Consistency of units should be followed while performing simulations on L

October 10, 2019

Consistency of units should be followed while performing simulations on L_S DYNA

The variation of different qualtities are derived and illustrated in the table.
Also the calculation depending upon the different unit systemare given below after the tables.
Table for unit consistency

Kg-m-s	Kg-cm-ms	Kg-cm-s	gm-mm-ms	g-cm-s	g-cm-µs	g-mm-s	Ton-mm-s	Slug-ft-s	Kg-mm-s	g-cm-ms	Kg-mm-ms
Mass(1kg)	1 kg	1kg	1000gm	1000gm	1000gm	1000gm	0.001 ton	1/14.5939	1kg	1000gm	1kg
Length(1m)	100cm	100cm	1000mm	100cm	100	1000 mm	1000mm	3.28 feet	1000mm	100 cm	1000mm
Time (1s)	1000ms	1s	1000ms	1s	1000000 µs	1s	1s	1s	1s	1000ms	1000ms
Force(1N)	110^-4 kgcm/ms²	110² kgcm/s²	1N	110⁵ gcm/s²	110^-7 gcm/µs²	110⁶ gmm/s²	1N	0.2248 slug*feet/s²	110³ kgmm/s²	110^-1 gcm/ms²	1N
Stress(1Pa)	110⁸ kg/cmms²	110^-2 kg/cms²	110^-6 gm/mmms²	110 g/cms²	110^-13 g/cmµs²	1pa	110^-6 ton/mms²	0.02089 slug/feet*s²	110^-3 kg/mms²	110^-5 g/cmms²	110^-6kg/mmms²
Energy(1N-m)	110^-2kgcm²/ms²	110⁴kgcm²/s²	110³gmmm²/ms²	110⁷gcm²/s²	110^-5gcm²/µs²	110^-2kgcm²/ms²	110^-3tonmm²/s²	10.75slug*ft²/s²	110⁶kgmm²/s²	110 gcm²/ms²	1N-m
Density 1kg/m³	1*10^-6kg/cm³	1*10^-6kg/cm³	1*10^-6gm/mm³	1*10^-6kg/cm³	1*10^-3g/cm³	1*10^-3g/cm³	1*10^-6ton/mm³	0.00194slugg/ft³	1*10^-6kg/mm³	1*10^-3g/cm³	1*10^-9kg/mm³
Young’s modulus 210 Gpa	21010 kg/cmms²	21010⁷ kg/cms²	21010³ gm/mmms²	21010¹⁰ g/cms²	21010^-2 g/cmµs²	210 gpa	21010³ ton/mms²	4.3810⁹ slug/fts²	21010⁶ kg/mms²	21010⁴ g/cmms²	210 gpa
Velocity 56.33 KMPH (	1.563 cm/ms	1563.88 cm/s	56.33 KMPH	1563.88 cm/s	0.00157 cm/µs	15.63 mm/s	15.63 mm/s	51.505 ft/s	15.63 mm/s	1.5702 cm/ms	56.33 KMPH
Gravity 9.8 m/s²	9.8*10^-4cm/ms²	9.8*10²cm/s²	9.8*10^-3,mm/ms²	9.8*10²cm/s²	9.8*10^-10cm/µs²	9.8*10³mm/s²	9.8*10³ mm/s²	32.17 ft/s²	9.8*10³mm/s²	9.8*10^-4cm/ms²	9.8*10^-3 mm/ms²

Mass ,length and time is self explanatory and there is no need to explain,as they are not derived quantities.
force calculation
1)Force is a derived quantity (1N) = kg*m/s^2 in (kg-m-s ) unit system.
2) unit system Kg-cm-ms
= 1*100/1000^2 =1*10^-4 kg*cm/ms²
^{unit conversion factor 10 ^-4}

3) unit system Kg-cm-s
= 1*100/1 =1*10^2 kg*cm/s²
unit conversion factor 10^2
4) unit system gm-mm-ms
= 1000*1000/(1000)^2 =1 N
5) unit system g-cm-s
= 1000*100/1 =1*10^5 g*cm/s²
unit conversion factor 10^5
6) unit system g-cm-us
= 1000*100/(1000000)^2 =1*10^-7 g*cm/us²
unit conversion factor 10^-7
7) unit system g-mm-s
= 1000*1000/1 =1*10^6 g*mm/s²
unit conversion factor 10^6
8) unit system ton-mm-s
= 0.001*1000/1 =1N
9) unit system slug-ft-s
=1/14.59 *3.28=0.2248 slug*ft/s^2

10) unit system kg-mm-s
= 1*100/1 =1*10^3 kg*mm/s²
unit conversion factor 10^3
11) unit system g-cm-ms
= 1000*100/(1000)^2 =1*10^-1 g*cm/ms²
unit conversion factor 10^-1
12) kg-mm-ms
1 N

stress calculation
1) unit system kg-m-s
1pa = kg/m*s^2
2) unit system (kg-cm-ms)
= 1/100*(1000)^2
=1*10^-8 kg/cm*ms^2
unit conversion factor =10^-8
3)unit system (kg-cm-s)
=1/100*1^2 =1*10^-2 kg/cm*s^2
unit conversion factor = 10^-2
4)unit system(gm-mm-ms)
= 1000/1000*(1000)^2
= 1*10^-6 gm/mm*ms^2
unit conversion factor = 10^-6
5) unit system (g-cm-s)
=1000/100*1
= 1*10 g/cm*s^2
unit conversion factor= 10
6) unit system (g-cm-us)
= 1000/100*(1000000)^2
= 1*10^-13 g/cm*us^2
unit conversion factor = 10^-13
7) unit system (g-mm-s)
=1000/1000*1^2
= 1 pa
8) unit system (ton-mm-s)
= 1*10^-3 /1000*1
= 1*10^-6
=1 mpa
9) unit system (slug-ft-s)
=0.2248/3.28^2
= 0.020 slug/ft*s^2
unit conversion factor =0.020
10) unit system( kg-mm-s)
= 1000/1000^2
= 1*10^-3 kg/mm*s^2
unit conversion factor= 10^-3
11) unit system (g-cm-ms)
= 0.1/10000
= 1*10^-5 g/cm*ms^2
unit conversion factor = 10^-5
12)unit system (kg-mm-ms)
= 1/1000^2
= 1*10^-6
= 1mpa
ENERGY CALCULATION

1) unit system(kg-m-s)
1 N-m = kg*m^2 /s^2
2) unit system(kg-cm-ms)
= 1*100^2 / (1000)^2
= 1*10^-2 kg*cm^2 /ms^2
unit conversion factor = 10^-2
3) unit system (kg-cm-s)
= 1*100^2 /1^2
= 1*10^4 kg*cm^2 /s^2
unit conversion factor = 10^4
4)unit system(gm-mm-ms)
= 1000*(1000)^2 /(1000)^2
= 1*10^3 gm*mm^2 /ms^2
unit conversion factor = 10^3
5) unit system (g-cm-s)
= 1000*100^2 / 1^2
= 1*10^7 g*cm^2 /s^2
unit conversion factor = 10^7
6) unit system (g-cm-us)
= 1000*(100)^2 / (1000000)^2
= 1*10^-5 g*cm^2 /us^2
unit conversion factor = 10^-5
7) unit system (g-mm-s)
= 1000*(1000)^2 / 1
= 1*10^9 g*mm^2 /s^2
unit conversion factor = 10^9
8) unit system = (ton-mm-s)
= 1*10^-3 *(1000)^2 /1^2
= 1*10^-3 ton*mm^2/s^2
unit conversion factor = 10^-3
9) unit system ( slug- ft- s)
= 1/14.5939 * (3.28)^2 /1^2
= 10.7584 slug*ft^2 /s^2
unit conversion factor -= 10.7584
10) unit system ( kg-mm-s)
= 1*1000^2 /1
= 1*10^6 kg*mm^2 /s^2
unitconversion factor = 10^6
11) unit system (g-cm-ms)
= 1000*100^2 /1000^2
= 1*10 g*cm^2 /ms^2
unit conversion factor = 10
12) unit system ( kg- mm- ms)
= 1*1000^2 / 1000^2
=1 N-m

density calculation
1) unit system (kg-m-s)
1 kg/m^3
2) unit system( kg-cm-ms)
= 1/ 100^3
= 1*10^-6 kg/cm^3
unit conversion factor 10^-6
3) unit system ( kg-cm-s)
= 1*10^-6 kg/cm^3
unit conversion factor 10^-6
4) unit system ( gm-mm-ms)
= 1000/(1000)^3
= 1*10^ -6 gm/ mm^ 3
unit conversion factir -= 10^-6
5)unit system( g-cm-s)
= 100/100^3
= 1*10^-3 g/cm^-3
unit conversion factor= 10^-3
6) unit system( g-cm-us)
= 1*10^-3 g/cm^3
unit conversion factor= 10^-3
7) unit system= (g-mm-s)
= 1000/(1000)^3
= 1*10^-6 g/mm^3
unit conversion factor = 10^-6
8) unit system (ton- mm-s)
= 1*10^-3 / (1000)^3
= 1*10^-6 ton/ mm^3
unit conversion factor 10^-6
9) unit system ( slug- ft- s)
= 1/14.5939*(3.28)^3
= 0.00194 slug/ ft^3
unit conversion factor = 0.00194
10) unit system ( kg-mm-s)
= 1/(1000)^3
= 1*10^-9 kg/ mm^3
unit cnoversion factor = 10^ -9
11) unit system ( g-cm-ms)
= 1000/(100)^3
= 1*10^-3 g/cm^3
12) unit system( kg-mm-ms)
= 1/(1000)^3
= 1*10^-9 kg/mm^3
unit conversion factior = 1*10^-9

young's modulus
1) unit system (kg-m-s)
210 Gpa = 210 *10^9 pa
= 210 *10^9 kg/m*s^2
2) unit system (kg-cm-ms)
= 210 *10^9 *1/ 100*(1000)^2
= 210*10^9 -10^ -8
= 210 *10 kg/cm*ms^2
unit conversion factor= 10
3) unit system = (kg-cm-s)
= 210 * 10^9 *1/100*1^2
= 210*10^7 kg/cm*s^2
unit conversion factor = 10^7
4)unit sysstem = (gm- mm-ms)
= 210*10^9 *1000/1000*(1000)^2
= 210*10^9 *10^-6
= 210*10^3 gm/mm(ms)^2
unit conversion factor = 10^3
5) unit system = (g-cm-s)
= 210*10^9 *1000/(100)*1^2
= 210*10^ 10 g/cm*s^2
unitconversion factor= 10^9
6) unit system = (g-cm-us)
= 210*10^9 * 1000/100*1000000
= 210*10^-12 g/cm*us^2
unit conversion factor= 10^-12
7) unit system ( g-mm-s)
= 210*10^9 * 1000/10001^2
= 210*10^9 g/mm*s^2
= 210 Gpa
8) unit system (ton-mm-s)
=210*10^9 *10^-3 / 1000*1^3
= 210*10^3 ton/mm*s^2
unit conversion factor = 10^3
9) unit system =(slug- ft-s)
= 210*10^9 *1/14.5939*(3.28)*1^2
= 4.38 *10^9 slug/ft*s^2
10) unit system (kg-mm-s)
= 210*10^9 *1/1000*1
= 210*10^6 kg/mm*s^2
11) unit system( g-cm-ms)
= 210*10^9 *1000/100*(1000)^2
= 210*10^4 g/cm*ms^2
12) unit system(kg-mm-ms)
= 210*10^9 *1/1000*(1000)^2
= 210Gpa

VELOCITY CALCULATION
1) unit system(kg-m-s)
56.53 KMPH
56.53*1000/3600 = 56.53 *5/18 m/s
2) unit system( g-cm-ms)
= 56.53*1000/3600 * 100/1000
=1.563 cm/ms
3)unit system ( kg-cm-s)
=56.53*1000/3600 * 100/1
= 1563.88 cm/s
4)unit system( gm-mm-ms)
= 56.53*1000/3600 * 1000/1000
= 56.53 KMPH
5) unitsystem( g-cm-s)
=56.53*1000/3600 *100/1
= 1563.88 cm/s
6) unit system( g-cm-us)
= 56.53*1000/3600 * 100/1000000
= 0.001570 cm/us
7)unit system = (g-mm-s)
= 56.53*1000/3600 * 1000/1
= 15.63 mm/s
8) ton-mm-s
=56.53*1000/3600 * 1000/1
=15.63 mm/s
9) slug-ft-s
=56.53*1000/3600 * 3.28/1
= 21.505 ft/s
10) kg-mm-s
= 15.63 mm/s
11) g-cm-ms
= 56.53* 1000/3600 * 100/1000
= 1.5702 cm/ms
12) kg-mm-ms
= 56.53 KMPH

For gravity calculation
1) kg-m-s
= 9.8 m/s^2
2) kg-cm-ms
= 9.8*100/1000^2
= 9.8*10^-4
unit conversion factor = 10^-4
3)kg-cm-s
=9.8*100/1^2
=9.8*10^2 cm/s^2
4) gm-mm-ms
=9.8*1000/(1000)^2
= 9.8*10^-3 mm/ms^2
unit conversion factor= 10^-3
5) g-cm-s
= 9.81*100/1
= 9.81 *10^2 cm/s^2
6) g-cm-us
= 9.81*100/(1000000)^2
= 9.8 *10^-10 cm/us^2
7) g-mm-s
= 9.8*1000/1^2
= 9.8*10^3 mm/s^2
8) ton-mm-s
= 9381*10^3 mm/s^2
9) slug-ft-s
= 9.8*3.28/1^2
=32.17 ft/s^2
10) kg-mm-s
= 9.8*10^3 mm/s^2
11) g-cm-ms
= 9.81 *100/(1000)^2
= 9.81 *10^-4 cm/ms^2
12) kg-mm-ms
= 9.8*10^-3 mm/ms^2

IN this way all the unit conversion factors are calculated in their respective unit system .
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MECHANICAL DESIGN ENGINEER

Consistency of units should be followed while performing simulations on L_S DYNA

Consistency of units should be followed while performing simulations on L_S DYNA

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