3.6.3. Examples of Calculation of the Allowable Torque and Allowable Moment of Inertia (HS180)

(1) Case #1 Simple two-dimensional model

Figure 3.11Two-Dimensional Load Model

M – Load weight

Jxx - Moment of inertia in the direction of the X axis at the center of the gravity of the load

Jyy - Moment of inertia in the direction of the Y axis at the center of the gravity of the load

Jzz - Moment of inertia in the direction of the Z axis at the center of the gravity of the load

Ja4 - Moment of inertia at the center of rotation of the R2 axis

Ja5 - Moment of inertia at the center of rotation of the B axis

Ja6 - Moment of inertia at the center of rotation of the R1 axis

☞ Load condition: Stainless Steel (with mass of 138.15 kg) with a width of 260 mm and a thickness of 260 mm

① Weight limit

Load weight:

② Limit of the allowable torque

The position of the center of gravity with respect to B axis: LX = 350 mm, LY = 0 mm and LZ = -60 mm

Each distance from B axis and R1 axis to the center of gravity can be calculated respectively as follows.

Distance with respect to the B axis

Distance with respect to the R1 axis

Load torque of the B axis

Load torque of the R1 axis

③ Limit of the allowable moment of inertia

The moments of inertia of the load at the center of gravity: Jxx= 1.56kgm2, Jyy= 1.56 kgm2, and Jzz= 1.56 kgm2

Moment of inertia of the B axis (Ja5)

Moment of inertia of the R1 axis (Ja6)

④ Conclusion

It is safe because all conditions of weight, torque, and moment of inertia satisfy the conditions of limit.

(2) Case #2 Complex three-dimensional model

Figure 3.12Two-Dimensional Shape of a Three-Dimensional Load Model

Combination of aluminum block shapes

(σ=0.0027 g/mm3: 176.3 kg)

m1 (60×300×300) 14.6kg

m2 (480×440×220) 125.4kg

m3 (280×300×160) 36.3kg

mi - Load weight of i block

LXi - Position of the center of gravity of i block in the direction of X axis

LYi - Position of the center of gravity of i block in the direction of Y axis

LZi - Position of the center of gravity of i block in the direction of Z axis

① Weight limit

Load weight:

② Limit of the allowable torque

The position of the center of gravity of all loads at the center of rotation of the B axis can be calculated as follows.

(Y축 대칭이므로)

Position of the center of gravity of all blocks with respect to B axis = 520.85mm, = 0mm, = -238.47mm

Distance from the B axis to the center of gravity

Distance from the R1 axis to the center of gravity

Load torque of the B axis

Load torque of the R1 axis

x1 y1 z1 – Lengths of m1 block in the x, y, and z directions respectively

x2 y2 z2 – Lengths of m2 block in the x, y, and z directions respectively

x3 y3 z3 – Lengths of m3 block in the x, y, and z directions respectively

LX1, LY1, LZ1 - Position of the center of gravity of m1 block at the center of rotation of the B axis

LX2, LY2, LZ2 - Position of the center of gravity of m2 block at the center of rotation of the B axis

LX3, LY3, LZ3 - Position of the center of gravity of m3 block at the center of rotation of the B axis

Jxx1, Jyy1, Jzz1 – Moment of inertia of each of x, y, and z axes at the center of gravity of m1 block.

Jxx2, Jyy2, Jzz2 – Moment of inertia of each of x, y, and z axes at the center of gravity of m2 block.

Jxx3, Jyy3, Jzz3 – Moment of inertia of each of x, y, and z axes at the center of gravity of m3 block.

Figure 3.13Three-Dimensional Shape of a Three-Dimensional Load Model