Simulating Basic Engineering Science Experiments using Dynamic Simulation

Simulating Basic Engineering Science Concepts using Dynamic Simulation

Bryan Hee Tze KeonLee Soo Leng

Politeknik Sultan Salahuddin Abdul Aziz Shah

htkbryan@psa.edu.mysllee@psa.edu.my

Abstract

Engineering Science is a basic course taught in all engineering programs in Malaysian Polytechnics in the first year of the program. For many students who do not have a strong foundation in physics in secondary school many of the concepts taught in the course will seem daunting. This paper examines the effectiveness of the Dynamic Simulation software in Autodesks Inventor Professional 2012 by trying to simulate two basic Physics concepts taught in the Engineering Science course at Malaysian Polytechnics. The conclusions from the simulations prove that the use of computer simulations can effectively demonstrate and simplify the learning of difficult to understand scientific concepts.

Concept 1: Simulating Newtons Second Law of Physics.

Newton Second law states that the acceleration (a) of a body is parallel and directly proportional to the net force (F) and inversely proportional to the mass (m), i.e., F=ma.

The experiment tries to prove Newtons law by simulating of two different object parts;. a table for the sliding to take place and a wooden block which will be subjected to two linear forces, one representing the User imposed driven Force and the other the force against the movement or assumed friction. (Appendix 1, Diagram 1)

Both parts were modeled in AutoDesk Inventor Professional 2012 separately and then assembled in the assembly environment of AutoDesk Inventor. In the assembly environment a mate constraint was laid between the wooden block and the table.

By selecting the environment tab and clicking dynamic simulation the motion study process came to being. After activating dynamic simulation, Autodesk Inventor automatically detects that the table which was already grounded in the assembly environment and automatically selects it to be grounded in the simulation environment. The woodblock was automatically located to mobile group. A Standard Joint was placed between the woodblock and the table.To complete the simulation I attached two loads. For Force 1, representing the friction force I assigned it a force of 0.8 N in the negative X direction. For the Force 2 which represented the User Imposed Force I gave it a value of 1 N in the positive X direction. For defining gravity I assigned it a value of 9810 mm/s2 which was the gravitational force in the Z direction. (Appendix 1, Diagram 2)

The mass of the woodblock was determined by selecting the body properties of the woodblock in the browser window.

To start the simulation one has to activate the simulation player. The Output Grapher is turned on to record and trace selected output that the user can select.

Discussion and ConclusionThe results obtained from the simulation are compared to results obtained from calculation.For a simple proof of the accuracy of the simulation, the acceleration information from the simulation (Appendix 1, Table 1 ) is attained giving the simulation an acceleration average of 15480 mm/s2 for the whole duration of the movement from the time = 0 to 0.2 seconds.

To prove the results theoretically,Using Newtons Second Law of Motion;F=ma , F= force applied, m= mass, a= accelerationF-friction=ma; where m=0.013kg , the driving force =1 N and friction value(force in the opposite direction as the driving force)= 0.8N1-0.8=0.013(a),0.2=0.013(a)a=15.3m/s2 or 15320mm/s2The percentage difference in results is given as (15480 15320)/ 15320 x 100 = 1.04 % where the effect of air friction was not taken into consideration.

Hence we can therefore conclude that the simulation faithfully confirms Newtons Second Law.Concept 2: Understanding the Law of Conservation of Energy: Simulating Motion using Newtons Cradle

The second experiment is about creating a basic Newton Cradle with two balls hanging from a frame and subjecting one stationary ball to a simulated collision with the main ball that is set to a fixed angle of 30 degrees. (Appendix 2, Diagram 4)

The assembly was modeled in two separate parts in AutoDesk Inventor Professional 2012. The first consists of a frame, next a set of rope and ball. Two set of rope and balls are attached to frame. The ball is made of steel and has a mass of 0.748kg. (Appendix 2, Diagram 5). In the Dynamic Simulation environment, the driving ball A was given a angle constraint of 30 degrees to the driven ball B to simulate the angle of release of the ball. Later a 2D contact was placed between both the balls. After placing the constraints, the simulation player was activated to run the simulation.

The experiment is designed to explain the Law of Conservation Energy that states the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time. For an isolated system, this law means that energy can change its location within the system, and that it can change form within the system, for instance chemical energy can become kinetic energy, but that energy can be neither created nor destroyed. In an ideal situation according to the Law of Conservation of Energy, Energy before collision = Energy after collisionFrom the simulation we would like to assume that, Maximum energy of driving ball A at the initial position = Total Energy at collision of driving ball A = Total Energy after collision of driven ball BEnergy State 1 = Energy State 2 = Energy State3 (See Discussion and Conclusion)and Conservation of Momentum states that the momentum before and after a collision are the same(Appendix 2, Diagram 6) shows the simulated movement of the balls from 0 to 0.28 seconds

Discussion and Conclusion

The conservation of momentum (mass x velocity) and kinetic energy (0.5 x mass x velocity2) can be used to find the resulting velocities for 2 colliding elastic balls. An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total kinetic energy before the encounter. Elastic collisions occur only if there is no net conversion of kinetic energy into other forms.

During the collision of small objects, kinetic energy is first converted to potential energy associated with a repulsive force between the particles (when the particles move against this force, i.e. the angle between the force and the relative velocity is obtuse), then this potential energy is converted back to kinetic energy (when the particles move with this force, i.e. the angle between the force and the relative velocity is acute).

The following results are calculated from the data obtained from the simulation. (Appendix 2, Table 1)Energy at State 1 or The Start Energy Before Ball A Is Released Maximum energy before the release of driving ball A (potential energy) at the initial time = 0 secondsEp= mgh where m = 0.748kg , g=9.81 m/s2 h=91.12 mm or 0.09112 m, time = 0 Seconds Ep = 0.748 x 9.81 x 0.09112= 0.6682 Joule

Energy at State 2 or the Total Energy of Driving Ball A Just Before First CollisionThe energy of the driving ball A after first collision at 0.28s;E = mv12 where m = 0.748kg and v1= 168 deg/s or 0.87962 m/s (conversion of tangential velocity at 0.28 sec) Degrees per second to Revolutions per minute conversion360 deg/s = 60 RPM or 1 Hz168 deg /s = 28 RPMV = Pi x D x RPMV= Tangential surface velocityD=Diameter or 2 times the length of the ropeWhere length of the rope which is 300mm or Diameter = 0.6 m, Pi = 3.1415Tangential Velocity = 3.1415 x 0.6x 28 = 52.7772m/min = 52.7772 m /60 sec = 0.87962m/s

Ek2 = (0.748) (0.87962)2 = 0.2893 Joule

The Potential energy of the driving ball at collision at 0.28s ; Ep2 = mgh where m= 0.748 kg g= 9.810 m/s2and h= 50.32 mm or 0.05032 m Ep2 = 0.748 x 9.81 x 0.05032 Ep2 = 0.3692 Joule Ep2 + Ek2= 0.3692 + 0. 2893 =0.6585 J

Energy at State 3 or The Total Energy Of Driven Ball B At 1st CollisionEnergy after collision for the driven ball B at 0.28s; Total Energy after collision for ball B=Ep3+ Ek3 Ep3 = mgh where m=0.748 kg, g=9.81ms-2, h=50.32mm or 0.05032 m Ep3 = (0.748)(9.81)(0.05032) = 0.3692 Joule Ek3 = mv2 where m=0.748 kg, v= 149.5 deg/s or 0.7854 m/s (Tangential velocity = Pi x D x RPM where Pi= 3.1415, D= 600 mm=0.6m 360 deg/s = 60 RPM or 1 Hz 149.5 deg /s = (149.5/360) x 60 = 25 RPM Therefore tangential velocity = 3.1415 x 0.6 x 25 = 47.125 /60 = 0.7854 m/s) Ek3 = (0.748) (0.7854)2 = 0.2307 Joule tangential velocity = 3.1415 x 0.6 x (14.9512/360 x60)/60 = 0.00415 m/s) Ek3 of ball-A = (0.748) (0.00415)2 = 0.00000644984 Joule negligible

Ep3 + Ek3= 0.3692 + 0.2307 = 0.5999 JouleFrom the calculations and results obtained from the simulation,Energy at State 1 = 0.6682 JouleEnergy at State 2 = 0.6585 JouleEnergy at state 3 = 0.5999 Joule

From the results we observe a decline in energy levels from the initial state, State 1 to the State 3 which is the state of the driven ball at 0.28 s. This is because of heat losses from the balls striking each other or friction losses from air resistance and the strings. These energy losses are why the balls eventually come to a stop. The higher the weight of steel reduces the relative effect of air resistance. The size of the steel balls is limited because the collisions may exceed the elastic limit of the steel, deforming it and causing heat losses.

Momentum has the special property that, in a closed system, it is always conserved, even in collisions and separations caused by explosive forces. Kinetic energy, on the other hand, is not conserved in collisions if they are inelastic. Since momentum is always conserved, the sum of the moment a before the collision must equal the sum of the moment a after the collision:

where u1 and u2 are the velocities before collision, and v1 and v2 are the velocities after collision.The results used for the calculation are taken just before and after the first collision time of 0.28 seconds; (Appendix2, Diagram 8) m1 = m2 = 0.748 kg , u1 = 0.8796 m/s or 149.5 deg/s u2 = 0 v1= 0.1044 m/s or 14.95 deg/s v2 = 0.7854 m/s or 149.5 deg/s

From the Law of Conservation of Momentum;Momentum before collision= Momentum after collisionm1 u1 + m2 u2 = m 1v 1 + m 2 v 2(0.748)(0.8796) + (0.748)(0) = (0.748)( 0.1044) + (0.748)(0.7854)0.6579 = 0.078 + 0.58740.6579 0.6654 The difference between the pre collision and post collision give an error of (0.6579 0.6654)/ 0.6654 x 100 = 1.13 %

In the ideal state where it is assumed that no energy loss occurs, the Law of Conservation Energy, the Law of Conservation of Momentum as predicted by Newtons Second Law of Physics can be relied on. The simulation of the collision in Inventor provides an almost realistic process of the movement, collision and the energy levels of the two balls that sit in the same cradle.

REFERENCES

NEWTONS SECOND LAW, Wikipedia, http://en.wikipedia.org/wiki/Newton%27s_laws_of_motionELASTIC COLLISION, Wikipedia. http://en.wikipedia.org/wiki/Elastic_collisionKINETIC ENERGY, Wikipedia. http://en.wikipedia.org/wiki/Kinetic_energyPOTENTIAL ENERGY, Wikipedia. http://en.wikipedia.org/wiki/Potential_energyACCELERATION, Wikipedia. http://en.wikipedia.org/wiki/AccelerationENERGY, Wikipedia. http://en.wikipedia.org/wiki/EnergyCOLLISION, Wikipedia. http://en.wikipedia.org/wiki/CollisionLAW OF CONSERVATION OF ENERGY, Wikipedia. http://en.wikipedia.org/wiki/Conservation_of_energy

KLETZ, T. CHUNG, P., BROOMFIELD, E. and SHEN-ORR, C,. Computer Control and Human Error, 1995, IChemE, Gulf Publishing Company, ISBN 0-88415-269-3

DELP, S. L., ANDERSON, F. C., ARNOLD, A. S., LOAN, P., HABIB, A., JOHN, T., GUENDELMAN, E., AND THELEN, D. G., 2007. Open sim: Open-source software to create and analyze dynamic simulations of movement.

THEETTEN, A., GRISONI, L., ANDRIOT, C., AND BARSKY, B.2008. Geometrically exact dynamic splines. Computer-Aided Design 40, 1, 35 48.

GREGOIRE, M., AND SCHO MER, E. 2007. Interactive simulation of one-dimensional flexible parts. Comput. Aided Des. 39 (Aug), 694707.

USING DYNAMIC SIMULATION TO IMPROVE PRODUCT DESIGN, 2006. Autodesk Inc. http://images.autodesk.com/adsk/files/dynamic_simulaton_whitepaper.pdf

APPENDIX 1

Diagram 1The setup of the simulation

Magnitude of Friction = 0.8 N

Magnitude of Driving Force = 1 N

Mass of woodblock=0.013kg

Diagram 2 Simulation before and after. Movement of wood block on table.

Diagram showing the simulation at the beginning

Output of acceleration of the wooden block versus time (mm/s2vs seconds)

Diagram 3Acceleration of wood block vs time taken

Table 1Acceleration of wood block vs time taken

Time ( s )A (Trace:1) - New_NewtonLaw2_bothForces.iaa ( mm/s^2 )

0.0000015274.70000

0.0100015272.80000

0.0200015269.40000

0.0300015272.00000

0.0400015292.50000

0.0500015343.20000

0.0600015425.30000

0.0700015518.50000

0.0800015590.20000

0.0900015621.90000

0.1000015620.10000

0.1100015603.00000

0.1200015584.00000

0.1300015568.80000

0.1400015558.30000

0.1500015551.40000

0.1600015547.10000

0.1700015544.40000

0.1800015542.70000

0.1900015541.60000

0.2000015541.00000

Average Acceleration15480.13810

APPENDIX 2

Height from ground = 91.12 mmLength of rope = 300 mm or 0.3 mDiagram 4 Newton Cradle and position of driving ball A and driven ball Bbefore and after collision

Diagram 5Newton Cradle Modeling Information

RopeSteel Ball

Ball Mass = 0.748 kg

Newtons Cradle showing frame and balls

Diagram 6 Newtons Cradle showing position of driving ball A before release at State 1 and after the first collision at 0.28 s State 2

Ball A Ball B 50.32 mm State 3 State 1 Ball B Ball A 91.12 mm 30 deg

Diagram 7 Output of velocity of driving ball A(spherical 3) and velocity of driven ball B (spherical 4) for 2 seconds

Table 2 Output velocity of driving ball A (spherical 3) versus output velocity of driven ball B (spherical 4) for 2 seconds

Time ( s )Driving Ball (A) ( deg/s )Driven Ball (B) ( deg/s )

0.000000.000000.00000

0.01000-9.208290.00000

0.02000-18.390900.00000

0.03000-27.522200.00000

0.04000-36.576600.00000

0.05000-45.528400.00000

0.06000-54.351900.00000

0.07000-63.021600.00000

0.08000-71.512000.00000

0.09000-79.797700.00000

0.10000-87.853400.00000

0.11000-95.654200.00000

0.12000-103.175000.00000

0.13000-110.392000.00000

0.14000-117.281000.00000

0.15000-123.819450.00000

0.16000-129.984000.00000

0.17000-135.753000.00000

0.18000-141.106000.00000

0.19000-146.023000.00000

0.20000-150.486000.00000

0.21000-154.479000.00000

0.22000-157.985000.00000

0.23000-160.991000.00000

0.24000-163.486000.00000

0.25000-165.458000.00000

0.26000-166.902000.00000

0.27000-167.810000.00000

0.28000-168.178000.00000

0.28194-14.95120149.50100

0.29000-14.93040149.34500

0.30000-14.86120148.71800

0.31000-14.74430147.61300

0.32000-14.58000146.03500

0.33000-14.36880143.99000

0.34000-14.11140141.48500

0.35000-13.80870138.53100

0.36000-13.46160135.13800

0.37000-13.07120131.31900

0.38000-12.63880127.08700

0.39000-12.16570122.46000

0.40000-11.65360117.45200

0.41000-11.10400112.08200

0.42000-10.51880106.36900

0.43000-9.89971100.33100

0.44000-9.2488493.98930

0.45000-8.5682687.36490

0.46000-7.8601580.47910

0.47000-7.1267973.35410

0.48000-6.3705366.01210

0.49000-5.5938258.47600

0.50000-4.7991350.76870

0.51000-3.9890342.91350

0.52000-3.1661234.93364

0.53000-2.3330526.85270

0.54000-1.4924718.69430

0.55000-0.6471110.48200

0.560000.200332.23959

0.570001.04713-6.00928

0.580001.89057-14.24090

0.590002.72793-22.43150

0.600003.55654-30.55740

0.610004.37372-38.59500

0.620005.17685-46.52080

0.630005.96336-54.31134

0.640006.73071-61.94326

0.650007.47644-69.39350

0.660008.19815-76.63910

0.670008.89353-83.65750

0.680009.56033-90.42650

0.6900010.19640-96.92430

0.7000010.79970-103.13000

0.7100011.36840-109.02200

0.7200011.90050-114.58000

0.7300012.39430-119.78700

0.7400012.84830-124.62300

0.7500013.26100-129.07200

0.7600013.63110-133.11600

0.7700013.95740-136.74200

0.7800014.23880-139.93600

0.7900014.47450-142.68631

0.8000014.66356-144.98200

0.8100014.80550-146.81400

0.8200014.89990-148.17700

0.8300014.94640-149.06400

0.8400014.94480-149.47200

0.84461134.54715-26.89130

0.85000134.45900-26.84970

0.86000133.96200-26.70600

0.87000133.03500-26.47650

0.88000131.68100-26.16190

0.89000129.90500-25.76310

0.90000127.71500-25.28160

0.91000125.11700-24.71890

0.92000122.12100-24.07666

0.93000118.73893-23.35710

0.94000114.98200-22.56254

0.95000110.86400-21.69550

0.96000106.40000-20.75880

0.97000101.60400-19.75540

0.9800096.49430-18.68870

0.9900091.08690-17.56200

1.0000085.40010-16.37890

1.0100079.45290-15.14320

1.0200073.26450-13.85900

1.0300066.85470-12.53040

1.0400060.24380-11.16160

1.0500053.45250-9.75696

1.0600046.50180-8.32109

1.0700039.41280-6.85854

1.0800032.20700-5.37401

1.0900024.90600-3.87227

1.1000017.53160-2.35812

1.1100010.10559-0.83641

1.120002.649830.68798

1.13000-4.813722.21017

1.14000-12.263103.72527

1.15000-19.676405.22844

1.16000-27.031806.71485

1.17000-34.307408.17974

1.18000-41.481519.61842

1.19000-48.5326011.02630

1.20000-55.4393012.39880

1.21000-62.1804013.73152

1.22000-68.7351015.02020

1.23000-75.0827016.26080

1.24000-81.2032017.44910

1.25000-87.0769018.58150

1.26000-92.6845419.65430

1.27000-98.0076020.66396

1.28000-103.0280021.60729

1.29000-107.7290022.48120

1.30000-112.0950023.28300

1.31000-116.1090024.00990

1.32000-119.7590024.65980

1.33000-123.0300025.23040

1.34000-125.9110025.71990

1.35000-128.3920026.12670

1.36000-130.4634726.44960

1.37000-132.1170026.68740

1.38000-133.3480026.83950

1.39000-134.1500026.90520

1.40000-134.5220026.88450

1.40651-36.40070122.56600

1.41000-36.34940122.50000

1.42000-36.12400122.04500

1.43000-35.78240121.19873

1.44000-35.32584119.96312

1.45000-34.75573118.34301

1.46000-34.07390116.34400

1.47000-33.28270113.97400

1.48000-32.38460111.24100

1.49000-31.38250108.15500

1.50000-30.27964104.72700

1.51000-29.07970100.96800

1.52000-27.7864096.89230

1.53000-26.4040092.51340

1.54000-24.9370087.84610

1.55000-23.3901082.90620

1.56000-21.7683077.71000

1.57000-20.0768072.27460

1.58000-18.3210066.61760

1.59000-16.5066060.75720

1.60000-14.6394054.71190

1.61000-12.7254048.50070

1.62000-10.7707042.14290

1.63000-8.7815735.65820

1.64000-6.7643729.06620

1.65000-4.7255622.38710

1.66000-2.6716515.64100

1.67000-0.609208.84804

1.680001.455192.02868

1.690003.51494-4.79674

1.700005.56345-11.60780

1.710007.59419-18.38420

1.720009.60066-25.10564

1.7300011.57640-31.75180

1.7400013.51520-38.30270

1.7500015.41080-44.73830

1.7600017.25710-51.03900

1.7700019.04813-57.18520

1.7800020.77820-63.15770

1.7900022.44180-68.93790

1.8000024.03355-74.50710

1.8100025.54830-79.84760

1.8200026.98110-84.94180

1.8300028.32750-89.77310

1.8400029.58300-94.32530

1.8500030.74360-98.58300

1.8600031.80560-102.53200

1.8700032.76550-106.15800

1.8800033.62011-109.44900

1.8900034.36680-112.39300

1.9000035.00300-114.98000

1.9100035.52680-117.20000

1.9200035.93640-119.04600

1.9300036.23050-120.51100

1.9400036.40810-121.58900

1.9500036.46870-122.27700

1.9600036.41200-122.57200

1.96792112.94600-43.95270

1.97000112.89400-43.90500

1.98000112.43000-43.59110

1.99000111.60400-43.13700

2.00000110.41900-42.54435

9