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Measurement of Cone Shaft and Cone Sleeve of High-speed Wire Rolling Mill’s Roller ABSTRACT To obtain good assembly performance when transferring roll moment, a cone fit is adopted between cone shaft and cone sleeve of roller of high-speed wire rolling mill. This paper introduces an automatic cone measuring method, dissertates the principle of taking reference cylindrical surface of the roller as measuring reference to measure cones, and the main characteristics of the associated horizontal automatic cone measuring instrument. Measuring error of the instrument is also analyzed. The instrument uses grating transducers for cone diameter measurements and for axial positioning of transducer. The measuring error for diameter measurement is 1.4μm,the axial positioning error is less than 0.01mm, and the relative error for taper measurement is less than 2×10-3.Since the instrument is equipped with data acquisition system, many parameters and actual profile of the measured cone can be obtained according to the collected measuring data. Furthermore, virtual assembly of corn shaft with cone sleeve can be carried out on the computer, and the actual assembly effect of cone shaft with cone sleeve can be observed so that selective assembly with higher accuracy can be realized to the fullest extent. Keywords: rolling mill, roller, grating transducer, stepping motor, virtual assembly 1. INTRODUCTION Compared with smooth cylindrical fit, cone fit has advantages of automatic alignment, higher coaxiality, easy to adjust the degree of tightness, closer fit, easy to disassemble, etc. Therefore, it is widely used in mechanical facilities. Now, the rolling speed of high-speed wire rolling has exceeded 100m/s. To adapt to this speed, cone fit with good performance must be adopted between cone shaft and cone sleeve of high-speed wire rolling mill’s roller otherwise the roller of the mill will have some run-out so that the rolling speed and rolling benefit can’t be ensured. The inspection of the cone has two methods: composite inspection and monomial inspection. Cone gauges are used for composite inspection while goniometers, indexes, sine bars, angular blocks are used in monomial inspection for measuring parameters of cone tolerance[2]. This paper introduces an automatic cone measuring method, together with an associated horizontal automatic cone measuring instrument. The instrument measures cone shaft and cone sleeve under the condition that taking reference cylindrical surface of the roller as measuring reference. Parameters of the roller are: the maximum diameter of measured cone shaft is 241mm,the length range of measured cone shaft is 647mm~985mm, the maximum diameter of measured cone sleeve is 192mm, the length range of measured cone sleeve is 647mm~985mm and the normal taper of measured cone is 1:12. The tolerance requirement of the cone is that the allowable variation in diameter should be within 1±0.003mm when axial displacement is 12mm[1]. 2. PRINCIPLE OF MEASUREMENT Two grating transducers are located at both side of the cone, they are parallel and at right angle with the axis of the cone. The measurement begins at the bigger end of measured cone to ensure the measuring accuracy. The size of the diameter measured equals to the sum of the two transducer readings. One measurement is done for every 0.9o rotation of the cone, i.e. 400 measurements are done for a full circumference. One circumference measurements are done for every 1mm axial interval. The measuring procedure ends when measurements for the circumference at the smaller end of the cone have completed .At the section which is L apart from bigger end (the diameter is D) of the cone, Assume that the theoretical diameter of the section is d, measured diameter is C = (D ? d ) / L (1) d = D ? C - L (2) D = d ? d = d ? (D ?-L) = d + L ? D (3) Where C is the normal taper of the cone, d is the measuring error of diameter sleeve of the roller, the allowable variation in diameter should be within10.003mm when axial displacement is 12mm. Therefore,the measuring error of the instrument for measuring diameter should not exceed 3 m. 3. COMPOSITION OF THE INSTRUMENT Fig.1 automatic cone measuring instrument The instrument consists of four parts: mechanical system, measuring system, dada acquisition system and data processing system, control system for axial movement and radial rotation. (1) Mechanical system Mechanical system of the instrument includes bed plate, left and right supports for supporting roller, and workbench of measurement. Mechanical system has two functions. The first is to support measured cone to rotate, and the second is to support grating transducer to do rectilinear movement along the cone axis. When in measuring operation, support the cone on two supports with two centers at the beginning, then start the motors to locate transducer in its axial place with horizontal grating, and alternatively, to locate transducer in its radial place by driving the cone to rotate with a deflectable rod. (2) Measuring system Measuring system is mainly made up of grating transducers and measuring circuit. It is used for axial locating and diameter measurements. Grating transducer has characteristics such as high accuracy, fine resolution, broad measuring range, strong ability to resist disturbance, etc. The accuracy of ordinary grating transducer can reach to 0.5μm /300mm; the resolution can reach to 0.05μm. The measuring circuits for grating transducer include subdivision circuit, direction identification circuit, counting circuit, and display circuit. In our design, the resolution and measuring accuracy of the grating transducer for diameter measurements are 0.5μm and 1μm/20mm; the resolution and measuring accuracy of the grating transducer for axial locating are 0.5μm and 1μm/20mm, respectively. (3) Dada acquisition system and data processing system The function of dada acquisition system and data processing system is to collect measured data such as diameters，angles, axial positions, and then input these data to the computer through standard RS-232C seria interface for data processing, so that measuring results and actual cone profile of the measured cone can be obtained.Since the Baud rate of serial communication is set to 9600bps, the system can transmit 1200 bytes in a second. The total number of measured data is about 400×100=40000 while 9 bytes are needed to store one measured ata..So the time required to do whole measurement is approximate 40000×9/1200=300s, or about 5 minutes. (4) Control system for axial movement and radial rotation Fig.2 the interface of control operation The function of control system is to control stepping motors by which the rotation and axial rectilinear movement can be implemented. The core of control system is a parallel interface board. Figure 2 shows the interface of control operation. By operations within this interface, starting and stopping of motors, control of rotating direction and speed and locating of the transducer along cone axis, can be realized. The stepping angle of stepping motor is 0.045o; Accuracy of 0.01mm can be obtained for rectilinear movement control by means of driving mechanisms such as gears, ballscrews, etc. 4. EVALUATION OF THE MEASURED CONE Once the measurement is finished, evaluation of the measured cone can be made from 400×100 measured data. According to the definition of taper, there are two methods which can be used to get the actual taper of the measured cone. (1) Both 400 measured data measured on sections of bigger end and smaller end of the cone are processed separately with least square method. D' and d ' , the diameters of two circles determined by least square method, can be found out. Then, we can find out L, the axial distance between these two sections, from locating dimensions. According to equation Ca= (D'?d ' ) / L' , the actual taper of measured cone can be calculated. (2) Total 400×100 data are processed with least square method and the equation of the tapered face determined by least square method can be calculated. After two appropriate sections are chosen, we can calculate and d”, the diameters of two sections and L" ,the distance between twosections, and then, the actual taper of measured cone can be calculated according to equation Ca = (D"?d " ) / L" . This instrument adopts the second evaluation method. Other parameters such as standard deviation of taper, maximum deviation of taper and minimum deviation of taper can also be calculated while further data processing work is done. To enhance the visualizability of measuring results, processing of visualization has been adopted. The actual profile of tapered face can be displayed on the screen of computer in the form of grid according to measured data. Figure 3 is the actual profile of a tapered face. If you click any point on the profile, the axial position and the diameter of the section at which the point is locating, and deviations, can be printed，on the screen immediately. Besides, you can drag the actual profile with mouse so that you can observe the condition of an arbitrary position on the profile. This instrument can make virtual assembly of cone shaft and cone sleeve by computer. Numbering for cone shafts and cone sleeves and then save their measuring results. When they are to be used, virtual assembly can be made by computer by making use of saved result. Taking notice of the actual assembly effect of cone shaft and cone sleeve, selective assembly of cones with high accuracy can be realized to a great extent[3]. Fig.3 actual profile of a tapered face 5. CONCLUSIONS The measurement of cone shaft and cone sleeve of roller introduced in this paper takes reference cylindrical surface of roller as the reference of measurement. This is accordance with actual condition of cone fit, so that it has great advantage in principle.The horizontal automatic cone measuring instrument has characteristics such as simple in structure, convenient in adjustment and operation, high accuracy, broad measuring range, etc. The instrument has heavy load bearing capacity, large rigidity and enhanced adaptability. Grating transducers are used in measuring system for diameter measurement and axial positioning, and radial angular positioning is completed with stepping motor. So, the error for measuring diameter is less than 1.4μm and the relative error for measuring taper of cone is less than 2×10-3. Horizontal automatic cone measuring instrument is automated in great extent. The adoption of digital grating transducers which have high accuracy is propitious to the computer aided data acquisition and data processing. Large amount of digital information can be obtained from collected data after procedures of error separation, error correction and statistic analysis. With visualization technique the profile of measured cone can also be displayed on computer’s screen. It is of great importance that, using collected data, virtual assembly of cone shaft and cone sleeve can be realized so that selective assembly of cones with high accuracy can be realized to a great extent. REFERENCES [1] Rakesh Gupta. Prototyping and Design for Assembly Analysis Using Multimodal Virtual Environment[J]. Computer Aided Design. 1997, (29): 585-597 [2] Xu Kun, Wang Shao Tuan. Measurement of Cone’s Taper Angle in Same Direction. Tractor @ Farm Transporter. 2002, l3(3): 47 [3] Du Ming Fang, Zhang Yong Ming. Measurement and Data Processing of Circular Cone. Metrology & Measurement Technique. 2002, 29(4):10-11 [4] Li Xiao Qing, Zhang Fu Run, Yang Chu Min. Development of Special Measuring Tools for Small Diameter on Male Cone of Large-Sized Cone Parts. Tool Engineering. 2003, (5):44-46 [5] Yu Xin Hai, Chen Ping. Measurement of Large Diameter Cone with Universal Measuring Microscope. Practical Measurement technology. 2000,26(4):34-35 [6] Shi Jian Yao, Yang De Wang. Measurement of Cone Diameter and Error Analysis. Practical Measurement technology. 2000, 26(5):34-36 7 高速線材軋機(jī)軋輥的錐軸與錐套的檢測(cè) 摘要 當(dāng)更換軋輥時(shí)為了取得良好的裝配性能,高速線材軋機(jī)軋輥采用椎孔與錐套的配合。本文介紹了一種錐度的自動(dòng)測(cè)量方法，論述的原則是參照?qǐng)A柱表面作為測(cè)量錐度的標(biāo)準(zhǔn)。主要特色是橫向聯(lián)系錐自動(dòng)測(cè)量?jī)x器。對(duì)測(cè)量誤差的儀器進(jìn)行分析. 該儀器采用光柵位移傳感器錐直徑和軸向定位傳感器. m時(shí),軸向定位誤差小于0.01mm的, ,相對(duì)誤差為錐度測(cè)量小于2 × 10-3 .μ測(cè)量誤差直徑為1.4 。由于該儀器配備數(shù)據(jù)采集系統(tǒng), 許多參數(shù)和實(shí)際剖面測(cè)量的錐度可根據(jù)所收集的測(cè)量數(shù)據(jù)確定. 此外，錐軸與錐套可應(yīng)用電腦進(jìn)行虛擬裝配。可以觀察出錐軸與錐套的實(shí)際裝配效果，可以實(shí)現(xiàn)裝配精度最大程度的提高。 關(guān)鍵詞：軋機(jī)，軋輥，光柵傳感器，步進(jìn)電機(jī)，虛擬裝配 1.說(shuō)明 與光滑圓柱配合相比，錐度具有其獨(dú)特的優(yōu)點(diǎn)，例如：自動(dòng)定心，同軸度高，配合緊密，，容易調(diào)整松緊度，容易拆裝等。因此，它被廣泛應(yīng)用于機(jī)械裝置中?，F(xiàn)在，高線的軋制速度超過(guò)了100m/s。為了適應(yīng)這個(gè)速度，采用錐軸和錐套相配合的軋輥具有良好的表現(xiàn)，否則軋輥將會(huì)跑偏使得軋制速度和軋制受益不能保證。 有兩個(gè)方法用來(lái)檢查錐度：綜合檢查和單項(xiàng)檢查. 圓錐量是用于綜合檢查,而指標(biāo)、正弦、角度是用于單項(xiàng)檢查錐度公差。本文介紹了一種錐自動(dòng)測(cè)量方法,連同相關(guān)臥式錐自動(dòng)測(cè)量?jī)x器.該儀器在軋制條件下以圓柱表面作為參考測(cè)量了錐軸和錐套。軋制參數(shù)如下: 最大測(cè)量錐軸直徑241mm ，其測(cè)量錐軸長(zhǎng)度范圍為647mm ~ 985mm ,測(cè)量軸套的最大直徑為192mm,測(cè)量軸套的長(zhǎng)度范圍為647mm~985mm，通常測(cè)量錐度是1：12。錐度的公差要求是，當(dāng)軸向位移為12mm時(shí)，直徑的公差為1±0.003mm。 2.測(cè)量原則 兩個(gè)光柵傳感器分別位于錐軸兩邊, 他們是平行的,與主軸配以合適的角度. 檢測(cè)從測(cè)量較大一端的錐度開(kāi)始，以確保測(cè)量的準(zhǔn)確性.測(cè)量直徑的大小等于傳感器讀數(shù)之和。錐體每旋轉(zhuǎn)0.9 o做一次測(cè)量，即整個(gè)周長(zhǎng)測(cè)量400次。一個(gè)周長(zhǎng)測(cè)量做每軸0.79區(qū)間. 測(cè)量程序結(jié)束時(shí),測(cè)量的周長(zhǎng)較小一端的錐度已完成. 在其中一段是:遠(yuǎn)離錐度大端的l（直徑為D），假設(shè)理論測(cè)量直徑是d，測(cè)量值即為軋輥的軸套的直徑。 C = (D ? d ) / L (1) d = D ? C - L (2) D = d ? d = d ? (D ?-L) = d + L ? D (3) 式中：c——錐度的正常值， d——直徑的測(cè)量誤差， 軸向位移是12mm時(shí)，直徑的容許誤差小于10.003mm。因此,儀器的測(cè)量誤差在測(cè)量直徑時(shí)不得超過(guò)3米. 3.設(shè)備的結(jié)構(gòu)分析 圖1 錐度自動(dòng)測(cè)量?jī)x 該設(shè)備由四部分組成：機(jī)械系統(tǒng)，測(cè)量系統(tǒng)，數(shù)據(jù)采集系統(tǒng)和數(shù)據(jù)處理系統(tǒng)，控制系統(tǒng)用于控制軸向運(yùn)動(dòng)和徑向旋轉(zhuǎn). ⑴ 機(jī)械系統(tǒng) 設(shè)備的機(jī)械系統(tǒng)包括：底板,左,右支托輥, 和測(cè)量工作臺(tái).機(jī)械系統(tǒng)有兩個(gè)功能：一種是用于測(cè)量錐體轉(zhuǎn)動(dòng), 而后者則是用于使光柵傳感器沿著錐軸做直線運(yùn)動(dòng).在測(cè)量操作中，首先用兩個(gè)頂錐支撐住錐軸，然后啟動(dòng)馬達(dá)使位于軸向與橫向光柵的傳感器工作，同時(shí)，靠錐軸驅(qū)動(dòng)的徑向傳感器同時(shí)旋轉(zhuǎn)。 ⑵ 測(cè)量系統(tǒng) 測(cè)量系統(tǒng)主要由光柵傳感器及測(cè)量電路組成。它是用于軸向定位和測(cè)量直徑。光柵傳感器的特點(diǎn),如高精度,高分辨率,量程寬, 抗干擾能力強(qiáng)等。普通光柵傳感器的準(zhǔn)確性可達(dá)到0.5m/300mm，而結(jié)果的精度可達(dá)到0.05m。光柵傳感器的測(cè)量電路包括細(xì)分電路,方向識(shí)別電路,計(jì)數(shù)電路,顯示電路.我們?cè)O(shè)計(jì)時(shí)，傳感器的結(jié)果和測(cè)量精度分別達(dá)到0.5m和1m/20mm。軸向定位傳感器的結(jié)果和測(cè)量精度分別達(dá)到0.5m和1m/20mm。 ⑶ 數(shù)據(jù)采集和數(shù)據(jù)處理系統(tǒng) 數(shù)據(jù)采集和數(shù)據(jù)處理系統(tǒng)的功能是收集測(cè)量的數(shù)據(jù)如直徑、角度、軸向位置，然后把數(shù)據(jù)輸入采用RS-232C標(biāo)準(zhǔn)接口的計(jì)算機(jī)，因此可以得到測(cè)量結(jié)果和實(shí)際的錐度輪廓。由于串行通信波特率設(shè)置為9600bps ,該系統(tǒng)可每秒傳輸1200字節(jié)。當(dāng)儲(chǔ)存一次測(cè)量數(shù)據(jù)需要9字節(jié)時(shí)，測(cè)量數(shù)據(jù)的總計(jì)個(gè)數(shù)為400×100=40000，因此做完整個(gè)測(cè)量所需的時(shí)間總共為40000×9/1200=300秒，大約為五分鐘。 ⑷軸向運(yùn)動(dòng)和徑向旋轉(zhuǎn)的控制系統(tǒng) 圖2 控制操作的界面 該控制系統(tǒng)功能是控制步進(jìn)電機(jī)的旋轉(zhuǎn)和可實(shí)現(xiàn)的軸向直線運(yùn)動(dòng). 核心控制系統(tǒng)是一個(gè)并行接口板. 圖2顯示控制操作的界面.在該界面內(nèi)操作，可以實(shí)現(xiàn)啟動(dòng)和停止發(fā)動(dòng)機(jī),控制旋轉(zhuǎn)方向和定位傳感器沿錐軸的速度。步進(jìn)電機(jī)的步進(jìn)角為0.045 o ; 精度達(dá)0.01mm ,可作直線運(yùn)動(dòng)的控制手段和驅(qū)動(dòng)機(jī)制,就像齒輪、滾珠絲杠等. 4.錐度測(cè)量的評(píng)價(jià) 一旦測(cè)量結(jié)束，測(cè)量錐度的評(píng)價(jià)由400x100的測(cè)量數(shù)據(jù)獲得。根據(jù)錐度的定義有兩種方法可以用來(lái)獲得實(shí)際測(cè)量錐度。 ⑴ 錐軸的大端和小端的測(cè)量數(shù)據(jù)都是通過(guò)最小二乘法處理的。 D'和 d '都是通過(guò)最小二乘法計(jì)算得來(lái)的。然后，我們可以找見(jiàn)L，兩段之間多軸向距離，來(lái)自于定位尺寸。根據(jù)公式：Ca= (D'?d ' ) / L' ,可以計(jì)算出測(cè)量的真正錐度。 ⑵ 共有400X100個(gè)數(shù)據(jù)和圓錐表面的計(jì)算式都是通過(guò)最小二乘法計(jì)算得來(lái)的。當(dāng)選擇了適當(dāng)?shù)恼鹿?jié)后，我們可以計(jì)算出d "，前兩截面的直徑，和L"，兩截面之間的距離，然后測(cè)量的錐度可以通過(guò)式子Ca = (D"?d " ) / L"計(jì)算而得出。 這種儀器采用第二種評(píng)價(jià)方法. 其它參數(shù)如標(biāo)準(zhǔn)偏差錐度, 最大偏差錐度、最小偏差錐度也可以通過(guò)進(jìn)一步的數(shù)據(jù)處理工作完成. 為了提高測(cè)量結(jié)果的可視化，已經(jīng)采用了可視化的加工過(guò)程。根據(jù)測(cè)量數(shù)據(jù)，實(shí)際的錐面輪廓可以通過(guò)坐標(biāo)顯示于計(jì)算機(jī)屏幕上。圖3 是實(shí)際錐面的輪廓圖。如果你點(diǎn)擊輪廓的任意一點(diǎn)，該截面的軸向位置和直徑即可顯示。此外，你還可以用鼠標(biāo)拖動(dòng)實(shí)際輪廓,讓你可以觀察到的任意位置的概況. 這種儀器可以通過(guò)電腦做錐軸與錐套的虛擬裝配.為錐軸和錐套編號(hào),然后保存它的測(cè)量結(jié)果.當(dāng)他們被用到時(shí)，利用保存結(jié)果可在電腦上實(shí)現(xiàn)虛擬裝配。標(biāo)記錐軸與錐套的實(shí)際裝配效果可以在很大程度上提高裝配精度。 圖3 錐度的實(shí)際輪廓圖 5. 結(jié)論 本文中對(duì)錐軸和錐套的測(cè)量參照了圓柱面軋輥的測(cè)量。它與錐度的實(shí)際工作狀況相符合，所以原則上具有很大的優(yōu)越性。臥式錐自動(dòng)測(cè)量?jī)x器有其自身的特點(diǎn),如結(jié)構(gòu)簡(jiǎn)單,便于調(diào)試和運(yùn)行, 精度高,量程寬等.同時(shí)該儀器具有沉重的承載能力,剛度大,增強(qiáng)了適應(yīng)性. 光柵傳感器,用于測(cè)量系統(tǒng)的直徑和軸向定位, 徑向角定位是由步進(jìn)馬達(dá)完成的. 因此，測(cè)量誤差小于1.4m，相對(duì)測(cè)量錐度誤差小于2×10-3。 臥式錐自動(dòng)測(cè)量?jī)x器在很大程度上實(shí)現(xiàn)了自動(dòng)化. 采用數(shù)字式光柵傳感器在于精度高,同時(shí)順利的完成了計(jì)算機(jī)數(shù)據(jù)采集和數(shù)據(jù)處理. 可從收集到的大量的數(shù)據(jù)數(shù)字化信息進(jìn)行誤差分離, 糾錯(cuò),并施行統(tǒng)計(jì)分析. 應(yīng)用可視化技術(shù)，剖面測(cè)量錐度也可以顯示在計(jì)算機(jī)屏幕上. 更加重要的是,利用所收集的數(shù)據(jù), 可實(shí)現(xiàn)虛擬裝配錐軸與錐套,可以實(shí)現(xiàn)裝配精度在很大程度的提高。 參考文獻(xiàn) [1] 勒凱什普塔，《樣機(jī)和裝配的設(shè)計(jì)在多式聯(lián)合虛擬環(huán)境中的應(yīng)用》，《電腦輔助設(shè)計(jì)》，1997, (29): 585-597 [2] 徐坤，王紹褍，《在同一方向上測(cè)量錐體的圓錐角》，《拖拉機(jī)和農(nóng)用運(yùn)輸車》，2002, l3(3): 47 [3] 杜眀芳，張永明《錐度的測(cè)量和數(shù)據(jù)處理》，《精密測(cè)量技術(shù)》，2002, 29(4):10-11 [4] 李曉慶，張福云，楊楚敏《大型圓錐體上的小錐徑測(cè)量工具的發(fā)展》，《工程工具》，2003, (5):44-46 [5] 余新海，陳萍《用測(cè)量顯微鏡測(cè)量大錐徑》，《實(shí)際測(cè)量技術(shù)》2000,26(4):34-35 [6] 石建要，楊德旺《錐徑測(cè)量和誤差分析》，《實(shí)際測(cè)量技術(shù)》2000, 26(5):34-36 7 7