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

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

 

(1)   Case #1 Simple 2-D model

 

 

Figure 3.11 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

If you apply the B and R1 axis length limit in the torque map, it is shown 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 center Jxx= 1.56kgm2, Jyy= 1.56 kgm2, Jzz= 1.56 kgm2

B axis inertia moment (Ja5)

R1 axis inertia moment (Ja6) (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 3.12 3-D load model 2-D shape

 

Combination of block forms of carbon steel (S45C) for the structure of a machinery

(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  = 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 3.13 3-D load model 3-D shape

 

③    Permitted inertia moment limit

 

Table 3‑3 Inertia moment from weight center by block

Block weight [kg]	Weight center (Lx, LY, LZ) [m]	Jxx	Jyy	Jzz
m1 (14.6)	(0.25, 0, 0)	0.219 kgm2	0.114 kgm2	0.114 kgm2
m2 (125.4)	(0.48, 0, -0.26)	2.530 kgm2	2.915 kgm2	4.433 kgm2
m3 (36.3)	(0.89, 0, -0.26)	0.350 kgm2	0.314 kgm2	0.509 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