finite element modeling and simulation of the

FINITE ELEMENT MODELING AND SIMULATION OF THE TRANSPORT BEHAVIOR OF A TUNNELING RIG

Ulf Sellgren

MMK Document Data File: mosaik\reports\atlas_2.doc Date: 2000-08-16 Confidentiality: Full version (Atlas Copco only)

Stockholm 2000

Technical Report Machine Elements Department of Machine Design Royal Institute of Technology (KTH) S-100 44 Stockholm, Sweden

SUMMARY The presented work was performed in the MOSAIC project which is a joint project between Atlas Copco Rock Drills AB, ABB Robotics Products AB, and the Department of Machine Design at the Royal Institute of Technology (KTH). The essence of the MOSAIC approach to behavior modeling of complex systems is to support behavior analysis and simulation in an iterative and thus complex engineering process, by using encapsulated submodels of components and of their interfaces. An existing Ansys FE model of an Atlas Copco tunneling rig has been reorganized, modularized, and adapted to allow for a wide range of simulations and analyses of its physical behavior. In this report the model is used to study some aspects of the dynamic behavior at transport. For the types of simulations that have been presented here, the finite element approach has proved to be useful. Analyses of the simulation results show that a transient force acting in any direction will generate considerable motions and vibrations in the lateral direction. This effect is caused by a set of highly coupled modes in the 2-3 Hz frequency range. Parameter studies indicate that the lateral motions during transport can be significantly reduced by increasing the stiffness of the front wheels, or by adding a pair of extra front wheels. With the present version of Ansys, a general driving case, with the purpose to simulate the dynamic behavior due to the nonlinear contact between wheel and ground, can not efficiently be simulated. A thorough study of a realistic driving case in rough terrain requires a more sophisticated tire model, e.g. the Delft Tire model that has been implemented in the Adams software. Such a detailed study probably also requires an elastic systems model, i.e. a configuration of flexibile submodels such as finite element models. This can be accomplished by exporting component modes for each elastic submodel from Ansys to the Adams software and then mounting instances of the detailed tire model to the flexible submodels in Adams.

2

CONTENTS

1 2 3

4 5 6

SUMMARY CONTENTS INTRODUCTION BEHAVIOR MODEL OF A MOBILE RIG TRANSPORT CASE 3.1 Modal characteristics 3.2 Transient excitation 3.3 Parameter studies DISCUSSION ACKNOWLEDGEMENTS REFERENCES

APPENDIX A: A RIG WITH TWO BOOMS – MOBILE REQUENCIES APPENDIX B: A RIG WITH TWO BOOMS ON LEGS – MODES APPENDIX C: RIG WITH TWO BOOMS – TRANSIENT SIMULATIONS APPENDIX D: RIG WITH TWO BOOMS – PARAMETER STUDIES APPENDIX E: ANSYS MACRO LIBRARY TO CONFIGURE A SYSTEM APPENDIX F: ANSYS MODEL OF BVX96_LE (Confidential) APPENDIX G: ANSYS WHEEL MODEL MACRO

3

2 3 4 6 8 8 10 12 13 14 14

15 18 23 28 32 36 50

1 INTRODUCTION Tunneling in hard rock is typically performed with blasting techniques. Tunneling consists of a sequence of activities, starting with the drilling of a pattern of three to five meter long blast holes, then charging them with explosives, controlled blasting of the rock, and ventilation of the gases. After the rock has been transported away, the sequence can be repeated. From an efficiency point of view, it is highly desirable to minimize the deviation from the target profile for the tunnel, as well as minimize the damage of the surrounding rock, as indicated in figure 1A. This can be achieved with a combination of high precision drilling and a controlled blasting sequence for an ideal distribution of explosives. Any deviation from the ideal pattern of colinear and parallel blast holes will increase the size of the crack zone (see figure 1B). A

B Crack zones

Target profile

Figure 1. Efficient blasting in A and the effect of a reduced drilling and/or blasting accuracy in B.

The introduction of the pusher-leg drilling in the 1940’s, usually referred to as the Swedish method, began a rapid development of tunneling and mining efficiency. The productivity in terms of drilled meters per operator and hour increased dramatically in the 1960s with the introduction of pneumatic rock drills mounted on mobile rigs (see figure 2). The excavation technique was developed further a decade later, when the first generation of hydraulic rock drills were introduced. Since then, this technique has been significantly improved.

Productivity development

Figure 2. Productivity development, from Atlas Copco.

In figure 3, we can see a mobile rig, which is used for tunneling applications, equipped with two boomers and a service platform. The rig, which is an Atlas Copco product, is a complex

4

system with long and slender mechanical parts, hydraulic actuators, sensors and a control system.

Figure 3. A mobile rig with two robot boomers and a service platform in action, from Atlas Copco.

The system is highly stressed during normal drilling operation, and there are increasing customer demands on the performance, with precision and speed as crucial parameters. The drilling speed can be improved by increasing the force and/or the frequency. Significant dynamic loads are generated during regular transport, i.e. rolling motion, of the rig. Finite element simulations of some aspects of the dynamic behavior during rolling motion is presented this report.

5

2 BEHAVIOR MODEL OF A MOBILE RIG An FE model of the Atlas Copco boomer BUT35L was presented in Sellgren (1999). The model of the boomer system was configured from model modules, i.e. models of subsystems (see figure 4), that were interconnected with connect features on a systems level. But35L connect_features

actuators

back plate

boomer_body

telescope

feed_and_drilling

Figure 4. The subsystems of the BUT35L FE model, from Sellgren (1999).

In the project with the number NO100 BVX 96 L2, an Ansys beam model of BVX 96 L2 was developed by CAMATEC for Atlas Copco. This model was developed as a tool to study the quasi-static behavior of the rig during transport. The Booms and the service platform were not included in the model. The influences from these subsystems were treated as static forces acting on the rig. In order to make the rig model useful for configuration studies and for simulations for various types of behavior, the Ansys model has been modified (see appendix F) and reorganized. Figures 5 and 6 show a hierarchical and a topological view, respectively, of a rig with two instances of the BUT35 boom model connected. The boom model is not decomposed in the topological view. The rig is composed of a model of the front part and the rear part of the rig, respectively. These two submodels are connected by a steering joint, which is a revolute joint with the unrestrained degree of freedom in the vertical direction, and a linear hydraulic actuator. Each wheel is modeled as an idealized linear stiffness matrix, i.e. the Ansys Matrix27 element type (ANSYS, 1998), connecting the center point of the wheel to a ground node. In the present model the vertical wheel stiffness is approximated as twice the secant-stiffness defined by the static compression of the wheel due to the dead weight. Furthermore, the wheel stiffness in the lateral and longitudinal directions are defined as equal to the vertical stiffness. An Ansys macro that is used to define a wheel submodel is listed in appendix G. A more sophisticated wheel model aimed for rolling contact would require that each wheel is connected to the rig with revolute joint features and not rigidly attached as in this model.

6

L2C Boomer

L2C

But35L_left

Wheels

connect_feature s

But35L_right

actuators

Connect_features

L2C_rear

Actuator s

L2C_front

back _plat e

boom_body

telescope

feeding_and_drilling

Connect_features

Figure 5. A hierarchical view of the systems model.

L2C_rear

Actuator Revoute_ joint Attachment

Ball_joint L2C_front

But35L_left

Revoute_ joint

Attachment

Attachment

Attachment Wheel_ rear_ right

Wheel_ rear_ left

But35L_right Attachment Attachment Wheel_ front_ left

Wheel_ front_ right

Figure 6. A topological view of the rig model with connects features realizing the interfaces between the submodels.

7

3 TRANSPORT CASE The weight of an L2C rig with two booms is approximately 27000 kg. The front wheel pair has to carry most of the weight. The center of gravity of a rig ewuipped with booms is thus located in front of the geometric center of the rig where the revolute joint is located. This large offset between this steering joint and the center of gravity gives rise to a characteristic motion during normal transport. The motion is somteimes referred to as a ”lizard-walk”.

3.1 Modal characteristics The eigenfrequencies that are below 10Hz for an L2C rig on four wheels with the booms in transport position are listed in figure 7. The corresponding mode shapes are plotted in appendix A. The modal data for a rig on four legs, i.e. it is ready for drilling operation, is listed in appendix B. The mass and stiffness for each mode is also listed in figure 7. The mass mi for mode number i is defined here as: mi = DTi MD i where M is the mass matrix and Di is eigenvector i normalized with the largest component equal to one. The corresponding modal stiffness ki is: 2 k i = mi (2πf i ) where fi is the frequency in Hertz of mode number i. A mode with a relatively large mass can be characterized as a global mode and a mode with a small mass as a local mode. The nine modes with the largest modal mass are labeled in the rightmost plot in figure 7. frequency modal (Hz) mass 0.97 5167 1.14 4443 1.41 3 1.50 120 1.52 218 1.71 1211 1.77 4 1.81 39 2.29 10865 2.39 16041 2.71 24782 2.74 5248 3.49 8491 3.92 4651 4.40 128 4.97 35 5.11 149 5.48 155 5.92 98 7.59 1 8.36 0.2 8.61 3 8.86 44 9.57 17

modal stiffness 190300 228600 200 10700 19800 139600 500 5100 2250000 3619200 7174600 1556000 4089500 2814500 98100 33900 153400 183200 135100 2400 700 7500 136200 61900

Rig on wheels - modal mass 11 0.9

normalized modal mass

mode number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

10

0.6

9 13 0.3 1

12

2

14

6 0

0

1

2

3

4

5

6

7

8

frequency (Hz)

Figure 7. Frequencies, masses and stiffnesses for the lowest modes.

8

9

10

In figure 8, the modal mass for the lowest eigenfrequencies are decomposed into the three global directions. It is clear that modes 9 to 12, i.e. between 2.3 and 2.7 Hz, are very active in all three global directions. In figure 9, it can be seen that these modes have significant eigenvector components in all three global translational directions at the center of the front wheels. An excitation in any direction at a front wheel will thus initiate lateral as well as longitudinal and vertical vibrations in the front rig and the boomer systems. Rig on wheels - modal mass components direction

normalized modal mass

0.9

Directions for rig with two booms

longitudinal vertical lateral

0.6

0.3

y

z

0

x

0

1

2

3

4

5

6

7

8

9

10

frequency (Hz)

Figure 8. Modal mass decomposed into the three global directions. Rig on wheels - eigenvector components 1

direction 0.8

longitudinal vertical lateral

relative amplitude

0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1

0

1

2

3

4

5

6

7

8

9

10

frequency (Hz)

Figure 9. Eigenvector component for the translational degrees of freedom at the center point of the left front wheel.

9

3.2 Transient excitation ”Some aspects of the ”lizard-walk” of the Atlas Copco Rocket Boomer L2D was studied by Sjögren (1999). He combined an Adams rigid body model with a simplified wheel submodel and hydraulic actuators. The wheel and the actuators were flexible submodels. The dynamic behavior was studied by applying a sine-shaped force acting at the center of the left front wheel. The same concept has been used here. The sensitivity of the rig to excitation forces in the front wheel to ground contact was studied by applying a force with a duration of 0.2 s at the left front wheel center (see figure 10). The force was independently applied in the longitudinal, lateral, and vertical directions, which correspond to the global x, z and y directions, respectively. Rig with two booms Left front wheel center y

z

x

250

60

force spectra (kN)

applied force (kN)

70

50 40 30 20

200 150 100 50

10 00

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0

2

0

2

time (s)

4

6

8

10

frequency (Hz)

Figure 10. Applied force at the left front wheel center. Fourier spectra of the force in the right figure.

Figure 11 shows the absolute displacement time-history for the service platform attachment feature located on the rig. We can clearly see that forces acting in the longitudinal direction will cause significant movements also in the lateral direction. A Fourier-spectra of the movements for a force acting in the longitudinal, vertical, and lateral direction, respectively, is shown in figure 12. Here we can see that forces acting in any direction on a front wheel will cause significant lateral movements.

Rig with two booms Steering joint a1 y

z

Fx(t)

x

absolute movement of point a1 (m)

0.01 0.008

direction

0.006

longitudinal vertical lateral

0.004 0.002 0 -0.002 -0.004 -0.006 -0.008 -0.01

0

0.2

0.4

0.6

0.8

1

1.2

1.4

time (s)

Figure 11. Displacement history at mating feature a1 for a longitudinal force.

10

1.6

1.8

2

Vertical excitation

Fourier amplitudes at point a1 (m)

Fourier amplitudes at point a1 (m)

Fourier amplitudes at point a1 (m)

Longitudinal excitation direction

0.08 0.07 0.06

longitudinal vertical lateral

0.07 0.06 0.05

0.05

0.04

0.04

0.03

0.03

0.02

0.02

0.01

0.01 0

direction

0.08

longitudinal vertical lateral

0

2

4

6

frequency (Hz)

8

0

10

0

2

4

6

8

10

frequency (Hz)

Lateral excitation 0.06

direction

0.05

longitudinal vertical lateral

0.04 0.03

Rig with two booms Mating feature a1

0.02

y

0.01 0 0

2

4

6

8

10

z

x

frequency (Hz)

Figure 12. Displacement history at mating feature a1 for a longitudinal, vertical, and a lateral force.

11

3.3 Parameter studies A conceptual parameter study was performed to investigate the effect on the magnitude of the lateral movements by changing some of the model parameters. The following five cases were studied for a lateral force acting at the center of the front left wheel: 1 - Original model (as presented above in chapter 3.2). 2 - A rig with a completely rigid steering joint. 3 - The stiffness of the front wheels increased with a factor of two. 4 - The stiffness of the rear wheels increased with a factor of two. 5 - The stiffness of all four wheels increased with a factor of two.

Point a1 - vertical movement (m)

The lateral and vertical movement of point a1 for the five model variants are shown in figure 13. The maximum lateral and vertical movements for each model is represented as a box surrounding the motion envelope. One observation is that the lateral motion can be significantly reduced by increasing the stiffness of the front wheels or by adding a pair of front wheels. Lateral excitation

0.006 0.004 0.002 0 -0.002 -0.004

Front wheels: 2xstiffness Rear wheels: 2xstiffness All wheels: 2xstiffness Original rig Rigid mid joint

-0.006 -0.008 -0.01 -0.01

-0.005

0

0.005

0.01

Point a1 - lateral movement (m)

Figure 13. Displacement history at mating fetaure a1 for a variation in some model parameters.

12

4 DISCUSSION The behavior of a rig has previously been studied by Sjögren (1999) with a rigid body approach, i.e. the Adams software, combined with a hydraulic system and instances of a flexible wheel model. Similar types of simulations have been performed with a finite element based Ansys model. For the latter type of simulations, which have been presented in this report, the finite element approach has proved to be quite useful. Analyses of the simulation results show that transient forces on the front wheels acting in any direction will generate considerable motions and vibrations in the lateral direction. This effect is caused by a set of highly coupled modes that can be found in the 2-3 Hz frequency range. Simulations indicate that the lateral movements can be significantly reduced with an increased stiffness of the front wheels. A general driving case, with the purpose to simulate the dynamic behavior due to the nonlinear contact between wheel and ground can not be simulated with the present version of Ansys. Linear vibrations based on modal superposition can though be performed as random simulations for known forces that can be defined as a power spectrum density (PSD) spectrum. A more thorough study of a realistic driving case on rough terrain would require a more general tire model, e.g. the Delft Tire model that is available in the Adams software package (ADAMS,1999). Observe that this wheel model was not used by Sjögren (1999). A detailed simulation with a comprehensive wheel model would probably require an elastic systems model, i.e. a composition of flexibile submodels. This can for example be accomplished by exporting component modes as a modal neutral file (MNF) from Ansys to Adams (ADAMS, 1999). The standard Ansys macro adams.mac can be used for that purpose.

13

5 ACKNOWLEDGEMENTS This work was financially supported by the National Board for Industrial and Technical Development (NUTEK) and by grant from Volvo Research Foundation. The supervision of Professor Sören Andersson is gratefully acknowledged. The support from Dr. Kenneth Weddfeldt, Atlas Copco Rock Drills AB, is also acknowledged.

6 REFERENCES ADAMS, 1999, “ADAMS Users Manual”, MDI. ANSYS, 1998, ”Theory Reference manual”, Eight edition, ANSYS Inc. Sellgren, U., 1999, “Finite Element Modeling and Optimization of a Robot Boomer”, Technical report, TRITA – MMK 1999:21, Department of Machine Design, Royal Institute of Technology, Stockholm, Sweden. Sjögren, F., 1999, “ADAMS-simulering av Atlas Copco Rocket Boomer L2D. Undersökning av odämpad girvinkelrörelse”, (Confidential), Mechanical Dynamics Sweden AB

14

APPENDIX A: RIG WITH TWO BOOMS – MOBILE FREQUENCIES The weight of an L2C rig with two booms is approximately 27000 kg. The eigenfrequencies that are below 10Hz for such a rig on four wheels with the booms in transport position are listed in figure A1. The mass and stiffness for each mode is also listed in figure A1. A mode with a relatively large mass can be characterized as a global mode and a mode with a small mass as a local mode. The nine modes with the largest modal mass are labeled in the rightmost plot in figure A1. The mass mi for mode number i is defined here as: mi = DTi MD i where M is the mass matrix and Di is eigenvector i normalized with the largest component equal to one. The corresponding modal stiffness ki is: 2 k i = mi (2πf i ) where fi is the frequency in Hertz of mode number i. frequency modal (Hz) mass 0.97 5167 1.14 4443 1.41 3 1.50 120 1.52 218 1.71 1211 1.77 4 1.81 39 2.29 10865 2.39 16041 2.71 24782 2.74 5248 3.49 8491 3.92 4651 4.40 128 4.97 35 5.11 149 5.48 155 5.92 98 7.59 1 8.36 0.2 8.61 3 8.86 44 9.57 17

modal stiffness 190300 228600 200 10700 19800 139600 500 5100 2250000 3619200 7174600 1556000 4089500 2814500 98100 33900 153400 183200 135100 2400 700 7500 136200 61900

Rig on wheels - modal mass 11 0.9

normalized modal mass

mode number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

10

0.6

9 13 0.3 1

12

2

14

6 0

0

1

2

3

4

5

6

7

8

9

10

frequency (Hz)

Figure A1. Frequencies, masses and stiffnesses for the lowest modes. Rig on wheels - modal mass components direction

Directions for rig with two booms

normalized modal mass

0.9

longitudinal vertical lateral

0.6

0.3

y

z

0

x

0

1

2

3

4

5

frequency (Hz)

Figure A2. Mass components for the lowest modes.

15

6

7

8

9

10

The shape of the twenty lowest modes are plotted in figures A3 and A4. Modes 1, 2, 6, and 9 to 14 can be characterized as global modes. All other modes are of a local character. The local modes may although cause local behavior that can severely affect the global performance and reliability. f1=0.97 Hz

f2=1.14 Hz

Y

Y

Z

X

Z

X

Y

X

Y

X

Z

Z

f4=1.50 Hz

f3=1.41 Hz Y

Y Z

X

Y

Z

X

Y

X

X

Z

Z

f5=1.52 Hz

f6=1.71 Hz

Y

Y

Z

X

Z

X

Y

X

Y

X

Z

Z

f8=1.81 Hz

f7=1.77 Hz Y

Y

Z

X

Z

Y

X

Y

X

X

Z

Z

f10=2.39 Hz

f9=2.29 Hz Y

Y

Z

X

Z

X

Y

X

Y

X

Z

Z

Figure A3. The then lowest frequencies and the corresponding mode shapes.

16

f11=2.71 Hz

f12=2.74 Hz Y

Y Z

X

Z

X

Y

X

Y

X

Z

Z

f13=3.49 Hz

f14=3.92 Hz Y

Y Z

X

Z

X

Y

X

Y

X

Z

Z

f15=4.40 Hz

f16=4.97 Hz Y

Y Z

X

Z

X

Y

X

Y

X

Z

Z

f17=5.11 Hz

f18=5.48 Hz

Y

Y

Z

X

Z

X

Y

X

Y

X

Z

Z

f19=5.92 Hz

f20=7.59 Hz

Y

Y

Z

X

Y

X

Z

X

Y

X

Z

Z

Figure A4. Frequencies and shapes for modes eleven to twenty.

17

APPENDIX B: RIG WITH TWO BOOMS ON LEGS - MODES The weight of an L2C rig with two booms is approximately 27000 kg. The eigenfrequencies that are below 10Hz for such a rig on four wheels with the booms in transport position are listed in figure B1. The mass and stiffness for each mode is also listed in figure B1. A mode with a relatively large mass can be characterized as a global mode and a mode with a small mass as a local mode. The nine modes with the largest modal mass are labeled in the rightmost plot in figure B1. The mass mi for mode number i is defined here as: mi = DTi MD i where M is the mass matrix and Di is eigenvector i normalized with the largest component equal to one. The corresponding modal stiffness ki is: 2 k i = mi (2πf i ) where fi is the frequency in Hertz of mode number i. frequency (Hz) 1.32 1.41 1.51 1.51 1.74 1.77 1.77 1.88 3.41 4.93 6.13 6.76 7.21 7.25 7.39 7.73 8.31 8.39 8.61 11.47 11.72 12.07 12.50 13.16

modal modal mass stiffness 4351 300000 3 200 679 61000 41 3800 1648 198000 142 18000 2411 299000 19 2600 2820 1295000 523 502000 2749 4074000 1905 3436000 1834 3765000 1596 3314000 2925 6312000 5840 13753000 10777 29386000 1402 3900000 884 2586000 4531 23524000 2594 14067000 18 103000 266 1640000 600 4101000

Rig on legs - modal mass

0.6

0.5

normalized modal mass

mode number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

17 0.4

0.3 16 0.2

1 9

7

0.1

11

15 12

13

5

18

14 0

0

1

2

3

4

5

6

7

8

9

10

frequency (Hz)

Figure B1. Frequencies, masses and stiffnesses for the lowest modes. Rig on legs - modal mass components

0.6

direction longitudinal vertical lateral

Directions for rig with two booms

normalized modal mass

0.5

y

z

0.4

0.3

0.2

0.1

0

x

0

1

2

3

4

5

frequency (Hz)

Figure B2. Mass components for the lowest modes.

18

6

7

8

9

10

The shape of the twenty lowest modes are plotted in figures B3 and B4. Modes 1, 6, 7, 9 and 11 to 18 can be characterized as global modes. All other modes are of a local character. The local modes may although cause local behavior that can severely affect the global performance and reliability. f2=1.41 Hz

f1=1.32 Hz

Y

Y

Z

X

Z

X

Y

X

Y

X

Z

Z

f4=1.51 Hz

f3=1.51 Hz

Y

Y Z

X

Z

X

Y

X

Y

X

Z

Z

f6=1.77 Hz

f5=1.74 Hz

Y

Y Z

X

Z

X

Y

X

Y

X

Z

Z

f8=1.88 Hz

f7=1.77 Hz

Y

Y

Z

X

Z

X

Y

X

Y

X

Z

Z

f10=4.93 Hz

f9=3.41 Hz

Y

Y

Z

X

Z

X

Y

X

Y

X

Z

Z

Figure B3. The then lowest frequencies and the corresponding mode shapes.

19

f12=6.76 Hz

f11=6.13 Hz

Y

Y Z

X

Y

X

Z

Z

X

Y

X

Z

f14=7.25 Hz

f13=7.21 Hz

Y

Y Z

X

Z

X

Y

X

Y

X

Z

Z

f16=7.73 Hz

f15=7.39 Hz

Y

Y Z

X

Y

X

Z

Y

X

X

Z

Z

f18=8.39 Hz

f17=8.31 Hz

Y

Y Z

X

Z

X

Y

X

Y

X

Z

Z

f20=11.47 Hz

f19=8.61 Hz

Y

Y

Z

X

Z

X

Y

X

Y

X

Z

Z

Figure B4. Frequencies and shapes for modes eleven to twenty.

20

APPENDIX C: RIG WITH TWO BOOMS – TRANSIENT SIMULATIONS C.1 Loading and monitoring points The time history as well as the frequency content of the force used in the simulations is plotted in figure C2. The force is applied at the left front wheel center (see figure C1), either as a longitudinal force in the global x direction, a lateral force in the z direction, or as a vertical force in the y-direction.

Rig with two booms Left front wheel center y

z

x

Figure C1. The force is applied at the left front wheel center.

250

60

force spectra (kN)

applied force (kN)

70

50 40 30 20 10 00

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

200 150 100 50 0

2

0

2

time (s)

4

6

8

10

frequency (Hz)

Figure C2. Tme history and Fourier spectra for the applied force.

Some simulation motion results, i.e. translations and rotations, are plotted for the the service platform mating feature a1, and the steering joint that connect the front and rear parts of the rig (see figure C3). Point a2f is located on the front part and point a2r is located on the rear part. Cylinder forces are also plotted for the two lift cylinders lc11 and lc12 on the left boom.

Rig with two booms Steering joint (a2f,a2r) a1 y

z

Lift cylinders lc11 lc12 Fx(t)

x

Figure C3. Results are ploptted for three monitoring points and two hydraulic cylinders.

21

C.2 Longitudinal pulse at left front wheel Point a1 - absolute movement response spectra (m)

0.01

Point a1 - absolute movement (m)

0.008 0.006 0.004 0.002 0 -0.002

direction

-0.004

longitudinal vertical lateral

-0.006 -0.008 -0.01 0

0.2

0.4

0.6

0.8

1 1.2 time (s)

1.4

1.6

1.8

2

direction

0.14

longitudinal vertical lateral

0.12 0.1 0.08 0.06 0.04 0.02 0 0

2

Point a1 - vertical movement (mm)

2.5 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 -2.5 -2

-1

0 1 2 3 Point a1 - lateral movement (mm)

4

Figure C4. Transient reponse at point a1.

22

4 6 frequency (Hz)

8

10

0.1

0.05

0

-0.05

rotational direction -0.1

longitudinal axis lateral axis vertical axis

-0.15

-0.2 0

0.2

0.4

0.6

0.8

1 1.2 time (s)

1.4

1.6

1.8

2

Point a2f to a2r - relative rotation response spectra (degrees)

Point a2f to a2r - relative rotation (degrees)

0.15

1.4

1.2

1

0.8

0.6

0.4

0.2

0 0

2

4 6 frequency (Hz)

8

10

0.1

0.05

0

-0.05

rotational direction

-0.1

longitudinal axis lateral axis vertical axis

-0.15

-0.2 0

0.2

0.4

0.6

0.8

1 1.2 time (s)

1.4

1.6

1.8

2

Figure C5. Relative rotation at the joint and absolute rotation at mating feature a2f. 350

Lift cylinder

Lift cylinder

cylinder lc12 cylinder lc11

cylinder lc12 cylinder lc11

600 Lift cylinder force spectra (kN)

300 Left lift cylinder forces (kN)

Point a2f - absolute rotation (degrees)

0.15

250

200

150

100

50

500

400

300

200

100

0

0 0

2

4

6 frequency (Hz)

8

10

0

2

4

6 frequency (Hz)

Figure C6. Time history of the absolute values for the cylinders forces (left), and the frequency content (right).

23

8

10

C.3 Vertical pulse at left front wheel 0.16 Point a1 - absolute movement response spectra (m)

0.015

direction Point a1 - absolute movement (m)

0.01

longitudinal vertical lateral

0.005

0

-0.005

-0.01

0.14

direction

0.12

longitudinal vertical lateral

0.1 0.08 0.06 0.04 0.02 0

-0.015 0

0.2

0.4

0.6

0.8

1 1.2 time (s)

1.4

1.6

1.8

2

0

2

Point a1 - vertical movement (m)

0.01 0.008 0.006 0.004 0.002 0 -0.002 -0.004 -0.006 -0.008 -0.01 -0.01

-0.005

0 0.005 0.01 Point a1 - lateral movement (m)

0.015

Figure C7. Transient reponse at point a1.

24

4 6 frequency (Hz)

8

10

Point ba2f to a2r - relative rotation response spectra (degrees)

Point a2f to a2r - relative rotation (degrees)

0.2

rotational direction 0.15

longitudinal axis lateral axis vertical axis

0.1 0.05 0 -0.05 -0.1 -0.15 -0.2

0

0.2

0.4

0.6

0.8

1 1.2 time (s)

1.4

1.6

1.8

2

1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0

2

4 6 frequency (Hz)

8

10

0.5

rotational direction

Point a2f - absolute rotation (degrees)

0.4

longitudinal axis lateral axis vertical axis

0.3 0.2 0.1 0 -0.1 -0.2 -0.3

0

0.2

0.4

0.6

0.8

1 1.2 time (s)

1.4

1.6

1.8

2

Figure C8. Relative rotation at the joint and absolute rotation at mating feature a2f.

800

Lift cylinder

450

700 Lift cylinder force spectra (kN)

400 Left lift cylinder forces (kN)

Lift cylinder

cylinder lc12 cylinder lc11

350 300 250 200 150

cylinder lc12 cylinder lc11

600 500 400 300 200

100 100

50

0

0 0

2

4 6 frequency (Hz)

8

0

10

2

4 6 frequency (Hz)

Figure C9 Time history of the absolute values for the cylinders forces (left), and the frequency content (right).

25

8

10

C.4 Lateral pulse at left front wheel 0.015

Point a1 - absolute movement (m)

Point a1 - absolute movement response spectra (m)

direction longitudinal vertical lateral

0.01

0.005

0

-0.005

-0.01

-0.015 0

0.2

0.4

0.6

0.8

1 1.2 time (s)

1.4

1.6

1.8

2

direction

0.09

longitudinal vertical lateral

0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 0

2

8 6

Point a1 - vertical movement (mm)

4 2 0 -2 -4 -6 -8 -10

-8

-6

-4

-2 0 2 4 6 8 Point a1 - lateral movement (mm)

10

Figure C10. Transient reponse at point a1.

26

4 6 frequency (Hz)

8

10

Point a2f to a2r - relative rotation response spectra (degrees)

Point a2f to a2r - relative rotation (degrees)

0.2

0.1

0

-0.1

rotational direction -0.2

longitudinal axis lateral axis vertical axis

-0.3

0

0.2

0.4

0.6

0.8

1 time (s)

1.2

1.4

1.6

1.8

2

3

2.5

2

1.5

1

0.5

0 0

2

4 6 frequency (Hz)

8

10

0.25

rotational direction

Point a2f - absolute rotation (degrees)

0.2

longitudinal axis lateral axis vertical axis

0.15 0.1 0.05 0 -0.05 -0.1 -0.15 -0.2 -0.25 0

0.2

0.4

0.6

0.8

1 1.2 time (s)

1.4

1.6

1.8

2

Figure C11. Relative rotation at the joint and absolute rotation at mating feature a2f.

Lift cylinder

350

Lift cylinder force spectra (kN)

Left lift cylinder forces (kN)

300

Lift cylinder

700

cylinder lc12 cylinder lc11

250 200 150

600 500 400 300

100

200

50

100

0

cylinder lc12 cylinder lc11

0 0

2

4 6 frequency (Hz)

8

10

0

2

4 6 frequency (Hz)

8

Figure C12 Time history of the absolute values for the cylinders forces (left), and the frequency content (right).

27

10

APPENDIX D: RIG WITH TWO BOOMS – PARAMETER STUDIES D.1 Loading and monitoring points The same force and loading poin as in appendix C was used here (see figure D1). The results plotted in appendix C may thus be treated as results for the original model.

Left front wheel center y

applied force (kN)

70

Rig with two booms

60 50 40 30 20 10

z

x

00

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

time (s)

Figure D1. Force applied at the left front wheel center.

Some simulation motion results, i.e. translations and rotations, are plotted for the the service platform mating feature a1, and the steering joint that connect the front and rear parts of the rig (see figure D3).

Rig with two booms Mating feature a1 y

z

x Figure D2. .

28

Point a1 absolute movement response spectra (m)

D.2 Rigid steering joint – lateral pulse at left front wheel

Point a1 - absolute movement (m)

0.01

0.005

0

-0.005

direction longitudinal vertical lateral

-0.01

direction

0.14

longitudinal vertical lateral

0.12 0.1 0.08 0.06 0.04 0.02 0

-0.015 0

0.2

-10

-8

0.4

0.6

0.8

1 time (s)

1.2

1.4

1.6

1.8

0

2

2

4 6 frequency (Hz)

8

10

8

Point a1 - vertical movement (mm)

6 4 2 0 -2 -4 -6 -8 -6

-4 -2 0 2 4 6 Point a1 - lateral movement (mm)

8

10

rotational direction

0.2

Point a2f to a2r - relative rotation (degrees)

Point a2f - absolute rotation (degrees)

Figure D3. Transient reponse at point a1.

longitudinal axis lateral axis vertical axis

0.15 0.1 0.05 0 -0.05 -0.1

0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8

-0.15

-1 0

0.2

0.4

0.6

0.8

1 1.2 time (s)

1.4

1.6

1.8

2

0

0.2

0.4

0.6

0.8

1 1.2 time (s)

1.4

1.6

Figure D4. Relative rotation at the joint and absolute rotation at mating feature a2f.

29

1.8

2

direction

6 Point a1 - absolute movement (mm)

Point a1 - absolute movement response spectra (m)

D.3 2 times front wheel stiffness – lateral pulse at left front wheel

longitudinal vertical lateral

4

2

0

-2

-4

-6

direction

0.06

longitudinal vertical lateral

0.05

0.04

0.03

0.02

0.01

0

0

0.2

0.4

0.6

0.8

1 1.2 time (s)

1.4

1.6

1.8

0

2

2

4 6 frequency (Hz)

8

10

4 6 frequency (Hz)

8

10

Point a1 - vertical movement (mm)

4 3 2 1 0 -1 -2 -3 -4 -4

-2

0 2 4 Point a1 - lateral movement (mm)

6

rotational direction

0.15

longitudinal axis lateral axis vertical axis

0.1 0.05 0 -0.05 -0.1 -0.15 -0.2

0

0.2

0.4

0.6

0.8

1 1.2 time (s)

1.4

1.6

1.8

2

Point a2f to a2r -relative rotation response spectra (degrees)

Point a2f to a2r - relative rotation (degrees)

Figure D5. Transient reponse at point a1.

1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0

0

2

Figure D6. Relative rotation at the joint and absolute rotation at mating feature a2f.

30

D4. CONCLUSIONS – LATERAL PULSE AT LEFT FRONT WHEEL

Point a1 - vertical movement (m)

The lateral and vertical movement of point a1 for these five models are shown in figure D7. The maximum lateral and vertical movements for each model are represented as a box surrounding the motion envelope.

Lateral excitation

0.006 0.004 0.002 0 -0.002 -0.004

Front wheels: 2xstiffness Rear wheels: 2xstiffness All wheels: 2xstiffness Original rig Rigid mid joint

-0.006 -0.008 -0.01 -0.01

-0.005

0

0.005

0.01

Point a1 - lateral movement (m)

Figure D7.

31

APPENDIX E: ANSYS MACRO LIBRARY TO CONFIGURE A SYSTEM

help !*********************************************** !* !* rig_3.lib - 2000-05-29 !*!* External routines called: !* atlas.lib !* !* rockl2ct – mount a full rig model with two booms and four wheels and performa transient simulation for !* a lateral excitation force acting in the center of the front left wheel. !* !* Execute macro: !* *ulib,rig_3,lib !* *use,rockl2ct !* subadams - transform rig (l2c) to adams cs and extract adams !* substructure files from ansys submodel !* subasc - dump ansys substructure file to an ascii file !* !* 1999-11-11 !* !* rocket - mount rig (l2c) with 2 boomer model (but36l_j.ans) instances !* and attach them !* rocky - environment for rocket (wheel axle fixes and lizard axelerations) !* and simulation !* rig_init - initial rig parameter data !* l2c - rig model !* fixes - fixed displacements !* lizard - lizard accelerations arounbd vertical axis !* at wheel axle centres !* environ - environment model !* simulate - perform single step simulation !* rig_post !* !* bvx96_le - original rig model, rearranged and converted to SI units !* load - load behavior module (connected model) !* /eof rockl2ct /output,l2cnwty,out /filenam,l2cnwty ! full model (rig + 2 booms, 4 wheels) *ulib,atlas,lib *use,pos_10 ! transport configuration *ulib,rig_3,lib fini /prep7 init_sys=25 csys,0 clocal,init_sys,0,1.955,1.585,0.950 fini *use,load,'but35l_j' /prep7

32

csys,0 clocal,init_sys,0,1.955,1.585,-0.950 numoff,node,40 fini *use,load,'but35l_j' fini /prep7 numoff,node,200 fini *use,rig_init *use,load,'l2c_nw' ! l2cnwt_zw - regular rig without wheels ! ! front wheels *use,wheel,16,28,'z',2.e6,2.e6,2.e6,585. !center,ground,direction,kx,ky,kz,mass *use,wheel,46,29,'z',2.e6,2.e6,2.e6,585. !center,ground,direction,kx,ky,kz,mass ! rear wheels *use,wheel,126,30,'z',2.e6,2.e6,2.e6,585. !center,ground,direction,kx,ky,kz,mass *use,wheel,156,31,'z',2.e6,2.e6,2.e6,585. !center,ground,direction,kx,ky,kz,mass ! fini /prep7 ! right boom (z+) to rig *ulib,atlas,lib *use,attach,23,279 *use,attach,53,239 !*** *use,attach,1,101 ! rigid steering joint !*** *use,attach,2,102 ! rigid steering joint *ulib,rig_3,lib fini *use,ground,'wheel' save /title,L2c Fy(left front wheel)=63kN,0.2s *use,bump,63662.,'z',0.2,2.0,46 !l2cnw_ty /output /eof rig_init !*********************************************** !* LUTKRAFT=54200 Gy=9.82 HAST=0.0001084404E3 ! (rot acceleration)/g [rad/s2)]/[m/s2]? CSYS,0 styrv=0 !*** /FILNAME,BVX_L2_LIZZ /COM, /COM, /FDELE,TRI,DELE /FDELE,EMAT,DELE /FDELE,ESAV,DELE /eof load !******************************************************** !* Load model (imported from atlas.lib) !* Input parameter: !* arg1 - model name (extension= .ans) !* Entry point: any ! fini

33

/input,arg1,ans /eof ground !*********************************************** ! arg1 - 'wheel' support of the four wheels ! 'leg' support of the four legs fini /prep7 *if,arg1,'eq','wheel',then cmsel,s,mates(8,1) cmsel,a,mates(9,1) cmsel,a,mates(10,1) cmsel,a,mates(11,1) d,all,all,0.0 nsel,all *else cmsel,s,mates(4,1) cmsel,a,mates(5,1) cmsel,a,mates(6,1) cmsel,a,mates(7,1) d,all,all,0.0 nsel,all *endif fini /eof bump !************************************************* !* arg1 - force in the center of the left front wheel !* arg2 - direction !* arg3 - duration !* arg4 - total simulation time !* arg5 - node !* forc=arg1 tforce=arg3 ttot=arg4 fini /solu antype,trans trnopt,full ! full transient option lumpm,on ! lumped mass esel,s,elem,,144,145 esel,a,elem,,62,63 outres,esol,all esel,all outres,nsol,all !nlgeom,on !nropt,*** eqslv,sparce ! sparse=sparse direct solver,front=frontal solver kbc,0 ! ramped loading time,tforce/2 deltim,tforce/4,tforce/4,tforce/4 !dt,dtmin,dtmax *if,arg2,eq,'x',then f,arg5,fx,forc *elseif,arg2,eq,'y' f,arg5,fy,forc *else

34

f,arg5,fz,forc *endif solve time,tforce *if,arg2,eq,'x',then f,arg5,fx,0.0 *elseif,arg2,eq,'y' f,arg5,fy,0.0 *else f,arg5,fz,0.0 *endif solve time,ttot solve fini save /eof

35

APPENDIX F: ANSYS MODEL OF BVX96_LE (Confidential) Listed below is an Ansys model of rig L2C without wheels. The submodels are interconnected. This model is a modified version of the Ansys model developed by CAMATEC for Atlas Copco in the project NO100 BVX 96 L2. L2c_nw.ans: !/////////////////////////////////////////////////////////////////////////////////////////////////// ! file name: l2c_nw.ans ! connected model of rig L2C, with no wheels ! 1999-11-11 ! 2000-05-29 - modified boom and service platform connection points !///////////////////////////////////////////////// ! component front - front nodes ! component rear - rear nodes ! !/////////////////////////////////////////////////////////////////////////////////////////////////// !* Entry point: any ! ! loop DOF parameters and define them if they currently do not exist *get,par_stat,parm,styrv,type *if,par_stat,lt,0,then ! parameter undefined styrv=0 ! *endif fini /PREP7 ! *get,i_sys,active,,csys ! get active coordinate system *get,i_typ,active,,type ! get active element type *get,i_mat,active,,mat ! get active material *get,i_real,active,,real ! get active real constant r_max=i_real mat_max=i_mat /title,BVX 96 L2 /stitle,2,Steering angle%styrv% !///////////////////////////////////////////////////////////////////////// !Boom frame - 'abstract' representation !********************************************************** fini /prep7 N, 1, 0., .451, .0 N, 2, 0., .081, .0 N, 3, .162, .180, .450 N, 4, 1.070, .180, .450 N, 5, 1.430, .180, .450 N, 6, 1.756, .568, .450 N,24, 1.756, .568, .450 N, 7, 2.200, .568, .450 N, 8, 2.394, .568, .450 N,25, 2.394, .568, .450 N, 9, 2.497, .568, .450 N,10, 3.000, .280, .450 N,11, 3.100, .280, .450 N,12, 3.100, .133, .997 ! N,13, 3.100, -.006, 1.517 ! N,14, 3.100, -.434, 1.517 ! N,15, 2.200, .270, .527 !

36

N,16, 2.200, .270, 1.070 ! N,28, 2.200, .270-.640, 1.070 ! N,17, .162, .451, .450 ! N,18, .162, .081, .450 N,19, 2.394, .765, .450 N,20, 1.756, .765, .450 N,21, 1.766, 1.172, .514 N,22, 1.766, 1.172, .950 ! N,23, 1.955, 1.585-0.469, .950 N,33, .162, .180, -.450 N,34, 1.070, .180, -.450 N,35, 1.430, .180, -.450 N,36, 1.756, .568, -.450 N,26, 1.756, .568, -.450 N,37, 2.200, .568, -.450 N,38, 2.394, .568, -.450 N,27, 2.394, .568, -.450 N,39, 2.497, .568, -.450 N,40, 3.000, .280, -.450 N,41, 3.100, .280, -.450 N,42, 3.100, .133, -.997 N,43, 3.100, -.006,-1.517 N,44, 3.100, -.434,-1.517 N,45, 2.200, .270, -.527 N,46, 2.200, .270,-1.070 N,29, 2.200, .270-.640,-1.070 N,47, .162, .451, -.450 N,48, .162, .081, -.450 N,49, 2.394, .765, -.450 N,50, 1.756, .765, -.450 N,51, 1.766, 1.172, -.514 N,52, 1.766, 1.172, -.950 N,53, 1.955, 1.585-0.469, -.950 N,54, 3.100, .400, .0 N,55, .162, .451, .0 N,56, .162, .081, .0 N,57, 1.766, 1.172, .0 N,58, .908, .261, -.239 N,59, 2.200, .270, .0 N,60, 1.955, 1.585-0.469, .0 ! mat_max=mat_max+1 mat,mat_max mp,EX,,20.6e10 ! generic steel mp,alpx,,0.0 ! ! !Real constants r_max=r_max+1 real,r_max R,r_max,.1,1e-3,1e-3,.100,.100,, Rmore,,1e-3 et,,beam4 *get,et_max,etyp,,num,max type,et_max E,1,55 E,2,56 ! r_max=r_max+1 real,r_max

! ! ! !

!Styv

37

R,r_max,11840.e-6,264e-6,26.7e-6,.200,.360,, Rmore,,1.63e-6 E,3,4 E,4,5 E,5,6 ! r_max=r_max+1 real,r_max R,r_max,17020.e-6,476e-6,43.4e-6,.200,.400,, Rmore,,6.31e-6 E,6,7 E,7,8 E,8,9 ! r_max=r_max+1 real,r_max R,r_max,11870.e-6,270e-6,26.1e-6,.200,.363,, Rmore,,1.6e-6 E,9,10 ! r_max=r_max+1 real,r_max R,r_max,.1,1e-3,1e-3,.100,.100,, Rmore,,1e-3 E,10,11 ! r_max=r_max+1 real,r_max R,r_max,21469.e-6,132e-6,445e-6,.440,.200,, Rmore,,320e-6

!Boom frame beam 1

!Boom frame beam 2

!Boom frame beam 3

!Rigid

!Outer ”Domkrafts” beam

E,11,12 E,11,54 ! r_max=r_max+1 real,r_max R,r_max,12346.e-6,41.0e-6,109e-6,.261,.152,, !Inner ”Domkrafts” beam Rmore,,95.1e-6 E,12,13 ! r_max=r_max+1 real,r_max R,r_max,.1,1e-3,1e-3,.100,.100,, !Rigid Rmore,,1e-3 E,13,14 E,24,20 E,7,15 E,25,19 ! r_max=r_max+1 real,r_max R,r_max,16000.e-6,85.3e-6,27.7e-6,.200,.240,, !Boom console foot Rmore,,3.3e-6 E,19,20 ! r_max=r_max+1 real,r_max R,r_max,.1,1e-3,1e-3,.100,.100,, !Rigid Rmore,,1e-3

38

E,20,21 ! r_max=r_max+1 real,r_max R,r_max,29688.e-6,275e-6,275e-6,.305,.305,, Rmore,,550e-6 E,21,22 E,21,57 ! r_max=r_max+1 real,r_max R,r_max,35940.e-6,274e-6,1044e-6,.600,.243,, Rmore,,461e-6 E,22,23 ! r_max=r_max+1 real,r_max R,r_max,.1,1e-3,1e-3,.100,.100,, Rmore,,1e-3 E,15,16 E,3,17 E,3,18 E,15,59 ! r_max=r_max+1 real,r_max R,r_max,25050.e-6,62.8e-6,61.0e-6,.185,.162,, Rmore,,55e-6 E,17,55 E,18,56 ! ****************************** ! Left r_max=r_max+1 real,r_max R,r_max,11840.e-6,264e-6,26.7e-6,.200,.360,, Rmore,,1.63e-6 E,33,34 E,34,35 E,35,36 ! r_max=r_max+1 real,r_max R,r_max,17020.e-6,476e-6,43.4e-6,.200,.400,, Rmore,,6.31e-6 E,36,37 E,37,38 E,38,39 ! r_max=r_max+1 real,r_max R,r_max,11870.e-6,270e-6,26.1e-6,.200,.363,, Rmore,,1.6e-6 E,39,40 ! r_max=r_max+1 real,r_max R,r_max,.1,1e-3,1e-3,.100,.100,, Rmore,,1e-3 E,40,41

!Boom console tube

!Boom console plate

!Rigid

!Steering joint console boom frame

!Boom frame beam 1

!Boom frame beam 2

!Boom frame beam 3

!Rigid

39

! r_max=r_max+1 real,r_max R,r_max,21469.e-6,132e-6,445e-6,.440,.200,, Rmore,,320e-6 E,41,42 E,41,54 ! r_max=r_max+1 real,r_max R,r_max,12346.e-6,41.0e-6,109e-6,.261,.152,, Rmore,,95.1e-6 E,42,43 ! r_max=r_max+1 real,r_max R,r_max,.1,1e-3,1e-3,.100,.100,, Rmore,,1e-3 E,43,44 E,26,50 E,37,45 E,27,49 ! r_max=r_max+1 real,r_max R,r_max,16000.e-6,85.3e-6,27.7e-6,.200,.240,, Rmore,,3.3e-6 E,49,50 ! r_max=r_max+1 real,r_max R,r_max,.1,1e-3,1e-3,.100,.100,, Rmore,,1e-3 E,50,51 ! r_max=r_max+1 real,r_max R,r_max,29688.e-6,275e-6,275e-6,.305,.305,, Rmore,,550e-6 E,51,52 E,51,57 ! r_max=r_max+1 real,r_max R,r_max,35940.e-6,274e-6,1044e-6,.600,.243,, Rmore,,461e-6 E,52,53 ! r_max=r_max+1 real,r_max R,r_max,.1,1e-3,1e-3,.100,.100,, Rmore,,1e-3 E,45,46 E,33,47 E,33,48 E,45,59 ! r_max=r_max+1 real,r_max

!Outer ”Domkrafts” beam

!Inner ”Domkrafts” beam

!Rigid

!Boom console foot

!Rigid

!Boom console tube

!Boom console plate

!Rigid

40

R,r_max,25050.e-6,62.8e-6,61.0e-6,.185,.162,, !Steering joint console boom frame Rmore,,55e-6 E,47,55 E,48,56 ! r_max=r_max+1 real,r_max R,r_max,.1,1e-3,1e-3,.100,.100,, !Rigid Rmore,,1e-3 E,34,58 !******** ! masses *get,i_mat,active,,mat mat_max=i_mat+1 et,,mass21,,0,2 ! dir par to global, 3D mass wo rot mass *get,et_max,etyp,,num,max ! get maximum element type ! type,et_max r_max=r_max+1 r,r_max, 1834. real,r_max e, 6 !Mass front wagon e,36 r_max=r_max+1 r,r_max, 695. real,r_max e, 7 ! Mass front wagon e,37 r_max=r_max+1 r,r_max, 422. real,r_max e, 3 !Mass service platform e,33 r_max=r_max+1 r,r_max, 315. real,r_max e, 4 ! Mass service platform e,34 ! ! front component cm,front,node fini !//////////////////////////////////////////////////////// ! motor frame - 'abstract' representation fini /prep7 csys,0 CLOCAL,11,0,0,0,0,0,0,180+styrv ! N,101, .0, .451, .0 N,102, .0, .081, .0 N,103, .340, .261, -.436 N,104, .867, .605, -.436 N,105, 1.250, .605, -.436 N,106, 1.565, .605, -.436 N,107, 1.565, .435, -.436 !N,108, N,109, 2.020, .605, -.436 N,110, 2.020, .435, -.436

41

N,111, 2.610, .605, -.436 N,112, 2.610, .205, -.436 N,113, 2.610, .205, -.510 N,114, 2.670, .205, -.510 N,115, 2.670, .205, -.664 N,116, 2.510, .205, -.664 N,117, 2.510, -.473, -.664 N,118, 2.670, .205, -.940 N,119, 3.397, .205, -.940 !N,120 N,121, 4.310, .450, -.700 N,122, 1.250, 1.100, -.436 N,123, 1.250, 1.700, -.436 N,124, .892, 1.100, -.700 N,125, 1.792, .270, -.436 N,126, 1.792, .270, -1.070 N, 30, 1.792, .270-.640, -1.070 ! rear wheel - right ground (z+) N,127, .340, .451, -.436 N,128, .340, .081, -.436 ! !Vänster N,133, .340, .261, .436 N,134, .867, .605, .436 N,135, 1.250, .605, .436 N,136, 1.565, .605, .436 N,137, 1.565, .435, .436 !N,138, N,139, 2.020, .605, .436 N,140, 2.020, .435, .436 N,141, 2.610, .605, .436 N,142, 2.610, .205, .436 N,143, 2.610, .205, .510 N,144, 2.670, .205, .510 N,145, 2.670, .205, .664 N,146, 2.510, .205, .664 N,147, 2.510, -.473, .664 N,148, 2.670, .205, .940 N,149, 3.397, .205, .940 !N,150 N,151, 4.310, .450, .700 N,152, 1.250, 1.100, .436 N,153, 1.250, 1.700, .436 N,154, .892, 1.100, .700 N,155, 1.792, .270, .436 N,156, 1.792, .270, 1.070 N, 31, 1.792, .270-.640, 1.070 ! rear wheel - left ground (z-) N,157, .340, .451, .436 N,158, .340, .081, .436 ! !Mitten N,161, .340, .451, .0 N,162, .340, .081, .0 N,163, 1.565, .270, .0 N,164, 1.792, .270, .0 N,165, 2.020, .270, .0 N,166, 4.310, .450, .0 N,167, 4.535, .450, .0 N,168, .030, .261, .280 !

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et,,beam4 *get,et_max,etyp,,num,max type,et_max mat_max=mat_max+1 mat,mat_max mp,EX,,20.6e10 ! generic steel mp,alpx,,0.0 ! r_max=r_max+1 real,r_max R,r_max,.1,1e-3,1e-3,.100,.100,, !Rigid Rmore,,1e-3 E,101,161 E,102,162 E,103,127 E,103,128 E,133,157 E,133,158 E,133,168 ! r_max=r_max+1 real,r_max R,r_max,11600.e-6,10.6e-6,21.5e-6,.150,.132,, !Steering joint console motor frame Rmore,,3.2e-6 E,127,161 E,157,161 E,128,162 E,158,162 ! r_max=r_max+1 real,r_max R,r_max,5944.e-6,89.1e-6,4.8e-6,.100,.340,, !Motor frame beam Rmore,,0.3e-6 E,103,104 E,133,134 E,104,105 E,134,135 E,105,106 E,135,136 E,106,109 E,136,139 E,109,111 E,139,141 ! r_max=r_max+1 real,r_max R,r_max,.1,1e-3,1e-3,.100,.100,, !Rigid Rmore,,1e-3 E,106,107 E,136,137 E,109,110 E,139,140 E,163,164 E,164,165 E,125,126 E,155,156 E,125,164 E,155,164 ! r_max=r_max+1

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real,r_max R,r_max,7200.e-6,1.0e-6,19.4e-6,.180,.040,, !Wheel axel console Rmore,,3.3e-6 E,107,163 E,137,163 E,110,165 E,140,165 ! r_max=r_max+1 real,r_max R,r_max,.1,1e-3,1e-3,.100,.100,, !Rigid Rmore,,1e-3 E,111,112 E,141,142 E,112,113 E,142,143 E,113,114 E,143,144 E,115,116 E,145,146 E,116,117 E,146,147 ! r_max=r_max+1 real,r_max R,r_max,5020.e-6,31e-6,12e-6,.120,.220,, !Front after frame beam Rmore,,28.5e-6 E,114,115 E,144,145 E,115,118 E,145,148 E,114,144 ! r_max=r_max+1 real,r_max R,r_max,6664.e-6,43.7e-6,11.1e-6,.117,.250,, !After frame beam side 1 Rmore,,40.4e-6 E,118,119 E,148,149 ! r_max=r_max+1 real,r_max R,r_max,3000.e-6,7.4e-6,2.1e-6,.085,.150,, !After fram beam side 2 Rmore,,0.1e-6 E,119,121 E,149,151 ! r_max=r_max+1 real,r_max R,r_max,4860.e-6,18.9e-6,41.8e-6,.250,.150,, ! Rear after frame beam Rmore,,40.5e-6 E,121,166 E,151,166 ! r_max=r_max+1 real,r_max R,r_max,.1,1e-3,1e-3,.100,.100,, !Rigid Rmore,,1e-3 E,166,167

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! r_max=r_max+1 real,r_max R,r_max,7600.e-6,91.4e-6,0.3e-6,.020,.380,, !Hydraulic tank console Rmore,,0.96e-6 E,105,122 E,135,152 E,122,123 E,152,153 ! r_max=r_max+1 real,r_max R,r_max,4940.e-6,25.1e-6,0.16e-6,.020,.247,, ! Hydraul tank console stuff Rmore,,0.62e-6 E,123,153 ! r_max=r_max+1 real,r_max R,r_max,.1,1e-3,1e-3,.100,.100,, !Rigid Rmore,,1e-3 E,122,124 E,152,154 !******** ! masses *get,i_mat,active,,mat mat_max=i_mat+1 et,,mass21,,0,2 ! dir par to global, 3D mass wo rot mass *get,et_max,etyp,,num,max ! get maximum element type type,et_max r_max=r_max+1 r,r_max, 593. real,r_max e,163 !Mass pendel axel e,165 ! r_max=r_max+1 r,r_max, (611+250+186) real,r_max e,119 !Mass after frame, counterweight backmotv, ”v-vinda”,scrubber e,149 ! r_max=r_max+1 r,r_max, 300. real,r_max e,118 !Mass after frame e,148 ! r_max=r_max+1 r,r_max, (437+143) real,r_max e,121 !Mass jet-anol and rear counterweight e,151 e,166 ! r_max=r_max+1 r,r_max, 755. real,r_max e,105 !Mass motor frame e,135

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! r_max=r_max+1 r,r_max, 503. real,r_max e,106 !Mass motor frame e,136 ! r_max=r_max+1 r,r_max, 905. real,r_max e,124 !Mass power unit e,154 ! r_max=r_max+1 r,r_max, 484. real,r_max e,103 !Mass counterweight steering joint e,133 ! r_max=r_max+1 r,r_max, 817. real,r_max e,104 !Mass counterweight steering joint e,134 ! nsel,all nsel,u,node,,front cm,rear,node nsel,all fini !////////////////////////////////////////////////////////// !* Sub system 1 !* steering cylinder fini /prep7 et,,link8 *get,et_max,etyp,,num,max type,et_max mat_max=mat_max+1 mat,mat_max mp,EX,,8.e9 ! mp,alpx,,1.0 ! r_max=r_max+1 real,r_max R,r_max,12272.e-6 !Steering cylinder E,58,168 fini !////////////////////////////////////////////////////////// fini /prep7 ! !Service platform et,,beam4 *get,et_max,etyp,,num,max type,et_max mat_max=mat_max+1 mat,mat_max mp,EX,,20.6e10 ! generic steel mp,alpx,,0.0 !

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r_max=r_max+1 real,r_max R,r_max,.1,1e-3,1e-3,.100,.100,, !Rigid Rmore,,1e-3 E,57,60 fini !///////////////////////////////////////////////////////// ! connect features (interface realizations) ! revolute joint connections fini /prep7 csys,init_sys et,,combin7 *get,et_max,etyp,,num,max ! get maximum element type rj_k1=1.e10 ! x-y siffness rj_k2=1.e10 ! z stiffnes rj_k3=1.e10 rj_k4=0.0 r_max=r_max+1 r,r_max,rj_k1,rj_k2,rj_k3,rj_k4 ! K1,K2,K3,K4,CT,TF type,et_max real,r_max e,1,101,2 e,2,102,1 fini !///////////////////////////////////////////////////////////////////////////////////////////////////////////// ! ball joint connections fini /prep7 !Connection - boom console and boom frame CP,next,UX,6,24 CP,next,UY,6,24 CP,next,UZ,6,24 ! CP,next,UX,8,25 CP,next,UY,8,25 CP,next,UZ,8,25 ! CP,next,UX,36,26 CP,next,UY,36,26 CP,next,UZ,36,26 ! CP,next,UX,38,27 CP,next,UY,38,27 CP,next,UZ,38,27 fini !///////////////////////////////////////////////////////////////////////////////////////////////////////////// !* meta data !* fini /prep7 n_mates=11 *get,pstat,parm,mates,type *if,pstat,lt,0,then *dim,mates,char,n_mates,3 *else mates(1)= *dim,mates,char,n_mates,3 *endif

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mates(1,1)='boom_rig' mates(1,2)='attach' mates(1,3)='abstract' nsel,s,node,,23 cm,mates(1,1),node nsel,all mates(2,1)='boom_lef' mates(2,2)='attach' mates(2,3)='abstract' nsel,s,node,,53 cm,mates(2,1),node nsel,all mates(3,1)='observat' mates(3,2)='attach' mates(3,3)='abstract' nsel,s,node,,60 cm,mates(3,1),node nsel,all ! mates(4,1)='leg_fr_r' mates(4,2)='contact' mates(4,3)='abstract' nsel,s,node,,14 cm,mates(4,1),node nsel,all mates(5,1)='leg_fr_l' mates(5,2)='contact' mates(5,3)='abstract' nsel,s,node,,44 cm,mates(5,1),node nsel,all mates(6,1)='leg_re_r' mates(6,2)='contact' mates(6,3)='abstract' nsel,s,node,,117 cm,mates(6,1),node nsel,all mates(7,1)='leg_re_l' mates(7,2)='contact' mates(7,3)='abstract' nsel,s,node,,147 cm,mates(7,1),node nsel,all ! mates(8,1)='wheel_fl' mates(8,2)='contact' mates(8,3)='abstract' nsel,s,node,,29 cm,mates(8,1),node nsel,all mates(9,1)='wheel_fr' mates(9,2)='contact' mates(9,3)='abstract' nsel,s,node,,28 cm,mates(9,1),node nsel,all mates(10,1)='wheel_rl' mates(10,2)='contact' mates(10,3)='abstract'

! right boom ! type ! level_of_abstraction

! left boom ! type ! level_of_abstraction

! service paltform ! type ! level_of_abstraction

! front right leg ! type ! level_of_abstraction

! front left leg ! type ! level_of_abstraction

! rear right leg ! type ! level_of_abstraction

! rear left leg ! type ! level_of_abstraction

! front left wheel ! type ! level_of_abstraction

! front right wheel ! type ! level_of_abstraction

! rear left wheel ! type ! level_of_abstraction

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nsel,s,node,,31 cm,mates(10,1),node nsel,all mates(11,1)='wheel_rr' ! rear left wheel mates(11,2)='contact' ! type mates(11,3)='abstract' ! level_of_abstraction nsel,s,node,,30 cm,mates(11,1),node nsel,all ! model_st='connected' ! model_state abstract='abstract' ! level_of_abstraction ! ! dimensionality and physical dofs *get,pstat,parm,dimnam,type *if,pstat,eq,-1,then n_dim=3 *dim,dimnam,character,n_dim ! *else n_dim=3 dimnam(1)= *dim,dimnam,character,n_dim ! *endif dimnam(1)='x' dimnam(2)='y' dimnam(3)='z' ! *get,pstat,parm,phys,type *if,pstat,eq,-1,then nphys=6 *dim,phys,character,nphys ! *else nphys=6 phys(1)= *dim,phys,character,nphys ! *endif phys(1)='ux' phys(2)='uy' phys(3)='uz' phys(4)='rotx' phys(5)='roty' phys(6)='rotz' ! ! condensation sets cmsel,s,mates(1,1) cmsel,a,mates(2,1) cmsel,a,mates(3,1) cmsel,a,mates(4,1) cmsel,a,mates(5,1) cmsel,a,mates(6,1) cmsel,a,mates(7,1) !***cmsel,a,mates(8,1) !***cmsel,a,mates(9,1) !***cmsel,a,mates(10,1) !***cmsel,a,mates(11,1) cm,static,node nsel,all cm,dynamic,node cm,full,node

49

nsel,all fini !/////////////////////////////////////////////////////////////////////////////////////////////////////////////

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APPENDIX G: ANSYS WHEEL MODEL MACRO wheel !/////////////////////////////////////////////////////////////// ! Create an abstracted wheel for Ansys ! Input arguments: ! arg1 - centre node # ! arg2 - ground node # ! (arg2 - wheel radius (m)) ! arg3 - axial direction (x/y/z) ! arg4 - stiffness in radial direction (N/m) ! arg5 - stiffness in axial direction (N/m) ! arg6 - stiffness in rotational direction (N/m) ! arg7 – wheel mass (kg) fini kx=2.e6 ! default axial stiffness ky=2.e6 ! default radial stiffness kz=2.e6 ! default lateral stiffness m_trans=585. ! default mass =0 *if,arg4,ne,0,then kx = arg4 *endif *if,arg5,ne,0,then kz = arg5 *endif *if,arg6,ne,0,then ky = arg6 *endif *if,arg7,ne,0,then m_trans = arg7 *endif /prep7 !Wheel k2=0 ! symmetric matrices k3=4 ! 12 x 12 stiffness matrix k4=1 ! print element matrix at beginning of solution phase et,,matrix27,,k2,k3,k4 *get,et_max,etyp,,num,max type,et_max r_max=r_max+1 real,r_max R,r_max, kx, 0., 0., 0., 0., 0. ! c1 - c6 Rmore, -kx, 0., 0., 0., 0., 0. ! c7 -c12 Rmore, ky, 0., 0., 0., 0., 0. ! c13-c18 Rmore, -ky, 0., 0., 0., 0., kz ! c19-c24 Rmore, 0., 0., 0., 0., 0.,-kz ! c25-c30 Rmore, 0., 0., 0., 0., 0., 0. ! c31-c36 Rmore, 0., 0., 0., 0., 0., 0. ! c37-c42 Rmore, 0., 0., 0., 0., 0., 0. ! c43-c48 Rmore, 0., 0., 0., 0., 0., 0. ! c49-c54 Rmore, 0., 0., 0., kx, 0., 0. ! c55-c60 Rmore, 0., 0., 0., ky, 0., 0. ! c61-c66 Rmore, 0., 0., kz, 0., 0., 0. ! c67-c72 Rmore, 0., 0., 0., 0., 0., 0. ! c73-c78 e,arg1,arg2 !

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! wheel mass et,,mass21,,0,2 ! dir par to global, 3D mass wo rot mass *get,et_max,etyp,,num,max ! get maximum element type type,et_max r_max=r_max+1 r,r_max, arg7 real,r_max e,arg1 !Wheel mass ! k2= k3= k4= kx= ky= kz= m_trans= fini /eof

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