Calculatig the iitial force The iitial force of the gas sprig ca be calculated as the sealed area of the pisto rod or the pisto (depedig o desig) multiplied by the pressure iside the gas sprig. The larger the effective cross sectioal area of the pisto rod or the pisto, the more powerful the gas sprig will be. This explais why a Bore Sealed sprig, like the CU sprig is more powerful tha a Pisto Rod Sealed sprig, like the TU sprig with the same outer body diameter. Derived from the iformatio above the gas sprig force ca be writte as: F gas sprig (N) = p d seal 2 π 40 p (bar) = Charge Pressure d seal (mm) = Dyamic Seal Diameter Example I A TU 1500 sprig (see page 2.6/24) should be modified to give a iitial force of 12 000 N (at 20 C). = p stadard F required F required = 12 000 N I the table for the TU 1500 the followig values ca be foud: p stadard tadard tadard = 150 bar The chargig pressure that should be used will the be: = 150 12 000 = 120 bar Adjustig the iitial force As see from formula the force from ay give gas sprig ca be chaged by chagig the gas pressure. I cases where a o stadard iitial force is required the followig formula should be applied. = p stadard F required tadard F required (N) = The required iitial force tadard (N) = Stadard iitial force (at p stadard ) p stadard (bar) = Stadard chargig pressure A gas pressure of 120 bar will give the desired iitial force of 12 000 N. The stadard iitial force, tadard ad the stadard chargig pressure at 20 C are give for each model i the catalogue. Isothermic force icrease As the gas sprig is compressed the gas pressure iside the sprig will rise resultig i a icreased gas sprig force. The gas pressure icrease (ad force icrease) is determied by the followig gas laws. The ideal gas law p V = R T p (bar) = gas pressure V (l) = gas volume (mole) = molecular quatity R (Nm/ K) = gas costat = 8.314 T ( K) = temperature
For a closed system, as the gas sprig, where the temperature is kept costat (isothermic process) this formula ca be simplified to: p V = costat (Boyles law) Calculatig the gas pressure at a certai poit of the stroke (S) ca be performed i the followig way: p o V o = p s V s p o (bar) V o (l) p s (bar) V s (l) = iitial pressure = iitial volume = pressure at stroke S = volume at stroke S By combiig this with the followig ca be derived to calculate the force at ay positio of the stroke. - 1- (N) = force at the used stroke S F iit,actual (N) = iitial force at curret chargig pressure (mm) = used stroke (mm) = omial stroke for the sprig (N) = omial iitial force of the sprig F ed (N) = force at full omial stroke, ad F ed,om are give for each model i the catalogue. If the force has ot bee chaged (the charge pressure has ot bee modified) will be the same as the which is the value give i the catalogue. Note! All ed forces, stated i the catalogue are the isothermic ed forces. Example II What is the sprig force of a TU 1500 100 whe compressig the sprig 80 mm? = 80 mm The table for the TU 1500 (see page 2.6/24) will give the followig values: = 100 mm = 23 000 N = (80 mm) = 20 800 N If the temperature of the gas sprig is kept costat, (isothermic process), the sprig will give a force of 20 800 N whe compressed 80 mm. Polytropic force icrease For most applicatios the temperature iside the gas sprig will ot stay costat durig the stroke. For these applicatios the followig formula should be used to calculate the true force icrease (polytropic process). - 1-100 100-80 1- - 23 000 1- Where is called the polytropic expoet. Depedig o how fast the gas sprig is compressed ad the iitial gas pressure, the -value will be betwee 1 ad 1.55. For a ormal applicatio i a press tool ad a chargig pressure of 150 bar, a value of 1.4 ca be used.
S, om ad F ed,om are give for each model i the catalogue. If the force has ot bee chaged (the charge pressure has ot bee modified) will be the same as the which is the value give i the catalogue. Note! All ed forces, stated i the catalogue are the isothermic ed forces. Example III What is the polytropic ed force of a TU 1500-100, whe usig a stroke of 80 mm i a ormal press applicatio?, polytropic - 1- Iitial force depedig o temperature The temperature of the itroge gas affects the pressure i, ad the force of, the gas sprig. The forces give i the catalogue are based o a temperature of 20 C. Usig the same basic as before the pressure ad force at other temperatures ca be calculated as follows: p 0 p 1 = ( K) = Referece temperature ( K) = Gas sprig temperature F ed,om = 100 mm = 80 mm = 23 000 N = 1.4 ( ormal press applicatio ) p 1 = p 0 As the force is proportioal to the pressure, it ca also be writte as:, polytropic (80 mm) =, polytropic (80 mm) = 23 700 N 100 100-80 1-23 000 1.4 = F 0 Example IV A gas sprig with a iitial force of 15000 N at 20 C is used i such a way that the gas sprig temperature is icreased to 60 C. What iitial force will the sprig have at 60 C? Solutio usig = F 0 F 0 = 273 + 60 C = 333 K = 273 + 20 C = 293 K = 333 = 17 000 N 293
The Safer Choice 1 ABOUT THE COMPANY 2 GAS SPRINGS INCLUDING STANDARD MOUNTS 3 SPECIAL MOUNTS 4 GAS LINK SYSTEM 5 PROBLEM SOLVERS AND ACCESSORIES 6 LIFTERS 7 MACHINE AND VEHICLES 8 SERVICE AND MAINTENANCE 9 PIERCING AND FORMING UNITS / CAMS 10 CONTROLLABLE GAS SPRINGS For more iformatio see our website www.kaller.com