn)行回歸分析和網(wǎng)絡(luò)分析來準(zhǔn)確預(yù)測(cè)熱量誤差是不可能的。 為了能夠獲得機(jī)床熱量行為的全面理解以及正確的判斷誤差模型，形成了一種測(cè)量方法。滾珠排列是把一系列的滾珠按相等的間隔固定在頂梁上。 在加工期間，誤差是根據(jù)之前建立的模型進(jìn)行預(yù)測(cè)并通過在實(shí)際過程中用額外的信號(hào)和自由回路進(jìn)行改正的。 (2) The speed spect rum 。其次，溫度傳感器的線會(huì)或多或少影響機(jī)器的運(yùn)轉(zhuǎn)。所以，熱量誤差主要關(guān)注在光軸上。此處，由切割過程而引起的熱量作用沒有被考慮進(jìn)來。根據(jù)已有的數(shù)據(jù)發(fā)現(xiàn)熱量誤差的改變是和時(shí)間成正比的。試驗(yàn)表明這種不同由 7μm 減少到 2μ