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: In the Z88 commander launch Z88X, press Button DXF --> Z88I* (default), Run Button.

LINUX/UNIX: In the Z88 commander press button DXF --> Z88I* under CAD converters.

Z88O, look at finite element structure. Proceed as follows:

Windows: In the Z88 commander launch Z88O, Run Button. Use the Wireframe Mode. Switch on Mouse (4th button from left). You may also label the nodes and elements: Menu > Labels > Label All.

LINUX/UNIX: In the Z88 commander launch Z88O, Run Button. Use the Wireframe Mode. Switch on Mouse (7th button from top). You may also label the nodes and elements: Menu > Labels > Label All.

Z88F, calculates displacements. Proceed as follows:
Windows: In the Z88 commander press button Z88F, CD Button (is default), Run Button.
LINUX/UNIX: In the Z88 commander press button Z88F -C.

Z88D, calculates stresses. Proceed as follows:
Windows: In the Z88 commander press button Z88D, Run Button.
LINUX/UNIX: In the Z88 commander press button Z88D.

Z88E, nodal forces calculation. Proceed as follows:
Windows: In the Z88 commander press button Z88E, Run Button.
LINUX/UNIX: In the Z88 commander press button Z88E.

Z88O, look at the deflected finite element structure. Proceed as follows:

Windows, LINUX/UNIX: Choose Deflected. The deflections are magnified per default by the factor 100 which is not enough for this example. Enter 1,000 each for FUX, FUY and FUZ in Menu > Factors > Deflections.

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 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 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 XY pane, deflected with nodal numbers

View of XZ pane, deflected with coarse plot of the Z deflections (Button Deflections Z). Compare this to the exact values in Z88O2.TXT.