Chap, 5.2 The fundamental law of gearing() O2N2 OP r2 五=b1= Const r2 b2 onst b2 The fundamental law of gearing The ratio of the driving gear radius to the driven gear radius remains constant as the teeth move into and out of mesh
. . 2 1 2 1 1 2 2 1 2 1 2 1 2 1 2 2 1 1 1 2 Const r r r r m Const r r r r r r O P O P O N O N m b b i n out V b b i n out V = = = = = = = = = = = = The fundamental law of gearing The ratio of the driving gear radius to the driven gear radius remains constant as the teeth move into and out of mesh. Chap.5.2 The fundamental law of gearing(7) r1 r2
Important lines Tangency of the both base circles Vbp (基圆公切线) is the common norma K Line of action(力作用线) Axis of transmission(啮合线或传动线) Conclusion: these three lines are the same line
Important lines Conclusion: these three lines are the same line. Axis of transmission(啮合线或传动线) Line of action（力作用线） Tangency of the both base circles （基圆公切线）is the common normal . rbp rbg rp rg
Chap, 5.2 The fundamental law of gearing( 了3. Pressure angle(节圆压力角) Driving r The pressure angle in a gearset defined as the angle between the axis of transmission or line of action (common normal) and the direction of velocity at the pitch point. n r Meshing angle(啮合角) r Standard value of the pressure angle are 1450 200 and 250. 200 is the most commonly used
Chap.5.2 The fundamental law of gearing(8) 3. Pressure angle（节圆压力角） The pressure angle in a gearset is defined as the angle between the axis of transmission or line of action(common normal) and the direction of velocity at the pitch point. Standard value of the pressure angle are 14.50, 200 and 250. 200 is the most commonly used. Meshing angle(啮合角)
rb
Chap 5.2 The fundamental law of gearing(9) 4. Changing Center Distance C AO out b2=Const fi a cos a +rb2 -acos=a' a=const. a cosa=lbl +r2
4. Changing Center Distance Chap.5.2 The fundamental law of gearing(9) 1 2 'cos ' b b a = r + r 1 2 ''cos '' b b a = r + r a'cos' = a''cos'' = const. . 1 2 1 2 1 2 Const r r r r m b b i n out V = = = = =