??? 摘 要: 介紹了在Pro/E環(huán)境下，實(shí)現(xiàn)格利森制弧齒錐齒輪副的造型方法和步驟，從原理出發(fā)，利用方程建立漸開(kāi)線(xiàn)，從而保證齒形的準(zhǔn)確性。通過(guò)建立齒輪中各變量與模數(shù)、齒數(shù)等基本參數(shù)的關(guān)系，實(shí)現(xiàn)了不同模數(shù)、齒數(shù)齒輪的快速造型，提高了設(shè)計(jì)效率。
??? 關(guān)鍵詞：漸開(kāi)線(xiàn)；弧齒錐齒輪；Pro/E
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??? 弧齒錐齒輪根據(jù)齒形的不同分為奧利康制和格利森制[1]。作為基礎(chǔ)傳動(dòng)件，用于傳遞相交軸之間的運(yùn)動(dòng)和動(dòng)力，并廣泛應(yīng)用于航空、航海、汽車(chē)、拖拉機(jī)、機(jī)床等行業(yè)中。傳統(tǒng)的格利森弧齒錐齒輪的造型是已知齒輪的參數(shù)，利用嚙合原理的方法建立齒面方程，由齒面方程獲得大量齒面數(shù)據(jù)點(diǎn)，再由數(shù)據(jù)點(diǎn)嚙合出齒面模型[2-3]。由于此種方法需要較多的嚙合原理知識(shí)和大量的數(shù)據(jù)處理工作，不易被工程技術(shù)人員掌握。因此，尋找一種快捷有效的弧齒錐齒輪造型方法和性能分析有著重要的現(xiàn)實(shí)意義。
1造型方法
1.1設(shè)計(jì)參數(shù)
??? 設(shè)計(jì)參數(shù)包括：分度圓直徑D；基圓直徑DB；齒頂圓直徑DA；齒根圓直徑DF；齒寬B；齒基高HB；錐距PX；齒頂高HA；齒根高HF；全齒高H；分錐角DELTAD等；大端尺寸：分度圓直徑DZ，齒頂圓直徑DZa，齒根圓直徑DZf，基圓直徑FZb。小端尺寸：分度圓直徑dZ，齒頂圓直徑dza，齒根圓直徑dZf，基圓直徑dZb。
??? 輸入表1中各參數(shù)，定義基本參數(shù)M、Z、B、CX等值，通過(guò)關(guān)系式定義其余各參數(shù)的數(shù)值[4-5]。
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1.2創(chuàng)建基本曲線(xiàn)
??? (1)首先將基準(zhǔn)平面TOP向右平移一段距離D/2×tan(DELTA)，創(chuàng)建基準(zhǔn)軸A1基準(zhǔn)點(diǎn)PNT 0。在FRONT平面內(nèi)，以PNT 0為頂點(diǎn)繪制4條斜線(xiàn)，分別為分錐、根錐、基錐和頂錐母線(xiàn)。定義分錐母線(xiàn)終點(diǎn)尺寸為d2=D /2，與水平中心線(xiàn)夾角為d1=DELTA,與大背錐母線(xiàn)的夾角d3=90°；頂錐母線(xiàn)終點(diǎn)尺寸為d6=DA/2；根錐母線(xiàn)終點(diǎn)尺d5=DF/ 2；基錐母線(xiàn)中點(diǎn)尺寸d4=DB/2。繪制大、小端背錐母線(xiàn)，其間距離為d7=B，且均垂直于分錐母線(xiàn)。同時(shí)創(chuàng)建基準(zhǔn)點(diǎn)PNT 1和PNT 2。如圖1 所示(其中d…為Pro/E中自動(dòng)生成的尺寸代碼)。
??? (2)過(guò)背錐母線(xiàn)分別做兩個(gè)垂直于中心平面FRONT面的輔助平面DTM 2和DTM 3。在這兩個(gè)平面內(nèi)分別繪制各基礎(chǔ)圓曲線(xiàn)，同時(shí)分別繪制2條過(guò)中心的豎直線(xiàn)，為以后創(chuàng)建坐標(biāo)系做準(zhǔn)備。如圖2所示。
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??? (3)創(chuàng)建輔助坐標(biāo)系，繪制大、小端齒廓漸開(kāi)線(xiàn)。首先創(chuàng)建大端的漸開(kāi)線(xiàn)的參考坐標(biāo)系CS1，小端漸開(kāi)線(xiàn)參考坐標(biāo)系CS3。兩坐標(biāo)系分別位于齒輪中心軸與兩輔助平面的交點(diǎn)處，Z軸垂直于所建輔助平面DTM 2和DTM 3。然后繪制漸開(kāi)線(xiàn)，以FRONT面作為齒廓中心角的角分面。繪制漸開(kāi)線(xiàn)時(shí)必須保證兩漸開(kāi)線(xiàn)FRONT面對(duì)稱(chēng)，才能保證背錐面上齒廓完全符合理論要求。設(shè)參數(shù)t=0～1，因此，在Pro/E草圖環(huán)境中，笛卡兒坐標(biāo)系下的漸開(kāi)線(xiàn)參數(shù)方程為[6]：
??? 
??? 最終生成的輔助坐標(biāo)系和大、小端齒廓漸開(kāi)線(xiàn)如圖 3 所示。
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??? (4)創(chuàng)建掃描軌跡和齒廓線(xiàn)。根據(jù)齒廓中心角以及齒寬等參數(shù)的關(guān)系創(chuàng)建輔助平面DTM 4和DTM 5， 以DTM 5為對(duì)稱(chēng)面分別鏡像兩條漸開(kāi)線(xiàn)，經(jīng)過(guò)旋轉(zhuǎn)生成如圖4 所示的齒廓線(xiàn)；以分錐母線(xiàn)為參考，分別生成輔助平面DTM 6和投影曲面。在輔助平面DTM 6中根據(jù)刀具半徑、螺旋角和齒輪的旋轉(zhuǎn)方向繪制圓弧。將圓弧向投降平面投影，生成如圖4所示的掃描軌跡[7]。
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??? (5)生成完整模型。通過(guò)掃描混合命令沿投影曲線(xiàn)，生成第一個(gè)齒廓，之后通過(guò)復(fù)制、陣列得到其他齒形。定義旋轉(zhuǎn)角度d111=360/Z，陣列個(gè)數(shù)p112=Z-1，得到完整非等頂隙弧齒錐齒輪的模型，同樣的方法可得到小齒輪的模型，如圖 5 所示為大小弧齒錐齒輪模型圖。圖 6 所示為弧齒錐齒輪副裝配圖。
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??? 由于齒輪的各個(gè)參數(shù)與齒輪的模數(shù)M、齒數(shù)Z和分錐角THETA等建立了關(guān)系,? 因此只要按設(shè)計(jì)要求修改模數(shù)、齒數(shù)等參數(shù)以及掃描曲線(xiàn)，就可得到不同弧齒錐齒輪副[8-10]。為以后的分析計(jì)算提供了方便。
??? 本文介紹了格利森制非等頂隙的漸開(kāi)線(xiàn)弧齒錐齒輪副的造型方法，按照此種方法將參數(shù)稍做改動(dòng)就可以創(chuàng)建等頂隙的漸開(kāi)線(xiàn)弧齒錐齒輪副。
參考文獻(xiàn)
[1]?蔡春源．新編機(jī)械設(shè)計(jì)手冊(cè). 沈陽(yáng)：遼寧科學(xué)技術(shù)出版社，1993.
[2]?安虎平, 孟剛. 齒輪漸開(kāi)線(xiàn)齒面及其三維實(shí)體建模[J]. 機(jī)械研究與應(yīng)用，2006, 15 (5).
[3]?路懿, 陳修龍. 圓錐齒輪實(shí)體參數(shù)化逆向造型設(shè)計(jì)[J]. 計(jì)算機(jī)輔助設(shè)計(jì)與圖形學(xué)學(xué)報(bào)，2003, 15(1).
[4]?孫桓，陳作模. 機(jī)械原理. 北京：高等教育出版社，1996.
[5]?譚雪松. 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title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" 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title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" 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