Week - 1 - Consistency of units
Objective:To convert given system of units into desired unit system with conversion factors.
Data given:
MASS 1kg
LENGTH 1m
TIME 1s
FORCE 1N
STRESS 1Pa
ENERGY 1Nm
DENSITY 1Kg/m3
YOUNG'S Modulus 210GPa
Velocity 56.33KMPH
GRAVITY 9.8m/s2
1)Coversion of SI unit to gm/mm/ms system
Mass:1 kg=1000 gm=10^3 g
Length:1 m=100 cm=1000 mm
Time :1 s=1000 ms
Force:1 N=1xkgx(m/s^2)
=1x(10^3 gm)x(10^3mm)/(10^6ms^2
=1x(gm)x(mm)/(s^2)
Stress:1Pa=1N/m
Stress:1Pa=1N/m^2
=1000g*(1000)^2mm^2/(1000)^2ms^2
=10^(-6)g/mm*ms2
Multiplication factor=10^-6
Energy:
1 J=1N-m=1kg*m2/s2
=1000g*(1000)^2mm^2/(1000)^2ms^2
=10^3 gmm^2/ms^2
Multiplication factor=10^3
Density:
1 kg/m^3=(1000)g/(1000)^3
=10^(-6)g/mm^3
Multiplication factor=10^-6
Young's Modulus:
210 Gpa=210*10^9 kg/m-s^2
=210*10^9*(1000)g/(1000)mm*(1000)^2 ms^2
=210*10^3 g/mm*ms^2
Multiplication factor=10^3
Velocity:
56.33 kmph=56.33*10^6mm/(3600*1000ms)
=15.647mm/ms
conversion factor=1
Gravity:
9.8m/s^2=9.8*(1000)mm/(1000)^2 ms^2
=10^-3mm/ms^2
Conversion factor=10^-3
| Mass | Length | Time | Force | Stress | Energy | Density | Young's Modulus | Velocity | Gravity | |
| kg m s | 1 kg | 1 m | 1s | 1 N=1 kg*m/s^2 | 1Pa=1 kg/ms^2 | 1j=1 Nm=1 kg*m^2/s^2 | 1kg/m^3 |
210 Gpa=210*10^9 kg/ms^2 |
15.647m/s | 9.8 m/s^2 |
| kg cm ms | 1 kg | 10^2 cm | 10^3 ms | 10^-4 kg*cm/ms^2 | 10^-9kg/cm*ms^2 | 10^-2kg*cm^2/ms^2 | 10^-6 kg/cm^3 | 2100kg/cm*ms^2 | 1.5647 cm/ms | 9.8*10^-4 |
| kg cm s | 1 kg | 10^2 cm | 1 s | 10^2 kg cm/s^2 | 10^-2kg/cm*s^2 | 10^4 kg*cm^2/s^2 | 10^-6kg/cm^3 | 210*10^7kg/cm*s^2 | 1564.7cm/s | 9.8*10^2cm/s^2 |
| gm mm ms | 10^3 gm | 10^3 mm | 10^3 ms | 1 gm*mm/ms^2 | 10^-6 gm/mm*ms^2 | 10^3 gm*mm^2/ms^2 | 10^-6 gm/mm^3 | 210*10^3 gm/mm*ms^2 | 15.647 mm/ms | 9.8*10^-3 mm/ms^2 |
| gm cm s | 10^3 gm | 10^2 cm | 10^6 ms | 10^-7 gm cm/ms^2 | 10^-11 gm/cm*ms^2 | 10^-5 gm*cm^2/ms^2 | 10^-3 gm/cm^3 | 2.10 gm/cm ms^2 | 15.647*10^-4 cm/ms | 9.8*10^-10 cm/ms^2 |
| g mm s | 10^3 gm | 10^3 mm | 1 s | 10^6 gm*mm/s^2 | 1 gm/mm s^2 | 10^9 gm*mm^2/s^2 | 10^-6 gm/mm^3 | 2.10*10^11 gm/mm*s^2 | 15647 mm/s | 9.8*10^3 mm/s^2 |
| g cm ms | 10^3 gm | 10^2 cm | 10^6 ms | 10^-7 gm*cm/ms^2 | 10^-11 gm/cm*ms^2 | 10^-5 gm*cm^2/ms^2 | 10^-3 gm/cm^3 | 2.10 gm/cm ms^2 | 15.647*10^-4 cm/ms | 9.8*10^-10 cm/ms^2 |
| ton mm s | 10^-3 ton | 10^3 mm | 1 s | 1 ton*mm/s^2 | 10^-6 ton/mm*s^2 | 10^-6 gm/mm^3 | 10^3 ton*mm^2/s^2 |
2.10*10^12 gm/mm*s^2 |
15647 mm/s | 9.8*10^3 mm/s^2 |
| slug ft s | 0.068 slug | 3.28 ft | 1 s | 0.2246 slug*ft/s^2 | 0.0208 slug/ft s^2 |
0.7366 slug ft^2/sec |
1.93*10^-3 slug/ft^3 |
4.368*10^9 slug/ft s^2 | 51.322 ft/s | 32.144 ft/s^2 |
| kg mm s | 1 kg | 10^3 mm | 1 s | 10^3 kg*mm/s^2 | 10^-3 kg*mm/s^2 |
10^6 kg*mm/s^2 |
10^-9 kg/mm^3 |
210*10^6kg/mm*s^2 | 115647 mm/s | 9.81*10^3 mm/s^2 |
| gm cm ms | 10^3 gm | 10^2 cm | 10^3 s | 0.1 gm*cm/ms^2 | 10^-5 gm/cm*ms^2 | 10 gm*cm/ms^2 | 10^-3 gm/cm^3 | 210*10^4 gm/cm*ms^2 | 1.5647 cm/ms | 9.8*10^-4 cm/ms^2 |
| kg mm ms | 1 kg | 10^3 mm | 10^3 s | 10^-3 kg mm/ms^2 | 10^-9 kg mm/ms^2 | 1 kg*mm/ms^2 | 10^-9 kg/mm^3 | 210 kg/mm*ms^2 | 15.647 mm/ms | 9.8*10^-3 mm/ms^2 |
Conclusion:
1) As LS-Dyna is not having any specific unit system we have to define specific unit system.
2) Converson factor plays an important role in unit transfer.