3.6.3. Example of permitted torque and inertia moment calculation

(1) Case #1 Simple 2-D model

Figure 3.10 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 weigh t: 138.15 ≤ 180 kg

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

Length in B axis 𝐿𝐵 = √0.352 + 0.062 = 0.355 m

Length in R1 axis 𝐿𝑅1 = 0.06 m

Load torque of axis B 𝑇𝐵 = 𝑀𝑔𝐿𝐵 = 49.04 kgfm ≤ 110 kgfm

Load torque of axis R1 𝑇𝑅1 = 𝑀𝑔𝐿𝑅1 = 8.29 kgfm ≤ 58 kgfm

③ Permitted inertia moment limit

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

kgm2

B axis inertia moment (Ja5)

𝐽𝑎5 = 𝑀𝐿2𝐵 + 𝐽𝑦𝑦 = 138.15× 0.3552 + 1.56 = 18.97 ≤ 106 kgm2

R1 axis inertia moment (Ja6)

𝐽𝑎6 = 𝑀𝐿2𝑅1 + 𝐽𝑥𝑥 = 138.15× 0.062 + 1.56 = 2.06 ≤ 56 kgm2

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 3.11 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 : 176.3 ≤180 kg

② Permitted torque limit

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

center as follows.

(Y축 대칭이므로)

The weight center location for the total load from the B axis rotation center = 520.85mm, = 0mm, = -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 3.12 3-D load model 3-D shape