机械原理 英汉双语 教学课件 ppt 作者 张春林 Chapter 8 Design of Gear Trains

Chapter 8 Design of Gear Trains,8.1 Classification of Gear Trains,A gear train is a combination of gears used to transmit motion from one shaft to another. Fig 8-1a shows a gear box in an automobile; there are many pairs of gears to transmit different motion. Fig 8-1b shows a quartz watch in which the hour hand, minute hand and second hand rotate as their definite gear ratios to indicate the times.,Fig.8-1 Application of gear trains(轮系的应用) 1、2clutch (离合器) 3、4driving shaft (输入轴) 5gear train (轮系),1.Ordinary Gear Trains,1) Simple ordinary gear train. It is a gear train in which each shaft carries only one gear, as shown in Fig 8-2a. 2) Compound gear train. It is a gear train in which at least one shaft carries more than one gear, as shown in Fig 8-2b. This will be a parallel or series parallel arrangement, rather than the pure series connections of the simple gear trains. 3) Reverted gear train. If the axes of input gear and output gear in a compound gear train are coincident, this is called a reverted gear train, as shown in Fig 8- 2c.。,Fig.8-2 Classification of ordinary gear trains (定轴轮系分类),2.Epicyclic Gear Trains,A gear train having a relative motion of axes is called a epicyclic gear train or planetary gear train, as shown in Fig 8-3a. If the axes of the gears in an epicyclic gear train are fixed, these gears are called sun gears or central gears, such as gears 1 and 3 in Fig 8-3a, denoted as K. The gear whose axis rotates about the axes of the sun gears is the planet gear, such as gear 2. The link which is pivoted to the frame at point O and carries the planet gear 2 to maintain gears 1, 2 and 3 in mesh is the arm or planet carrier, denoted as H.,Fig.8-3 Epicyclic gear train (周转轮系),3.Combined Gear Trains,Fig.8-4 Combined gear trains (混合轮系),Quite often a gear train may contain the combination of ordinary gear trains and epicyclic gear trains or some planetary gear trains. Fig 8-4a shows a gear train which consists of an ordinary gear train and a planetary gear train. Fig 8-4b shows a gear train which consists of two planetary gear trains in series connection.,8.2 Ratio of Ordinary Gear Trains,we will study how to determine the ratios of the gear trains. The ratio of a gear train is that the angular velocity of the input gear is divided by the angular velocity of the output gear, denoted as:,Where in is the angular velocity of the input gear, and out is the angular velocity of the output gear.,Fig.8-5 Planar ordinary gear trains(平面定轴轮系),(1) Parallel axis ordinary gear trains The following example will provide us with a general rule to determine the ratio of ordinary gear trains.,Equation can be written as:,（2） Spatial ordinary gear trains The formula of calculating the ratio is the same with the parallel gear trains, but the (-1) m can not be used to determine the rotating direction of the output gear. A spatial ordinary gear train is illustrated in Fig 8-6, and all the numbers of teeth of gears are known.,Fig.8-6 Spatial ordinary gear trains (空间定轴轮系),(3) Summary,1) The angular velocity ratio of an ordinary gear train is equal to the product of driven tooth numbers divided by the product of driving tooth numbers. 2) The angular velocity ratio of an ordinary gear train is also equal to the product of the angular velocity ratio of each pair of meshing gears. 3) The idle gear, whose number of teeth is canceled in equation calculating the ratio, hence is used to change the direction of rotation. 4) If all the shafts are parallel in the gear train, the sign of the train value depends on the number of the external gears.,Example 8-1 Fig 8-7a illustrates a spatial gear train, in which all the numbers of teeth of gears are known. The worm is the driving gear and has a right hand. Determine the angular velocity ratio i15.,Fig.8-7 Ratio of the spatial ordinary gear trains (空间定轴轮系的传动比),8.3 Ratio of Epicyclic Gear Trains,1.Converted Gear Train,Consider the epicyclic gear train shown in Fig 8-8a, in which the absolute velocities of gears 1, 2, 3 and the arm H are 1, 2, 3 and H respectively. Now, suppose that the train is inverted at an angular velocity which is equal to that of the arm but the direction is opposite, then the arm is considered to be in stationary, see Fig 8-8b. We call this inverted train a converted gear train, which an imaginary ordinary gear train.,Fig.8-8 Ratio of the epicyclic gear trains (周转轮系传动比),Tab 8-1,The angular velocities of gears 1, 2, 3 and the arm H in the converted train are H 1 , H 3, H 2 and H H respectively. The absolute angular velocities of all the members and the angular velocities relative to the arm are shown in Tab 8-1.,In the converted gear train, if gear 1 and gear 3 are input and output gears, the ratio is as follows:,This equation can solve the ratios of any epicyclic gear train, but basic principle must be made clear, for example, iH1ki1k. Its value is iH1k=H1/Hk ,and its value is i1k=1/k. It must be emphasized that the first ar and