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Challenge

Week - 1 - Consistency of Units

DDinesh N29 Sept 2022
LS-DYNA

CONSISTENCY OF UNITS

AIM :

Convertion of given measurement values to different unit systems

OBJECTIVE:

  • To give an explanation about a change of SI units to gm/mm/ms units.
  • To make an table content of remaining values of conversion from SI units to different unit values as per requirement.
  • To find out different conversion factors for different unit system.

DATA BASE:

INTRODUCTION: LS-DYNA TOOL USED IN DIFFERENT CIRCUMSTANCES

  • Different industries use different system of units as per their convenience.
  • The units for the basic measurement quantities, mass distance and time - dictate how the other derived quantities will be expressed. For example, automotive industries use kg,mm,ms as their standard unit system.
  • Construction industries are likely to use tonne,m,s as their unit system. Similarly, PCB simulation in electronic industry uses gm, micrometer,ms as their system of units.
  • LS-DYNA doesn't have a default system of units. User needs to input material properties and physical dimensions according to a consistent system of units as per their choice. This warrants that to use LS-DYNA in different circumstances, users has to be conversant with converting quantities from one system of units to another.

PROCEDURAL STEPS:

1.DETAILED CALCULATION OF CONVERTION FROM SI UNITS( kg m s) to gm/mm/ms units

  1. Mass-1kg

1kg=1000 gm = 10^3gm.

conversion factor = 10^3gm.

2. Length-1m

1m = 1000 mm = 10^3mm.

conversion factor = 10^3mm.

3. Time-1s

1s = 1000 ms = 10^3ms.

conversion factor = 10^3ms.

4. Force-1N

1N = kg.m / s^2

kg.m / s^2 = (1000 gm )*[(1000 mm) / (1000)^2 ms^2 ] = 1 gm.mm/ms^2.

Conversion factor = 1.

5. Stress-1pa

1pa = 1N /m^2

1N /m^2 = (1 gm.mm/ms^2. ) / (1000^2 mm^2) = 10^-6 * (gm/ mm.ms^2 / mm^2 ) = 10^-6 gm / ms^2. mm

Conversion factor = 10^-6 .

6. Energy-1Nm

1 joule = 1Nm = (1 gm.mm/ms^2.) * (1000 mm ) = 10^3 * ( gm.mm/ms^2 )*( mm ) = 10^3 gm mm^2 / ms^2.

Conversion factor = 10^3.

7. Density - 1kg / m^3

1kg / m^3 = (1000 gm ) / (1000^3 mm^3) = 10^-6 gm / mm^3.

Conversion factor = 10^-6.

8. Youngs modulus-210 Gpa

1Gpa = 10^9 N /m^2 = 10^9 (1 gm.mm/ms^2. ) / (1000^2 mm^2) = (10^9 *10^-6 ) * (gm/ mm.ms^2 / mm^2 ) = 10^ 3 gm / ms^2. mm

210 Gpa = 210 . (10^ 3 gm / ms^2. mm )

Conversion factor = 10^3.

9. Velocity - 56.33 kmph

Velocity = 1kmph = (10^6 mm) / (3600 *1000 ms) = 277.77 mm/ms

Velocity = 56.33 * 0.277mm/ms = 15.64 mm/ms.

Conversion factor = 0.277

10. Gravity -9.8 m/s^2

Gravity = 9.8 m/s^2 = 9.8 *( 1000 mm ) / (1000^2 ms^2) = 9.8 * 10^-3 mm/ms^2

Conversion factor = 10^-3.

2. TABLE CONTENT OF DIFFERENT VALUES OF CONVERTION OF UNITS FROM SI UNITS.

Note : CF-conversion factor

S.No Mass CF Length CF Time CF Force CF Stress CF Energy CF Density CF Youngs modulus CF Velocity CF Gravity CF
SI units kg m sec 1 N N /m² Nm 1kg / m³ 210*10⁹ N/m² 56.33 kmph 9.8 m/s^2
Other unit systems
1 Kg cm ms 1 kg 1 10² cm 10² 10³ms 10³ 10⁻⁴ Kg.cm / ms² 10⁻⁴ 10⁻⁸ kg. / cm ms² 10⁻⁸ 10⁻² kg cm² / ms² 10⁻² 10⁻⁶ kg / cm³ 10⁻⁶ 2100 kg. / cm ms² 10⁻⁸ 1.564 cm /ms 0.027 9.8 *10⁻⁴cm /ms² 10⁻⁴
2 Kg cm s 1 kg 1 10² cm 10² 1 sec 1 10² kg cm / s² 10² 10⁻² kg / cm s² 10⁻² 10⁴ kg cm² / s² 10⁴ 10⁻⁶ kg / cm³ 10⁻⁶ 210*10⁷ kg / cm s² 10⁷ 1564.7 cm /s 27.77 9.8 *10² cm /s² 10²
3 Gm mm ms 10³ gm 10³ 10³ mm 10³ 10³ ms 10³ 1 gm mm / ms² 1 10⁻⁶ gm / mm ms² 10⁻⁶ 10³ gm mm² /ms² 10³ 10⁻⁶ gm /mm³ 10⁻⁶ 210*10³ gm / mm ms² 10³ 15.64 mm/ms 0.277 9.8 *10⁻³ mm / ms² 10⁻³
4 Kg m s 1 kg 1 1m 1 1 sec 1 1 Kg m / s² 1 1 kg / m s² 1 1 kg m² / s² 1 1kg / m³ 1 210*10⁹ kg / m s² 1 15.64 m /s 0.277 9.8 m / s² 1
5 Gm cm s 10³ gm 10³ 10² cm 10² 1 sec 1 10⁵ gm cm / s² 10⁵ 10 gm / cm s² 10 10⁷ gm cm² / s² 10⁷ 10⁻³ gm / cm³ 10⁻³ 210*10¹⁰gm / cm s² 10 1564.7 cm /s 27.77 9.8 *10² cm /s² 10²
6 Gm cm µs 10³ gm 10³ 10² cm 10² 10⁶ sec 10⁶ 10⁻⁷ gm cm / µs² 10⁻⁷ 10⁻¹¹ gm / cm µs² 10⁻¹¹ 10⁻⁵ gm cm² / µs² 10⁻⁵ 10⁻³ gm / cm³ 10⁻³ 210*10² gm / cm µs² 10⁻¹¹ 1.564*10⁻³ cm /µs 2.7 *10⁻⁵ 9.8 *10⁻¹⁰ cm/ µs² 10⁻¹⁰
7 Gm mm s 10³ gm 10³ 10³ mm 10³ 1 sec 1 10⁶ gm mm / s² 10⁶ 1 gm / mm s² 1 10⁹ gm mm² / s² 10⁹ 10⁻⁶ gm /mm³ 10⁻⁶ 210*10⁹ gm / mm s² 1 15647.22 mm /s 277.77 9.8 *10³ mm / s² 10³
8 Ton mm s 10⁻³ ton 10⁻³ 10³ mm 10³ 1 sec 1 1 ton mm / s² 1 10⁻⁶ ton / mm s² 10⁻⁶ 10³ ton mm² / s² 10³ 10⁻¹² ton / mm³ 10⁻¹² 210*10³ ton / mm s² 10⁻⁶ 15647.22 mm /s 277.77 9.8 *10³ mm / s² 10³
9 Slug ft s 0.068 slug 0.068 3.28 ft 3.3 1 sec 1 0.22 sl. ft / s² 0.22 0.020 sl / ft. s² 0.02 0.72 sl .ft² / s² 0.72 1.9 *10⁻³ sl / ft³ 1.9 *10⁻³ 4.2*10⁻⁹ sl / ft. s² 0.02 51.32 ft / sec 0.91 32.144 ft /s² 3.28
10 Kg mm s 1 kg 1 10³ mm 10³ 1 sec 1 10³ kg mm / s² 10³ 10⁻³ kg / mm s² 10⁻³ 10³ kg mm² / s² 10³ 10⁻⁹ kg / mm³ 10⁻⁹ 210*10⁶ kg / mm s² 10⁻³ 15647.22 mm /s 277.77 9.8 *10³ mm / s² 10³
11 Gm cm ms 10³ gm 10³ 10² cm 10² 10³ ms 10³ 0.1 gm cm / ms² 0.1 10⁻⁵ gm / cm ms² 10⁻⁵ 10 gmcm² / ms² 10 10⁻³ gm /mm³ 10⁻³ 210*10⁴ gm / cm ms² 10⁻⁵ 1.5647 cm / ms 0.027 9.8 *10⁻⁴ cm / ms² 10⁻⁴
12 Kg mm ms 1 kg 1 10³ mm 10³ 10³ ms 10³ 10⁻³ kg mm / ms² 10⁻³ 10⁻⁹ kg / mm ms² 10⁻⁹ 1 kg mm² /ms² 1 10⁻⁹ kg / mm³ 10⁻⁹ 210kg / mm ms² 10⁻⁹ 15.64 mm/ms 0.277 9.8 *10⁻³ mm / ms² 10⁻³

RESULT :

  1. Calculated detailed convertion factor about a change of SI units to gm/mm/ms units.
  2. Performed table content of conversion from SI units to different unit values as per requirement.
  3. Different conversion factors for different unit system was successfully found out.

LEARNING OUTCOME :

In this week 1 challenge i came to know,

  1. How to do calculate convertion factor from SI units to diffrent unit systems.
  2. How to do make an table contents of conversion from SI units to different unit values for comparison purpose as per requirement.
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