Ι = m1・ + m2・ 3 a1 2 3 a2 2 Ι = m・ 12 a2 Ι = m・ 12 a2 Ι = m1・ + m2 ・ 12 4a1 2 + b2 12 4a2 2 + b2 Ι = m・ 12 a2 + b2 Ι = m・ 5 2r2 Ι = m・ 4 r2 + m2・a2 2 + K 3 a1 2 Ι = m1・ (Ex.) Refer to 7 when the shape of m2 is spherical. K = m2・ 5 2r2 1. Find the moment of inertia ΙB for the rotation of shaft (B). 2. Then, replace the moment of inertia ΙB around the shaft (A) by ΙA b a ΙA = ( )2・ΙB 1. Thin bar 2. Thin bar 3. Thin rectangular plate (cuboid) 4. Thin rectangular plate (cuboid) 5. Thin rectangular plate (cuboid) 7. Sphere Position of rotation shaft: Diameter 6. Cylindrical shape (including a thin disk) Position of rotation shaft: Center axis 8. Thin disk (mounted vertically) Position of rotation shaft: Diameter 9. When a load is mounted on the end of the lever 10. Gear transmission a2 m2 m1 a1 r a b r r r a1 a2 b a1 a2 a a Number of teeth = a Number of teeth = b Ι = m・ 2 r2 Position of the rotation shaft: Passes through the center of gravity of the plate and perpendicular to the plate. (The same applies to thicker cuboids.) Position of rotation shaft: Perpendicular to a bar through one end Position of rotation shaft: Passes through the center of gravity of the bar. Position of rotation shaft: Passes through the center of gravity of a plate. Position of rotation shaft: Perpendicular to the plate and passes through one end. (The same applies to thicker cuboids.) L F ω L ω mg μ L mg Formulas for Moment of Inertia (Calculation of moment of inertia I ) Load Type Load Type Static load: Ts Resistance load: Tf Inertial load: Ta Only pressing force is necessary. (e.g. for clamping) Gravity or friction force is applied to rotating direction. Rotate the load with inertia.

・ ・ Ts = F・L Ts: Static load (N・m) F : Clamping force (N) L : Distance from the rotation center to the clamping position (m) Gravity is applied to rotating direction. Tf = m・g・L Friction force is applied to rotating direction. Tf = μ・m・g・L Ta = I・ω ・ ・2π/360 (Ta = I・ω ・ ・0.0175) Ta: Inertial load (N・m) I : Moment of inertia (kg・m2) ω ・・ : Angular acceleration/angular deceleration (°/sec2) ω : Angular speed (°/sec) Tf: Resistance load (N・m) m: Load mass (kg) g : Gravitational acceleration 9.8 (m/s2) L : Distance from the rotation center to the point of application of the gravity or friction force (m) μ : Friction coefficient Necessary torque T = Ts Necessary torque T = Tf x 1.5 Note 1) Necessary torque T = Ta x 1.5 Note 1) . Resistance load: Gravity or friction force is applied to rotating direction. Ex. 1) Rotation shaft is horizontal (lateral), and the rotation center and the center of gravity of the load are not concentric. Ex. 2) Load moves by sliding on the floor. . The total of resistance load and inertial load is the necessary torque. T = (Tf + Ta) x 1.5 . Not resistance load: Neither gravity or friction force is applied to rotating direction. Ex. 1) Rotation shaft is vertical (up and down). Ex. 2) Rotation shaft is horizontal (lateral), and rotation center and the center of gravity of the load are concentric. . Necessary torque is inertial load only. T = Ta x 1.5 Note 1) To adjust the speed, margin is necessary for Tf and Ta. I: Moment of inertia kg・m2 m: Load mass kg 2 Model Selection Series LER