混砂機傳動裝置的設(shè)計,混砂機傳動裝置的設(shè)計,混砂機,傳動,裝置,設(shè)計
山西農(nóng)業(yè)大學(xué)工程技術(shù)學(xué)院
畢業(yè)設(shè)計說明書（論文）
題 目：混砂機傳動裝置設(shè)計
作 者： 馮少龍 班級： 06級雙學(xué)位班
學(xué) 院：工程技術(shù)學(xué)院
專 業(yè)：農(nóng)業(yè)機械及其自動化
指 導(dǎo) 者：
評 閱 者：
2008 年 6月 山西 太谷
混砂機傳動裝置的設(shè)計
摘要：設(shè)計混砂機斜齒傳動裝置主要是設(shè)計其中的減速器，而減速器的設(shè)計又是機械設(shè)計的基礎(chǔ)，是培養(yǎng)機械設(shè)計能力的基礎(chǔ)。其目的就是：通過減速器的設(shè)計，綜合運用機械設(shè)計課程和其他選修課程的理論和實際知識，掌握機械設(shè)計的一般規(guī)律，樹立正確的設(shè)計思路，培養(yǎng)分析和解決實際問題的能力。學(xué)會從機器功能的要求和實際需要出發(fā)，合理選擇傳動機構(gòu)類型并制定設(shè)計方案，正確計算零件的工作能力，確定它們的尺寸、形狀、結(jié)構(gòu)及材料，并考慮制造工藝、使用、維護、經(jīng)濟和安全等問題，培養(yǎng)機械設(shè)計能力。通過減速器的設(shè)計，學(xué)會運用標(biāo)準(zhǔn)、規(guī)范、手冊和查閱有關(guān)技術(shù)資料等，培養(yǎng)機械設(shè)計的基本技能。傳動裝置總體設(shè)計的內(nèi)容為確定傳動方案、選定電動機型號、計算總傳動比和合理分配各級傳動比，計算傳動裝置的運動和動力參數(shù)，為設(shè)計各級傳動件和裝配圖設(shè)計提供條件。在減速器的設(shè)計中學(xué)會使用機械設(shè)計的基本知識，掌握機械設(shè)計的方法，學(xué)會運用AutoCAD畫圖和使用word軟件中的更多附加工具，使自己的機械設(shè)計能力提高到一定的程度。
關(guān)鍵詞：減速器、電動機、傳動、齒輪
畢業(yè)設(shè)計說明書中文摘要
畢業(yè)設(shè)計說明書中文摘要
The designs of batch mill conveyer
Abstract:It mainly designs the decelerator among them to design of bantch mill conveyer transmission device, the design of training mechanical designed capacity .Its purpose is: Through the design of the decelerator, use machinery to design course, other theories of majoring in course first and practical intelligence synthetically,know the universal law that machinery is designed, establish the correct mentality of designing, cultivate the ability to analyse and solve practical problem. The society proceeds from the requirement for the function of the machine and actual need, choose organization’s type of the transmission and make the design plan rationally, calculate the ability to work of the part correctly, confirm their size,form, structure and material, consider such questions as manufacturing engineering, using, safeguarding, economy and security, etc, train mechanical designed capacity. Through the design of the decelerator, learn to use the standard, norm, manual and consult relevant technical data etc, basic kill of training machinery to be designed. Transmission device content that design not overall than and can’t assigned by transmission not at all levels rationally for confirming transmission scheme, selecting motor the types, calculation transmission not total of than, calculate sport and power parameter, transmission of device, offer the condition for designing the units at various levels and spreading moveable piece and installation diagram to design. Will use ABC that machinery is designed in the design middle school of the decelerator, grasp the method that machinery is designed, learn to use AutoCAD to draw and use more additional tools in word software, make one’s own mechanical designed capacity bring sure degree up to.
Keyword: Decelerator; motor; transmission; gear wheel.
目錄
1設(shè)計任務(wù) 1
1.1設(shè)計依據(jù)： 1
1.2減速器的用途及使用范圍 1
2傳動方案的確定 1
2.1分析傳動方案 1
2.2總體參數(shù)計算 2
2.2.1電動機的選擇 2
2.2.2計算總傳動比及分配各級的傳動比 3
3傳動系統(tǒng)的設(shè)計計算 4
3.1皮帶輪傳動的設(shè)計計算 4
3.2 鏈傳動的設(shè)計計算 7
3.3齒輪傳動的設(shè)計計算 8
3.3.1輸入軸的設(shè)計計算： 12
3.3.2輸出軸的設(shè)計計算： 17
4主要零件的強度校核及選型 22
4.1滾動軸承的選擇及計算 22
4.2鍵連接的選擇及校核計算 23
5主要設(shè)計結(jié)果 24
參考文獻 26
致謝 27
畢業(yè)設(shè)計（論文）評價表
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目錄
1設(shè)計任務(wù) 1
1.1設(shè)計依據(jù)： 1
1.2減速器的用途及使用范圍 1
2傳動方案的確定 1
2.1分析傳動方案 1
2.2總體參數(shù)計算 2
2.2.1電動機的選擇 2
2.2.2計算總傳動比及分配各級的傳動比 3
3傳動系統(tǒng)的設(shè)計計算 4
3.1皮帶輪傳動的設(shè)計計算 4
3.2 鏈傳動的設(shè)計計算 7
3.3齒輪傳動的設(shè)計計算 8
3.3.1輸入軸的設(shè)計計算： 12
3.3.2輸出軸的設(shè)計計算： 17
4主要零件的強度校核及選型 22
4.1滾動軸承的選擇及計算 22
4.2鍵連接的選擇及校核計算 23
5主要設(shè)計結(jié)果 24
參考文獻 26
致謝 27
混砂機傳動裝置的設(shè)計
1設(shè)計任務(wù)
1.1設(shè)計依據(jù)：
（1）工作機主軸上的功率=1.8kW；
（2）工作機主軸上的轉(zhuǎn)速=30r/min；
（3）工作情況：兩班制連續(xù)單向運轉(zhuǎn)，載荷有輕微沖擊；
（4）使用折舊器：8年；
（5）工作環(huán)境：室內(nèi)，灰塵較大，環(huán)境最高溫度為35；
（6）動力來源：電力，三相交流，電壓380/220V；
（7）檢修間隔期：四年一大修，二年一中修，半年一小修；
（8）制造條件及生產(chǎn)批量：一般機械廠制造，小批量生產(chǎn)。
1.2減速器的用途及使用范圍
本產(chǎn)品廣泛的應(yīng)用于化工、冶金、煤炭、水電、建材等部門。功能是中長距離水平輸送各種塊狀、粒狀等散裝物料，也可用來輸送成件物品。
2傳動方案的確定
2.1分析傳動方案
傳動方案一般用機構(gòu)運動簡圖表示，它能簡單明了地表示運動和動力的傳遞方式和路線以及各部件的組成和相互聯(lián)接關(guān)系。滿足工作機性能要求的傳動方案，可以由不同傳動機構(gòu)類型以不同的組合形式和布置順序構(gòu)成。合理的方案首先應(yīng)滿足工作機的性能要求，保證工作可靠，并且結(jié)構(gòu)簡單、尺寸緊湊、加工方便、成本低廉、傳動效率高和使用維護便利。一種方案要同時滿足這些要求往往是困難的，因此要通過分析比較多種方案，選擇能滿足重點要求的較好傳動方案。經(jīng)過分析，這里采用為一級圓柱齒輪封閉式減速器，它適合于繁重及惡劣條件下長期工作，使用維護方便能更好的滿足實際工況的需要。傳動方案如圖所示：
圖1傳動方案示意圖
2.2總體參數(shù)計算
2.2.1電動機的選擇
（1）電動機類型的選擇：Y系列三相異步電動機
（2）電動機功率選擇：
①傳動裝置的總功率：
②電機所需要的工作效率：
(3)確定電動機的轉(zhuǎn)速
圓錐齒輪傳動比范圍，V帶傳動，故總傳動比合理范圍為，因此電動機轉(zhuǎn)速合理范圍，符合這一范圍的同步轉(zhuǎn)速有750、1000、1500，選擇n=1000。
(4)確定電動機型號
根據(jù)以上選用的電動機類型，所需的額定功率及同步轉(zhuǎn)速，選定電動機型號為Y160L-6。其主要性能：額定功率為2.2KW；滿載轉(zhuǎn)速為710r/min；額定轉(zhuǎn)矩為2.0；質(zhì)量為147kg。
2.2.2計算總傳動比及分配各級的傳動比
(1)總傳動比：
(2)分配各級傳動比
①取一級圓錐齒輪傳動比（一級減速器i=3～6合理）
②
2.2.3運動參數(shù)及動力參數(shù)的計算
(1)計算各軸轉(zhuǎn)速
(2)計算各軸功率
(3)計算各軸轉(zhuǎn)矩
3傳動系統(tǒng)的設(shè)計計算
3.1皮帶輪傳動的設(shè)計計算
帶1：
（1）選擇普通V帶型號
查機械設(shè)計手冊得工作情況系數(shù)KA：KA=1.2，所以計算功率
Pca=KAP=1.22.096=2.512KW
根據(jù)Pca和n1查得：選用B型V帶
（2）確定帶輪基準(zhǔn)直徑
查手冊取主動輪基準(zhǔn)直徑dd1=120mm.
驗算帶的速度：
帶速合適。
計算從動輪基準(zhǔn)直徑dd2
根據(jù)手冊取dd2=340mm.
（3）確定V帶的基準(zhǔn)長度和傳動的中心距
根據(jù)0.7(dd2+dd1)
72000h
所以預(yù)算軸承合格。
II軸：
軸承6208的校核
由公式
所選軸承為深溝球軸承故ε=3
由表可查得C=25590N
n=30.19r/min
P=1.546W
=
=2764352h>72000h
所以預(yù)算軸承合格。
4.2鍵連接的選擇及校核計算
由公式=2T/dlr=4T/dhl≤
鍵一：
傳遞的轉(zhuǎn)矩28192.7
軸的直徑=30
鍵的類型取A型
鍵的截面尺寸108
鍵的長度45
鍵的有效長度35
由于鍵采用靜聯(lián)接，沖擊輕微，所以許用擠壓應(yīng)力為135
計算鍵的應(yīng)力
=18.52<滿足
所以該鍵安全。
鍵二：
傳遞的轉(zhuǎn)矩75776.3
軸的直徑=44
鍵的類型取A型
鍵的截面尺寸128
鍵的長度36
鍵的有效長度24.0
由于鍵采用靜聯(lián)接，沖擊輕微，所以許用擠壓應(yīng)力為135
計算鍵的應(yīng)力
=99.32<滿足
所以該鍵安全。
鍵三：
傳遞的轉(zhuǎn)矩203738.9
軸的直徑=35
鍵的類型取A型
鍵的截面尺寸108
鍵的長度32
鍵的有效長度22.0
由于鍵采用靜聯(lián)接，沖擊輕微，所以許用擠壓應(yīng)力為135
計算鍵的應(yīng)力
=126.54<滿足
所以該鍵安全
5主要設(shè)計結(jié)果
電動機功率：p=2.096
總傳動比：i=23.6
齒輪中心距：a=224mm
鏈輪中心距：a=594mm
6減速器附件的選擇
通氣器
由于在室內(nèi)使用，選通氣器（一次過濾），采用M10×1.5
油面指示器
選用游標(biāo)尺M12
起吊裝置
采用箱蓋吊耳、箱座吊耳
放油螺塞
選用外六角油塞及墊片M10×1.5
7滾動軸承的潤滑和密封
7.1潤滑方式的選擇
（1）潤滑劑的作用：潤滑對滾動軸承有重要意義，它可以降低摩擦阻力，提高散熱性能，減少接觸應(yīng)力，吸收振動，防止生銹等作用；
（2）潤滑方式選擇：采用飛濺潤滑方式，齒輪和軸可同時得到潤滑，易于維護。
（3）潤滑油牌號:SH0094-91中的680號潤滑油；
（4）換有周期：每半年全部更換一次（在正常工作狀態(tài)下）
7.2密封方式的選擇
輸出軸在端蓋處的密封因為，可采用氈圈油封。
輸入軸與端蓋配合處因，因此選用J型油封
參考文獻
[1]張祖立，機械設(shè)計［M］.第一版.北京.中國農(nóng)業(yè)出版社.2004
[2]吳宗澤，羅圣國.機械設(shè)計課程設(shè)計手冊.高等教育出版社.2003
[3]濮良貴，紀(jì)明剛.機械設(shè)計.第七版.高等教育出版社.2003
[4]陳作模，機械原理.第六版.高等教育出版社.2003
[5]張良成，材料力學(xué).第一版.中國農(nóng)業(yè)出版社.2003
[6]甘永立，幾何量公差于檢測.第六版.上?？茖W(xué)技術(shù)出版社.2004
[7]成大先，機械設(shè)計手冊.第四版.化學(xué)工業(yè)出版社.2002
[8]吳宗澤，機械設(shè)計禁忌800例.第二版.機械工業(yè)出版社.2006
[9]楊黎明，機械零件設(shè)計手冊.第一版.國防工業(yè)出版社.1987
[10]哈爾濱工業(yè)大學(xué)理論力學(xué)教研室.理論力學(xué)（Ⅰ）.第六版.高等教育出版社.2006
致謝
首先，我要感謝我的指導(dǎo)老師鄭老師，在設(shè)計和論文的撰寫過程中，他給了我很多幫助。并提出了寶貴意見，在此我向他以崇高的敬意和衷心的感謝。另外對給予我?guī)椭钠渌蠋熞惨徊⒅轮x。此外，對同組的同學(xué)表示感謝！
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黃河科技學(xué)院畢業(yè)設(shè)計（文獻翻譯） 第 27 頁
畢業(yè)設(shè)計
文獻翻譯
院（系）名稱
工學(xué)院機械系
專業(yè)名稱
機械設(shè)計制造及其自動化
學(xué)生姓名
王方成
指導(dǎo)教師
李安生
2012年 03 月 10 日
外文出處：Mechanism and Machine Theory
動力傳動圓錐漸開線齒輪的設(shè)計、制造和應(yīng)用
Dr. J. B?rner, K. Humm, Dr. F. Joachim, Dr. H. akaria,
ZF Friedrichshafen AG , 88038Friedrichshafen, Germany；
摘要：圓錐漸開線齒輪(斜面體齒輪)被用于交叉或傾斜軸變速器和平行軸自由側(cè)隙變速器中。圓錐齒輪是在齒寬橫斷面上具有不同齒頂高修正(齒厚)的直齒或斜齒圓柱齒輪。這類齒輪的幾何形狀是已知的，但應(yīng)用在動力傳動上則多少是個例外。ZF公司已將該斜面體齒輪裝置應(yīng)用于各種場合:4W D轎車傳動裝置、船用變速器(主要用于快艇)機器人齒輪箱和工業(yè)傳動等領(lǐng)域。斜面體齒輪的模數(shù)在0. 7 mm-8 mm之間，
交叉?zhèn)鲃咏窃?°- 25°。之間。這些邊界條件需要對斜面體齒輪的設(shè)計、制造和質(zhì)量有一個深入的理解。在錐齒輪傳動中為獲得高承載能力和低噪聲所必須進行的齒側(cè)修形可采用范成法磨削工藝制造。為降低制造成本，機床設(shè)定和由于磨削加工造成的齒側(cè)偏差可在設(shè)計階段利用仿真制造進行計算。本文從總體上介紹了動力傳動變速器斜面體齒輪的研發(fā)，包括:基本幾何形狀、宏觀及微觀幾何形狀的設(shè)計、仿真、制造、齒輪測量和試驗。
關(guān)鍵字：機械傳動 漸開線齒輪
1前言
在變速器中如果各軸軸線不平行的話，轉(zhuǎn)矩傳遞可采用多種設(shè)計，例如:傘齒輪或冠齒輪、萬向節(jié)軸或圓錐漸開線齒輪(斜面體齒輪)。圓錐漸開線齒輪特別適用于小軸線角度(小于15°)，該齒輪的優(yōu)點是在制造、結(jié)構(gòu)特點和輸入多樣性等方而的簡易。圓錐漸開線齒輪被用于直角或交叉軸傳動的變速器或被用于平行軸自由側(cè)隙工況的變速器。由于錐角的選擇并不取決于軸線交角，配對的齒輪也可能采用圓柱齒輪。斜面體齒輪可制成外嚙合和內(nèi)齒輪，整個可選齒輪副矩陣見表1，它為設(shè)計者提供了高度的靈活性。 圓錐齒輪是在齒寬橫截面上具有不同齒頂高修正(齒厚)量的直齒輪或斜齒輪。它們能與各種用同一把基準(zhǔn)齒條刀具切制成的齒輪相嚙合。斜面體齒輪的幾何形狀是已知的，但它們很少應(yīng)用在動力傳動上。過去，未曾對斜面體齒輪的承載能力和噪聲進行過任何大范圍的試驗研究。標(biāo)準(zhǔn)(諸如適用于圓柱齒輪的IS06336)、計算方法和強度值都是未知的。因此，必須開發(fā)計算方法、獲得承載能力數(shù)值和算出用于生產(chǎn)和質(zhì)量保證的規(guī)范。在過去的15年中，ZF公司已為錐齒輪開發(fā)了多種應(yīng)用:
1、輸出軸具有下傾角的船用變速[1、3]圖.1
2、轉(zhuǎn)向器[1]
3、機器人用小齒隙行星齒輪裝置(交叉軸角度1°一3°)[2]
4、商用車輛的輸送齒輪箱(垃圾傾倒車)
5、AWD用自動變速器[ 4]，圖2
2.齒輪幾何形狀
2. 1 宏觀幾何形狀
簡而言之，斜面體齒輪可看成是一個在齒寬橫截面上連續(xù)改變齒頂高修正的圓柱齒輪，如圖3。為此，根據(jù)齒根錐角δ刀具向齒輪軸線傾斜[ 1]。結(jié)果形成了齒輪基圓尺寸。
螺旋角，左/右
tanβ=tanβ·cosδ (l)
橫向壓力角 左/右
（2）
基圓直徑 左/右
(3)
左右側(cè)不同的基圓導(dǎo)致斜齒輪齒廓形狀的不均勻，圖3。采用齒條類刀具加工將使得齒根錐具有相應(yīng)的根錐角δ。齒頂角設(shè)計成這樣以使得頂端避免與被嚙合齒輪發(fā)生干涉，并獲得最大接觸區(qū)域。由此導(dǎo)致在齒寬橫截面上具有不同的齒高。由于幾何設(shè)計限制了根切和齒頂形狀，實際齒寬隨錐角增加而減小。錐齒輪傳動合適的錐角最大約為15°。
2. 2微觀幾何形狀
一對傘齒輪通常形成點狀接觸。除接觸外，在齒側(cè)還存在間隙，如圖7。齒輪修形設(shè)計的目的是減小這些間隙以形成平坦而均勻的接觸。通過逐步應(yīng)用嚙合定律有可能對齒側(cè)進行精確的計算[5],圖4。最后，在原始側(cè)生成半徑為rp和法向矢量為n的P1點。這生成速度矢量V及對于在嚙合一側(cè)所生成的點，有半徑矢量rp:
(4)
(5)
和速度矢量
（6）
角速度根據(jù)齒輪速比確定：
（7）
角度γ被反復(fù)迭代直至滿足下代。
(8)
嚙合點Pa偏轉(zhuǎn)角度
（9）
繞齒輪軸轉(zhuǎn)動，形成共軛點P。
3傳動裝置設(shè)計
3. 1根切和齒頂形狀
斜面體齒輪的可用齒寬受到大端齒頂形狀和小端根切的限制，見圖3。齒高愈高(為獲得較大的齒高變位量)，理論可用齒寬愈窄。小端根切和大端齒頂形狀導(dǎo)致齒高變位量沿齒寬方向發(fā)生變化。當(dāng)一對齒輪的錐角大致相同時可獲得最大的可用齒寬。若齒輪副中小齒輪愈小，則該小齒輪必須采用更小的錐角。齒頂錐角小于齒根錐角時，通常能在小端獲得有用的漸開線，而在大端處有足夠齒頂間隙，這時大端的齒頂形狀并不太嚴(yán)重。
3. 2工作區(qū)域和滑動速度
斜面體齒輪工作區(qū)域產(chǎn)生扭歪的原因是圓錐半徑有形成平行四邊形趨勢。另外，工作壓力角在齒寬橫截面方向的改變也造成工作區(qū)域的扭曲。圖5是一個例子。在交叉軸傳動的斜面體齒輪上存在一滾動軸;如同圓柱齒輪副的滾動點一樣，在該軸上不存在滑動。對于傾斜軸布置而言，在輪齒嚙合處總存在另外的軸向滑動。由于工作壓力角在齒寬橫截面上變化，從小端到大端的接觸區(qū)內(nèi)的接觸軌跡有很大的變化。因此，沿齒寬方向在齒頂和齒根處具有明顯不同的滑動速度。在齒輪中部，齒頂高修正的選擇是基于圓柱齒輪副的規(guī)范;在主動齒輪根部的接觸軌跡將小于齒頂?shù)慕佑|軌跡。圖6給出了斜面體齒輪副主動齒輪滑動速度的分布。
4接觸分析和修形
4. 1點接觸和間隙
在未修正齒輪傳動中，由于軸線傾斜，通常僅有一點接觸。沿可能接觸線出現(xiàn)的間隙可大致解釋為螺旋凸起和齒側(cè)廓線角度的偏差所致。圓柱齒輪左右側(cè)間隙與軸線交叉無關(guān)。對于螺旋齒輪而言，當(dāng)兩斜面體齒輪錐角大致相同時，其產(chǎn)生的間隙也幾乎相等。隨兩齒輪錐角和螺旋角不一致的增加，左右側(cè)間隙的不同程度也增加。
在工作壓力角較小時將導(dǎo)致更大的間隙。圖7給出了具有相同錐角交叉軸傳動的斜面體齒輪副所出現(xiàn)的間隙。圖8顯示了具有相同10°交叉軸線和30°螺旋角齒輪在左右側(cè)間隙方而的差異。兩側(cè)平均間隙的數(shù)值在很大程度上與螺旋角無關(guān)，但與兩齒輪的錐角相關(guān)。
螺旋角和錐角的選擇決定了齒輪左右側(cè)平均間隙的分布。傾斜軸線布置對接觸間隙產(chǎn)生額外影響。這將有效減少齒輪一側(cè)的螺旋凸形。如果垂直軸線與總基圓半徑相同，并且基圓柱螺旋角之差等于交叉軸角的話,間隙減小到零并出現(xiàn)線接觸。然而,在另一側(cè)將出現(xiàn)明顯的間隙。如果正交的軸線進一步擴大直至變成圓柱交叉軸螺旋齒輪副的話,其兩側(cè)間隙等同于較小的螺旋凸形。除螺旋凸形外,明顯的齒廓扭曲(見圖8)也是斜面體齒輪的間隙特征。隨螺旋角增加齒廓扭曲也隨之增加。圖9表明圖7所示齒輪裝置的齒廓是如何扭曲。為補償齒輪嚙合中所存在的間隙,必須采用齒側(cè)拓?fù)湫扌?該類修形可明顯補償螺旋凸形和輪廓扭曲。未對齒廓扭曲作補償?shù)脑?在工作區(qū)域僅有一個對角線狀的接觸帶,見圖10。
4.2 齒側(cè)修形
對于一定程度的補償而言,必需的齒面形狀可由實際間隙所決定。圖11給出了這些樣品的齒形幾何特征。采用修正后的接觸率得到了很大改善如圖12所示。為應(yīng)用在系列生產(chǎn)中,其目標(biāo)總是能使用磨床加工這類齒面,對此的選擇在第6節(jié)論述。除間隙補償外,齒頂修形也是有益的。修形減少了嚙合開始和結(jié)束階段的負(fù)荷,并能提供一較低的噪聲激勵源。然而,斜面體齒輪的齒頂修形在齒寬橫截面上的加工總量上和長度上是不同的。問題主要出現(xiàn)在具有一個大根錐角但頂錐角與根錐角存在偏差的齒輪上。因此齒頂修形在小端明顯大于大端。如齒輪需要在嚙合開始和結(jié)束處修形,則必須接受這種不均勻的齒頂修形。利用其它錐角如根錐角進行齒頂修形加工也是可行的。但是,這樣需要專門用于齒頂卸載的專用磨削設(shè)備。與范成法磨削方法無關(guān),齒側(cè)修正可采用諸如珩磨等手段;但在斜面體齒輪上應(yīng)用這些方法尚處在早期開發(fā)階段。5 承載能力和噪聲激勵
5.1 計算標(biāo)準(zhǔn)的應(yīng)用
斜面體齒輪齒側(cè)和根部承載能力僅可用圓柱齒輪的計算標(biāo)準(zhǔn)(ISO 6336, DIN 3990, AGMAC95) 作近似估算。具體計算時用圓柱齒輪副替代斜面體齒輪,用斜面體齒輪中部的齒寬來定義圓柱齒輪的參數(shù)。雖然斜面體齒輪齒廓是非對稱的,但在替代齒輪中可不予考慮。替代齒輪的中心距由斜面體齒輪中部齒寬處的工作節(jié)圓半徑確定。當(dāng)計及齒寬橫截面時,各項獨立的參數(shù)都會變化,這將明顯影響承載能力。
表2給出了影響齒根和齒側(cè)承載能力的主要因素。由于沿大端方向減小輪齒齒根圓角半徑所產(chǎn)生較大的凹口效應(yīng)阻止了根部齒厚的增加。另外,在大端處,較大的節(jié)圓直徑可獲得較小的切向力;然而,大端處的齒高變位量也隨之變小。由于主要影響得到很好的平衡,因此可用替代齒輪副獲得十分近似的承載能力計算結(jié)果。齒寬橫截面上的載荷分布可用齒寬系數(shù)(例如DIN/ISO標(biāo)準(zhǔn)中的K和K)表示和利用補充的負(fù)載曲線圖分析來確定。
5.2 輪齒接觸分析
如同在圓柱齒輪副中那樣,更精確的承載能力計算可采用三維輪齒接觸分析。同樣采用替代齒輪,而且齒側(cè)處接觸狀況被認(rèn)為非常理想。該齒側(cè)形狀通過疊加經(jīng)齒側(cè)修正的無負(fù)載接觸間隙而獲得。在這里,接觸線由替代齒輪所確定,它們和斜面體齒輪的接觸狀況稍有不同。圖13給出了以這方法獲得的載荷分布,并與已有的負(fù)載曲線圖作對比,兩者的相關(guān)性非常好。輪齒接觸分析也將生成一個作為激振源的由輪齒嚙合產(chǎn)生的傳動誤差。然而這僅能作為一個粗略的引導(dǎo)。在傳動誤差方面,斜面體齒輪接觸計算的不精確性是一個比載荷分布更大的影響因素。
5.3 采用有限元法的精確建模
斜面體齒輪的應(yīng)力也能利用有限元法計算。圖14是齒輪橫斷面建模的實例。圖15給出了使用PERMAS軟件由計算機生成的主動齒輪在嚙合位置的輪齒嚙合區(qū)模型和應(yīng)力分布計算值[7]。可對多個嚙
合位置進行計算,并能求出齒輪旋轉(zhuǎn)產(chǎn)生的傳動誤差。
5.4 承載能力和噪聲試驗
在交叉軸背靠背試驗臺上對AWD變速器進行試驗以測量其承載能力,圖16。試驗齒輪采用不同的修正,以確定它們對承載能力的影響。承載能力的試驗與有限元計算結(jié)果相當(dāng)吻合。值得注意的是,由于大端硬度提高使得載荷曲線圖朝大端由一個額外的移動。這種移動在替代的圓柱齒輪副計算中不能被辨別。在進行承載能力試驗的同時,傳動誤差和旋轉(zhuǎn)加速度的測量在通用噪聲試驗臺上進行,圖17。除了載荷影響外,這些試驗還測量了附加軸線傾斜所引起的噪聲激勵,關(guān)于軸線附加傾斜,試驗中未發(fā)現(xiàn)有明顯的影響。
6 仿真制造
借助于仿真制造,可獲得機床設(shè)置及連續(xù)范成磨削和產(chǎn)生齒廓扭曲的運動。齒廓受迫扭曲現(xiàn)象可在變速器設(shè)計階段就被認(rèn)識到并與承載能力及噪聲一并進行分析。斜面體齒輪制造仿真軟件由ZF公司開發(fā),詳見[9]。
6.1 適用于斜面體齒輪的制造方法斜面體齒輪僅可用范成法加工,因為齒廓形狀沿齒寬方向有明顯的變化。盡管是錐角非常小的斜面體齒輪,必須承認(rèn)在修整處理中仍然會出現(xiàn)齒廓角度偏差。滾刀最方便用于預(yù)切削。理論上也可采用刨削,但是,所需的運動在現(xiàn)有機床上很難實現(xiàn)。內(nèi)齒圓錐齒輪僅能用類似小齒輪的刀具精確制造,如果刀具軸線和工具軸線平行并且錐角是通過改變中心距生成的。如果內(nèi)齒輪利用軸線傾斜的小齒輪刀具如同加工差速器錐齒輪那樣來制造的話,將導(dǎo)致齒溝凸起和無修正運動的齒廓扭曲。對于小錐角而言這些偏差足夠小,可以被忽略。對于終加工,范成法螺旋磨削是一個最佳選擇。如果工件或機床夾具能被另外傾斜,也可采用部分范成法。如果齒輪錐角處于機床控制范圍內(nèi),拓?fù)淠ハ鞴に囈彩强赡艿?例如5軸機床),但是會耗費巨大的努力。原則上,珩磨等方法也能被用于加工,但是,在斜面體齒輪應(yīng)用這些方法仍需大量的開發(fā)工作。雙齒側(cè)范成法磨削工藝并利用中心距弧形減少方法可實現(xiàn)齒溝凸起的目標(biāo)。該方法所得到的齒廓扭曲與造成嚙合間隙的齒廓扭曲相反。因此該方法可在很大程度上補償齒廓扭曲并可承受比圓柱齒輪更大的載荷。
6.2 工件表面形狀
以下的關(guān)于工件描述被應(yīng)用在仿真中:
? 原始齒輪(留有磨削所需的余量)
?理想齒輪(來自齒輪數(shù)據(jù),無齒側(cè)修形)
?完成的齒輪(具有制造偏差和齒側(cè)修形)
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Foreign source ：Mechanism and Machine Theory
Application, Design, and Manufacturing of Conical Involute Gears for Power Transmissions
Dr. J. B?rner, K. Humm, Dr. F. Joachim, Dr. H. Yakaria,
ZF Friedrichshafen AG , 88038Friedrichshafen, Germany；
ABSTRACT: Conical involute gears (beveloids) are used in transmissions with intersecting or skew axes and for backlash-free transmissions with parallel axes. Conical gears are spur or helical gears with variable addendum modification (tooth thickness) across the face width. The geometry of such gears is generally known, but applications in power transmissions are more or less exceptional. ZF has implemented beveloid gear sets in various applications: 4WD gear units for passenger cars, marine transmissions (mostly used in yachts), gear boxes for robotics, and industrial drives. The module of these beveloids varies between 0.7 mm and 8 mm in size, and the crossed axes angle varies between 0°and 25°. These boundary conditions require a deep understanding of the design, manufacturing, and quality assurance of beveloid gears. Flank modifications, which are necessary for achieving a high load capacity and a low noise emission in the conical gears, can be produced with the continuous generation grinding process. In order to reduce the manufacturing costs, the machine settings as well as the flank deviations caused by the grinding process can be calculated in the design phase using a manufacturing simulation. This presentation gives an overview of the development of conical gears for power transmissions: Basic geometry, design of macro and micro geometry, simulation, manufacturing, gear measurement, and testing.
KEYWORDS: Mechanical transmission Involute gear
1 Introduction
In transmissions with shafts that are not arranged parallel to the axis, torque transmission ispossible by means of various designs such as bevel or crown gears , universal shafts , or conical involute gears (beveloids). The use of conical involute gears is particularly ideal for small shaft angles (less than 15°), as they offer benefits with regard to ease of production, design features, and overall input. Conical involute gears can be used in transmissions with intersecting or skew axes or in transmissions with parallel axes for backlash-free operation. Due to the fact that selection of the cone angle does not depend on the crossed axes angle, pairing is also possible with cylindrical gears. As beveloids can be produced as external and internal gears, a whole matrix of pairing options results and the designer is provided with a high degree of flexibility;
Table 1.
Conical gears are spur or helical gears with variable addendum correction (tooth thickness)
across the face width. They can mesh with all gears made with a tool with the same basic rack. The geometry of beveloids is generally known, but they have so far rarely been used in power transmissions. Neither the load capacity nor the noise behavior of beveloids has been examined to any great extent in the past. Standards (such as ISO 6336 for cylindrical gears ), calculation methods, and strength values are not available. Therefore, it was necessary to develop the calculation method, obtain the load capacity values, and calculate specifications for production and quality assurance. In the last 15 years, ZF has developed various applications with conical gears:
? Marine transmissions with down-angle output shafts /1, 3/, Fig. 1
? Steering transmissions /1/
? Low-backlash planetary gears (crossed axes angle 1…3°) for robots /2/
? Transfer gears for commercial vehicles (dumper)
? Automatic car transmissions for AWD /4/, Fig. 2
2 GEAR GEOMETRY
2.1 MACRO GEOMETRY
To put it simply, a beveloid is a spur gear with continuously changing addendum modification across the face width, as shown in Fig. 3. To accomplish this, the tool is tilted towards the gear axis by the root cone angle ? /1/. This results in the basic gear dimensions:
Helix angle, right/left
tanβ=tanβ·cosδ (1)
Transverse pressure angle right/left
(2)
Base circle diameter right/left
(3)
The differing base circles for the left and right flanks lead to asymmetrical tooth profiles at helical gears, Fig. 3. Manufacturing with a rack-type cutter results in a tooth root cone with root cone angle δ. The addendum angle is designed so that tip edge interferences with the mating gear are avoided and a maximally large contact ratio is obtained. Thus, a differing tooth height results across the face width.Due to the geometric design limits for undercut and tip formation, the possible face width decreases as the cone ngle increases. Sufficiently well-proportioned gearing is possible up to a cone angle of approx. 15°.
2.2 MICRO GEOMETRY
The pairing of two conical gears generally leads to a point-shaped tooth contact. Out-side this contact, there is gaping between the tooth flanks , Fig. 7. The goal of the gearing correction design is to reduce this gaping in order to create a flat and uniform contact. An exact calculation of the tooth flank is possible with the step-by-step application of the gearing law /5/, Fig. 4. To that end , a point (P) with the radiusrP1and normal vectorn1is generated on the original flank. This generates the speed vector V with
(4)
For the point created on the mating flank, the radial vector rp:
(5)
and the speed vector apply
(6)
The angular velocities are generated from the gear ratio:
(7)
The angle γ is iterated until the gearing law in the form
(8)
is fulfilled. The meshing point Pa found is then rotated through the angle
(9)
around the gear axis, and this results in the conjugate flank point P.
3 GEARING DESIGN
3.1 UNDERCUT AND TIP FORMATION
The usable face width on the beveloid gearing is limited by tip formation on the heel and undercut on the toe as shown in Fig. 3. The greater the selected tooth height (in order to obtain a larger addendum modification), the smaller the theoretically useable face width is. Undercut on the toe and tip formation on the heel result from changing the addendum modification along the face width. The maximum usable face width is achieved when the cone angle on both gears of the pairing is selected to be approximately the same size. With pairs having a significantly smaller pinion, a smaller cone angle must be used on this pinion. Tip formation on the heel is less critical if the tip cone angle is smaller than the root cone angle, which often provides good use of the available involute on the toe and for sufficient tip clearance in the heel.
3.2 FIELD OF ACTION AND SLIDING VELOCITY
The field of action for the beveloid gearing is distorted by the radial conicity with a tendency towards the shape of a parallelogram. In addition, the field of action is twisted due to the working pressure angle change across the face width. Fig. 5 shows an example of this. There is a roll axis on the beveloid gearing with crossed axes; there is no sliding on this axis as there is on the roll point of cylindrical gear pairs. With a skewed axis arrangement, there is always yet another axial slide in the tooth engagement. Due to the working pressure angle that changes across the face width, there is varying distribution of the contact path to the tip and root contact. Thus, significantly differing sliding velocities can result on the tooth tip and the tooth root along the face width. In the center section, the selection of the addendum modification should be based on the specifications for the cylindrical gear pairs; the root contact path at the driver should be smaller than the tip contact path. Fig. 6 shows the distribution of the sliding velocity on the driver of a beveloid gear pair.
4 CONTACT ANALYSIS AND MODIFYCATIONS
4.1 POINT CONTACT AND EASE-OFF
At the uncorrected gearing, there is only one point in contact due to the tilting of the axes. The gaping that results along the potential contact line can be approximately described by helix crowning and flank line angle deviation. Crossed axes result in no difference between the gaps on the left and right flanks on spur gears. With helical gearing, the resulting gaping is almost equivalent when both beveloid gears show approximately the same cone angle. The difference between the gap values on the left and right flanks increases as the difference between the cone angles increases and as the helix angle increases. This process results in larger gap values on the flank with the smaller working pressure angle. Fig.7 shows the resulting gaping (ease-off) for a beveloid gear pair with crossed axes and beveloid gears with an identical cone angle. Fig.8 shows the differences in the gaping that results for the left and right flanks for the same crossed axes angle of 10° and a helical angle of approx. 30°. The mean gaping obtained from both flanks is, to a large extent, independent of the helix angle and the distribution of the cone angle to both gears.
The selection of the helical and cone angles only determines the distribution of the mean gaping to the left and right flanks. A skewed axis arrangement results in additional influence on the contact gaping. There is a significant reduction in the effective helix crowning on one flank. If the axis perpendicular is identical to the total of the base radii and the difference in the base helix angle is equivalent to the (projected) crossed axes angle, then the gaping decreases to zero and line contact appears. However, significant gaping remains on the opposite flank. If the axis perpendicular is further enlarged up to the point at which a cylindrical crossed helical gear pair is obtained, this results in equivalent minor helix crowning in the ease-off on both flanks. In addition to helix crowning, a notable profile twist (see Fig. 8) is also characteristic of the ease-off of helical beveloids. This profile twist grows significantly as the helix angle increases. Fig.9 shows how the profile twist on the example gear set from Fig.7 is changed depending on the helix angle. In order to compensate for the existing gaping in the tooth engagement, topological flank corrections are necessary; these corrections greatly compensate for the effective helix crowning as well as the profile twist. Without the compensation of the profile twist, only a diagonally patterned contact strip is obtained in the field of action, as shown in Fig. 10.
4.2 FLANK MODIFICATIONS
For a given degree of compensation, the necessary topography can be determined from the existing ease-off. Fig. 11 shows these types of typographies, which were produced on prototypes. The contact ratios have improved greatly with these corrections as can be seen in Fig.12. For use in series production, the target is always to manufacture such topographies on commonly used grinding machines. The options for this are described in Section 6. In addition to the gaping compensation, tip relief is also beneficial. This relief reduces the load at the start and at the end of meshing and can also provide lower noise excitation. However, tip relief manufactured at beveloid gears is not constant in amount and length across the face width. The problem primarily occurs on gearing with a large root cone angle and a tip cone angle deviating from this angle. The tip relief at the toe is significantly larger than that at the heel. This uneven tip relief must be accepted if relief of the start and end of meshing is required. The production of tip relief using another cone angle as the root cone angle is possible; however, this requires an additional grinding step only for the tip relief. Independently of the generating grinding process, targeted flank topography can be manufactured by coroning or honing; the application of this method on beveloids, however, is still in the early stages of development.
5 LOAD CAPACITY AND NOISE EXCITATION
5. 1 APPLICATION OF THE CALCULATION STANDARDS
The flank and root load capacity of beveloid gearing can only approximately be deter-mined using the calculation standards (ISO6336, DIN3990,AGMA C95) for cylindrical gearing. A substitute cylindrical gear pair has to be used, which is defined by the gear parameters at the center of the face width. The profile of the beveloid tooth is asymmetrical; that can, however, be ignored on the substitute gears. The substitute center distance is obtained by adding up the operating pitch radii at the center of the face width.When viewed across the face width, individual parameters will change, which significantly influence the load capacity. Table 2 sh