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畢業(yè)設(shè)計（論文）
題目：雙軸無重力粉體混合機(jī)混合單元的設(shè)計
系 別 航空工程系
專業(yè)名稱 機(jī)械設(shè)計制造及其自動化
班級學(xué)號 088105403
學(xué)生姓名 陳強(qiáng)華
指導(dǎo)教師 張緒坤
二O一二 年 六 月
南昌航空大學(xué)科技學(xué)院學(xué)士學(xué)位論文
目 錄
1 緒論 1
1.1 混合設(shè)備在工業(yè)生產(chǎn)中的應(yīng)用 1
1.2 混合物料的種類及特性 2
2 混合罐結(jié)構(gòu)設(shè)計 2
2.1 罐體的尺寸確定及結(jié)構(gòu)選型 2
2.1.1 筒體及封頭型式 2
2.1.2 確定內(nèi)筒體和封頭的直徑 2
2.1.3 確定內(nèi)筒體高度H 3
2.1.4 選取夾套直徑 3
2.1.5 校核傳熱面積 3
2.2 內(nèi)筒體及夾套的壁厚計算 3
2.2.1 選擇材料，確定設(shè)計壓力 4
2.2.2 夾套筒體和夾套封頭厚度計算 5
2.2.3 內(nèi)筒體壁厚計算 6
2.3入孔選型及開孔補(bǔ)強(qiáng)設(shè)計 6
2.4混合器的選型 8
2.5混合附件 9
3 傳動裝置的設(shè)計 10
3.1 減速器和電動機(jī)的選型條件 10
3.2 電動機(jī)與減速器的選擇 10
3.3 聯(lián)軸器的選型 12
3.4 混合軸的設(shè)計及其結(jié)果驗證 12
3.5 軸與槳葉、聯(lián)軸器的連接 12
3.5.1 連接形式 12
3.5.2 聯(lián)軸器與軸的連接 13
3.6 軸承的設(shè)計與校核 13
3.6.1 混合軸受力模型選擇與軸長的計算 14
3.6.2 按扭轉(zhuǎn)變形計算計算混合軸的軸徑 17
3.6.3 根據(jù)臨界轉(zhuǎn)速核算混合軸軸徑 20
3.6.4 按強(qiáng)度計算混合軸的軸徑 23
3.6.5 按軸封處（或軸上任意點(diǎn)處處）允許徑向位移驗算軸徑 24
3.6.6 軸徑的最后確定 24
4 支撐裝置設(shè)計 24
4.1 混合機(jī)的支承部分 24
4.1.1 機(jī)座 25
4.1.2 軸承裝置 25
4.2 下支撐座的設(shè)計 26
4.2.1 軸承的選型 27
4.2.2 支撐套的設(shè)計 27
5 軸的密封 27
5.1 密封裝置的類型 27
5.2 軸的密封選擇 27
5.3 封口錐結(jié)構(gòu)選型與計算 28
結(jié) 論 32
參考文獻(xiàn) 33
致 謝 34
南昌航空大學(xué)科技學(xué)院學(xué)士學(xué)位論文
The design of double-axial without gravity powder mixer's mixing unit
Student name: Chen Qianghua Class: 088105403
Supervisor: Zhang Xukun
Abstract: Mixing can make two or more different substances dispersed into each other in each other, so as to achieve uniform mixing, that can also speed up the process of heat and mass transfer.In industrial production, mixing operation is started from the chemical industry, focusing on food, fiber, paper, petroleum, water treatment, as part of the process widely used. In industrial production, most of the mixing operations are mechanical mixing system to medium and low voltage vertical mixing equipment based steel containers. Mixing equipment mainly contains three major parts of mixing device,seal and mixed cans.
The design issue is mainly related to biaxial mixer weightless dust mixed reaction mixer unit design, including mixed cans, motor and reducer selection, support equipment design, shaft seal set design.
Keywords: Mixer Axis gravity Mixing unit Mechanical design
Signature of supervisor:
南昌航空大學(xué)科技學(xué)院學(xué)士學(xué)位論文
雙軸無重力粉體混合機(jī)混合單元的設(shè)計
1 緒論
混合可以使兩種或多種不同的物質(zhì)在彼此之中互相分散，從而達(dá)到均勻混合；也可以加速傳熱和傳質(zhì)過程。在工業(yè)生產(chǎn)中，混合操作時從化學(xué)工業(yè)開始的，圍繞食品、纖維、造紙、石油、水處理等，作為工藝過程的一部分而被廣泛應(yīng)用。
混合操作分為機(jī)械混合與氣流混合。氣流混合是利用氣體鼓泡通過液體層，對液體產(chǎn)生混合作用，或使氣泡群一密集狀態(tài)上升借所謂上升作用促進(jìn)液體產(chǎn)生對流循環(huán)。與機(jī)械混合相比，僅氣泡的作用對液體進(jìn)行的混合時比較弱的，對于幾千毫帕·秒以上的高粘度液體是難于使用的。但氣流混合無運(yùn)動部件，所以在處理腐蝕性液體，高溫高壓條件下的反應(yīng)液體的混合時比較便利的。在工業(yè)生產(chǎn)中，大多數(shù)的混合操作均系機(jī)械混合，以中、低壓立式鋼制容器的混合設(shè)備為主?；旌显O(shè)備主要由混合裝置、軸封和混合罐三大部分組成。
1.1 混合設(shè)備在工業(yè)生產(chǎn)中的應(yīng)用
混合設(shè)備在工業(yè)生產(chǎn)中的應(yīng)用范圍很廣，尤其是化學(xué)工業(yè)中，很多的化工生產(chǎn)都或多或少地應(yīng)用著混合操作。混合設(shè)備在許多場合時作為反應(yīng)器來應(yīng)用的。例如在三大合成材料的生產(chǎn)中，混合設(shè)備作為反應(yīng)器約占反應(yīng)器總數(shù)的99%。?；旌显O(shè)備的應(yīng)用范圍之所以這樣廣泛，還因混合設(shè)備操作條件（如濃度、溫度、停留時間等）的可控范圍較廣，又能適應(yīng)多樣化的生產(chǎn)?；旌显O(shè)備的作用如下：①使物料混合均勻；②使氣體在液相中很好的分散；③使固體粒子（如催化劑）在液相中均勻的懸??；④使不相溶的另一液相均勻懸浮或充分乳化；⑤強(qiáng)化相間的傳質(zhì)（如吸收等）；⑥強(qiáng)化傳熱。混合設(shè)備在石油化工生產(chǎn)中被用于物料混合、溶解、傳熱、植被懸浮液、聚合反應(yīng)、制備催化劑等。例如石油工業(yè)中，異種原油的混合調(diào)整和精制，汽油中添加四乙基鉛等添加物而進(jìn)行混合使原料液或產(chǎn)品均勻化?；どa(chǎn)中，制造苯乙烯、乙烯、高壓聚乙烯、聚丙烯、合成橡膠、苯胺燃料和油漆顏料等工藝過程，都裝備著各種型式的混合設(shè)備。
1.2 混合物料的種類及特性
混合物料的種類主要是指流體。在流體力學(xué)中，把流體分為牛頓型和非牛頓型。非牛頓型流體又分為賓漢塑性流體、假塑性流體和脹塑性流體。在混合設(shè)備中由于混合器的作用，而使流體運(yùn)動。
2 混合罐結(jié)構(gòu)設(shè)計
本課題的主要設(shè)計參數(shù)是：
1、生產(chǎn)率：5噸/時；
2、裝機(jī)容量：11千瓦；
3、分批混合：500kg/批；
4、產(chǎn)品質(zhì)量：混合均勻度變異系數(shù)cv≤5%；
5、能耗：耗電≤5kWh/t；
2.1 罐體的尺寸確定及結(jié)構(gòu)選型
2.1.1 筒體及封頭型式
選擇圓柱形筒體，采用標(biāo)準(zhǔn)橢圓形封頭
2.1.2 確定內(nèi)筒體和封頭的直徑
發(fā)酵罐類設(shè)備長徑比取值范圍是1.7~2.5，綜合考慮罐體長徑比對混合功率、傳熱以及物料特性的影響選取根據(jù)工藝要求，裝料系數(shù)，罐體全容積，罐體公稱容積（操作時盛裝物料的容積）。
初算筒體直徑
即
圓整到公稱直徑系列，去。封頭取與內(nèi)筒體相同內(nèi)經(jīng)，封頭直邊高度，
2.1.3 確定內(nèi)筒體高度H
當(dāng)時，查《化工設(shè)備機(jī)械基礎(chǔ)》表16-6得封頭的容積
，取
核算與
，該值處于之間，故合理。
該值接近，故也是合理的。
2.1.4 選取夾套直徑
表1 夾套直徑與內(nèi)通體直徑的關(guān)系
內(nèi)筒徑
夾套
由表1，取。
夾套封頭也采用標(biāo)準(zhǔn)橢圓形，并與夾套筒體取相同直徑
2.1.5 校核傳熱面積
工藝要求傳熱面積為，查《化工設(shè)備機(jī)械基礎(chǔ)》表16-6得內(nèi)筒體封頭表面積高筒體表面積為
總傳熱面積為
故滿足工藝要求。
2.2 內(nèi)筒體及夾套的壁厚計算
2.2.1 選擇材料，確定設(shè)計壓力
按照《鋼制壓力容器》（）規(guī)定，決定選用高合金鋼板，該板材在一下的許用應(yīng)力由《過程設(shè)備設(shè)計》附表查取，，常溫屈服極限。
計算夾套內(nèi)壓
介質(zhì)密度
液柱靜壓力
最高壓力
設(shè)計壓力
所以
故計算壓力
內(nèi)筒體和底封頭既受內(nèi)壓作用又受外壓作用，按內(nèi)壓則取，按外壓則取
2.2.2 夾套筒體和夾套封頭厚度計算
夾套材料選擇熱軋鋼板，其
夾套筒體計算壁厚
夾套采用雙面焊，局部探傷檢查，查《過程設(shè)備設(shè)計》表4-3得
則
查《過程設(shè)備設(shè)計》表4-2取鋼板厚度負(fù)偏差，對于不銹鋼，當(dāng)介質(zhì)的腐蝕性極微時，可取腐蝕裕量，對于碳鋼取腐蝕裕量，故內(nèi)筒體厚度附加量，夾套厚度附加量。
根據(jù)鋼板規(guī)格，取夾套筒體名義厚度。
夾套封頭計算壁厚為
取厚度附加量，確定取夾套封頭壁厚與夾套筒體壁厚相同。
2.2.3 內(nèi)筒體壁厚計算
①按承受內(nèi)壓計算
焊縫系數(shù)同夾套，則內(nèi)筒體計算壁厚為：
②按承受外壓計算
設(shè)內(nèi)筒體名義厚度，則，內(nèi)筒體外徑。
內(nèi)筒體計算長度。
則，，由《過程設(shè)備設(shè)計》圖4-6查得，圖4-9查得，此時許用外壓為：
不滿足強(qiáng)度要求，再假設(shè)，則，，
內(nèi)筒體計算長度
則，
查《過程設(shè)備設(shè)計》圖4-6得,圖4-9得，此時許用外壓為：
故取內(nèi)筒體壁厚可以滿足強(qiáng)度要求。
考慮到加工制造方便，取封頭與夾套筒體等厚，即取封頭名義厚度。按內(nèi)壓計算肯定是滿足強(qiáng)度要求的，下面僅按封頭受外壓情況進(jìn)行校核。封頭有效厚度。由《過程設(shè)備設(shè)計》表4-5查得標(biāo)準(zhǔn)橢圓形封頭的形狀系數(shù)，則橢圓形封頭的當(dāng)量球殼內(nèi)徑，計算系數(shù)A
查《過程設(shè)備設(shè)計》圖4-9得
故封頭壁厚取可以滿足穩(wěn)定性要求。
2.2.4 水壓試驗校核
①試驗壓力
內(nèi)同試驗壓力取
夾套實(shí)驗壓力取
②內(nèi)壓試驗校核
內(nèi)筒筒體應(yīng)力
夾套筒體應(yīng)力
而
故內(nèi)筒體和夾套均滿足水壓試驗時的應(yīng)力要求。
③外壓實(shí)驗校核
由前面的計算可知，當(dāng)內(nèi)筒體厚度取時，它的許用外壓為，小于夾套的水壓試驗壓力，故在做夾套的壓力實(shí)驗校核時，必須在內(nèi)筒體內(nèi)保持一定壓力，以使整個試驗過程中的任意時間內(nèi)，夾套和內(nèi)同的壓力差不超過允許壓差。
2.3 入孔選型及開孔補(bǔ)強(qiáng)設(shè)計
①入孔選型
選擇回轉(zhuǎn)蓋帶頸法蘭入孔，標(biāo)記為：入孔PN2.5,DN450,HG/T 21518-2005,尺寸如下表所示:
密封面
形式
公稱壓力PN（MP）
公稱直徑DN
突面
（RF）
螺柱
螺母
螺柱
總質(zhì)量
（）
數(shù)量
直徑長度
開孔補(bǔ)強(qiáng)設(shè)計
最大的開孔為入孔，筒節(jié)，厚度附加量，補(bǔ)強(qiáng)計算如下：
開孔直徑
圓形封頭因開孔削弱所需補(bǔ)強(qiáng)面積為：
入孔材料亦為不銹鋼0Cr18Ni9，所以
所以
有效補(bǔ)強(qiáng)區(qū)尺寸：
在有效補(bǔ)強(qiáng)區(qū)范圍內(nèi)，殼體承受內(nèi)壓所需設(shè)計厚度之外的多余金屬面積為：
故
可見僅就大于,故不需另行補(bǔ)強(qiáng)。
最大開孔為入孔，而入孔不需另行補(bǔ)強(qiáng)，則其他接管均不需另行補(bǔ)強(qiáng)。
2.4 混合器的選型
槳徑與罐內(nèi)徑之比叫槳徑罐徑比,渦輪式葉輪的一般為0.25~0.5，渦輪式為快速型，快速型混合器一般在時設(shè)置多層混合器，且相鄰混合器間距不小于葉輪直徑d。適應(yīng)的最高黏度為左右。
混合器在圓形罐中心直立安裝時，渦輪式下層葉輪離罐底面的高度C一般為槳徑的1~1.5倍。如果為了防止底部有沉降，也可將葉輪放置低些，如離底高度.最上層葉輪高度離液面至少要有1.5d的深度。
符號說明
——鍵槽的寬度
——混合器槳葉的寬度
——輪轂內(nèi)經(jīng)
——混合器槳葉連接螺栓孔徑
——混合器緊定螺釘孔徑
——輪轂外徑
——混合器直徑
——混合器圓盤的直徑
——混合器參考質(zhì)量
——輪轂高度
——圓盤到輪轂底部的高度
——混合器葉片的長度
——弧葉圓盤渦輪混合器葉片的弧半徑
——混合器許用扭矩
——輪轂內(nèi)經(jīng)與鍵槽深度之和
——混合器槳葉的厚度
——混合器圓盤的厚度
工藝給定混合器為六彎葉圓盤渦輪混合器，其后掠角為，圓盤渦輪混合器的通用尺寸為槳徑:槳長:槳寬，圓盤直徑一般取槳徑的，彎葉的圓弧半徑可取槳徑的。
查HG-T 3796.1~12-2005,選取混合器參數(shù)如下表
由前面的計算可知液層深度，而，故，則設(shè)置兩層混合器。為防止底部有沉淀，將底層葉輪放置低些，離底層高度為，上層葉輪高度離液面的深度，即。則兩個混合器間距為，該值大于也輪直徑，故符合要求。
2.5 混合附件
①擋板
擋板一般是指長條形的豎向固定在罐底上板，主要是在湍流狀態(tài)時，為了消除罐中央的“圓柱狀回轉(zhuǎn)區(qū)”而增設(shè)的。罐內(nèi)徑為，選擇塊豎式擋板，且沿罐壁周圍均勻分布地直立安裝。
3 傳動裝置的設(shè)計
3.1 減速器和電動機(jī)的選型條件
(1) 機(jī)械效率，傳動化，功率，進(jìn)出軸的許用扭距和相對位置。
(2) 出軸旋轉(zhuǎn)方向是單項或雙向。
(3) 混合軸軸向力的大小和方向。
(4) 工作平穩(wěn)性，如震動和荷載變化情況。
(5) 外形尺寸應(yīng)滿足安裝及檢修要求。
(6) 使用單位的維修能力。
(7) 經(jīng)濟(jì)性。
3.2電動機(jī)與減速器的選擇
混合設(shè)備的電動機(jī)通常選用普通異步電動機(jī)。澄清池混合機(jī)采用YCT系列滑差式電磁調(diào)速異步電動機(jī)，消化池混合機(jī)一般采用防爆異步電動機(jī)。
混合設(shè)備的減速器應(yīng)優(yōu)先選用標(biāo)準(zhǔn)減速器及專業(yè)生產(chǎn)廠產(chǎn)品，參考文獻(xiàn)[2]“標(biāo)準(zhǔn)減速器及產(chǎn)品”選用，其中一般選用機(jī)械效率較高的擺線針輪減速器或齒輪減速器：有防爆要求時一般不采用皮帶傳動：要求正反向傳動時一般不選用蝸輪傳動。電動機(jī)及減速機(jī)選用，見表3-1
表3-1電動機(jī)與減速器的選型
名稱
符號
單位
第一檔
第二檔
第三檔
混合器的轉(zhuǎn)速
n
r/min
7.5
5.9
3.64
混合功率
N
KW
0.34
0.16
0.04
電動機(jī)算功率
N=式中
k—工況系數(shù)24h連續(xù)運(yùn)行為1.2
=擺線針輪減速機(jī)傳動效率
=滾動軸承傳動效率
KW
0.46
0.22
0.05
選用電動機(jī)的功率
KW
0.8
0.4
0.4
電動機(jī)同步轉(zhuǎn)速
r/min
1500
1500
1500
減速比
200
254
412
選用減速器減速比
187
289
385
選用減速器輸出軸轉(zhuǎn)速
r/min
8
5.2
3.9
3.3 聯(lián)軸器的選型
根據(jù)機(jī)械設(shè)計手冊及混合機(jī)的類型選用凸緣聯(lián)軸器，由電機(jī)的尺寸選擇聯(lián)軸器軸徑d=65mm， L1=104mm，L2 =42mm，許用扭轉(zhuǎn)為850N.m，質(zhì)量為17.97Kg，標(biāo)記為：聯(lián)軸器D65-ZG，
3.4 混合軸的設(shè)計及其結(jié)果驗證
由上面所選聯(lián)軸器的類型初步確定混合軸小徑為：d1=65mm
下面來做軸徑的理論計算：
由《過程裝備設(shè)計》查的公式：
（3.1）
式中C2—按扭轉(zhuǎn)剛度計算系數(shù)，當(dāng)扭轉(zhuǎn)角為1/m時，C2=91.5
N—混合器的功率，單位KW
n—混合器的轉(zhuǎn)速，單位r/min
得：
第一檔：
第二檔：
第三檔：
經(jīng)上面計算所的結(jié)果可以看出3個軸徑的理論數(shù)值都小于65mm，故軸的小徑選：
d1=65mm
3.5 軸與槳葉、聯(lián)軸器的連接
3.5.1 連接形式
槳式混合器與軸的連接，當(dāng)采用槳葉一端煨成半個軸套，用螺栓將對開的軸套夾緊在混合軸上的結(jié)構(gòu)時D≤600mm時用一對螺栓鎖緊：D＞600mm時用兩對螺栓鎖緊。這種連接結(jié)構(gòu)為傳遞扭距可靠起見，宜用一穿軸螺栓使混合器與軸固定。
本設(shè)計由于軸選取D≤600mm，故選用一對螺栓縮緊裝置。
3.5.2 聯(lián)軸器與軸的連接
當(dāng)采用鍵和止動螺釘將混合器軸套固定在混合軸上的結(jié)構(gòu)時，鍵應(yīng)按GB1095-79《平鍵和鍵槽的剖面尺寸》選取?；旌掀鬏S套外勁D宜為軸徑D的1.6-2倍。軸套長度應(yīng)略大于軸套處槳葉寬度在軸線上的投影長度，但不小于D1。
由上面設(shè)計知：d1=65mm，再由文獻(xiàn)[4]查得，選取鍵為圓鍵，長度為85mm，寬度為18mm，厚度為14mm。
3.6 軸承的設(shè)計與校核
3.6.1 混合軸受力模型選擇與軸長的計算
軸長：
3.6.2 按扭轉(zhuǎn)變形計算計算混合軸的軸徑
軸的許用扭轉(zhuǎn)角，對單跨軸有；
混合軸傳遞的最大扭矩
上式中,，帶傳動取，
所以
根據(jù)前面附件的選型。取
根據(jù)軸徑計算軸的扭轉(zhuǎn)角
所以
3.6.3 根據(jù)臨界轉(zhuǎn)速核算混合軸軸徑
剛性軸（不包括帶錨式和框式混合器的剛性軸）的有效質(zhì)量等于軸自身的質(zhì)量加上軸附帶的液體質(zhì)量。
對單跨軸
所以
圓盤（混合器及附件）有效質(zhì)量的計算
剛性混合軸（不包括帶錨式和框式混合器的剛性軸）的圓盤有效質(zhì)量等于圓盤自身重量叫上混合器附帶的液體質(zhì)量
上式中：
——第個混合器的附加質(zhì)量系數(shù)，查表3.3.4—1
——第個混合器直徑，
——第個混合器葉片寬度，
葉片傾角，圓盤質(zhì)量
所以
作用集中質(zhì)量的單跨軸一階臨界轉(zhuǎn)速的計算
（1）兩端簡支的等直徑單跨軸，軸的有效質(zhì)量在中點(diǎn)處的相當(dāng)質(zhì)量為：
第個圓盤有效質(zhì)量在中點(diǎn)處的相當(dāng)質(zhì)量為：
所以
在點(diǎn)處的相當(dāng)質(zhì)量為：
所以
臨界轉(zhuǎn)速為：
所以
（2）一端固定另一端簡支的等直徑單跨軸，軸的有效質(zhì)量在中點(diǎn)處的相當(dāng)質(zhì)量為：
第個圓盤有效質(zhì)量在中點(diǎn)處的相當(dāng)質(zhì)量為：
所以
在點(diǎn)處總的相當(dāng)質(zhì)量為：
所以
臨界轉(zhuǎn)速為：
所以
（3）單跨混合軸傳動側(cè)支點(diǎn)的夾持系數(shù)的選取
傳動側(cè)軸承支點(diǎn)型式一般情況是介于簡支和固支之間，其程度用系數(shù)表示。采用剛性聯(lián)軸節(jié)時，,取。
所以
根據(jù)混合軸的抗震條件：當(dāng)混合介質(zhì)為液體—液體，混合器為葉片式混合器及混合軸為剛性軸時，且
所以滿足該條件。
3.6.4 按強(qiáng)度計算混合軸的軸徑
受強(qiáng)度控制的軸徑按下式求得：
式中：——軸上扭矩和彎矩同時作用時的當(dāng)量扭矩
——軸材料的許用剪應(yīng)力
軸上扭矩按下式求得：
——包括傳動側(cè)軸承在內(nèi)的傳動裝置效率，按附錄D選取，則
所以
軸上彎矩總和應(yīng)按下式求得：
（1） 徑向力引起的軸上彎矩的計算
對于單跨軸，徑向力引起的軸上彎矩可以近似的按下式計算：
第個混合器的流體徑向力應(yīng)按下式求得 ：
式中：——流體徑向力系數(shù)，按照附錄C. 2有
——第個混合器功率產(chǎn)生的扭矩
——第個混合器的設(shè)計功率，按附錄 C. 3有
兩個混合器為同種類型，，則
所以
所以
（2） 混合軸與各層圓盤的組合質(zhì)量按下式求得。
對于單跨軸：
——單跨軸段軸的質(zhì)量
所以
故
（3）混合軸與各層圓盤組合質(zhì)量偏心引起的離心力按下式求得。
對于單跨軸：
上式中，對剛性軸的初值取
——許用偏心距（組合件重心處），
——平衡精度等級，。一般取
所以
則
（4）混合軸與各層圓盤組合重心離軸承的距離按下式計算。
對于單跨軸：
所以
而
（5）由軸向推力引起作用于軸上的彎矩的計算。
的粗略計算：
當(dāng)或軸上任一混合器時，取
故
所以
所以
所以
前面計算中取軸徑為，故強(qiáng)度符合要求。
3.6.5 按軸封處（或軸上任意點(diǎn)處處）允許徑向位移驗算軸徑
因軸承徑向游隙、所引起軸上任意點(diǎn)離圖中軸承距離處的位移。
對于單跨軸：
軸承徑向游隙按照附錄C．1選取，因此
傳動側(cè)軸承游隙 （傳動側(cè)軸承為滾動軸承）
單跨軸末端軸承游隙 （該側(cè)軸承為滑動軸承）
當(dāng)時，求得的即為軸封處的總位移，
所以
由流體徑向作用力所引起軸上任意點(diǎn)離圖中軸承距離處的位移。
對于單跨軸：
兩端簡支的單跨軸
且,
而
所以
=
一端固支另一端簡支的單跨軸：
代入已知數(shù)據(jù)可得
由混合軸與各層圓盤（混合器及附件）組合質(zhì)量偏心引起的離心力在軸上任意點(diǎn)離圖中軸承距離處產(chǎn)生的位移按下式計算
對兩端簡支單跨軸：
代入已知數(shù)據(jù)可得
所以
對一端固支一端簡支單跨軸：
代入已知數(shù)據(jù)可得：
所以
一般單跨軸傳動側(cè)支點(diǎn)的夾持系數(shù)介于簡支和固支之間，此時值應(yīng)取式和式之中間值，查附錄C．4取
查附錄C．5得
所以
所以
總位移及其校核
對于剛性軸：
所以
驗算應(yīng)滿足下列條件：
軸封處允許徑向位移按下式計算：
——徑向位移系數(shù)，按附錄C．6．1選取
所以
則滿足
3.6.6 軸徑的最后確定
由以上分析可得，混合軸軸徑滿足臨界轉(zhuǎn)速和強(qiáng)度要求，故確定軸徑為。
混合軸軸封的選擇
機(jī)械密封是一種功耗小、泄漏率低、密封性能可靠、使用壽命長的旋轉(zhuǎn)軸密封。與填料密封相比，機(jī)械密封的泄漏率大約為填料密封的，功率消耗約為填料密封的。故采用機(jī)械密封。
4 支撐裝置設(shè)計
4.1混合機(jī)的支承部分
4.1.1機(jī)座
立式混合機(jī)設(shè)有機(jī)座，在機(jī)座上要考慮留有容納聯(lián)軸器，軸封裝置和上軸承等不見的空間，以及安裝操作所需的位置。
機(jī)座形式分為不帶支承的J-A型和帶中間支承的J-B型以及JXLD型擺線針輪減速器支架，由文獻(xiàn)[3]中的2.8用立式減速器的減速器機(jī)座的系列選用，當(dāng)不能滿足設(shè)計要求時參考該系列尺寸自行設(shè)計。
由于混合軸軸向力不大，聯(lián)軸器為夾殼式故選用J—A型機(jī)座，由于減速器軸徑為65mm，故選用J—A—65
該機(jī)座結(jié)構(gòu)如圖4-1所示
如圖4-1 上軸承支承裝置
4.1.2軸承裝置
上軸承：設(shè)在混合機(jī)機(jī)座內(nèi)。當(dāng)混合機(jī)軸向力較小時，可不設(shè)上軸承，(如J-A型機(jī)座)，但應(yīng)驗算減速機(jī)軸承承受混合軸向力的能力。當(dāng)混合機(jī)軸向力較大時，須設(shè)上軸承：若減速機(jī)軸與混合軸采用剛性連接，可在機(jī)座中設(shè)一個上軸承，以承擔(dān)混合機(jī)軸向立和部分勁向力，如圖(5-2)所示：若減速機(jī)軸用非剛性連接，可在機(jī)座中設(shè)兩個軸承。當(dāng)混合的軸向力很大時，減速機(jī)軸與混合軸應(yīng)用采用非剛性連接，應(yīng)在機(jī)座中設(shè)兩個上軸承或在機(jī)座中設(shè)一個上軸承并在容器內(nèi)或填料箱中再設(shè)支承裝置。
軸承蓋處的密封，一般上端用毛圈，下端采用橡膠油封。
4.2下支撐座的設(shè)計
4.2.1軸承的選型
底軸承：設(shè)在容器底部，起輔助支承作用，只承受勁向荷載。軸襯和軸套一般是整體式，安裝時先將軸承座對中，然后將支架焊于罐體上或?qū)⑤S承固定于池中預(yù)埋件上。
底軸承分以下兩種：
1. 罐裝底軸承：罐用底軸承用于容藥混合中，需加壓力清水潤滑，不能空罐運(yùn)轉(zhuǎn)，其結(jié)構(gòu)為滑動軸承形式。
(1) 適用于大直徑容器的三足式底軸承，如圖4-2所示，
圖4-2 三足底軸承
(2) 可折式底軸承可分為焊接式與鑄造式兩類。此種結(jié)構(gòu)形式可不拆混合軸即能將底軸拆下?？刹鹗降纵S承尺寸和零件材料。
2. 下底軸承：用于混合池或反應(yīng)池中。其結(jié)構(gòu)形式分為滾動軸承座和滑動軸承兩種：
(1) 滾動軸承座：在滾動軸承內(nèi)和滾動軸承座空間須填潤滑脂。滾動軸承必須嚴(yán)格密封，以防止泥沙和易沉物質(zhì)的磨損。
(2) 滑動軸承座：這種軸承必須注壓力清水進(jìn)行沖刷和潤滑，在混合機(jī)起動前應(yīng)先接通清水，水量不超過1L/min。
滑動軸承材料：滑動軸承中軸襯和護(hù)套的材料應(yīng)選擇兩中不會膠合的材料。橡膠軸承內(nèi)環(huán)工作面與軸的間隙可取0.05-0.2mm。在內(nèi)環(huán)工作面應(yīng)軸向均布6-8條梯形截面槽，尖角圓滑過渡。
4.2.2支撐套的設(shè)計
根據(jù)上面所選軸承知，支撐套的材料應(yīng)選45#鋼，且軸承套的內(nèi)徑為軸承的外徑。查國標(biāo)一般選20mm的板厚作為支撐套的原材料，該圖形設(shè)計由上面選擇的軸承座的類型根據(jù)文獻(xiàn)[3]選GPF-80型，如圖5-3所示：
圖4-3 下滑動軸承機(jī)座
5 軸的密封
5.1密封裝置的類型
用于機(jī)械混合反應(yīng)器的軸封主要有兩種：填料密封和機(jī)械密封。軸封的目的是避免介質(zhì)通過轉(zhuǎn)軸從混合容器內(nèi)泄漏或外部雜質(zhì)滲入混合容器內(nèi)。
5.2 軸的密封選擇
填料密封結(jié)構(gòu)簡單、制造容易，適用于非腐蝕性和弱腐蝕性介質(zhì)、密封要求不高、并允許定期維護(hù)的混合設(shè)備。
1．填料密封的結(jié)構(gòu)及工作原理
填料密封的結(jié)構(gòu)由：底環(huán)、本體、油環(huán)、填料、螺柱、壓蓋及油杯等組成。在壓蓋的壓力作用下，裝在混合軸與填料箱本體之間的填料，對混合軸表面產(chǎn)生徑向壓緊力。由于填料中含有潤滑劑，因此，在對混合軸產(chǎn)生徑向壓緊力的同時，使混合軸得到潤滑，而且阻止設(shè)備內(nèi)流體的逸出或外部流體的滲入，達(dá)到密封目的。
2．填料密封的選用
根據(jù)填料的性能選用：當(dāng)密封要求不高時，選用一般石棉或油浸石棉填料，當(dāng)密封要求高時，選用膨體聚四氟乙烯、柔性石墨等填料。各種填料材料的性能不同，按表選用。
填料名稱
介質(zhì)極限溫度oC
介質(zhì)極限壓力Mpa
線速度m/s
適用條件
油浸石棉填料
450
6
-
蒸汽、空氣、工業(yè)用水、重質(zhì)石油產(chǎn)品、弱酸性等
聚四氟乙烯
纖維編結(jié)填料
250
30
2
強(qiáng)酸、強(qiáng)堿、
有機(jī)溶劑
聚四氟乙烯
石棉盤根
260
25
1
酸堿、強(qiáng)腐蝕性溶液、化學(xué)試劑等
石棉線或石棉線與尼龍線浸漬聚四氟乙烯填料
300
30
2
弱酸、強(qiáng)堿、
各種有機(jī)溶劑等
柔性石墨填料
250-300
20
2
醋酸、硼酸、檸檬酸鹽酸等酸類
膨體聚四氟
乙烯石墨盤根
250
4
2
強(qiáng)酸、強(qiáng)堿、
有機(jī)溶液
因為在水處理中對密封要求不高，只要能夠阻止設(shè)備內(nèi)流體的逸出或外部流體的滲入，達(dá)到密封目的即可。根據(jù)以上的填料密封的介紹，本課題的密封裝置選用：油浸石棉填料填料密封。
5.3 封口錐結(jié)構(gòu)選型與計算
符號說明
——軸向力系數(shù)；
——封口錐的連接系數(shù)；
——內(nèi)筒體厚度附加量，；
——夾套厚度附加量，；
——容器內(nèi)徑，；
——夾套內(nèi)徑，；
——夾套封頭與容器封頭的連接園直徑，；
——容器外壁至夾套壁中面的距離
——封口錐連接的強(qiáng)度系數(shù)；
——與封口錐相接的夾套加強(qiáng)區(qū)的實(shí)際長度，或連接封口錐與夾套
的第一道環(huán)焊縫至折邊錐體切線的距離，；
——工作或試驗條件下容器內(nèi)的設(shè)計壓力，；
——工作或試驗條件下夾套或通道內(nèi)的設(shè)計壓力，；
——夾套或通道的許用內(nèi)壓力，；
——容器筒體的實(shí)際壁厚，；
——夾套筒體、封口錐或通道的實(shí)際壁厚，；
——夾套筒體、封口錐或通道的計算厚度，；
——容器殼體與夾套殼體的間距系數(shù)；
——容器殼體與夾套殼體強(qiáng)度比系數(shù)；
——封口錐連接長度系數(shù)；
——封口錐相對有效承載長度系數(shù)；
——封口錐過渡區(qū)轉(zhuǎn)角內(nèi)半徑系數(shù)；
——設(shè)計溫度下容器殼體材料的許用應(yīng)力，；
——設(shè)計溫度下夾套殼體或通道材料的許用應(yīng)力，；
——計算的焊縫系數(shù)；
——夾套筒體的縱焊縫系數(shù)；
——容器筒體的環(huán)焊縫系數(shù)；
——夾套筒體的縱焊縫系數(shù)；
選擇（a）型結(jié)構(gòu)
a. 軸向力系數(shù)A
式中：，
即，取
所以
輔助系數(shù)、、、、、、
容器殼體與夾套殼體的間距系數(shù)
上式中：
所以
因所選封口錐結(jié)構(gòu)為（a）型，故封口錐過渡區(qū)轉(zhuǎn)角內(nèi)半徑系數(shù)。
封口錐連接長度系數(shù)，對于有
容器殼體于夾套殼體強(qiáng)度比系數(shù)
計算的焊縫系數(shù)、
封口錐相對有效承載長度系數(shù)
所以
封口錐的連接系數(shù)
式中：
對于，
所以
則
對于，
所以
，
所以
則
封口錐的許用內(nèi)應(yīng)力
所以
封口錐壁厚應(yīng)等于或大于與其相連接的夾套筒體壁厚，故取封口錐壁厚為。
總 結(jié)
兩個多月的畢業(yè)設(shè)計在忙碌中就快要結(jié)束了,在這兩個多月的時間里,在畢業(yè)設(shè)計之余還要兼顧找工作,因此,在這段時間里我覺得生活非常的充實(shí).不但在畢業(yè)設(shè)計中鞏固了以前的知識,而且在人生道路上學(xué)到在校園學(xué)不到的社會交際.
畢業(yè)設(shè)計是大學(xué)四年所學(xué)知識的一個考察,它兼顧了四年中所學(xué)的基礎(chǔ)和專業(yè)知識,因此不同于以前的課程設(shè)計,畢業(yè)設(shè)計是課程設(shè)計一個質(zhì)的飛越.認(rèn)識到這點(diǎn),我對待畢業(yè)設(shè)計的態(tài)度也不敢懶散,一直抱以認(rèn)真謹(jǐn)慎的學(xué)習(xí)態(tài)度.
在接到畢業(yè)設(shè)計課題后首先要做的就是搜集各方面的資料，以前的課程設(shè)計都是老師給出的，不用自己去煩惱。但是畢業(yè)設(shè)計就不同了，它是一個綜合設(shè)計，很多資料，數(shù)據(jù)都需要自己通過各種途徑搜集得到。
雖然畢業(yè)設(shè)計內(nèi)容繁多，過程繁瑣但我的收獲卻更加豐富。提高是有限的但提高也是全面的，正是這一次設(shè)計讓我積累了無數(shù)實(shí)際經(jīng)驗，使我的頭腦更好的被知識武裝了起來，也必然會讓我在未來的工作學(xué)習(xí)中表現(xiàn)出更高的應(yīng)變能力，更強(qiáng)的溝通力和理解力。順利如期的完成本次畢業(yè)設(shè)計是我最大的動力，讓我了解專業(yè)知識的同時也對本專業(yè)的發(fā)展前景充滿信心。
在本次設(shè)計中，要用到許多基礎(chǔ)理論，由于有些知識已經(jīng)遺忘，這使我們要重新溫習(xí)知識，因此設(shè)計之前就對大學(xué)里面所涉及到的有關(guān)該課題的課程認(rèn)真的復(fù)習(xí)了一遍，開始對本課題的設(shè)計任務(wù)有了大致的了解，并也有了設(shè)計的感覺。同時，由于設(shè)計的需要，要查閱并收集大量關(guān)于機(jī)械制造方面的文獻(xiàn)，進(jìn)而對這些文獻(xiàn)進(jìn)行分析和總結(jié)，這些都提高了我們對于專業(yè)知識的綜合運(yùn)用能力和分析解決實(shí)際問題的能力。通過本次設(shè)計還使我更深切地感受到了團(tuán)隊的力量，在與同學(xué)們的討論中發(fā)現(xiàn)問題并及時解決問題，這些使我們相互之間的溝通協(xié)調(diào)能力得到了提高，團(tuán)隊合作精神也得到了增強(qiáng)。可以說，畢業(yè)設(shè)計體現(xiàn)了我們大學(xué)四年所學(xué)的大部分知識，也檢驗了我們的綜合素質(zhì)和實(shí)際能力
。
參考文獻(xiàn)
[1] 李慶華主編. 材料力學(xué) （第二版）.成都：西南交通大學(xué)出版社，2002
[2] 成大先主編. 機(jī)械設(shè)計手冊 （第四版）.北京：化學(xué)工業(yè)出版社，2002
[3] 朱孝錄主編. 機(jī)械傳動裝置選用手冊 .北京：機(jī)械工業(yè)出版社，1999
[4] 何鳴新、錢可強(qiáng)主編. 機(jī)械制圖 （第四版）.北京：高等教育出版社，2001
[5] 陳秀寧主編. 機(jī)械設(shè)計基礎(chǔ) （第二版）.杭州：浙江大學(xué)出版社，1999
[6] 唐金松主編. 簡明機(jī)械設(shè)計手冊.上海：上?？茖W(xué)技術(shù)出版社，1992
[7] 何鏡民主編. 公差配合使用指南.北京：機(jī)械工業(yè)出版社，1990
[8] 唐保寧、高學(xué)滿主編. 機(jī)械設(shè)計與制造簡明手冊.上海：同濟(jì)大學(xué)出版社，1993
[9] 甘永立主編. 幾何量公差與檢測. 上海：上?？茖W(xué)技術(shù)出版社，2005
[10] 方昆凡主編 . 公差與配合技術(shù)手冊.北京：北京出版社，1999
[11] 張祖立，機(jī)械設(shè)計，中國農(nóng)業(yè)出版社，2004.8。
[12] 哈爾濱工業(yè)大學(xué)，李益民，機(jī)械制造工藝設(shè)計簡明手冊，機(jī)械工業(yè)出版社，2008。
[13].化工輕工設(shè)備機(jī)械基礎(chǔ).成都：科技大學(xué)出版社，1988年
[14].過程裝備控制技術(shù)及應(yīng)用.北京：化學(xué)工業(yè)出版社.2001年
[15] 璞良貴，紀(jì)名剛主編.機(jī)械設(shè)計.第七版.北京：高等教育出版社，2001
[16] 金國淼等.攪拌設(shè)備(化工設(shè)備設(shè)計全書). 北京： 化學(xué)工業(yè)出版社，2002
[17] 徐灝主編，機(jī)械設(shè)計手冊.北京：機(jī)械工業(yè)出版社，1995.12
[18] 李克永.化工機(jī)械手冊. 天津: 天津大學(xué)出版社，1991.5
[19] Bd.H.Ernst．Die Hebezeuge，1999
[20] Lawrence S. Gould. Solid Modelers Are Doing More of the Manual Design Work
[21] Dirk Spindler Georg von Petery INA-Schaeffler KG. Angular Contact Ball
Bearings for a Rear Axle Differential.SAE ，2003
[22] Bathala C. Redlaty, V. S. Muvthy, Madaboosi S. Ananth, Chamarti D. P. Rao. Modeling of continuous Fertilizer Cranulation process for control. Part. Part. Syst. Charact 15(1998):156-160
致 謝
為期兩個多月的畢業(yè)設(shè)計就要結(jié)束了，我也順利的完成了我的課題設(shè)計，在此之際我要衷心的感謝在設(shè)計過程中一直幫助我的老師。
我要感謝張緒坤指導(dǎo)老師，老師在整個設(shè)計過程中對我的影響很大，設(shè)計過程中的很多個難點(diǎn)都是在老師的悉心指導(dǎo)下才克服的。也因為這樣，和老師之間存在著師生心理障礙一下全無，我也就大方的有問題就問，有想法就提，這也使得我能更多的發(fā)現(xiàn)設(shè)計中存在的問題，并解決問題。老師嚴(yán)謹(jǐn)?shù)闹螌W(xué)態(tài)度，淵博的專業(yè)知識，誨人不倦教學(xué)精神，在學(xué)術(shù)上和為人上都是我們的楷模和榜樣。同時我還要感謝跟我一起參與設(shè)計的同學(xué)，雖然我們課題不同，但是都能在討論中發(fā)現(xiàn)各自的問題，并互相提出解決的方法，設(shè)計能夠順利完成，也因為他們的幫助。
結(jié)束代表著新的開始，新的征程，本次的畢業(yè)設(shè)計將會成為我今后工作，學(xué)習(xí)生活中的一份堅實(shí)的基礎(chǔ)和保證。從中吸取的經(jīng)驗教訓(xùn)也將成為我們在今后生活道路上的一筆財富，挫折永遠(yuǎn)是前進(jìn)道路上所必須面對的，相信我們的未來會走的更好，也可以讓我們大學(xué)的老師放心。真心的感謝在大學(xué)幫助過我的老師和同學(xué)們，再次感謝你們！
34
Chemical Engineering Journal 78 (2000) 107113 Experimental investigation of the heat and mass transfer in a centrifugal uidized bed dryer M.H. Shi , H. Wang, Y .L. Hao Department of Power Engineering, Southeast University, Nanjing 210096, China Received 9 November 1998; received in revised form 25 June 1999; accepted 29 June 1999 Abstract An experimental study of the heat and mass transfer characteristics of wet material in a drying process in a centrifugal uidized bed (CFB) dryer was carried out. The rotating speed ranged from 300 to 500 rpm. Wet sand, glass beads and sliced food products were used as the testing materials. The gas temperature and the wet bulb temperature at the inlet and outlet, as well as the bed temperature, were measured. The moisture contents were determined instantaneously by the mass balance method in the gas phase. Inuences of the supercial gas velocity, particle diameter and shape, bed thickness, rotating speed of the bed and initial moisture on the drying characteristics were examined. One empirical correlation which can be used to calculate the heat transfer coefcients of the gas particles in the centrifugal uidized dryer were obtained. 2000 Elsevier Science S.A. All rights reserved. Keywords: Drying; Heat and mass transfer; Centrifugal uidized bed 1. Introduction Centrifugal uidized bed (CFB) drying is a new technol ogy in which the wet material undergoes a highly enhanced heat and mass transfer process in a centrifugal force eld by rotating the bed. The bed essentially is a cylindrical basket rotating around its symmetric axis with a porous cylindrical wall. The drying material is introduced into the basket and forced to form an annular layer at the circumference of the basket due to the large centrifugal forces produced by rota tion. The gas is injected inward through the porous cylin drical wall and the bed begins to uidize when the forces exerted on the material by the uidizing medium balance the centrifugal forces. Instead of having a xed gravitational eld as in a vertical bed, the body force in a centrifugal bed becomes an adjustable parameter that can be determined by the rotation speed and the basket radius. Minimum uidiza tion can, in principle, be achieved at any gas ow rate by changing the rotating speed of the bed. By use of a strong centrifugal eld much greater than gravity, the bed is able to withstand a large gas ow rate without the formation of large bubbles. Thus, the gassolid contact at a high gas ow rate is improved and heat and mass transfer can be achieved during the drying process. For this reason, the CFB dryer has received much attention in the drying industry. Corresponding author. Only a few research works dealing with drying in the CFB could be found in the literature. Lazar and Farkas 1,2 and Brown 3 have conducted the drying process in a CFB for sliced fruits and vegetables, while Carlson 4 investigated the drying of rice in the CFB. These research works are very instructive, but they are mainly focused on the possibility of an industrial application for CFB. The ow behaviour and drying characteristics in the CFB are very complicated and still unclear. A knowledge of heat transfer from the gas to the material is desirable in order to estimate the material surface temperature from the measured temperature of the gas. A quantitative knowledge of the heat transfer characteristics of CFBs is therefore necessary for design purposes 5. In this paper, an experimental study of the ow behaviour and gassolid heat and mass transfer characteristics in a CFB dryer was performed and the main factors which inuence the drying process were examined and discussed. 2. Experimental apparatus A schematic diagram of the experimental apparatus is shown in Fig. 1. A cylindrical basket rotated about a hor izontal axis is mounted in a sealed cylindrical casing. The basket is 200 mm in diameter and 80 mm in width. The side surface of the basket contains 3 mm diameter holes which serve as a gas distributor, with an open area of 22.7%. A 13858947/00/$ see front matter 2000 Elsevier Science S.A. All rights reserved. PII: S13858947(00)001480M.H. Shi et al. / Chemical Engineering Journal 78 (2000) 107113 109 Fig. 3. The uidized curve of sand in the CFB (d p D0.245 mm, nD400rpm). Material (up/down): (m/h) sand; (d/s) glass beads. speeds during the drying tests. In the initial uidizing stage, the pressure drop increases linearly with increasing gas ve locity. After reaching the critical point, the pressure drop will be almost constant. However, different results are observed for sliced and block materials. The pressure drop curve has a maximum value that corresponds with the critical uidiza tion point as shown in Fig. 4. In the initial uidizing stage, the pressure drop increases slowly with increasing gas ve locity. After reaching the critical point, the pressure drop will decrease with increasing gas velocity. This is because the selflock phenomenon of the sliced material under a cen trifugal force eld will be weakened and because the bed becomes uniform. This causes a decrease in the ow resis tance. Decreasing the bed rotating speed would decrease the bed pressure drop and the critical gas velocity remarkably, as also shown in Fig. 4. This is because decrease in the bed rotating speed would weaken the centrifugal force eld and cause the ow resistance to decrease. It can be seen from Fig. 4 that the critical uidized velocity for pieces of potato is somewhat smaller than that of blocks of potato owing to the Fig. 5. Intermittent drying curve in the CFB (sand, d p D0.411 mm, MD2.48 kg, !D41.9 rad s 1 , U 0 D1.71 m s 1 , H in D0.016 kg kg 1 ): (1) T g;in ; (2) T g;out ; (3) T b ; (4) R; (5) x. Fig. 4. The uidized curves for materials with different shapes: (4) pieces of potato 10 mm 10 mm 1.5 mm, nD300 rpm; (h) blocks of potato 5mm 5mm 5 mm, nD300 rpm; (s) block of potato 5 mm 5mm 5 mm, nD250 rpm. larger upwind surface area for pieces of material. Further more, pressure drop of the piece material bed is also smaller than that of the block material bed because the pieces of material show better uidization character in the CFB. The initial uidizing relationships obtained from the theoretical model for granular material 6 do not t the sliced mate rial. The initial uidizing conditions for the sliced material with different shapes should be determined experimentally and individually. 3.2. Drying curves Typical gas temperature and bed temperature curves as well as the drying curve of wet sand in the intermittent dry ing process are shown in Fig. 5. This shows that the drying110 M.H. Shi et al. / Chemical Engineering Journal 78 (2000) 107113 Fig. 6. Variations in the moisture content (Curve 6) and drying rate (Curve 7) for sliced potato. characteristics of materials like sand in the CFB, in which the moisture content is mainly surface water, are the same as in an ordinary dryer, i.e. the whole drying process can be divided into three stages. At a short initial stage, the material is preheated and the drying rate increases rapidly; the bed temperature is increased to a stable value. The second stage is a constant drying rate stage in which the heat transferred from gas to material is expended totally for evaporation of the surface water of the material. The material temperature remains constant and the drying rate is also constant. The last stage is called the falling rate stage in which the ma terial temperature increases gradually and the drying rate decreases until the end of drying. The drying behaviour for sliced food products in the CFB is somewhat different from sand as shown in Fig. 6. It is obvious that sliced potato has a drying character in the CFB that is basically similar to that in the conventional drying process. In the beginning, there is a short initial period. In this period, the bed material is preheated; the bed temper ature approaches a stable value quickly and the drying rate increases very rapidly. This initial period is followed by a period of a constant rate of drying. In the constant rate pe riod, the surface of the test material is covered with a thin water lm. The heat transferred from the gas ow to the ma terial is used completely to evaporate the moisture, so that the temperature of the sliced material remains at an equi librium temperature and the drying rate is at the maximum value. As the main moisture content in potato is cell water, the constant rate period is very short. The most important drying process is completed in the falling rate period. In the falling rate period, the dry layer appears and gradually becomes thicker near the surface owing to the larger trans port resistance of the inner moisture outward. This causes the heat transfer resistance to increase and the drying rate to decrease rapidly in the rst stage. After the dried layers temperature has increased to a certain value, a slow decrease in the drying rate occurs. This indicates that the falling rate period for the sliced potato in the CFB dryer can be divided into two different stages. This is signicant for engineering design and operation. The experimental results show that the pieces of potato in the drying process have a larger drying rate and a shorter drying time than blocks of potato in the CFB. This is be cause the transport distance of moisture from the inner cell to the outer evaporating surface in the pieces of ma terial is much shorter than in the blocks of material; in particular, the second stage of the falling rate period is shorter for the pieces of material during the drying process. In general, because the sliced material could be uidized and mixed very well in the CFB, the drying time is ex tremely short. For example, the drying time is 15 times shorter in the CFB for sliced potato than in the tunnel dryer and ve times shorter than in the conventional uidized dryer. 3.3. Inuences of the operational parameters 3.3.1. Supercial gas velocity It is obvious that an increase in the supercial velocity would increase the degree of uidization, and thus, the heat and mass transfer between the gas and the solid phase would be greatly enhanced. This causes the drying rate to be larger and the drying time to be shorter, as shown in Fig. 7. The critical moisture content would be increased with increas ing gas velocity, indicated by the broken line in Fig. 7. For food material, the experimental results show that the dry ing rate in the constant rate period and the rst stage of the falling rate period would increase with increasing gas velocity in the low gas velocity range. Thus, the total dry ing time would be decreased. However, when the gas veloc ity is increased to a certain value, the constant rate period would disappear, the rst stage of the falling rate period Fig. 7. The inuence of supercial velocity on the moisture con tent (d p D0.411 mm, MD2.50 kg, !D41.9 rad s 1 , H in D0.016 kg kg 1 ): (1) U 0 D1.66 m s 1 ; (2) U 0 D2.17 m s 1 .M.H. Shi et al. / Chemical Engineering Journal 78 (2000) 107113 111 would decrease and the second stage would increase. The total drying time would remain unchanged; this is because the main water content in potato is the inner cell water and the main drying process is in the second stage of the falling rate period. With an increase in the inlet gas temperature, the drying rates in all drying periods increase and the total drying time will decrease. However, the increase in gas tem perature would be limited by the quality of the dried food products. In our test, the best inlet gas temperature is about 100110 C. The experimental results also show that pieces of radish with given dimensions show a larger drying rate than pieces of potato under the same operating conditions. This is be cause the microstructures of the test examples indicate that radish has a larger cell structure with a more regular ar rangement than potato, and furthermore, the liquid in the radish cell is less viscous; these structural characteristics make radish easy to dry. 3.3.2. Rotating speed At the same gas velocity, a decrease in the bed rotating speed will reduce the centrifugal force acting on the material and increase the uidized degree of the material; this causes the heat and mass transfer between the gas and the solid phase to increase. Thus, when decreasing the bed rotating speed, the drying rate will be larger, as shown in Fig. 8, and the drying process will be much more uniform over the whole bed. This means that, for a given material drying in the CFB, the bed rotating speed should be as low as possible until the uidization state cannot be maintained. When it is desired that the drying process be enhanced by increasing the gas velocity in the CFB dryer, the bed rotating speed must be increased simultaneously to avoid the drying material from blowing out of the bed. Theoretically, the bed can be operated in the optimum uidized condition at any gas velocity by regulating the bed rotating speed in the CFB. Fig. 8. The inuence of rotating speed (d p D0.411 mm, MD2.41 kg, U 0 D 1.43 m s 1 , H in D0.0123 kg kg 1 ): (1) !D52.4 rad s 1 ; (2) !D41.9 rad s 1 . Fig. 9. The inuence of particle diameter (MD2.4 kg, !D41.9 rad s 1 , U 0 D 1.43 m s 1 , H in D0.0123 kg kg 1 ): (1) d p D0.245 mm; (2) d p D0.411 mm. 3.3.3. Partial diameter Fig. 9 shows the inuence of particle diameter on the drying behaviour in the CFB. It is clear that, owing to the larger slip velocity between gas and solid particles for parti cles with larger diameters, the heat and mass transfer in the drying process would be enhanced; thus, the drying rate in the CFB would increase with increasing particle diameter as shown in Fig. 9. However, with increasing material dimen sions, the internal heat and mass transfer resistance would be increased; thus, for a given material to be dried, it is im portant to determine the optimum material dimensions in the drying process under certain given operating conditions. 3.3.4. Bed thickness Fig. 10 shows the effect of initial bed thickness on the drying process. It can be seen that, with increasing bed thick ness, the drying rate would be decreased; this is because the heat and mass transfer driving force between the gas and the solid phase is larger in the shallow bed situation. Fig. 10. The inuence of bed thickness (d p D0.411 mm, !D41.9 rad s 1 , U 0 D1.43 m s 1 , H in D0.0123 kg kg 1 ): (1) L 0 D30 mm; (2) L 0 D20 mm.112 M.H. Shi et al. / Chemical Engineering Journal 78 (2000) 107113 Fig. 11. The initial moisture content (d p D0.411 mm, MD2.48 kg, !D41.9 rad s 1 , U 0 D1.71 m s 1 , H in D0.016 kg kg 1 ): (1) x 0 D0.221 kg kg 1 ; (2) x 0 D0.0574 kg kg 1 . 3.3.5. The effect of initial moisture content It is obvious that a material with a large initial moisture content has a much longer drying time (Fig. 11), but the drying characteristics are the same. The only difference is in the duration of the constant rate stage. 3.4. The heat transfer correlation Sixtyve experimental runs of wet sand and glass beads were carried out under the conditions of a static bed thick ness range from 10 to 30 mm, Reynolds number from 5.47 to 35.3 and centrifugal force from 10.08 to 28 multiples of gravity. The heat transfer coefcients were converted into Nusselt numbers using the mean diameter and the thermal conductivity of air at the average temperature. The dimensionless correlation of heat transfer between gas and particles in the CFB during drying is obtained by use of a regression procedure. The exponent of the diffusivity ratio (Prandtl number) has been assumed to be 1/3; thus, Fig. 12. Comparison of experimental and calculated results. Nu D 5:33 10 5 Pr 1=3 Re 1:59 F 0:48 c L 0 d p 0:21 s g 0:79 (7) The suitable parameter ranges for the above two correla tions are ReD5.042.0, F c D10.028.0. In Eq. (7), the Nus selt number is dened as NuDhd p / ; the Reynolds number is ReD g U 0 d p / ; the Prandtl number is PrDc pg / ; and then, dimensionless centrifugal force is dened as F c Dr 0 ! 2 /g. Comparison of the experimental heat transfer data with the values calculated by Eq. (7) is shown in Fig. 12. The deviation for all test data obtained in this work is within 25%. 4. Conclusions 1. The CFB may be operated in the packed bed, incipient uidization or uidized bed states at a given gas velocity. Steady uidized states can be maintained at large gas ow rates by using a strong centrifugal force eld. 2. There is no evident active region near the distributor of the CFB. The gassolid heat transfer comes under the inuence of the supercial gas velocity, particle diameter, particle shape factor, particle density, bed thickness and rotational speed of the bed. 3. The drying process can be divided into three stages in the CFB dryer and the drying rate increases with increas ing supercial gas velocity and particle diameter and de creasing bed rotating speed and initial bed thickness. 4. Sliced food products can be uidized and mixed very well in the CFB. The pressure drop curve has a max imum value and the critical uidized parameters vary with the shape and dimensions of the drying prod ucts and the material itself, as well as the operating conditions. 5. Sliced food products can be dried very well and ef ciently. The main process of drying is within the falling rate period; the drying rate depends on the shape, dimen sions and material of the drying products, as well as the operating conditions. 5. Nomenclature a particle surface per unit volume (m 2 m 3 ) c pg , c ps specic heat of gas or solid (J kg 1 C 1 ) d p mean particle diameter (m) D AB molecule diffusivity (m 2 s 1 ) F c dimensionless centrifugal force, r 0 ! 2 /g G mass ow rate of gas (kg s 1 ) h heat transfer coefcient (W m 2 C 1 ) H width of bed (m); wettability of gas (kg kg 1 ) L 0 xed bed thickness (m) M weight of dried material (kg)M.H. Shi et al. / Chemical Engineering Journal 78 (2000) 107113 113 n rotating speed of the bed (rpm) Nu Nusselt number, hd p / 1P pressure drop (kPa) Pr Prandtl number, c pg / R drying rate (kg m 2 s 1 ) Re Reynolds number, U 0 d p / T temperature ( C) U 0 supercial gas velocity (m s 1 ) x moisture content (kg kg 1 ) Greek letters porosity heat conductivity (W m 1 C 1 ) viscosity of gas (kg m 1 s 1 ) kinematic viscosity of gas (m 2 s 1 ) g , s density of gas or solid (kg m 3 ) s sphericity ! angular velocity (rad s 1 ) Acknowledgements This project was supported by the National Natural Sci ence Foundation of China. References 1 M.E. Lazar, D.F. Farkas, The centrifugal uidized bed. 2. Drying studies on piece form foods, J. Food Sci. 36 (1971) 315319. 2 M.E. Lazar, D.F. Farkas, J. Food Sci. 44 (1979) 242246. 3 G.E. Brown, D.F. Farkas, Centrifugal uidized bed, Food Technol. 26 (12) (1972) 2330. 4 R.A. Carlson, R.L. Roberts, D.F. Farkas, Preparation of quick cooking rice products using a centrifugal uidized bed, J. Food Sci. 41 (1976) 11771179. 5 D.F. Hanni, D.F. Farkas, G.E. Brown, Design and operating parameters for a continuous centrifugal uidized bed drier, J. Food Sci. 41 (1976) 11721176. 6 C.I. Metcalfe, J.R. Howard, Fluidization, Cambridge University Press, Cambridge, 1978, pp. 276327.