8.4 Ratio of Combined Gear Trains We must be able to visualize how the gear train works so as to separate it out from the combined gear train. Before calculating the speed ratio of a combined gear train, some rules must be cleared. 1) How many elementary gear trains are there in the combined gear train? 2) Analyzing the connection of the elementary gear trains. 3) Write the speed ratio of the elementary gear trains independently, then simultaneously solve these equations. First,the ordinary gear trains must be found out by inspection if there are some ordinary gear trains,then the epicyclic gear train.Finally,it is necessary to find out how the several gear trains are connected together.When several gears are in mesh,and their axes are fixed,it is an ordinary gear train.When several gears are in mesh,in which there are one er more planet gears and they are in mesh with sun gears,it is an epicyclic gear train.Usually,the tandem,closed and superimpose connection are often used in combined gear train. 1.Tandem Combined Gear TrainsIn this gear train,the output shaft of the first train is the input shaft of the latter train.Therefore the total ratio is the product of the ratios of all the gear trains.Example 8-4 Fig 8-12 shows a combined gear train in which the numbers of teeth of gears =20, =40, =20, =30, =80,and the driving speed of gear 1 is =300r/min. Determine the speed of the arm.SolutionThe ordinary gear train consists of gears 1 and 2 in which their shafts are all fixed,and the planetary gear train consists of gears ,3,4 and the arm H,in which gear 3 is the planet gear,and gears and 4 are the sun gears.The output speed of the first train is equal to the input speed of the latter train.For the planetary gear train,we have: For the ordinary gear train,we have: Simultaneously solving the two equations and substituting and ,the result is as follow: The minus sign indicates that the direction of rotation of the arm is opposite to that of the driving gear 1.Fig.8-12Tandem combined gear train (串联式混合轮系)2. Closed Combined Gear Trains If two output members,or two input members,or an input member and an output members of a differential gear train are connected by an ordinary gear train,such a combined train is said to be a closed combined gear train. We can write the speed ratio formula of the differential gear train and the ordinary gear train respectively;then solve them simultaneous. Example 8-5 Fig 8-13 shows a reducer of an electric hoister, in which the numbers of teeth of gears are =24, =52, =21，=78，=18，=30， =78. Determine the gear ratio .SolutionGear 1,2,3 and 5(arm H) constitute a differential gear train,in which gear 3 and gear 5(arm H) are the two output gears.Gears ,4 and 5 constitute an ordinary gear train.Gear 3 and gear 5,two output gears,of the differential gear train are connected by the ordinary gear train.It is a closed combined gear train.From the differential gear train,we have: From the ordinary gear train,we have: Simultaneously solving the two equations and substituting ,the result is as follows: Thus: Fig.8-13Reducer of the electrichoister (电动卷扬机减速器)