3.6.3. Example of permitted torque and inertia moment calculation (HS180 Case)

(1) Case #1 Simple 2-D model

Figure 3.7 2-D load model

M - Load weight

Jxx - Inertia moment in X direction from weight center of load

Jyy - Inertia moment in Y direction from weight center of load

Jzz - Inertia moment in Z direction from weight center of load

Ja4 - Inertia moment from R2 axis rotation center

Ja5 - Inertia moment from B axis rotation center

Ja6 - Inertia moment from R1 axis rotation center

☞ Load condition: Stainless steel with length and width of 260mm and thickness of 260mm (Mass 138.15kg)

① Weight limitation

Load weight:

② Permitted torque limit

Location of B axis weight center LX = 350mm, LY = 0mm, LZ = -60mm

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

B axis based length

R1 axis based length

Load torque of axis B

Load torque of axis R1

③ Permitted inertia moment limit

Inertia moment of load from the weight Jxx= 1.56kgm2, Jyy= 1.56 kgm2, Jzz= 1.56 kgm2

B axis inertia moment (Ja5)

R1 axis inertia moment (Ja6)

④ Conclusion

It is safe because the weight, torque and inertia moment all satisfy the limited condition.

(2) Case #2 Complicated 3-D model

Figure 3.8 3-D load model 2-D shape

Aluminum block shape combination

(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 - Weight of i block load

LXi - Weight center location in X axis direction of I block

LYi - Weight center location in Y axis direction of I block

LZi - Weight center location in Z axis direction of I block

① Weight limitation

Load weight:

② Permitted torque limit

You can calculate the weight center location for the total load from the B axis rotation center as follows.

(Symmetric to Y axis)

The weight center location for the total load from the B axis rotation center Lx = 520.85mm, Ly = 0mm, LZ = -238.47mm

Distance from the axis B to center of gravity

Distance from the axis R1 to center of gravity

Load torque of axis B

Load torque of axis R1

x1 y1 z1 – x, y and z direction length of block m1

x2 y2 z2 – x, y and z direction length of block m2

x3 y3 z3 – x, y and z direction length of block m3

LX1, LY1, LZ1 – Weight center location of block m1 from B axis rotation center

LX2, LY2, LZ2 - Weight center location of block m2 from B axis rotation center

LX3, LY3, LZ3 - Weight center location of block m3 from B axis rotation center

Jxx1, Jyy1, Jzz1 –Inertia moment by x, y and z axis from the weight center of block m1

Jxx2, Jyy2, Jzz2 –Inertia moment by x, y and z axis from the weight center of block m2

Jxx3, Jyy3, Jzz3 –Inertia moment by x, y and z axis from the weight center of block m3

Figure 3.9 3-D load model 3-D shape