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摘 要
輪椅是年老體弱者以及下肢傷殘者必不可少的代步工具,但障礙物卻使輪椅受到很大限制?,F(xiàn)代由于采用了傳統(tǒng)的輪式結構,只能夠在平地上行走,面對臺階、樓梯這樣比較復雜的地形卻顯得無能為力。電動性輪椅設計是采用輪腿式機器人結構,正常行駛時輪式工作,采用四輪驅動;遇到障礙時腿式工作,從而適應大多數(shù)地形;車身則采用自動導軌式調平結構,該結構簡單,調節(jié)方便。本次設計的主要工作包括:確定輪椅的工作方式以及工作結構形式、主體尺寸,并確定各主要零、部件的結構尺寸及其選型。
關鍵詞:輪椅 電動輪椅 輪腿式機器人
Abstract
Wheelchairs are frail elderly and the disabled limb indispensable means of transport, but the obstacles while filling the wheelchair is very restricted. As with a traditional modern wheeled structure, can only walk on flat ground, facing steps, stairs, but this is more complex terrain powerless. High-pass design is the use of a wheelchair wheel legged robot structure, normal driving wheel work, the use of four-wheel drive; encounter obstacles leg work to accommodate most of the terrain; body is leveling automatic slide-type structure, the structure is simple, easy to adjust. The design of the main tasks include: determining wheelchair work and the working structure, body size, and identify the major components and parts of the structure size and selection.
Keywords: wheelchair high adoption round legged robot
一、引 言
1.1 電動輪椅國內外發(fā)展情況
隨著社會的發(fā)展和人類文明程度的提高,人們特別是殘疾人愈來愈需要運用現(xiàn)代高新技術來改善他們的生活質量和生活自由度。因為各種交通事故、天災人禍和種種疾病,每年均有成千上萬的人喪失一種或多種能力(如行走、動手能力等)。
隨著人口的增長和醫(yī)療技術的進步,社會老齡化問題已成為很多國家不得不認真對待的重要問題之一。智能輪椅能夠幫助老年人和殘障人士獨立的生活,節(jié)省家庭護理費用,減輕社會負擔。許多國家投入較多資金研究智能輪椅,涌現(xiàn)出許多成果,但由于價格和實用性的原因使它們暫時只能作為實驗產品。
智能輪椅作為移動機器人的一種,主要用來輔助老年人和殘疾人的日常生活和工作,是對他們弱化的機體功能的一種補償.智能輪椅在作為代步工具的同時又可以使用攜帶的機器手臂完成簡單的日?;顒?使他們重新獲得生活能力,找回自立、自尊的感覺,重新融入社會.因而,智能輪椅的研究得到越來越多的關注
本設計的研究目標:在最經濟的條件下,設計出一件最實用、最簡易操作的電動輪椅,功能齊全、結構簡單、適用于傷殘人士、且能達到消費者需求水準的一件市場普及化產品。
主要特色:功能齊全、結構簡便、使用方便、價格適當、安全系數(shù)強
電動輪椅技術及其產業(yè)化
1.產品特點
電動輪椅作為一種安裝有傳感器,具有良好的智能控制功能的電動輪椅,不但具有普通的當前市面上電動輪椅所具有的所有功能,而且可以實現(xiàn)更加友好的人機接口和良好的操作性能。例如,可以實現(xiàn)避碰功能和導航功能,甚至可以實現(xiàn)利用無線方式將使用者的位置和基本狀態(tài)傳送給醫(yī)護人員和家人實現(xiàn)實時監(jiān)控。
2.國內外研究現(xiàn)狀及發(fā)展趨勢(含文獻綜述):
自動輪椅作為醫(yī)療護理領域的服務機器人,其應用大量使用了移動機器人技術在自動輪椅的研究中涉及到的關鍵技術有導航系統(tǒng)、控制和能源系統(tǒng)、人機接口
??????? 但由于整個輪椅系統(tǒng)以人為中心,所以在研究中要解決的核心是輪椅的安全導航問題所謂導航即是指移動機器人按照預先給定的任務命令,根據已知的地圖信息作出全局路徑規(guī)劃,并在行進過程中,不斷感知周圍的局部環(huán)境信息,自主地作出各種決策,并隨時調整自身位姿,引導自身安全行駛到達目標位置
智能輪椅作為醫(yī)療護理領域的服務機器人,其應用大量使用了移動機器人技術。在智能輪椅的研究中涉及到的關鍵技術有導航系統(tǒng)、控制和能源系統(tǒng)、人機接口,但由于整個輪椅系統(tǒng)以人為中心,所以在研究中要解決的核心是輪椅的安全導航問題。所謂導航即是指移動機器人按照預先給定的任務命令,根據已知的地圖信息作出全局路徑規(guī)劃,并在行進過程中,不斷感知周圍的局部環(huán)境信息,自主地作出各種決策,并隨時調整自身位姿,引導自身安全行駛到達目標位置。
隨著社會的發(fā)展和人類文明程度的提高,人們特別是殘疾人愈來愈需要運用現(xiàn)代高新技術來改善他們的生活質量和生活自由度。因為各種交通事故、天災人禍和種種疾病,每年均有成千上萬的人喪失一種或多種能力(如行走、動手能力等)。因此,對用于幫助殘障人行走的機器人輪椅的研究已逐漸成為熱點,如西班牙、意大利等國,中國科學院自動化研究所也成功研制了一種具有視覺和口令導航功能并能與人進行語音交互的智能輪椅。
???????近幾年來我國輪椅車的生產近幾年有了較大的發(fā)展,據中商情報網監(jiān)測數(shù)據顯示,目前全國規(guī)模以上輪椅生產企業(yè)約有30多家企業(yè),主要集中在東部及沿海發(fā)達地區(qū),外商投資輪椅生產企業(yè)在中國輪椅行業(yè)占絕對領導地位。近年來隨著人口老齡化到來及我國殘疾人康復事業(yè)的發(fā)展,這為輪椅生產企業(yè)提供了良好的空間和廣闊的市場前景。
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3.同國外產品的綜合比較
技術水平方面:與國外相比國內已經基本上沒有差距,在某些方面甚至還具有一定優(yōu)勢。
生產工藝方面:雖然與國外相比還有一定差距,但通過分析解剖國外產品特點,利用自身優(yōu)勢可以在較短時間內縮小這種差距。研發(fā)和生產成本方面:與國外相比,國內具有相當大的優(yōu)勢。市場潛力方面:國內電動輪椅市場剛剛啟動,尚沒有強有力的競爭對手,市場潛力非常大。
4.國內現(xiàn)有企業(yè)情況介紹
首先,國內尚無具備智能輪椅生產的企業(yè),現(xiàn)有的輪椅生產企業(yè)還主要定位在電動輪椅的生產上。且由于國內目前上不具備研制開發(fā)高性能電動輪椅控制器的能力,國內的生產企業(yè)的電動輪椅產品基本上都采用了國外的電動輪椅控制器,甚至部分企業(yè)的電動驅動總成也采用了外購方式,因此國內現(xiàn)有企業(yè)的產品成本居高不下,影響了市場購買能力的形成。同時由于不得不采用價格昂貴的進口控制器,國內電動輪椅產品的市場售價長期以來居高不下,難以為普通用戶接受,也直接影響了電動輪椅市場的啟動。
5.國家產業(yè)支持
國家科技發(fā)展部門已經看到智能輪椅產業(yè)的發(fā)展契機,已經從國家的產業(yè)發(fā)展角度來對其未來的發(fā)展進行支持。
下圖是普通輪椅圖
圖1-1-1 電動輪椅運動控制系統(tǒng)示意圖
下圖為設計的電動輪椅產品圖
圖1-1-2 電動輪椅運動控制系統(tǒng)示意圖
圖1-1-3 電動輪椅運動控制系統(tǒng)示意圖
1.2 設計內容
本設計的是為殘疾人士和老年人設計一款電動輪椅。
電動輪椅作為老年人和殘疾人的代步工具,有著嚴格的技術要求。輪椅優(yōu)良的驅動性能和嚴格的安全性保障是首要的技術要求。
技術要求主要如下
1. 基本驅動功能
輪椅的模擬給定是由操縱桿發(fā)出的, 由速度檔位設置按鍵來設定輪椅最高和最低運行速度。輪椅在起/制動時必須平滑穩(wěn)定和安全。電動輪椅對電機的起/制動快速性沒有特殊要求, 但對機械特性有相對較高的要求。輪椅必須能夠至少爬行5°的坡, 能夠在草地等比較糟糕的路況下運行, 能夠在左/右驅動輪處于不同路面時正常運行。
2.故障檢測及保護
控制器應能自動進行故障診斷、定位和報警,并對一些常見故障進行顯示。當輪椅運行時如果檢測出故障, 系統(tǒng)能夠使輪椅安全停止并鎖定;當輪椅靜止時出現(xiàn)故障, 系統(tǒng)應能夠立即鎖定輪椅
1.3 設計思路
本品設計的路線是在普通輪椅上增加電路和電動機,用電能來取代手動,從而使傷殘人士和老年人更方便使用輪椅。電機選擇的是Y160M1,連接電路來帶動鏈條連接機構。用單片機輸出、輸入信號,連接到輪椅扶手上的控制器,當控制器給出命令的時候,單片機驅動電路,再通過電機帶動鏈條,使整個輪椅能運動起來。
本款電動輪椅最快速度為10km/h,具備轉向、加速、減速、剎車功能。
二、系統(tǒng)方案
2.1 機械系統(tǒng)方案
圖2-1-1 電動輪椅運動控制系統(tǒng)示意圖
上圖1為輪椅運動控制系統(tǒng)組成??梢? 電動輪椅運動控制系統(tǒng)主要由操縱桿信號處理部分、電機控制部分和輪椅狀態(tài)檢測分組成。操縱桿輸出的信號經過操縱桿信號處理部分后被合成為帶起/制動S曲線和死區(qū)的輪椅的速度和方向給定值。這個給定值就是用戶給控制器的控制指令。電機控制部分接收用戶的指令和反饋信號來合成電機驅動信號和其他控制信號。這部分是輪椅運動控制系統(tǒng)的核心部分。電機檢測部分檢測電機和控制器的工作狀態(tài)。這些檢測信號被用作電機的控制信號和其它部分的控制信號。
1.1 操縱桿輸出信號速度給定合成由于操縱桿輸出是二維的隨著位置變化而成比例變化的電壓信號, 故非常適合用來控制電動輪椅。用戶前后推動操縱桿可以控制輪椅的運行速度, 左/右推動可以控制輪椅的轉向方向和轉向速度的大小。下面介紹怎樣把一個二維的操縱桿
輸出信號轉換為速度和轉向控制指令。如果把操縱桿的信號看作是二維輸出信號,分別在二維坐標系中用X軸和Y軸表示[ 1 ]。
圖2-1-2 操縱桿輸出信號矢量合成示意圖
可以將X軸信號看作是輪椅的轉向速度給定信號, 而Y軸信號則可以看作是輪椅的前向和后向速度給定信號。因此, 如果用戶想要轉向和前進,則可將輪椅的運動方向看作是X和Y的矢量合成,如圖2中所示F。而左/右電機的速度給定Sl 和Sr可從下式得出[ 2 ] :
Sl =Cx Fx +Cy Fy±Smax(1)
Sr =- Cx Fx +Cy Fy±Smax(2)
其中, 設Smax為速度給定最大值, Cx代表輪椅的轉向速度特性, 而Cy 則代表輪椅在前向和反向的速度特性。如果以上公式的計算結果大于了輪椅最大轉向速度, 則用最大轉向速度代替計算結果。
圖3表示以不同角度旋轉操縱桿時, 輪椅的左/右輪速度給定曲線。如果Sl 和Sr 的值都是正的, 則輪椅向前前進轉向, 否則是后退轉向。當輪椅向左轉時, 右輪正向轉動, 左輪反向轉動或保持不變; 相反, 當輪椅向右轉時, 左輪正向轉動, 右輪反向轉動或保持不變。當一個輪保持不轉動而另外一個輪轉動時, 輪椅做原地360°轉彎。
圖2-1-3 以不同角度旋轉操縱桿時輪椅的左/右輪的速度曲線
1.2 速度給定的S曲線設計
(1) 設計思路。S曲線本身是一個非線性函數(shù),其合成和編程都非常復雜。S曲線的形狀如圖4虛線所示。在輪椅起動時應該是一個拋物線形狀, 然后是輪椅的加速過程, 直至輪椅最大速度后, 加速度為零, 輪椅以恒定最大給定速度運行; 制動時,輪椅先以直線的斜率減速, 最后在拋物線段舒緩地停止。本文用圖4中的一個折線近似地代替S曲線,用三段折線用來模擬拋物線。這使得編程非常簡單,實踐證明, 控制效果非常理想。
圖2-1-4 輪椅速度給定的S曲線示意圖
(2) 實現(xiàn)方法。利用中斷時間和人體對加速度變化率的敏感特性來實現(xiàn)。根據人體對加速度和加速度變化率的敏感特性知, 當加速度或減速度最大值不大于1.5 m / s2、平均加減速度不低于0.5 m / s2、加速度變化率小于1.5 m / s3 時, 人體的舒適感比較好。設系統(tǒng)的中斷周期為T, 直線的斜率為K, 規(guī)定輪椅在t時間內加速到速度給定最大值Smax , 則:
K =Smaxt/T=SmaxtT (3)
圖4中, 三段線段斜率比值為: K1 ∶K2 ∶K3 = 1 ∶1.92 ∶2.6。具體程序實現(xiàn)見第四節(jié)。在本系統(tǒng)的設計中, K1、K2、K3 都被設置為可編程調節(jié)參數(shù),用戶可以根據自己的舒適性要求來進行相應調整。
2.2 控制方案設計
對調速系統(tǒng)來說, 用轉速負反饋可以獲得比較滿意的靜、動態(tài)性能。但是, 在本文的電動輪椅運動控制系統(tǒng)的設計中要實現(xiàn)轉速負反饋是非常困難的, 因為無法安裝轉速檢測裝置。故在設計中采用電壓負反饋和電流補償?shù)目刂品椒╗ 3 ]。如果忽略電樞壓降, 則直流電動機的轉速近似與電樞兩端電壓成正比, 所以電壓負反饋基本上能夠代替轉速負反饋的作用。采用電壓負反饋和電流補償控制的調速系統(tǒng)原理圖如圖5所示
圖2-2-1 電壓負反饋和電流補償控制的調速系統(tǒng)原理圖
其中, V +、V - 分別為電動機兩端的電壓。它們同時被送入DSP 的AD采樣通道中, 在軟件中對V +、V - 進行差分得到電機兩端的電壓。這樣可以消除由于電源電壓波動等因素引起的電機端電壓的誤差。R1、R2 是采樣電阻, 之所以有兩個采樣電阻, 是因為文中所討論的電動輪椅控制系統(tǒng)采用雙極性模式, 可在四象限運行。由如圖5所示的H橋可知, R2、R1可分別檢測電機的正反向電流。對應的系統(tǒng)控制方框圖如圖6所示。
2.3 總體方案:
在多次觀察了普通輪椅之后,發(fā)現(xiàn)在普通輪椅的座位底部安裝雙電動機,然后把鏈條安裝在雙電動機的連桿上,利用單片機來輸出、輸入信號,在單片機和雙電動機的電路連接下,使整個設計機構有一個完整的回路。從而實現(xiàn)這款電動輪椅的運行。
整個設計思路其實比較是簡單的,在安裝了設計電路后,通過電動機做功來帶動鏈條傳動,來實現(xiàn)電動輪椅行走、加速、減速、剎車的各項功能。
三、機械結構設計
3.1 鏈條傳動設計
雙電機組合帶動鏈條,以電動機產生動力,電帶動電動機上的桿和錐齒輪,通過鏈條的連接機構,而帶動車輪連桿上的鏈輪,這樣形成一個整體機構過程。
開啟電源后,當控制器發(fā)出運行命令時,信號通過單片機電路與電動機連接,電動機開始啟動,通過鏈條的傳動,帶動車輪向前或者向后行駛。
3.2 電動機的選用
本設計用的是雙電機組合,所以在選擇電動機時,依照電動輪椅運行時最大速度10km/h,來選擇電動機。
=
=
選擇的電動機是Y160M1 電動機轉速720
車輪的轉速:
則:
實際功率:
傳動比:
3.3 驅動電路設計
在本設計系統(tǒng)中,選用的是ST公司的L298N電機專用驅動芯片。該芯片的主要特點是:工作電壓高,最高工作電壓可達46V;輸出電流大,瞬間峰值電流可達3A,持續(xù)工作電流為2A;內含兩個H橋的高電壓大電流全橋式驅動器,可以用來驅動直流電動機和步進電動機、繼電器、線圈等感性負載;采用標準邏輯電平信號控制;具有兩個使能控制端,在不受輸入信號影響的情況下允許或禁止器件工作有一個邏輯電源輸入端,使內部邏輯電路部分在低電壓下工作;可以外接檢測電阻,將變化量反饋給控制電路。
圖3-3-1 電動輪椅運動控制系統(tǒng)示意圖
圖中電源和地之間接入了去耦電容,在電機線圈兩端分別接入二極管進行過流保護。
四、控制系統(tǒng)設計
4.1 控制系統(tǒng)軟件設計
輪椅運動控制系統(tǒng)總的流程如圖7所示。本文設計的輪椅控制系統(tǒng)是純數(shù)字化控制。系統(tǒng)軟件采用匯編語言編寫, 代碼運行效率高; 采用模塊化的程序設計方法, 各功能模塊之間除接口變量外互相獨立。
圖4-1-1 輪椅運動控制系統(tǒng)總程序流程圖
五、總 結
5.1 設計總結
本文以電動輪椅運動控制為背景,依據系統(tǒng)控制方案編制了相應的控制軟件, 軟件模塊化并考慮了參數(shù)修改和運行狀態(tài)顯示等功能。經調試和試運行, 技術指標達到了預期要求。從考慮人的舒適性和可靠性出發(fā), 提出了基于電壓檢測的功率管故障及主電路故障判斷、定位的實施方案, 并給出了速度給定S曲線計算公式和軟件編程算法。運行效果良好。操縱桿是輪椅運動速度方向和大小的給定裝置。
通過分析其原理導出了計算公式, 并通過軟件實現(xiàn)取得了良好效果??傊? 本文完成了輪椅運動控制器設計、調試和試運行, 各項指標均達到了預期目標, 驗證了硬、軟件方案正確性及可行性。
本文的項目設計以《國家高技術研究發(fā)展計劃(863計劃)先進制造技術
領域“服務機器人”重點項目2006年度課題申請指南》中課題l——智能輪椅關
鍵技術、單元部件及目標產品的研發(fā)的主要考核指標為參考技術標準,目標是
構建一個為老年人和殘疾人服務的電動輪椅。
從電動輪椅功能的角度對輪椅的硬件系統(tǒng)進行模塊化設計,將電動輪
椅分為機械結構、驅動、控制三部分。重點介紹了電動輪椅控制系統(tǒng),最主要的是設計了DA轉換平臺,成功接管了智能輪椅核心控制器。利用控制器,成功實現(xiàn)電動控制系統(tǒng)。
在設計電路控制器的工作,讓單片機開發(fā)板通過程序直接控制輪椅運動。
5.2 展望
如前所述,本課題設計電動輪椅控制系統(tǒng),基本達到了實用性
的要求。但由于多方面的原因,該系統(tǒng)需要進一步的改進與完善,還存在著很
多不足。
在采用輪椅控制器控制電機時沒有加入測速環(huán)節(jié)構成閉環(huán)反饋控制系
統(tǒng)。由于每個用戶的體重不同,且輪椅行駛的路面情況不同,根據直流電機負
載特性曲線可知,輪椅的實際電機轉速將會與設定值不同,這在實際應用中是
不應該出現(xiàn)的,雖然在短時間內實現(xiàn)了低成本的控制,仍然無法達到最智能的效果。
缺乏機器視覺技術的應用。本項目中圖像傳感器僅應用于路徑跟
蹤,沒有開發(fā)復雜的圖像處理與識別算法,且此處僅適用于跟蹤白色路面上的
黑色路標,使用場合有限。應用先進的機器視覺技術能夠大大提高輪椅的自主
性和智能化。
61
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外文翻譯
GEAR AND SHAFT INTRODUCTION
Si Tuzhong
Abstract: The important position of the wheel gear and shaft can falter in traditional machine and modern machines.The wheel gear and shafts mainly install the direction that delivers the dint at the principal axis box.The passing to process to make them can is divided into many model numbers, useding for many situations respectively.So we must be the multilayers to the understanding of the wheel gear and shaft in many ways .
Key words: Wheel gear;Shaft
In the force analysis of spur gears, the forces are assumed to act in a single plane. We shall study gears in which the forces have three dimensions. The reason for this, in the case of helical gears, is that the teeth are not parallel to the axis of rotation. And in the case of bevel gears, the rotational axes are not parallel to each other. There are also other reasons, as we shall learn.
Helical gears are used to transmit motion between parallel shafts. The helix angle is the same on each gear, but one gear must have a right-hand helix and the other a left-hand helix. The shape of the tooth is an involute helicoid. If a piece of paper cut in the shape of a parallelogram is wrapped around a cylinder, the angular edge of the paper becomes a helix. If we unwind this paper, each point on the angular edge generates an involute curve. The surface obtained when every point on the edge generates an involute is called an involute helicoid.
The initial contact of spur-gear teeth is a line extending all the way across the face of the tooth. The initial contact of helical gear teeth is a point, which changes into a line as the teeth come into more engagement. In spur gears the line of contact is parallel to the axis of the rotation; in helical gears, the line is diagonal across the face of the tooth. It is this gradual of the teeth and the smooth transfer of load from one tooth to another, which give helical gears the ability to transmit heavy loads at high speeds. Helical gears subject the shaft bearings to both radial and thrust loads. When the thrust loads become high or are objectionable for other reasons, it may be desirable to use double helical gears. A double helical gear (herringbone) is equivalent to two helical gears of opposite hand, mounted side by side on the same shaft. They develop opposite thrust reactions and thus cancel out the thrust load. When two or more single helical gears are mounted on the same shaft, the hand of the gears should be selected so as to produce the minimum thrust load.Crossed-helical, or spiral, gears are those in which the shaft centerlines are neither parallel nor intersecting. The teeth of crossed-helical fears have point contact with each other, which changes to line contact as the gears wear in. For this reason they will carry out very small loads and are mainly for instrumental applications, and are definitely not recommended for use in the transmission of power. There is on difference between a crossed helical gear and a helical gear until they are mounted in mesh with each other. They are manufactured in the same way. A pair of meshed crossed helical gears usually have the same hand; that is ,a right-hand driver goes with a right-hand driven. In the design of crossed-helical gears, the minimum sliding velocity is obtained when the helix angle are equal. However, when the helix angle are not equal, the gear with the larger helix angle should be used as the driver if both gears have the same hand.
Worm gears are similar to crossed helical gears. The pinion or worm has a small number of teeth, usually one to four, and since they completely wrap around the pitch cylinder they are called threads. Its mating gear is called a worm gear, which is not a true helical gear. A worm and worm gear are used to provide a high angular-velocity reduction between nonintersecting shafts which are usually at right angle. The worm gear is not a helical gear because its face is made concave to fit the curvature of the worm in order to provide line contact instead of point contact. However, a disadvantage of worm gearing is the high sliding velocities across the teeth, the same as with crossed helical gears.
Worm gearing are either single or double enveloping. A single-enveloping gearing is one in which the gear wraps around or partially encloses the worm.. A gearing in which each element partially encloses the other is, of course, a double-enveloping worm gearing. The important difference between the two is that area contact exists between the teeth of double-enveloping gears while only line contact between those of single-enveloping gears. The worm and worm gear of a set have the same hand of helix as for crossed helical gears, but the helix angles are usually quite different. The helix angle on the worm is generally quite large, and that on the gear very small. Because of this, it is usual to specify the lead angle on the worm, which is the complement of the worm helix angle, and the helix angle on the gear; the two angles are equal for a 90-deg. Shaft angle.
When gears are to be used to transmit motion between intersecting shaft, some of bevel gear is required. Although bevel gear are usually made for a shaft angle of 90 deg. They may be produced for almost any shaft angle. The teeth may be cast, milled, or generated. Only the generated teeth may be classed as accurate. In a typical bevel gear mounting, one of the gear is often mounted outboard of the bearing. This means that shaft deflection can be more pronounced and have a greater effect on the contact of teeth. Another difficulty, which occurs in predicting the stress in bevel-gear teeth, is the fact the teeth are tapered.
Straight bevel gears are easy to design and simple to manufacture and give very good results in service if they are mounted accurately and positively. As in the case of squr gears, however, they become noisy at higher values of the pitch-line velocity. In these cases it is often good design practice to go to the spiral bevel gear, which is the bevel counterpart of the helical gear. As in the case of helical gears, spiral bevel gears give a much smoother tooth action than straight bevel gears, and hence are useful where high speed are encountered.
It is frequently desirable, as in the case of automotive differential applications, to have gearing similar to bevel gears but with the shaft offset. Such gears are called hypoid gears because their pitch surfaces are hyperboloids of revolution. The tooth action between such gears is a combination of rolling and sliding along a straight line and has much in common with that of worm gears.
A shaft is a rotating or stationary member, usually of circular cross section, having mounted upon it such elementsas gears, pulleys, flywheels, cranks, sprockets, and other power-transmission elements. Shaft may be subjected to bending, tension, compression, or torsional loads, acting singly or in combination with one another. When they are combined, one may expect to find both static and fatigue strength to be important design considerations, since a single shaft may be subjected to static stresses, completely reversed, and repeated stresses, all acting at the same time.
The word “shaft” covers numerous variations, such as axles and spindles. Anaxle is a shaft, wither stationary or rotating, nor subjected to torsion load. A shirt rotating shaft is often called a spindle.
When either the lateral or the torsional deflection of a shaft must be held to close limits, the shaft must be sized on the basis of deflection before analyzing the stresses. The reason for this is that, if the shaft is made stiff enough so that the deflection is not too large, it is probable that the resulting stresses will be safe. But by no means should the designer assume that they are safe; it is almost always necessary to calculate them so that he knows they are within acceptable limits. Whenever possible, the power-transmission elements, such as gears or pullets, should be located close to the supporting bearings, This reduces the bending moment, and hence the deflection and bending stress.
Although the von Mises-Hencky-Goodman method is difficult to use in design of shaft, it probably comes closest to predicting actual failure. Thus it is a good way of checking a shaft that has already been designed or of discovering why a particular shaft has failed in service. Furthermore, there are a considerable number of shaft-design problems in which the dimension are pretty well limited by other considerations, such as rigidity, and it is only necessary for the designer to discover something about the fillet sizes, heat-treatment, and surface finish and whether or not shot peening is necessary in order to achieve the required life and reliability.
Because of the similarity of their functions, clutches and brakes are treated together. In a simplified dynamic representation of a friction clutch, or brake, two inertias I1 and I2 traveling at the respective angular velocities W1 and W2, one of which may be zero in the case of brake, are to be brought to the same speed by engaging the clutch or brake. Slippage occurs because the two elements are running at different speeds and energy is dissipated during actuation, resulting in a temperature rise. In analyzing the performance of these devices we shall be interested in the actuating force, the torque transmitted, the energy loss and the temperature rise. The torque transmitted is related to the actuating force, the coefficient of friction, and the geometry of the clutch or brake. This is problem in static, which will have to be studied separately for eath geometric configuration. However, temperature rise is related to energy loss and can be studied without regard to the type of brake or clutch because the geometry of interest is the heat-dissipating surfaces. The various types of clutches and brakes may be classified as fllows:
1. Rim type with internally expanding shoes
2. Rim type with externally contracting shoes
3. Band type
4. Disk or axial type
5. Cone type
6. Miscellaneous type
The analysis of all type of friction clutches and brakes