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

3.6.2. 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

③     Permitted inertia moment limit

 

Table 3‑4 Inertia moment from weight center by block

Block weight (kg)	Weight center (Lx, LY, LZ)	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.

 

n  Torque Map

 

 

 

Figure3.10 Wrist axis Torque lead