Привод коническо-цилиндрический. Рабочие чертежи на выходной вал редуктора, колесо коническое

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методике расчета конических передач изложенной в [1] отсутствует требование об округлении значения внешнего

окружного модуля до стандартного в соответствии с ГОСТ 9563-60, принимаем значение внешнего окружного модуля равным  mte=1,8 мм.

Уточняем значение внешнего диаметра колеса de2=mte*z2=1,8*100=180 мм.                                                                                                                                                                                                                                                                                                                                                                                                                                             

Определим углы делительных конусов[1, c.70].

шестерни ctgd1=u=4;    d1=140;

колеса d2=90-d1=900-140=740                                                                                                                                                                                                                                                                                                                                                                                                                

Определим внешнее конусное расстояние

 мм

Длина зуба b=ybReRe=0,285*92,8=26,4 мм. Округлим рассчитанное значение длины зуба до ближайшего целого значения и примем b= 26 мм.                                                                                                                                                                                                                                                                                                                                                                                                                                         

Внешний делительный диаметр шестерни

de1=mte*z1=1,8*25=51 мм.                                                                                                                                                                                                                                                                                                                                                                                                                                                

Средний делительный диаметр шестерни

d1=2*(Re-0,5b)sind1=2*(92,8-0,5*26)*sin140=44,5 мм.       

Внешние диаметры шестерни и колеса

dae1=de1+2*mtecosd1=51+2*1,8*cos 140=54,5 мм.                                               

dae2=de2+2mte*cosd2=180+2*1,8*cos760=182,7 мм.                                                                                                                                                                                                                                                                                                                                                                                                                                         

Средний окружной диаметр

m=d1/z1=44,5/25=1,78 мм.                                                                                                                                                                                                                                                                                                                                                                                                                                              

Коэффициент ширины шестерни по среднему диаметру

ybd=b/d1=26/44,5=0,59                                                                                                                                                                                                                                                                                                                                                                                                                        

Средняя окружная скорость колес

v=w1d1/2=149,6*44,5/2=3,33 м/с.                                                                                                                                                                                                                                                                                                                                                                                                                                               

По рекомендации [1, c.32] принимаем 8-ю степень точности

4.3 Расчет и проверка контактных напряжений

При ybd=0,59 консольном расположении колес и твердости НВ<350 коэффициент учитывающий распределение нагрузки по длине зуба KHb=1,24 [1, табл.3.5].

Коэффициент, учитывающий распределение нагрузки между прямыми зубьями KHa=1,0.                                                                                                                                                                                                                                                                                                                                                                                                                                           

Коэффициент, учитывающий динамическую нагрузку в зацеплении, для прямозубых колес при v<5 м/с, KHv=1,05 . Тогда [1, ф. 27]

Для проверки контактных напряжений определяем коэффициент нагрузки:

KH=KHbKHaKHv=1,24*1,05*1=1,3.                                                                                                                                                        

 МПа

Расчет проверки контактных напряжений следует признать удовлетворительным, так как рассчитанное значение контактного напряжения меньше допускаемого равного  sH=626 МПа

4.4 Проверка зубьев на выносливость при изгибе

Определим силы в зацеплении:

Окружная сила: Ft1,2=2T1/d1=2*25,4*103/44,5=1143,5 H                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     

радиальная сила шестерни, равная осевой силе колеса

Fr1=Fa2=Ft1,2*tga*cosδ1=1143,5*tg20*cos140=403,6 H

осевая сила  шестерни равная радиальной силе колеса

Fa1=Fr2=Ft1,2tgδ1=1143,5*tg140=100,6 Н

Напряжение при изгибе определяется как  [1, с.50]

sF=FtKFYF/q*b*m<=[sF]

Коэффициенты нагрузки KF=KFbKFv=1,4*1,45=2,03                                                                                                                                                                                                                                                                                                                 

 При ybd=0,59 консольном расположении колес на валах  и твердости                                                                                                                                                                                                                                                                           

 НВ<=350 значение KFb=1,4 [1, табл.3.7]                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      При твердости НВ<350, скорости v=2.41 м/с KFv=1,45 [1, табл.4.9]

YF- коэффициент формы зуба выбираем в зависимости от эквивалентных чисел                                                                                                                                                                                                                                                                                                                                      зубьев [1, с. 42]:                                                                                                                                                                                                                                                                                                                                               

для шестерни zv1=z1/cosd1=25/cos140=25,8                                                YF1=3,9                                                                                                                               YF1=                     3,68  ;                                                                                                         

для колеса zv2=z2 /cosd2=100/cos740=412                             YF2=3,6                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           YF2=                                                                                             3,6                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                

Допускаемое напряжение при проверке зубьев на выносливость по напряжениям                                                                                                                                                                                                                                                                                                                                                                       

изгиба [sF]=s0Flimb/[SF] [1, c. 43]                          

По табл.3.9  [1] для стали 40Х улучшенной при твердости НВ<350s0Flimb=1,8*HB                                                                                                                                                                                                                                                                                                                                                 

Для шестерни s0Flimb1=1,8*350=630 МПа                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               

для колеса s0Flimb2=1,8*325=585 МПа                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     

Коэффициент запаса прочности [SF]=[SF]`[SF]``=1,75*1=1,75                                                                                                          =     1,75                                                                                                                                                                                                            

Для стали 40Х, термической обработке - улучшение коэффициент, учитывающий нестабильность свойств материала конического колеса [SF]=1,75 [1, табл.3.9];

полагая, что заготовки будут получены поковкой, коэффициент [SF]``=1

Допускаемые напряжения при расчете зубьев на выносливость:                                                                                                                                                                                                                                                                                                                                                                    

для шестерни  [sF]=630*0,75/1,75=270 МПа

для  колеса [sF]=585*0,75/1,75=251 МПа                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 

Для шестерни отношение [sF]/YF1=270/3,9=69                                                                                                                                                                                                                                                                                                                                    

Для колеса отношение [sF2]/YF2=251/3,6=70

Дальнейший расчет ведем для зубьев шестерни, так как полученное отношение для

нее меньше                                                                                                                                                                                                                                                                                                                                               

sF2=1143,5*2,03*3,9/(0,85*26*1,8)=117,5< 251  МПа.       

5. Расчёт открытой цилиндрической передачи.

5.1 Выбор материала для зубчатых колес и определение допускаемых напряжений

Так как в задании нет особых требований в отношении габаритов передачи, выбираем материалы  со средними механическими характеристиками [1. табл. 3.3]: для шестерни сталь 45, термическая обработка -улучшение, твердость НВ 230, для колеса сталь 45, термическая обработка-улучшение , твердость НВ 200

Допускаемые контактные напряжения                                                                                                                                                                                                                                                                                                                                                                          

[sH]=sHlimbKHL/[SH]                                                                                                                                                                                                                                                                                                                                                          

где sHlimb предел контактной выносливости при базовом числе циклов                                                                                                                                                                                                                                                                                                                                                                   

По табл. 3.2 [1] для углеродистых сталей с твердостью поверхностей зубьев менее НВ 350 и термической обработкой (улучшение)                                                                                                                                                                                                                                                                                                                                                                                                        

sHlimb=2НВ+70

KHL-коэффициент долговечности; при числе циклов нагружения больше базового, что имеет место при длительной эксплуатации редуктора, принимают KHL=1, коэффициент безопасности                                                                                                                                                                                                                                                                                                                                                                          

[SH]=1,1                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             

Для прямозубых колес расчетное допускаемое контактное напряжение                                                                                                                                                                                                                                                                                                                                                                                             

[sH]= [sH2]                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   

для шестерни [sH1]=(2НВ1+70)*КHL/[SH]=(2*230+70)1/1,1=482                                                                                                                                                                  700                                                                                                                                       

для колеса [sH2]=(2НВ2+70)*КHL/[SH]=(2*200+70)1/1,1=428                                                                                                                                                                   654,5                                                                                                                                    

Расчетное допускаемое контактное напряжение                                                                                                                                                                                                                                                                                                                                                                           

 [sH]=[sH]2=428 МПа

 Коэффициент КHb. Несмотря на симметричное расположение колес относительно опор, примем выше так как со стороны закрытой конической передачи действуют силы, вызывающие дополнительную деформацию ведущего вала и ухудшающие контакт зубьев. Принимаем предварительно по табл. 3.1 [1], как в случае несимметричного расположения колес значение KHb=1,25

Принимаем для прямозубых колёс коэффициент ширины венца по межосевому расстоянию yba=b/aw=0,25

5.2 Расчет геометрических размеров цилиндрической передачи

мм

Где Ка=49,5 – для прямозубых передач

Ближайшее значение межосевого расстояния по ГОСТ 2185-66 аw= 160 мм                                                                                                                                                                                                                                           мм.                                                                                                                      

Нормальный модуль                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 

 mn=(0,01…0,02)aw=(0,01…0,02)*160=1,6…3,2 мм                                                                                                                                                                                                                                                                                                                                            

принимаем по ГОСТ 9563-60 mn= 2 мм 

Определим числа зубьев зубчатой пары

Суммарное число зубьев                                                                                                                                                                                                                                                                                                                                                                    

 zS=2aw/mn=2*160/2=160;

округлим значение до ближайшего целого числа zå=160

Число зубьев шестерни                                                                                                                                                                                                                                                              

 z1=zS/(u2+1)=160/(1,9+1)=55,17

округлим значение до ближайшего целого числа z1=55       

Число зубьев колеса                                                                                                                                                                                                                                                  

 z2=zS-z1=160-55=105                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    

После всех округлений уточним межосевое расстояние                                                                                                                                                                                                                                                                                                                                                                          

 aw=0,5(z1+z2)mn=0,5(35+ 112)*2=112 мм                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         

Основные размеры шестерни и колеса:                                                                                                                                                                                                                                                                                                                                                                                 

Диаметры делительные:                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        

     d1=mn*z1=2*55=110 мм                                                                                                                                                                                                                                                                                                                                                                                                                                                         

     d2=mn*z2=2*105=210 мм                                                                                                                                                                                                                                                                                                                                                          

Диаметры вершин зубьев:                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       

da1=d1+2*mn=110+2*2=114 мм;                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      

da2=d2+2*mn=210+2*2=214 мм;                

Ширина колеса b2=yba*aw=0,25*160=40 мм                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  

Ширина шестерни b1=b2+5= 40+5=45 мм

5.3 Расчет и проверка контактных напряжений

Коэффициент ширины шестерни по диаметру                                                                                                                                                                                                                                                                                                                                                                             

ybd=b1/d1=45/110=0,41                                                                                                                                                                                                                                                                                                                          

Окружная скорость колёс                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         

u=w1*d1/2=37,4*110/2*103=2,06 м/с                                                                                                                                                                                                                                                                                                                                                                                                                                                                 

Степень точности передачи: для прямозубых колёс при скорости до 10 м/с следует принять 8-ю степень точности.

Коэффициент нагрузки                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            

 KH=KHbKHaKHu.

По табл. 3.5 [1] при ybd=0,41 твёрдости НВ<350 и несимметричном расположении колес коэффициент KHb=1,04

По табл. 3.4 [1]  при v= 2,06 м/с и 8-ой степени точности KHa=1                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       

По табл. 3.6 [1] для прямозубых колёс при скорости менее 5 м/с коэффициент KHu=1,05                                                                                                                                                                                                                                                                                                                                                                              

Таким образом, KH=1,04*1,05*1=1,113                                                                                                                                                                                                                                                                                                                                  

Проверяем контактные напряжения                                                                                                                                                                                                                                                                                                                                                                                              

 МПа

5.4 Проверка зубьев на выносливость при изгибе

Определим силы в зацеплении:

окружная Ft=2T3/d2=2*179,9*103/210=1713 H                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            

радиальная  Fr=Ft*(tga)=1713*(tg20)=623 H

Осевая сила в прямозубой цилиндрической передаче равна

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