??? 摘 要: 介紹了在Pro/E環(huán)境下,，實現(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),，利用方程建立漸開線,，從而保證齒形的準確性,。通過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,，實現(xiàn)了不同模數(shù)、齒數(shù)齒輪的快速造型,，提高了設(shè)計效率,。
??? 關(guān)鍵詞：漸開線；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)傳動件，用于傳遞相交軸之間的運動和動力,，并廣泛應(yīng)用于航空,、航海、汽車,、拖拉機,、機床等行業(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，再由數(shù)據(jù)點嚙合出齒面模型[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)實意義,。
1造型方法
1.1設(shè)計參數(shù)
??? 設(shè)計參數(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
??? (1)首先將基準平面TOP向右平移一段距離D/2×tan(DELTA)，創(chuàng)建基準軸A1基準點PNT 0,。在FRONT平面內(nèi),，以PNT 0為頂點繪制4條斜線，分別為分錐,、根錐,、基錐和頂錐母線。定義分錐母線終點尺寸為d2=D /2,，與水平中心線夾角為d1=DELTA,與大背錐母線的夾角d3=90°,；頂錐母線終點尺寸為d6=DA/2,；根錐母線終點尺d5=DF/ 2,；基錐母線中點尺寸d4=DB/2。繪制大,、小端背錐母線,，其間距離為d7=B，且均垂直于分錐母線,。同時創(chuàng)建基準點PNT 1和PNT 2,。如圖1 所示(其中d…為Pro/E中自動生成的尺寸代碼),。
??? (2)過背錐母線分別做兩個垂直于中心平面FRONT面的輔助平面DTM 2和DTM 3。在這兩個平面內(nèi)分別繪制各基礎(chǔ)圓曲線,，同時分別繪制2條過中心的豎直線,，為以后創(chuàng)建坐標系做準備。如圖2所示,。
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??? (3)創(chuàng)建輔助坐標系,，繪制大、小端齒廓漸開線,。首先創(chuàng)建大端的漸開線的參考坐標系CS1,，小端漸開線參考坐標系CS3。兩坐標系分別位于齒輪中心軸與兩輔助平面的交點處,，Z軸垂直于所建輔助平面DTM 2和DTM 3,。然后繪制漸開線，以FRONT面作為齒廓中心角的角分面,。繪制漸開線時必須保證兩漸開線FRONT面對稱，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,，笛卡兒坐標系下的漸開線參數(shù)方程為[6]：
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??? 最終生成的輔助坐標系和大,、小端齒廓漸開線如圖 3 所示,。
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??? (4)創(chuàng)建掃描軌跡和齒廓線。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為對稱面分別鏡像兩條漸開線,，經(jīng)過旋轉(zhuǎn)生成如圖4 所示的齒廓線,；以分錐母線為參考,，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。通過掃描混合命令沿投影曲線,，生成第一個齒廓,，之后通過復(fù)制,、陣列得到其他齒形,。定義旋轉(zhuǎn)角度d111=360/Z，陣列個數(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)計要求修改模數(shù),、齒數(shù)等參數(shù)以及掃描曲線,，就可得到不同弧齒錐齒輪副[8-10],。為以后的分析計算提供了方便,。
??? 本文介紹了格利森制非等頂隙的漸開線弧齒錐齒輪副的造型方法，按照此種方法將參數(shù)稍做改動就可以創(chuàng)建等頂隙的漸開線弧齒錐齒輪副,。
參考文獻
[1]?蔡春源．新編機械設(shè)計手冊. 沈陽：遼寧科學技術(shù)出版社,，1993.
[2]?安虎平, 孟剛. 齒輪漸開線齒面及其三維實體建模[J]. 機械研究與應(yīng)用，2006, 15 (5).
[3]?路懿, 陳修龍. 圓錐齒輪實體參數(shù)化逆向造型設(shè)計[J]. 計算機輔助設(shè)計與圖形學學報,，2003, 15(1).
[4]?孫桓,，陳作模. 機械原理. 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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