A quick stress calculation method for flexspline in harmonic actuators based on the finite element method

Figures & data

Figure 1. FEM model calculates FS stress.

Figure 2. The change of the FS’s profile when working.

Figure 3. FS node force model.

Table 1. The stiffness matrix is obtained by adding the extended matrices

	Column 1	Column 2	Column 3		Column n-1	Column n
	of matrix	of matrix	of matrix		of matrix	of matrix
Row 1 of matrix	$K_{11}^1$	$K_{12}^1$
Row 2 of matrix	$K_{21}^1$	$K_{22}^1+K_{22}^2$	$K_{23}^2$
Row 3 of matrix	$K_{32}^2$	$K_{33}^2+K_{33}^3$
				$\ddots$
Row n- 1 of matrix					$K_{n,n}^{n-1}+K_{n,n}^n$	$K_{n,n+1}^n$
Row n of matrix					$K_{n+1,n}^n$	$K_{n+1,n+1}^n$

Figure 4. Bar with a rotation joint and a translation joint.

Figure 5. The process of building the displacement matrix of the element system.

Table 2. Programmatically determine the detailed drawing of the tooth profile

(defun tk ()

(setq p0 (getpoint “center coordinates:”)

r (getdist “radius:”)

alpha 0

m1 (polar p0 (*90(/pi 180))r))

(command “circle” p0 r”“)

(command “pdmode” 34)

(command “point” m1)

(white ($<=$ alpha 30)

(setq p1 (polar p0 (*(/pi 180)(+alpha 90)) r)

p2 (polar p1(*(/pi 180) alpha)(*r alpha(/pi180))))

(command “pline” m1 p2”“)

(set m1 p2)

(setq alpha (+alpha 0.1))

))

Figure 6. Completed FS and CS design drawing.

Figure 7. The design, model, and neutral curve measurement results of the FS.

Figure 8. Computational simulation results on cosmos design star