5

5.3 TRANSMISSION CAM WITH CAM ELEMENTS NO.5

Copy the example file B3_X.DXF to Z88X.DXF.

B3_X.DXF ---> Z88X.DXF input file for CAD converter Z88X

CAD:

You should only look within this example at the CAD FE structure without producing it. This comes with later examples. Import Z88X.DXF into your CAD program and view it. Usually you would draw or model the structure in your CAD system. Do not change anything and leave your CAD program without saving, converting etc. If you do not have any suitable CAD system, then drop this step.

Z88:

Z88X, conversion from Z88X.DXF to Z88I1.TXT, Z88I2.TXT and Z88I3.TXT. Windows: Compute > Z88X > Type Conversion > 5 from Z88X.DXF to Z88I*.TXT (the default) > Compute > Go, UNIX: pushbutton DXF <-> Z88 with radiobutton DXF -> I* (Z88-Commander) or z88x -iafx ("i all from dxf") (console or X-term).

Z88P, look at finite element structure. First delete the file Z88P.STO. Then Z88P loads the structure file Z88I1.TXT per default. Windows and UNIX: You can delete Z88P.STO directly in the Z88 Commander. Then launch the plot program. Windows: Plot > Z88P UNIX: with the Z88-Commander pushbutton Plot feature and radiobutton Z88P or enter from an X-term z88p.

Z88F, calculates deflections. You can use the Compactmode: Windows: Compute > Z88F > Mode > Compactmode, > Compute > Go, UNIX: pushbutton Z88F with radiobutton Compact M (Z88-Commander) or z88f -c (console or X-term).

Z88D, calculates stresses. Windows: Compute > Z88D > Compute > Go, UNIX: pushbutton Z88D (Z88-Commander) or z88d (console or X-term).

Z88E, nodal forces calculation. Windows: Compute > Z88E > Compute > Go, UNIX: pushbutton Z88E (Z88-Commander) or enter z88e from a console or X-term.

Z88P, look at the deflected finite element structure. The displacements are multiplied per default by the factor 100, which is a bit too little for this example. Windows: Plot > Z88P > Factors > Deflections > enter 1000 for FUX, FUY and FUZ each, > Structure > Deflected UNIX: with the Z88-Commander pushbutton Plot feature and radiobutton Z88P or enter from an X-term z88p. Enter 1000 into the textfields FUX, FUY and FUZ, either a Return for each textfield or press pushbutton Regen. Click radiobutton Deflected.

Basically, the calculation and displaying of von Mises stresses is not provided in Z88 for cams No.5, because newer literal sources state correctly that reduced stresses for cams and other machinery parts under dynamic loads do not only depend on the normal and direct stresses (which are computed by Z88), but also on stress concentration factors (impossible to calculate in Z88 and other FEA systems) and other factors.

Task: A transmission cam is designed as follows:

* Cam section, D= 30 mm, L = 30 mm , fixed bearing at the left end

* Gear wheel 1, reference circle D = 45 mm, L = 20 mm

* Cam section, D = 35 mm, L = 60 mm, moveable bearing in the middle

* Gear wheel 2, reference circle D = 60 mm, L = 15 mm

* Cam section, D = 40 mm, L = 60 mm, moveable bearing at the right end

For the loads we picture the cam with the following coordinate system: If we look onto the cam as the main view, then the origin should be at the left end in the middle of the cam. X runs along the cam, Z runs to the upper direction, Y runs in the rear.

Gear wheel 1 gets the following loads in the (physical) point X1 = 40, Y1 = -22.5, Z1 = 0: Fx1 = -10,801 N, Fy1 = 6,809 N, Fz1 = 18,708 N. Fx1 results in a bending moment M1 around the Z axis of -243,023 Nmm.

Gear wheel 2 gets the following loads in the (physical) point X2 = 117.5, Y2 = 0, Z2 = 30: Fx2 = 8,101 N, Fy2 = -14,031 N, Fz2 = -5,107 N. Fx2 results in a bending moment M2 around the Y axis of -243,030 Nmm.

This results in loads in XY and XZ plane. The "physical" points do not exist in the FE calculation, of course, because a cam element is formed analytically only of two points along an axis. The Y and Z coordinates are always 0.

The cam is subdivided into eight cam elements No.5 = 9 nodes. The bearings are assumed in the nodes 1, 5 and 9. Very important: Node 1 is fixed in addition in the degree of freedom 4 (the torsion degree of freedom) in order to compute the torsion angle between the two gears. Otherwise, the structure is statically underdefined !

5.3.1 Input

This example can almost be entered easier by editor into a file than with CAD. The CAD use has real advantages for the examples 1, 2, 5 and 6. Both ways are shown below:

With CAD program:

Proceed according to the description of chapter 2.7. Do not forget to write the element information on the layer Z88EIO by TEXT function:

FE 1 5 (1st finite element type 5)

FE 2 5 (2nd finite element type 5)

FE 3 5 (3rd finite element type 5)

FE 4 5 (4th finite element type 5)

FE 5 5 (5th finite element type 5)

FE 6 5 (6th finite element type 5)

FE 7 5 (7th finite element type 5)

FE 8 5 (8th finite element type 5)

Write the general information and material information on the layer Z88GEN :

Z88I1.TXT 3 9 8 54 3 0 0 0 (3-Dim, 9 nodes, 8 elements, 54 DOF, 3 mat infos, flags 0 )

MAT 1 1 3 206000 0.3 1 30 (1st mat info for ele 1 to ele 3, Young's,Poisson's,QPARA)

MAT 2 4 6 206000 0.3 1 35 (2nd mat info for ele 4 to ele 6, Young's,Poisson's,QPARA)

MAT 3 7 7 206000 0.3 1 40 (3rd mat info for ele 7 to ele 7, Young's,Poisson's,QPARA)

(INTORD is set here to 1, has no influence)

As cam elements No.5 are structure elements (thus not subdividable like finite elements), the mesh generator cannot be used. You can immediately write the boundary conditions with the TEXT function on the layer Z88RBD:

Z88I2.TXT 18 (18 Boundary conditions altogether)

RBD 1 1 1 2 0 (1.BC: Node 1, DOF 1 (=X) fixed)

RBD 2 1 2 2 0 (2.BC: Node 1, DOF 2 (=Y) fixed)

RBD 3 1 3 2 0 (3.BC: Node 1, DOF 3 (=Z) fixed)

RBD 4 1 4 2 0 (4.BC: Node 1, DOF 4 (=torsion) fixed)

RBD 5 3 1 1 -10801 (5.BC: Node 3, DOF 1 (=X), load -10,801 N)

RBD 6 3 2 1 +6809 (6.BC: Node 3, DOF 2 (=Y), load 6,809 N)

RBD 7 3 3 1 +18708 (7.BC: Node 3, DOF 3 (=Z), load 18,708 N)

RBD 8 3 4 1 -420930 (8.BC: Node 3, DOF 4 (torsion) -420,930 Nmm)

RBD 9 3 6 1 -243023 (9.BC: Node 3, DOF 6 (bend. moment around Z),-243,023Nmm)

RBD 10 5 2 2 0

RBD 11 5 3 2 0

RBD 12 7 1 1 +8101

RBD 13 7 2 1 -14031

RBD 14 7 3 1 -5107

RBD 15 7 4 1 +420930

RBD 16 7 5 1 -243030

RBD 17 9 2 2 0

RBD 18 9 3 2 0

... And write on the layer Z88GEN onto any free place of your drawing the stress parameters for the stress calculation:

Z88I3.TXT 0 0 0 (any stress parameters for Trusses No.4)

Export the drawing as DXF file with the name Z88X.DXF and then launch the CAD converter Z88X with the option "from Z88X.DXF to Z88I*.TXT" (DXF -> I*). The CAD converter will produce the input files Z88I1.TXT, Z88I2.TXT, Z88I3.TXT.

With an editor:

Enter the structure data into Z88I1.TXT by editor (cf. section 3.2):

3 9 8 54 3 0 0 0 (3D, 9 Node, 8 Ele, 54 DOF, 3 E-Gesetze, Flags 0)

1 6 0 0 0 (Node 1, 6 DOF, X-, Y- und Z-Koordinate)

2 6 30 0 0 (Node 2, 6 DOF, X-, Y- und Z-Koordinate)

3 6 40 0 0

4 6 50 0 0

5 6 80 0 0

6 6 110 0 0

7 6 117.5 0 0

8 6 125 0 0

9 6 185 0 0

1 5 (Element 1, cam No.5)

1 2 (Coincidence Ele 1)

2 5 (Element 2, type 5)

2 3 (coincidence Ele 2)

.......... (Elemente 3 to 7 dropped here)

8 5

8 9

1 3 206000 0.3 1 30 (mat info from Ele 1 to 3,Young's,Poisson's, QPARA= 30)

4 6 206000 0.3 1 35 (mat info from Ele 4 to 6,Young's,Poisson's, QPARA= 35)

7 7 206000 0.3 1 40 (mat info from Ele 7 to 7,Young's,Poisson's, QPARA= 40)

INTORD is set here to 1, has no influence.

The boundary conditions Z88I2.TXT:

18 (18 Boundary conditions)

1 1 2 0 (1.BC: Node 1, DOF 1 (=X) fixed)

1 2 2 0 (2.BC: Node 1, DOF 2 (=Y) fixed)

1 3 2 0 (3.BC: Node 1, DOF 3 (=Z) fixed)

1 4 2 0 (4.BC: Node 1, DOF 4 (=torsion) fixed)

3 1 1 -10801 (5.BC: Node 3, DOF 1 (=X), load -10,801 N)

3 2 1 +6809 (6.BC: Node 3, DOF 2 (=Y), load 6,809 N)

3 3 1 +18708 (7.BC: Node 3, DOF 3 (=Z), load 18,708 N)

3 4 1 -420930 (8.BC: Node 3, DOF 4 (torsion) -420,930 Nmm)

3 6 1 -243023 (9.BC: Node 3, DOF 6 (bend. moment around Z),-243,023Nmm)

5 2 2 0

5 3 2 0

7 1 1 +8101

7 2 1 -14031

7 3 1 -5107

7 4 1 +420930

7 5 1 -243030

9 2 2 0

9 3 2 0

The parameter file for the stress processor Z88I3.TXT can have any content (cf. sections 3.5 and 4.4), because Gauss points, radial and tangential stresses as well as calculation of the von Mises stresses has no significance for Cam Elements No.5.

CAD and editor:

Because now the structure data Z88I1.TXT, the boundary conditions Z88I2.TXT and the header file for the stress processor Z88I3.TXT (with any content) do exist, you can launch

>Z88F Cholesky solver for computing the deflections

>Z88D stress processor

>Z88E nodal force processor

5.3.2 Results

The Cholesky solver Z88F provides the following output files:

Z88O0.TXT stores the processed structure data. For documentation purposes.

Z88O1.TXT stores the processed boundary conditions: For documentation purposes.

Z88O2.TXT, the displacements, the main task and solution of the FEA problem.

The stress processor Z88D internally uses the calculated displacements from Z88F and stores

Z88O3.TXT, the calculated stresses. The results in Z88O3.TXT do not depend on the header parameters in Z88I3.TXT for Cam Elements No.5.

The nodal force processor Z88E internally uses the calculated deflections of Z88F and stores

Z88O4.TXT, the computed nodal forces. Keep in mind, that the "forces" of the DOF 4, 5 and 6 are really moments, because the DOF 4, 5 and 6 are rotations.

The following pictures of the plot program show the deflected structure for FUX, FUY and FUZ = 1,000 each (magnifications of the deflections):

View of undeflected structure with node labels and deflected structure in space

View of X-Z plane, undeflected and deflected

View of X-Y plane, undeflected and deflected