technical report year-number - sbel

Technical Report 2012-01

A Comparison of Chrono::Engine’s Primitive Joints with

ADAMS Results

Rebecca Shotwell

Simulation-Based Engineering Lab

University of Wisconsin - Madison

March 2012

2

Abstract

Chrono::Engine software offers a powerful simulation capability. This software has been used to

create million-body models; with further improvements, the simulation of increasingly larger

models could be feasible. This capability is predicted to lead to a better understanding of

granular materials, contributing to many areas of research. However, these capabilities are only

useful if they are shown to agree well with reality. Beginning at a simple level, a study was

conducted to compare the simulation of primitive joints in the Chrono::Engine simulation

package with the MSC/ADAMS commercial software package. This simple effort provides a

measure for the accuracy with which the software models the interaction of a joint and two

bodies. This allows more complex analyses to be carried out with knowledge of the software’s

accuracy at this level.

Contents

1 Introduction ............................................................................................................................. 3

2 Models & Results .................................................................................................................... 4 2.1 Simple Pendulums ............................................................................................................ 5

2.1.1 Revolute Joint ........................................................................................................... 5

2.1.2 Hooke Joint ............................................................................................................. 11 2.1.3 Spherical Joint ......................................................................................................... 16

2.2 Sliding Joints .................................................................................................................. 20 2.2.1 Translational Joint ................................................................................................... 20 2.2.2 Cylindrical Joint ...................................................................................................... 35

2.2.3 Planar Joint.............................................................................................................. 47 3 Conclusion ............................................................................................................................ 58

4 Acknowledgements ............................................................................................................... 58 5 References ............................................................................................................................. 59

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1 Introduction The capability to simulate billion-body models will, perhaps, soon be a reality. As computing

power and simulation methods improve, the size of simulations can continue to grow [4].

Simulating many-body systems is important to the study of granular materials, since, in this

field, it can be very difficult, if not impossible, to accurately measure the parameters of the

particles [5]. Furthermore, simulation can be used to test new designs in low- or zero-gravity or

other conditions that are infeasible to access or create in the real world [1].

While simulating granular materials clearly can offer many benefits over conducting physical

experiments, this capability cannot be fully utilized until it is known to what extent simulation

mirrors reality. Validation is essential to knowing whether simulations are modeling reality well,

but to conduct a validation, measurements of reality are necessary. Since it is difficult to

measure the parameters of granular materials, this study starts by comparing a simpler set of

models involved in the multibody dynamic simulation of granular material: primitive joints.

This effort, while not directly addressing the issue of validating granular material simulations,

provides assurance that the software behaves correctly for two bodies; it follows that the

software should behave correctly for 20 bodies, 2,000 bodies, or 2,000,000 bodies. By

comparing a more basic piece of the simulation software, one can check for inaccuracies while

also providing a stepping stone for further comparison and validation.

The software in question in this effort, Chrono::Engine [6,7], has been used to create and

simulate large, many-body granular material models, such as the one pictured in Figure 1, which

consists of 50,000 ellipsoidal particles [2]. MSC/ADAMS, a well-known and well-validated

software package [3], provided proven values with which the Chrono::Engine results were

compared. Primitive joint models were created in both software packages and direct

measurements (position, velocity, acceleration, joint reaction force, and joint reaction torque)

from the simulation of these models were examined.

Figure 1: Granular simulation of 50,000 ellipsoidal particles, simulated using Chrono::Engine

1

1 A video rendering of this simulation can be viewed at http://sbel.wisc.edu/Animations/.

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2 Models & Results This study compared the simulation of primitive joints in Chrono::Engine and MSC/ADAMS

2010 (ADAMS). By considering the measured position, velocity, acceleration, joint reaction

force, and joint reaction torque results from simple models in these two software packages, the

project analyzed one basic piece of the Chrono::Engine software.

To carry out this comparison, a simple model was created for each of a list of primitive joints,

shown in Table 1. Identical versions of each model were made in Chrono::Engine and ADAMS.

Then the results generated by the simulation of this model in the two software packages were

compared. The models each contain one primitive joint which connects a moving body to a

fixed body (the ground). There are no applied forces in the models; the bodies are acted on only

by gravity. Keeping the models simple allows the results to be more easily analyzed.

The joints that were analyzed in this study are listed in Table 1, with data on the number of

degrees of freedom allowed and removed by each joint. The “other” columns in the table refer to

the angled directions of translation and axes of rotation. For example, for the angled

translational joint, the “other” direction of translation refers to a path that is negative 45 degrees

from the positive x axis. The orientation is explained further in the description of the

translational joint models.

For the first three joints listed in Table 1 (the “pendulum joints”: the revolute, Hooke, and

spherical joints), the models created for the comparison, one of which is shown in Figure 2, each

consist of a simple pendulum: one link that is fixed at one end to the ground, allowing the other

end to move freely.

Three models were created for each of the remaining three joints from Table 1 (the “slider

joints”: the translational, cylindrical, and planar joints) to consider three different joint

orientations; examples of these models can be seen in Figure 17. In each model, a body is fixed

to the ground through its center of mass by the joint in question. In the first model for each joint,

the joint is oriented vertically, offering no resistance to the body’s downward motion due to

gravity. In the second model, the joint is oriented horizontally; thus, the joint holds the body in

place and prevents it from falling. In the third model, the joint is placed at an angle of negative

45 degrees from the positive x axis (horizontal). Thus, the joint allows the body to slide down

the incline in the positive x, negative y direction.

Table 1: List of joints considered in this validation and the degrees of freedom (DOF) allowed and removed

by each joint. The “other” columns refer to translational paths and rotational axes that are not oriented

along the x, y, or z axes.

Joint

Translations Allowed

Translational DOF

Rotations Allowed

Rotational DOF

DOF Removed by Joint x y z Other x y z Other

Revolute Joint - - - - 0 - - x - 1 5

Hooke Joint - - - - 0 x - x - 2 4

Spherical Joint - - - - 0 x x x - 3 3

Translational Joint

Vertical x x - - 1 - - - - 0 5

Horizontal x - - - 1 - - - - 0 5

Angled - - - x 1 - - - - 0 5

5

Cylindrical Joint

Vertical - x - - 1 - x - - 1 4

Horizontal x - - - 1 x - - - 1 4

Angled - - - x 1 - - - x 1 4

Planar Joint

Vertical x x - - 2 - - x - 1 3

Horizontal x - x - 2 - x - - 1 3

Angled - - x x 2 - - - x 1 3

A right hand coordinate system is used for each model with the y axis oriented vertically (up =

positive), the x axis oriented horizontally (right = positive), and the z axis oriented perpendicular

to the page (outward = positive). In all the models, gravity acts in the negative y direction with a

magnitude of 9.80665 [m/s2] (the default in ADAMS). Also, time, distance, force, and torques

are measured in units of seconds (s), meters (m), Newtons (N), and Newton-meters (N-m),

respectively, for each model. The metric prefixes “nano-”, for 1E-9, and “zepto-”, for 1E-21, are

used as scaling factors for plotting purposes to better show results with very small magnitudes.

2.1 Simple Pendulums This section presents models using revolute joints, Hooke joints, and spherical joints. Each

model is a simple pendulum, consisting of a link that is connected to the ground by each

respective joint (see Figure 2). The link in each model has a mass of 1 kg, a length of 4 meters,

and a moment of inertia of 1 kg-m2. The pendulum is initially oriented along the positive x axis

with no initial velocity; it is then allowed to move due to gravity.

Figure 2: Screenshot of the revolute joint pendulum model in ADAMS

2.1.1 Revolute Joint

This section presents the results for the revolute joint pendulum model, which is created by

connecting a link to the ground using a revolute joint. The results from the simulation of the

model are shown in Figures 3-7 and in Table 2. The position and velocity results from

Chrono::Engine (Chrono) and ADAMS (Adams) (see Figures 3 & 4) show good agreement with

only small, though apparently increasing, errors in the x and y directions. The acceleration

results, shown in Figure 5, have more discrepancies, the most significant of which is the spike

that occurred in the Chrono::Engine simulation at a time of just past 1 second; this is obvious in

6

the x, y, and error acceleration plots, and can also be seen as a small inconsistency in the x, y,

and error velocity plot in Figure 4. The joint reaction forces (in Figure 6) have poor agreement

between the two software packages for the forces in the x and y directions; the shapes of the

force plots are different, as are the values of the force. However, as is shown by the fact that the

magnitudes of the forces are very similar, the difference in the x and y directions is mainly due

only to a difference in the definitions of the reference frames. Finally, the reaction torque results

(see Figure 7) show more differences between the Chrono::Engine and ADAMS results. While

Chrono::Engine shows constant results, the ADAMS results vary with time. Overall, these

differences in the results are extremely small since the units are in Newton-nanometers.

Figure 3: Position results for the revolute joint pendulum simulations

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Figure 4: Velocity results for the revolute joint pendulum simulations

8

Figure 5: Acceleration results for the revolute joint pendulum simulations

9

Figure 6: Joint reaction force results for the revolute joint pendulum simulations

Figure 7: Joint reaction torque results for the revolute joint pendulum simulations

Table 2: Position, velocity, acceleration, reaction force, and reaction torque data for revolute joint pendulum

simulations; the % Error is calculated as the difference in the averages divided by the ADAMS average value

Revolute Joint Data Chrono Adams Difference % Error

Position X (m)

Minimum -2.0000 -2.0000 0.0000

10

Maximum 2.0000 2.0000 0.0000

Average 0.2272 0.2351 0.0079 3.375%

Position Y (m)

Minimum -2.0022 -2.0000 0.0022

Maximum 1.5110E-03

1.5613E-17 1.5110E-03

Average -0.9683 -0.9679 0.0004 -0.044%

Position Magnitude (m)

Minimum 2.0000 2.0000 0.0000

Maximum 2.0029 2.0000 0.0029

Average 2.0011 2.0000 0.0011 0.053%

Velocity X (m/s)

Minimum -5.6039 -5.5942 0.0097

Maximum 5.6029 5.5924 0.0105

Average -0.7039 -0.6972 0.0067 -0.967%

Velocity Y (m/s)

Minimum -3.4803 -3.4751 0.0052

Maximum 3.4808 3.4728 0.0079

Average -0.2523 -0.2647 0.0124 -4.689%

Velocity Magnitude (m/s)

Minimum 0.0209 0.0000 0.0209

Maximum 5.6046 5.5945 0.0101

Average 3.4714 3.4696 0.0018 0.053%

Acceleration X (m/s2)

Minimum -12.2612 -11.7582 0.5031

Maximum 40.3267 11.7624 28.5643

Average -0.5224 -0.6020 0.0796 -13.221%

Acceleration Y (m/s2)

Minimum -17.4894 -7.8453 9.6441

Maximum 69.9675 15.6811 54.2864

Average 0.7589 0.6679 0.0910 13.621%

Acceleration Magnitude (m/s2)

Minimum 7.8453 7.8453 0.0000

Maximum 80.7570 15.6830 65.0740

Average 11.1939 10.9404 0.2535 2.317%

Reaction Force X (N)

Minimum -89.3853 -11.7624 77.6229

Maximum 9.1704 11.7582 2.5878

Average -12.4215 0.6020 13.0234 2163.539%

Reaction Force Y (N)

Minimum -1.9613 -25.4877 23.5264

11

Maximum 1.9613 -1.9613 3.9226

Average 0.2347 -10.4745 10.7093 -102.241%

Reaction Force Magnitude (N)

Minimum 1.9613 1.9613 0.0000

Maximum 89.3877 25.4889 63.8988

Average 12.9084 12.7391 0.1693 1.329%

Torque X (N-m)

Minimum 0.0000 -5.7909E-18 5.7909E-18

Maximum 0.0000 5.7909E-18 5.7909E-18

Average 0.0000 6.8082E-19 6.8082E-19 100.000%

Torque Y (N-m)

Minimum 0.0000 -5.7908E-18 5.7908E-18

Maximum 0.0000 -1.8082E-34 1.8082E-34

Average 0.0000 -2.8025E-18 2.8025E-18 -100.000%

Torque Magnitude (N-m)

Minimum 0.0000 5.7909E-18 5.7909E-18

Maximum 0.0000 5.7909E-18 5.7909E-18

Average 0.0000 5.7909E-18 5.7909E-18 100.000%

2.1.2 Hooke Joint

The Hooke joint is analyzed in the same manner as the revolute joint, by creating a simple

pendulum using the joint. The results from the model simulations are shown in Figures 8-12 and

in Table 3. The position and velocity results (see Figures 8 & 9) show good agreement; the most

noticable discrepancy is in the position magnitude generated by Chrono::Engine. While

ADAMS shows a constant value, the Chrono::Engine results vary slightly with time. For the

aceleration results (see Figure 10), the shapes of the plots generated by Chrono::Engine and

ADAMS are the same, but Chrono::Engine shows frequent spikes that deviate from these curves.

These spikes can also be seen in the joint reaction force results (see Figure 11); additionally,

these results illustrate a difference in the definition of the reference frames (as in the revolute

joint analysis). Overall, the mean force magnitude value is very similar between the

Chrono::Engine and ADAMS results. The joint reaction torque results (see Figure 12) show

similar mean values, though the ADAMS results have values deviating from the constant

Chrono::Engine values.

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Figure 8: Position results for the Hooke joint pendulum simulations

Figure 9: Velocity results for the Hooke joint pendulum simulations

13

Figure 10: Acceleration results for the Hooke joint pendulum simulations

Figure 11: Joint reaction force results for the Hooke joint pendulum simulations

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Figure 12: Joint reaction torque results for the Hooke joint pendulum simulations

Table 3: Data for the position, velocity, acceleration, reaction forces, and reaction torques for the Hooke joint

pendulum simulations

Hooke Joint Data Chrono Adams Difference % Error

Position X (m)

Minimum -2.0000 -2.0000 0.0000

Maximum 2.0000 2.0000 0.0000

Average 0.2322 0.2351 0.0029 1.244%

Position Y (m)

Minimum -2.0022 -2.0000 0.0022

Maximum 0.0003 0.0000 0.0003

Average -0.9661 -0.9679 0.0018 -0.186%


Minimum 2.0000 2.0000 0.0000

Maximum 2.0024 2.0000 0.0024

Average 2.0011 2.0000 0.0011 0.053%

Velocity X (m/s)

Minimum -5.6031 -5.5932 0.0100

Maximum 5.6025 5.5930 0.0095

Average -0.7027 -0.6972 0.0055 -0.784%

Velocity Y (m/s)

Minimum -3.4790 -3.4753 0.0038

Maximum 3.4814 3.4737 0.0076

Average -0.2543 -0.2647 0.0104 -3.925%

15


Minimum 0.0109 0.0000 0.0109

Maximum 5.6032 5.5942 0.0090

Average 3.4632 3.4696 0.0064 0.185%


Minimum -16.0568 -11.7572 4.2996

Maximum 14.7991 11.7593 3.0398

Average -0.6059 -0.6020 0.0040 -0.661%


Minimum -7.8585 -7.8453 0.0132

Maximum 17.9218 15.6751 2.2467

Average 0.6209 0.6679 0.0471 7.048%


Minimum 7.5232 7.8453 0.3221

Maximum 20.2514 15.6816 4.5698

Average 10.9545 10.9405 0.0140 0.128%


Minimum -29.2810 -11.7593 17.5217

Maximum 0.6417 11.7572 11.1155

Average -12.2866 0.6020 12.8885 2141.105%


Minimum -1.9613 -25.4818 23.5204

Maximum 1.9623 -1.9613 3.9236

Average 0.2390 -10.4746 10.7136 -102.282%


Minimum 1.9613 1.9613 0.0000

Maximum 29.2881 25.4858 3.8024

Average 12.7123 12.7392 0.0269 0.211%

Torque X (N-m)

Minimum 0.0000 0.0000 0.0000

Maximum 0.0000 0.0000 0.0000

Average 0.0000 0.0000 0.0000 100.000%

Torque Y (N-m)

Minimum 0.0000 0.0000 0.0000

Maximum 0.0000 0.0000 0.0000

Average 0.0000 0.0000 0.0000 100.000%

Torque Z (N-m)

Minimum 0.0000 0.0000 0.0000

Maximum 0.0000 0.0000 0.0000

Average 0.0000 0.0000 0.0000 -100.000%


16

Minimum 0.0000 0.0000 0.0000

Maximum 0.0000 0.0000 0.0000

Average 0.0000 0.0000 0.0000 100.000%

2.1.3 Spherical Joint

The final simple pendulum model is created using a spherical joint. The plots shown in Figures

13-16 and the data in Table 4 summarize the results from the simulations. The position and

velocity results (see Figures 13 & 14) show good agreement between the Chrono::Engine and

ADAMS results, with the most notable discrepancy being the difference in the position

magnitude results. The Chrono::Engine acceleration results, shown in Figure 15, have slight

deviations from the ADAMS results, though overall the mean values agree between the two

software packages. The joint reaction torques also have slight deviations in the Chrono::Engine

results; additionally, they illustrate the same differences in definition that were seen in the other

simple pendulum model results. Finally, the reaction torques in all directions are zero.

Figure 13: Position results for spherical joint pendulum simulations

17

Figure 14: Velocity results for spherical joint pendulum simulations

Figure 15: Acceleration results for spherical joint pendulum simulations

18

Figure 16: Joint reaction forces for the spherical joint pendulum simulations

Table 4: Data for position, velocity, acceleration, and reaction forces for the spherical joint simulations

Spherical Joint Data Chrono Adams Difference % Error

Position X (m)

Minimum -2.0000 -2.0000 0.0000

Maximum 2.0000 2.0000 0.0000

Average 0.2262 0.2351 0.0089 3.788%

Position Y (m)

Minimum -2.0022 -2.0000 0.0022

Maximum 2.2264E-04 1.5613E-17 2.2264E-04

Average -0.9702 -0.9679 0.0023 -0.234%

Position Z (m)

Minimum 0.0000 2.9525E-18 2.9525E-18

Maximum 0.0000 2.9525E-18 2.9525E-18

Average 0.0000 2.9525E-18 2.9525E-18 100.000%


Minimum 2.0000 2.0000 0.0000

Maximum 2.0023 2.0000 0.0023

Average 2.0011 2.0000 0.0011 0.053%

Velocity X (m/s)

Minimum -5.6037 -5.5946 0.0091

Maximum 5.6031 5.5933 0.0098

Average -0.7021 -0.6972 0.0049 -0.698%

Velocity Y (m/s)

19

Minimum -3.4775 -3.4748 0.0027

Maximum 3.4820 3.4730 0.0090

Average -0.2579 -0.2647 0.0067 -2.541%

Velocity Z (m/s)

Minimum 0.0000 0.0000 0.0000

Maximum 0.0000 3.9979E-33 3.9979E-33

Average 0.0000 1.9990E-33 1.9990E-33 100.000%


Minimum 0.0125 0.0000 0.0125

Maximum 5.6037 5.5946 0.0091

Average 3.4751 3.4695 0.0056 0.162%


Minimum -12.0535 -11.7612 0.2923

Maximum 13.1144 11.7610 1.3534

Average -0.5978 -0.6019 0.0041 -0.688%


Minimum -7.8453 -7.8453 0.0000

Maximum 16.8781 15.6836 1.1946

Average 0.6552 0.6678 0.0126 1.885%

Acceleration Z (m/s2)

Minimum 0.0000 7.9959E-34 7.9959E-34

Maximum 0.0000 7.9959E-34 7.9959E-34

Average 0.0000 7.9959E-34 7.9959E-34 100.000%


Minimum 7.8453 7.8453 0.0000

Maximum 17.4872 15.6836 1.8036

Average 10.9466 10.9403 0.0063 0.057%


Minimum -26.6869 -11.7610 14.9259

Maximum 0.0079 11.7612 11.7533

Average -12.3058 0.6019 12.9078 2144.340%


Minimum -1.9613 -25.4902 23.5289

Maximum 1.9614 -1.9613 3.9227

Average 0.2332 -10.4745 10.7076 -102.226%

Reaction Force Z (N)

Minimum 0.0000 -8.9000E-34 1.9613

Maximum 0.0000 -8.9000E-34 26.6869

Average 0.0000 -8.9000E-34 12.7286 -1.430E+36


Minimum 1.9613 1.9613 0.0000

20

Maximum 26.6869 25.4902 1.1967

Average 12.7286 12.7390 0.0105 0.082%

2.2 Sliding Joints This section presents models of “sliding” joints: translational joints, cylindrical joints, and planar

joints. Each model consists of a 1-kg block which is connected to the ground by a sliding joint.

For each joint, three types of models were created with different orientations of the joint:

vertical, horizontal, or angled (see Figure 17). In the models with the vertically-oriented joint,

the block should fall straight down, unimpeded by the joint. With the horizontally-oriented joint,

the joint prevents the block from falling (due to gravity), so the block does not move. For the

angled orientation, the joint has an angle of negative 45 degrees from the x-axis (in the x-y

plane). Therefore, the block slides (due to gravity) along the joint in the positive x, negative y

direction. In each model, there is no initial velocity or applied forces; the block is acted on by

only gravity and the joint. The results from these models, in both Chrono and Adams, are shown

in the following subsections.

Figure 17: Screenshots of translational joint models in ADAMS; the joints are oriented, from left to right,

vertically, horizontally, and at an angle

2.2.1 Translational Joint

Models were created in each Chrono and Adams to show translational joints with three different

orientations: vertical, horizontal, and angled.

2.2.1.1 Translational Joint – Vertical

In this model, a vertically-oriented translational joint connects a block to the ground. The block

should fall straight down (in the y direction) due to gravity, with no resistance from the joint.

The results from the simulation of this model are shown in Figures 18-22 and Table 5. The

position results (see Figure 18) show that there is good agreement in the y direction and, overall,

in the magnitude, though the Chrono::Engine results in the x direction show some discrepancy

from the expected ADAMS-calculated value of zero. The position data in the z direction is zero.

For the velocity, shown in Figure 19, again, the y-direction results and the magnitude results

show good agreement, but the Chrono::Engine results in the x and z directions show non-zero

results with growing magnitudes. The acceleration results (see Figure 20) in the x and z

directions again disagree between Chrono::Engine and ADAMS. Also, the Chrono::Engine

results in the y direction and the magnitude show deviations from the constant value calculated

by ADAMS, though the mean values agree between the two software packages. The joint

21

reaction forces, seen in Figure 21, show some small differences between Chrono::Engine and

ADAMS (perhaps partially due to the differences in reference frame definition). Finally, the

joint reaction torques (see Figure 22) show the Chrono::Engine results as zero while the ADAMS

results deviate from this value.

Figure 18: Position results for vertically-oriented translational joint model simulations

22

Figure 19: Velocity results for vertically-oriented translational joint model simulations

23

Figure 20: Acceleration results for vertically-oriented translational joint model simulations

24

Figure 21: Joint reaction force results for vertically-oriented translational joint model simulations

Figure 22: Joint reaction torque results for the vertically-oriented translational joint simulations

Table 5: Data for position, velocity, acceleration, reaction forces, and reaction torques for the vertically-

oriented translational joint simulations

Translational Joint - Vertical Data Chrono Adams Difference % Error

Position X (m)

Minimum 2.1536E-12 0.0000 2.1536E-12

25

Maximum 1.1879E-06 0.0000 1.1879E-06

Average 3.9901E-07 0.0000 3.9901E-07 -

Position Y (m)

Minimum -19.9293 -19.6133 0.3160

Maximum -3.6132E-05 0.0000 3.6132E-05

Average -6.6942 -6.5650 0.1292 -1.968%


Minimum 3.6132E-05 0.0000 3.6132E-05

Maximum 19.9293 19.6133 0.3160

Average 6.6942 6.5650 0.1292 1.968%

Velocity X (m/s)

Minimum 1.1220E-09 -2.4019E-15 1.1220E-09

Maximum 1.1735E-06 0.0000 1.1735E-06

Average 5.8641E-07 -1.2010E-15 5.8641E-07 -4.883E+10

Velocity Y (m/s)

Minimum -19.6883 -19.6133 0.0750

Maximum -0.0188 0.0000 0.0188

Average -9.8383 -9.8066 0.0317 -0.323%

Velocity Z (m/s)

Minimum 0.0000 -1.2010E-15 1.2010E-15

Maximum 0.0000 0.0000 0.0000

Average 0.0000 -6.0048E-16 6.0048E-16 -100.000%


Minimum 0.0188 0.0000 0.0188

Maximum 19.6883 19.6133 0.0750

Average 9.8383 9.8066 0.0317 0.323%


Minimum 5.8411E-07 -1.2010E-15 5.8411E-07

Maximum 5.8493E-07 -1.2010E-15 5.8493E-07

Average 5.8452E-07 -1.2010E-15 5.8452E-07 -4.867E+10


Minimum -9.8067 -9.8067 0.0001

Maximum -9.8066 -9.8067 0.0000

Average -9.8067 -9.8066 2.4793E-06 0.000%


Minimum 0.0000 -6.0048E-16 6.0048E-16

Maximum 0.0000 -6.0048E-16 6.0048E-16

Average 0.0000 -6.0048E-16 6.0048E-16 -100.000%


Minimum 9.8066 9.8067 5.0000E-05

Maximum 9.8067 9.8067 6.0000E-05

26

Average 9.8067 9.8066 2.4793E-06 0.000%


Minimum 0.0000 1.2010E-15 1.2010E-15

Maximum 0.0000 1.2010E-15 1.2010E-15

Average 0.0000 1.2010E-15 1.2010E-15 100.000%


Minimum 5.8411E-07 -1.8385E-31 5.8411E-07

Maximum 5.8493E-07 -1.8385E-31 5.8493E-07

Average 5.8452E-07 -1.8385E-31 5.8452E-07 -3.179E+26


Minimum 0.0000 6.0048E-16 6.0048E-16

Maximum 0.0000 6.0048E-16 6.0048E-16

Average 0.0000 6.0048E-16 6.0048E-16 100.000%


Minimum 5.8411E-07 1.3427E-15 5.8411E-07

Maximum 5.8493E-07 1.3427E-15 5.8493E-07

Average 5.8452E-07 1.3427E-15 5.8452E-07 4.353E+10

Reaction Torque X (N-m)

Minimum 0.0000 -1.1777E-14 1.1777E-14

Maximum 0.0000 0.0000 0.0000

Average 0.0000 -6.5691E-16 6.5691E-16 -100.000%

Reaction Torque Y (N-m)

Minimum 0.0000 -1.2120E-30 1.2120E-30

Maximum 0.0000 6.0938E-31 6.0938E-31

Average 0.0000 -1.9835E-31 1.9835E-31 -100.000%

Reaction Torque Z (N-m)

Minimum 0.0000 0.0000 0.0000

Maximum 0.0000 2.3164E-14 2.3164E-14

Average 0.0000 4.5532E-15 4.5532E-15 100.000%

Reaction Torque Magnitude (N-m)

Minimum 0.0000 0.0000 0.0000

Maximum 0.0000 2.5465E-14 2.5465E-14

Average 0.0000 4.7581E-15 4.7581E-15 100.000%

2.2.1.2 Translational Joint – Horizontal

This model has a translational joint which is oriented horizontally; the joint should hold the

block in place and prevent it from falling due to gravity. The results from the model simulations

are shown in Figures 23-25 and Table 6. The position results are all zero. The ADAMS velocity

results (see Figure 23) show increasing differences from the expected, Chrono::Engine-

calculated value of zero. ADAMS also shows non-zero (though very small) values for

acceleration (see Figure 24). While the joint reaction force results (see Figure 25) in the y

27

direction are opposite in sign due to differences in the definnition of the reference frames, the

force magnitude results agree very well.

Figure 23: Velocity results for the horizontally-oriented translational joint model simulations

Figure 24: Acceleration results for the horizontally-oriented translational joint model simulations

28

Figure 25: Joint reaction force results for the horizontally-oriented translational joint simulations

Table 6: Data for velocity, acceleration, and joint reaction forces for the horizontally-oriented translational

joint simulations

Translational Joint - Horizontal Data Chrono Adams Difference

Velocity X (m/s)

Minimum 0.0000 0.0000 0.0000

Maximum 0.0000 1.2010E-15 1.2010E-15

Average 0.0000 6.0048E-16 6.0048E-16

Velocity Z (m/s)

Minimum 0.0000 0.0000 0.0000

Maximum 0.0000 7.3538E-32 7.3538E-32

Average 0.0000 3.6769E-32 3.6769E-32


Minimum 0.0000 0.0000 0.0000

Maximum 0.0000 1.2010E-15 1.2010E-15

Average 0.0000 6.0048E-16 6.0048E-16


Minimum 0.0000 6.0048E-16 6.0048E-16

Maximum 0.0000 6.0048E-16 6.0048E-16

Average 0.0000 6.0048E-16 6.0048E-16


Minimum 0.0000 3.6769E-32 3.6769E-32

Maximum 0.0000 3.6769E-32 3.6769E-32

Average 0.0000 3.6769E-32 3.6769E-32

29


Minimum 0.0000 6.0048E-16 6.0048E-16

Maximum 0.0000 6.0048E-16 6.0048E-16

Average 0.0000 6.0048E-16 6.0048E-16


Minimum 0.0000 6.0048E-16 6.0048E-16

Maximum 0.0000 6.0048E-16 6.0048E-16

Average 0.0000 6.0048E-16 6.0048E-16


Minimum -9.8067 9.8067 19.6133

Maximum -9.8067 9.8067 19.6133

Average -9.8066 9.8066 19.6133


Minimum 0.0000 3.6769E-32 3.6769E-32

Maximum 0.0000 3.6769E-32 3.6769E-32

Average 0.0000 3.6769E-32 3.6769E-32


Minimum 9.8067 9.8067 0.0000

Maximum 9.8067 9.8067 0.0000

Average 9.8066 9.8066 0.0000

2.2.1.3 Translational Joint – Angled

In this model, the translational joint is oriented at an angle of negative 45 degrees from the x axis

(in the x-y plane). The block is then allowed to fall due to gravity. The simulation results are

shown in Figures 26-29 and Table 7. The position and velocity results, shown in Figures 26 &

27, have similarly shaped curves and overall good agreement. The position results in the z

direction are zero. The mean values of the Chrono::Engine acceleration results (see Figure 28)

are very similar to the ADAMS results, though the Chrono::Engine deviations seem to be

increasing with time. The Chrono::Engine joint reaction force results, pictured in Figure 29,

show the same deviations as in the acceleration results. The plots in the x and y directions also

illustrate a difference in the definition of the reference frames. Overall, the mean value of the

joint reaction forces agrees well between Chrono::Engine and ADAMS. The reaction torques in

all directions are zero.

30

Figure 26: Position results for the angled translational joint model simulations

31

Figure 27: Velocity results for the angled translational joint model simulations

32

Figure 28: Acceleration results for the angled translational joint model simulations

33

Figure 29: Joint reaction force results for the angled translational joint model simulations

Table 7: Data for position, velocity, acceleration, and joint reaction forces for the angled translational joint

model simulations

Translational Joint - Angled Data Chrono Adams Difference % Error

Position X (m)

Minimum 0.0005 0.0000 0.0005

Maximum 9.9514 9.8067 0.1447

Average 3.3385 3.2825 0.0560 1.705%

Position Y (m)

Minimum -9.9514 -9.8067 0.1447

Maximum -0.0005 0.0000 0.0005

Average -3.3385 -3.2825 0.0560 -1.705%


Minimum 0.0007 0.0000 0.0007

Maximum 14.0734 13.8687 0.2047

Average 4.7213 4.6422 0.0791 1.705%

34

Velocity X (m/s)

Minimum 0.0489 0.0000 0.0489

Maximum 9.8377 9.8067 0.0311

Average 4.9163 4.9033 0.0130 0.264%

Velocity Y (m/s)

Minimum -9.8377 -9.8067 0.0310

Maximum -0.0489 0.0000 0.0489

Average -4.9163 -4.9033 0.0130 -0.264%

Velocity Z (m/s)

Minimum 0.0000 0.0000 0.0000

Maximum 0.0000 8.4921E-16 8.4921E-16

Average 0.0000 4.2461E-16 4.2461E-16 100.000%


Minimum 0.0692 0.0000 0.0692

Maximum 13.9126 13.8687 0.0439

Average 6.9527 6.9343 0.0183 0.264%


Minimum 4.9009 4.9033 0.0024

Maximum 4.9070 4.9033 0.0037

Average 4.9033 4.9033 5.1653E-06 0.000%


Minimum -4.9057 -4.9033 0.0024

Maximum -4.8997 -4.9033 0.0036

Average -4.9033 -4.9033 6.9008E-06 0.000%


Minimum 0.0000 4.2461E-16 4.2461E-16

Maximum 0.0000 4.2461E-16 4.2461E-16

Average 0.0000 4.2461E-16 4.2461E-16 100.000%


Minimum 6.9343 6.9343 1.9000E-05

Maximum 6.9344 6.9343 2.1000E-05

Average 6.9343 6.9343 1.3140E-06 0.000%


Minimum 0.0000 4.9033 4.9033

Maximum 0.0000 4.9033 4.9033

Average 0.0000 4.9033 4.9033 100.000%


Minimum 6.9310 4.9033 2.0276

Maximum 6.9395 4.9033 2.0362

Average 6.9344 4.9033 2.0310 41.422%

35


Minimum 0.0000 4.2461E-16 4.2461E-16

Maximum 0.0000 4.2461E-16 4.2461E-16

Average 0.0000 4.2461E-16 4.2461E-16 100.000%


Minimum 6.9310 6.9343 0.0034

Maximum 6.9395 6.9343 0.0052

Average 6.9344 6.9343 9.6777E-06 0.000%

2.2.2 Cylindrical Joint

The following three simulations compare, between Chrono::Engine and ADAMS, cylindrical

joints with three different orientations.

2.2.2.1 Cylindrical Joint – Vertical

This model consists of a block which is connected to the ground by a vertically-oriented

cylindrical joint. Thus, the block should fall, due to gravity, with no resistance from the joint.

The results from the model simulations are presented in Figures 30-34 and Table 8. The

Chrono::Engine position and velocity results (see Figures 30 & 31) show some discrepancies in

the z direction, though, overall, the shapes of the curves agree well between the two software

packages. The acceleration results, pictured in Figure 32, also have discrepancies in the z

direction, as well as in the x direction. Further, Chrono::Engine shows deviations in the y

direction and magnitude that seem to be increasing with time. However, the mean value of the

Chrono::Engine acceleration magnitude results agrees well with the corresponding ADAMS

value. The reaction forces (see Figure 33), in a manner similar to the vertically-oriented

translational joint model, show discrepancies between the two software packages’ results.

Chrono::Engine calculated a small, non-zero value for the force magnitude, while the ADAMS

magnitude results are zero. Finally, for the joint reaction torques, shown in Figure 34,

Chrono::Engine calculated a value of zero in every direction, while the ADAMS results show

some very small deviations from this value.

36

Figure 30: Position results for the vertically-oriented cylindrical joint model simulations

Figure 31: Velocity results for the vertically-oriented cylindrical joint model simulations

37

Figure 32: Acceleration results for the vertically-oriented cylindrical joint model simulations

Figure 33: Joint reaction force results for the vertically-oriented translational joint model simulations

38

Figure 34: Joint reaction torque results for the vertically-oriented cylindrical joint model simulations

Table 8: Data for position, velocity, acceleration, joint reaction forces, and joint reaction torques for the

vertically-oriented cylindrical joint model simulations

Cylindrical Joint - Vertical Data Chrono Adams Difference % Error

Position Y (m)

Minimum -19.8963 -19.6133 0.2830

Maximum -2.4132E-05 0.0000 2.4132E-05

Average -6.6751 -6.5650 0.1101 -1.676%

Position Z (m)

Minimum -1.1859E-06 0.0000 1.1859E-06

Maximum -1.4384E-12 0.0000 0.0000

Average -3.9787E-07 0.0000 0.0000 -


Minimum 2.4132E-05 0.0000 2.4132E-05

Maximum 19.8963 19.6133 0.2830

Average 6.6751 6.5650 0.1101 1.676%

Velocity X (m/s)

Minimum 0.0000 -2.4019E-15 2.4019E-15

Maximum 0.0000 0.0000 0.0000

Average 0.0000 -1.2010E-15 1.2010E-15 -100.000%

Velocity Y (m/s)

Minimum -19.6717 -19.6133 0.0584

Maximum -0.0154 0.0000 0.0154

Average -9.8198 -9.8066 0.0131 -0.134%

39

Velocity Z (m/s)

Minimum -1.1725E-06 -1.2010E-15 1.1725E-06

Maximum -9.1694E-10 0.0000 9.1694E-10

Average -5.8530E-07 -6.0048E-16 5.8530E-07 -9.747E+10


Minimum 0.0154 0.0000 0.0154

Maximum 19.6717 19.6133 0.0584

Average 9.8198 9.8066 0.0131 0.134%


Minimum 0.0000 -1.2010E-15 1.2010E-15

Maximum 0.0000 -1.2010E-15 1.2010E-15

Average 0.0000 -1.2010E-15 1.2010E-15 -100.000%


Minimum -9.8067 -9.8067 0.0001

Maximum -9.8066 -9.8067 0.0000

Average -9.8066 -9.8066 0.0000 0.000%


Minimum -5.8505E-07 -6.0048E-16 5.8505E-07

Maximum -5.8428E-07 -6.0048E-16 5.8428E-07

Average -5.8452E-07 -6.0048E-16 5.8452E-07 -9.734E+10


Minimum 9.8066 9.8067 0.0000

Maximum 9.8067 9.8067 0.0001

Average 9.8066 9.8066 0.0000 0.000%


Minimum 0.0000 1.2010E-15 1.2010E-15

Maximum 0.0000 1.2010E-15 1.2010E-15

Average 0.0000 1.2010E-15 1.2010E-15 100.000%


Minimum 5.8428E-07 -1.8385E-31 5.8428E-07

Maximum 5.8506E-07 -1.8385E-31 5.8506E-07

Average 5.8452E-07 -1.8385E-31 5.8452E-07 -3.179E+26


Minimum 0.0000 6.0048E-16 6.0048E-16

Maximum 0.0000 6.0048E-16 6.0048E-16

Average 0.0000 6.0048E-16 6.0048E-16 100.000%


Minimum 5.8428E-07 1.3427E-15 5.8428E-07

Maximum 5.8506E-07 1.3427E-15 5.8506E-07

Average 5.8452E-07 1.3427E-15 5.8452E-07 4.353E+10

40

Torque X (N-m)

Minimum 0.0000 -1.1777E-14 1.1777E-14

Maximum 0.0000 0.0000 0.0000

Average 0.0000 -6.5691E-16 6.5691E-16 -100.000%

Torque Y (N-m)

Minimum 0.0000 -1.2120E-30 1.2120E-30

Maximum 0.0000 6.0938E-31 6.0938E-31

Average 0.0000 -1.9835E-31 1.9835E-31 -100.000%

Torque Z (N-m)

Minimum 0.0000 0.0000 0.0000

Maximum 0.0000 2.3164E-14 2.3164E-14

Average 0.0000 4.5532E-15 4.5532E-15 100.000%


Minimum 0.0000 0.0000 0.0000

Maximum 0.0000 2.5465E-14 2.5465E-14

Average 0.0000 4.7581E-15 4.7581E-15 100.000%

2.2.2.2 Cylindrical Joint – Horizontal

In this model, the cylindrical joint is oriented horizontally. The joint stops the block from falling

due to gravity. The results from the simulation of this model are presented in Figures 35-37 and

Table 9. The position data are zero. For the velocities, shown in Figure 35, Chrono::Engine

calculates a value of zero in every direction, while ADAMS shows very small, though increasing

non-zero values. For the accelerations, pictured in Figure 36, ADAMS again deviates from the

expected value of zero. The joint reaction force magnitude results (see Figure 37) show very

good agreement.

41

Figure 35: Velocity results for the horizontally-oriented cylindrical joint model simulations

Figure 36: Acceleration results for the horizontally-oriented cylindrical joint model simulations

42

Figure 37: Joint reaction force results for the horizontally-oriented cylindrical joint model simulations

Table 9: Data for velocity, acceleration, and joint reaction forces for the horizontally-oriented cylindrical

joint model simulations

Cylindrical Joint - Horizontal Data Chrono Adams Difference

Velocity X (m/s)

Minimum 0.0000 0.0000 0.0000

Maximum 0.0000 1.2010E-15 1.2010E-15

Average 0.0000 6.0048E-16 6.0048E-16

Velocity Y (m/s)

Minimum 0.0000 0.0000 0.0000

Maximum 0.0000 2.7572E-64 2.7572E-64

Average 0.0000 1.3786E-64 1.3786E-64

Velocity Z (m/s)

Minimum 0.0000 0.0000 0.0000

Maximum 0.0000 7.3538E-32 7.3538E-32

Average 0.0000 3.6769E-32 3.6769E-32


Minimum 0.0000 0.0000 0.0000

Maximum 0.0000 1.2010E-15 1.2010E-15

Average 0.0000 6.0048E-16 6.0048E-16


Minimum 0.0000 6.0048E-16 6.0048E-16

Maximum 0.0000 6.0048E-16 6.0048E-16

Average 0.0000 6.0048E-16 6.0048E-16

43


Minimum 0.0000 1.3786E-64 1.3786E-64

Maximum 0.0000 1.3786E-64 1.3786E-64

Average 0.0000 1.3786E-64 1.3786E-64


Minimum 0.0000 3.6769E-32 3.6769E-32

Maximum 0.0000 3.6769E-32 3.6769E-32

Average 0.0000 3.6769E-32 3.6769E-32


Minimum 0.0000 6.0048E-16 6.0048E-16

Maximum 0.0000 6.0048E-16 6.0048E-16

Average 0.0000 6.0048E-16 6.0048E-16


Minimum 0.0000 -6.0048E-16 6.0048E-16

Maximum 0.0000 -6.0048E-16 6.0048E-16

Average 0.0000 -6.0048E-16 6.0048E-16


Minimum -9.8067 -9.8067 0.0000

Maximum -9.8067 -9.8067 0.0000

Average -9.8066 -9.8066 0.0000


Minimum 0.0000 -7.3538E-32 7.3538E-32

Maximum 0.0000 -7.3538E-32 7.3538E-32

Average 0.0000 -7.3538E-32 7.3538E-32


Minimum 9.8067 9.8067 0.0000

Maximum 9.8067 9.8067 0.0000

Average 9.8066 9.8066 0.0000

2.2.2.3 Cylindrical Joint – AngledThe cylindrical joint in this model is oriented with an angle

of negative 45 degrees from the x-axis. The block slides along this incline due to gravity. The

results from the model simulations are shown in Figures 38-41 and Table 10. The position and

velocity (see Figures 38 & 39) show similarly shaped curves in both Chrono::Engine and

ADAMS. The mean values of the accelerations, shown in Figure 40, also agree well, though

Chrono::Engine calculated values that deviate from this mean value, while the ADAMS values

are constant over time. The same deviations can be seen in the joint reaction force results in

Figure 41. Also notable from the force results is the differences in the definition of the reference

frames, shown by the differences in the results of the x and y directions of the force. The joint

reaction torques in all directions are zero.

44

Figure 38: Position results for the angled cylindrical joint model simulations

Figure 39: Velocity results for the angled cylindrical joint model simulations

45

Figure 40: Acceleration results for the angled cylindrical joint model simulations

Figure 41: Joint reaction force results for the angled cylindrical joint model simulations

Table 10: Data for position, velocity, acceleration, and joint reaction forces for the angled cylindrical joint

model simulations

Cylindrical Joint - Angled Data Chrono Adams Difference % Error

Position X (m)

Minimum 1.4985E-05 0.0000 1.4985E-05

46

Maximum 9.9480 9.8067 0.1414

Average 3.3393 3.2825 0.0568 1.731%

Position Y (m)

Minimum -9.9480 -9.8067 0.1414

Maximum -1.4985E-05 0.0000 1.4985E-05

Average -3.3393 -3.2825 0.0568 -1.731%

Position Z (m)

Minimum 0.0000 0.0000 0.0000

Maximum 0.0000 0.0000 0.0000

Average 0.0000 0.0000 0.0000 -


Minimum 2.1192E-05 0.0000 2.1192E-05

Maximum 14.0686 13.8687 0.1999

Average 4.7225 4.6422 0.0803 1.731%

Velocity X (m/s)

Minimum 0.0086 0.0000 0.0086

Maximum 9.8361 9.8067 0.0294

Average 4.9119 4.9033 0.0086 0.175%

Velocity Y (m/s)

Minimum -9.8361 -9.8067 0.0294

Maximum -0.0086 0.0000 0.0086

Average -4.9119 -4.9033 0.0086 -0.175%

Velocity Z (m/s)

Minimum 0.0000 0.0000 0.0000

Maximum 0.0000 8.4921E-16 8.4921E-16

Average 0.0000 4.2461E-16 4.2461E-16 100.000%


Minimum 0.0121 0.0000 0.0121

Maximum 13.9103 13.8687 0.0416

Average 6.9465 6.9343 0.0122 0.175%


Minimum 4.9009 4.9033 0.0024

Maximum 4.9058 4.9033 0.0025

Average 4.9033 4.9033 0.0000 0.000%


Minimum -4.9057 -4.9033 0.0024

Maximum -4.9008 -4.9033 0.0025

Average -4.9033 -4.9033 0.0000 0.000%


Minimum 0.0000 4.2461E-16 4.2461E-16

47

Maximum 0.0000 4.2461E-16 4.2461E-16

Average 0.0000 4.2461E-16 4.2461E-16 100.000%


Minimum 6.9343 6.9343 1.9000E-05

Maximum 6.9344 6.9343 3.1000E-05

Average 6.9343 6.9343 7.4380E-08 0.000%


Minimum 0.0000 4.9033 4.9033

Maximum 0.0000 4.9033 4.9033

Average 0.0000 4.9033 4.9033 100.000%


Minimum -6.9344 4.9033 11.8377

Maximum -6.9344 4.9033 11.8377

Average -6.9344 4.9033 11.8377 241.421%


Minimum 0.0000 4.2461E-16 4.2461E-16

Maximum 0.0000 4.2461E-16 4.2461E-16

Average 0.0000 4.2461E-16 4.2461E-16 100.000%


Minimum 6.9309 6.9343 0.0034

Maximum 6.9379 6.9343 0.0035

Average 6.9344 6.9343 3.3967E-06 0.000%

2.2.3 Planar Joint

Models were created in Chrono::Engine and ADAMS with three different orientations of planar

joints.

2.2.3.1 Planar Joint – Vertical

In this model, a block is connected to the ground by a vertically-oriented planar joint. Therefore,

the block is allowed to fall due to gravity. The results from the simulation of this model are

shown in Figures 42-45 and Table 11. While the Chrono::Engine position and velocity results in

the x direction (see Figures 42 & 43) show some discrepancies from the expected value of zero,

the y-direction and magnitude results agree well overall. The x-direction Chrono::Engine results

for the acceleration (see Figure 44) also show a different value than the ADAMS results, and the

y-direction and magnitude acceleration Chrono::Engine results have deviations from the mean

value that seem to be increasing with time. However, the mean value of the Chrono::Engine

acceleration results agrees well with the ADAMS results. Finally, the Chrono::Engine reaction

force magnitude (see Figure 45) shows a small difference from the expected, ADAMS-calculated

value of zero.

48

Figure 42: Position results for the vertically-oriented planar joint model simulations

Figure 43: Velocity results for the vertically-oriented planar joint model simulations

49

Figure 44: Acceleration results for the vertically-oriented planar joint model simulations

Figure 45: Joint reaction force results for the vertically-oriented planar joint model simulations

Table 11: Data for position, velocity, acceleration, and joint reaction forces for the vertically-oriented planar

joint simulations

Planar Joint - Vertical Data Chrono Adams Difference % Error

Position X (m)

Minimum 1.9461E-12 0.0000 1.9461E-12

50

Maximum 1.1973E-06 0.0000 1.1973E-06

Average 4.0331E-07 0.0000 4.0331E-07 -

Position Y (m)

Minimum -20.0880 -19.6133 0.4747

Maximum 0.0000 0.0000 0.0000

Average -6.7665 -6.5650 0.2015 -3.069%


Minimum 3.2651E-05 0.0000 3.2651E-05

Maximum 20.0880 19.6133 0.4747

Average 6.7665 6.5650 0.2015 3.069%

Velocity X (m/s)

Minimum 1.0666E-09 0.0000 1.0666E-09

Maximum 1.1782E-06 0.0000 1.1782E-06

Average 5.9034E-07 0.0000 5.9034E-07 -

Velocity Y (m/s)

Minimum -19.7670 -19.6133 0.1537

Maximum -0.0179 0.0000 0.0179

Average -9.9043 -9.8066 0.0977 -0.996%

Velocity Z (m/s)

Minimum 0.0000 -7.3538E-32 7.3538E-32

Maximum 0.0000 0.0000 0.0000

Average 0.0000 -3.6769E-32 3.6769E-32 -100.000%


Minimum 0.0179 0.0000 0.0179

Maximum 19.7670 19.6133 0.1537

Average 9.9043 9.8066 0.0977 0.996%


Minimum 5.8411E-07 0.0000 5.8411E-07

Maximum 5.8493E-07 0.0000 5.8493E-07

Average 5.8452E-07 0.0000 5.8452E-07 -


Minimum -9.8067 -9.8067 5.0000E-05

Maximum -9.8066 -9.8067 5.0000E-05

Average -9.8066 -9.8066 1.4050E-06 0.000%


Minimum 0.0000 -3.6769E-32 3.6769E-32

Maximum 0.0000 -3.6769E-32 3.6769E-32

Average 0.0000 -3.6769E-32 3.6769E-32 -100.000%


Minimum 9.8066 9.8067 5.0000E-05

51

Maximum 9.8067 9.8067 5.0000E-05

Average 9.8066 9.8066 1.4050E-06 0.000%


Minimum 5.8411E-07 -2.7572E-64 5.8411E-07

Maximum 5.8493E-07 -2.7572E-64 5.8493E-07

Average 5.8452E-07 -2.7572E-64 5.8452E-07 -2.120E+59


Minimum 0.0000 7.3538E-32 7.3538E-32

Maximum 0.0000 7.3538E-32 7.3538E-32

Average 0.0000 7.3538E-32 7.3538E-32 100.000%


Minimum 5.8411E-07 7.3538E-32 5.8411E-07

Maximum 5.8493E-07 7.3538E-32 5.8493E-07

Average 5.8452E-07 7.3538E-32 5.8452E-07 7.949E+26

2.2.3.2 Planar Joint – Horizontal

This planar joint is oriented horizontally, thus it prevents the block from falling due to gravity.

In this way, the block should not move. The results from the model’s simulations are presented

in Figures 46 & 47 and Table 12. The position results are zero in all directions. For the velocity

results, seen in Figure 46, Chrono::Engine calculated the expected value of zero, while ADAMS

shows increasing, non-zero results. ADAMS also shows non-zero values for the accelerations

(seen in Figure 47). The reaction force results in the y direction and the force magnitude (see

Figure 48) agree very well between the two software packages.

Figure 46: Velocity results for the horizontally-oriented planar joint model simulations

52

Figure 47: Acceleration results for the horizontally-oriented planar joint model simulations

Figure 48: Joint reaction force results for the horizontally-oriented planar joint model simulations

Table 12: Data for velocity, acceleration, and joint reaction forces for the horizontally-oriented planar joint

model simulations

Planar Joint - Horizontal Data Chrono Adams Difference

Velocity X (meters/second)

53

Minimum 0.0000 0.0000 0.0000

Maximum 0.0000 2.4019E-15 2.4019E-15

Average 0.0000 1.2010E-15 1.2010E-15

Velocity Z (m/s)

Minimum 0.0000 0.0000 0.0000

Maximum 0.0000 1.2010E-15 1.2010E-15

Average 0.0000 6.0048E-16 6.0048E-16


Minimum 0.0000 0.0000 0.0000

Maximum 0.0000 2.6854E-15 2.6854E-15

Average 0.0000 1.3427E-15 1.3427E-15


Minimum 0.0000 1.2010E-15 1.2010E-15

Maximum 0.0000 1.2010E-15 1.2010E-15

Average 0.0000 1.2010E-15 1.2010E-15


Minimum 0.0000 6.0048E-16 6.0048E-16

Maximum 0.0000 6.0048E-16 6.0048E-16

Average 0.0000 6.0048E-16 6.0048E-16


Minimum 0.0000 1.3427E-15 1.3427E-15

Maximum 0.0000 1.3427E-15 1.3427E-15

Average 0.0000 1.3427E-15 1.3427E-15


Minimum 0.0000 1.2010E-15 1.2010E-15

Maximum 0.0000 1.2010E-15 1.2010E-15

Average 0.0000 1.2010E-15 1.2010E-15


Minimum -9.8067 9.8067 19.6133

Maximum -9.8067 9.8067 19.6133

Average -9.8066 9.8066 19.6133


Minimum 0.0000 6.0048E-16 6.0048E-16

Maximum 0.0000 6.0048E-16 6.0048E-16

Average 0.0000 6.0048E-16 6.0048E-16


Minimum 9.8067 9.8067 0.0000

Maximum 9.8067 9.8067 0.0000

Average 9.8066 9.8066 0.0000

54

2.2.3.3 Planar Joint – Angled

In this final model, the planar joint is oriented at an angle of negative 45 degrees. The block

slides downward, due to gravity, along the incline created by the joint. The simulation results

can be seen in Figures 49-52 and Table 13. The position and velocity curves (see Figures 49 &

50) show the same shape and overall good agreement. The Chrono::Engine acceleration results

(shown in Figure 51) deviate from the ADAMS values, though the mean values are very similar

between the two software packages. Finally, for the joint reaction forces, pictured in Figure 52,

Chrono::Engine calculated deviations similar to those seen in the acceleration results. There are

also differences in the x and y directions due to differences in the definition of the reference

frames. Despite these discrepancies, the mean values of the force magnitudes agree well.

Figure 49: Position results for the angled planar joint model simulations

55

Figure 50: Velocity results for the angled planar joint model simulations

Figure 51: Acceleration results for the angled planar joint model simulations

56

Figure 52: Joint reaction force results for the angled planar joint model simulations

Table 13: Data for position, velocity, acceleration, and joint reaction forces for the angled planar joint model

simulations

Planar Joint - Angled Data Chrono Adams Difference % Error

Position X (m)

Minimum 0.0000 0.0000 0.0000

Maximum 9.9667 9.8067 0.1600

Average 3.3312 3.2825 0.0487 1.483%

Position Y (m)

Minimum -9.9667 -9.8067 0.1600

Maximum -1.6377E-05 0.0000 1.6377E-05

Average -3.3312 -3.2825 0.0487 -1.483%


Minimum 2.3161E-05 0.0000 2.3161E-05

Maximum 14.0950 13.8687 0.2263

Average 4.7110 4.6422 0.0689 1.483%

Velocity X (m/s)

Minimum 0.0090 0.0000 0.0090

Maximum 9.8448 9.8067 0.0381

Average 4.8979 4.9033 0.0054 0.111%

Velocity Y (m/s)

Minimum -9.8448 -9.8067 0.0382

Maximum -0.0090 0.0000 0.0090

Average -4.8979 -4.9033 0.0054 -0.111%

57

Velocity Z (m/s)

Minimum 0.0000 -8.4921E-16 8.4921E-16

Maximum 0.0000 0.0000 0.0000

Average 0.0000 -4.2461E-16 4.2461E-16 -100.000%


Minimum 0.0127 0.0000 0.0127

Maximum 13.9227 13.8687 0.0540

Average 6.9267 6.9343 0.0077 0.111%


Minimum 4.9008 4.9033 0.0025

Maximum 4.9057 4.9033 0.0024

Average 4.9033 4.9033 1.5992E-05 0.000%


Minimum -4.9059 -4.9033 0.0026

Maximum -4.9009 -4.9033 0.0024

Average -4.9033 -4.9033 1.7149E-05 0.000%


Minimum 0.0000 -4.2461E-16 4.2461E-16

Maximum 0.0000 -4.2461E-16 4.2461E-16

Average 0.0000 -4.2461E-16 4.2461E-16 -100.000%

Acceleration Magnitude (m/s

2)

Minimum 6.9343 6.9343 1.9000E-05

Maximum 6.9344 6.9343 2.1000E-05

Average 6.9343 6.9343 5.8678E-07 0.000%


Minimum 0.0000 4.9033 4.9033

Maximum 0.0000 4.9033 4.9033

Average 0.0000 4.9033 4.9033 100.000%


Minimum 6.9308 4.9033 2.0274

Maximum 6.9378 4.9033 2.0344

Average 6.9343 4.9033 2.0310 41.421%


Minimum 0.0000 -4.2461E-16 4.2461E-16

Maximum 0.0000 -4.2461E-16 4.2461E-16

Average 0.0000 -4.2461E-16 4.2461E-16 -100.000%


Minimum 6.9308 6.9343 0.0036

Maximum 6.9378 6.9343 0.0034

Average 6.9343 6.9343 2.3380E-05 0.000%

58

3 Conclusion This effort was a straightforward means of (i) providing assurance that Chrono::Engine

simulations are accurate, and (ii) working towards validating the software’s many-body granular

material simulations. The comparison provides evidence that Chrono::Engine generates the

same or similar position, velocity, acceleration, and joint reaction force results for the primitive

joints considered. The study also highlighted some areas for further investigation, specifically,

the spikes in the acceleration and joint reaction forces for the revolute joint models and the

discrepancies in the joint reaction forces for the angled translational joint models. These topics

will be addressed more fully in future work.

To continue the effort of providing a measure of accuracy for Chrono::Engine, future work will

also include validations of the software’s granular material simulations against experimental

results. Comparing to ADAMS simulations, as in the current effort, is infeasible for use in

directly validating the simulation of granular materials due to the program’s limited efficiency

for even very small systems. Therefore, future direct validations of granular material simulations

will involve designing and creating physical models from which experimental data (such as mass

flow rate) will be gathered.

The direct validation process, outlined in the previous paragraph, is obviously not as

straightforward as creating models in ADAMS. This highlights the benefit of the current work in

that it provided a simple method for lending greater confidence in Chrono::Engine results,

bringing us one step closer to accurate, billion-body simulations.

4 Acknowledgements The author would like to thank Dan Negrut, Hammad Mazhar, and Justin Madsen for their

support and help with this report.

59

5 References [1] Mazhar, H., Quadrelli, M., Negrut, D., Using a Granular Dynamics Code to Investigate

the Performance of a Helical Anchoring System Design: Technical Report TR-2011-03,

2011, Simulation-Based Engineering Lab, University of Wisconsin - Madison.

[2] Mazhar, H., Granular Simulation of 50,000 Ellipsoids, http://sbel.wisc.edu/Animations/.

[3] MSC.Software, ADAMS Standard Documentation and Help, 2010, MSC Software

Corporation, ADAMS 2010.

[4] Negrut, D., A. Tasora, and M. Anitescu, Large-scale parallel multibody dynamics with

frictional contact on the GPU, in ASME 2008 Dynamic Systems and Control

Conference, E. Misawa, Editor 2008, ASME: Ann Arbor, MI.

[5] Pöschel, T. and T. Schwager, Computational granular dynamics: models and algorithms.

2005: Springer.

[6] Tasora, A. Chrono::Engine, 2012, Available from:

http://www.deltaknowledge.com/chronoengine/.

[7] Tasora, A., M. Silvestri, and P. Righettini, Architecture of the Chrono::Engine physics

simulation middleware, in ECCOMAS Multibody Dynamics Conference 2007: Milano.

p. 1-8.

http://www.deltaknowledge.com/chronoengine/

technical report year-number - sbel

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