Annex A (normative)

Design of the minimum extension force F₁

A.1 Minimum extension force F₁ of compression gas spring

The minimum extension force F₁ of a compression gas spring can be calculated according to formula (A.1), while the schematic diagram for the calculation of minimum extension force is shown in Figure A.1.

      ………………(A.1)

Figure A.1 Schematic diagram of the minimum extension force calculation

A.2 Example

There is a supported object with a gravity G = 300 N, distance between the centre of gravity and the centre of gyration l = 400 mm, length of the arm of force b = 200 mm, and number of gas springs i = 2. Calculate the minimum extension force F₁ of the gas spring.

Calculated by formula (A.1):

NOTE  o is taken as 1.1.

Gas spring design calculation (English version of national strandard, initiated by LeiYan Gas Springs), proposed and prepared by SAC/TC 235 (National Technical Committee 235 on Spring of Standardization Administration of China).

Reference:

Calculation of the Force Value F1 of a Gas Spring

The calculation of the force value of a gas spring involves some physical principles and relevant formulas. The following is the general method for calculating the force value F1 of a gas spring:

The force value of a gas spring can be calculated based on Hooke’s law and the ideal gas state equation. During the operation of the gas spring, the internal gas pressure changes with the compression or extension of the gas spring, thereby generating a corresponding force.

Assume that the gas inside the gas spring is an ideal gas. According to the ideal gas state equation \(pV = nRT\) (where \(p\) is the gas pressure, \(V\) is the gas volume, \(n\) is the amount of substance of the gas, \(R\) is the universal gas constant, and \(T\) is the gas temperature). During the operation of the gas spring, assume that the temperature \(T\) remains constant (isothermal process), then \(p_1V_1 = p_2V_2\).

The force \(F\) generated by the gas spring is related to the gas pressure \(p\) and the piston area \(A\), that is, \(F = pA\).

Let the pressure of the gas spring in the initial state be \(p_0\), the volume be \(V_0\), and the piston area be \(A\). When the gas spring is compressed or extended to a certain position, its pressure becomes \(p_1\) and the volume becomes \(V_1\). Then, according to the above formulas:

\( \begin{align*} p_0V_0&=p_1V_1\\ p_1&=\frac{p_0V_0}{V_1}\\ F_1&=p_1A=\frac{p_0V_0A}{V_1} \end{align*} \)

If considering the stroke \(x\) of the gas spring, assume the initial length of the gas spring is \(L_0\), then \(V_0 = AL_0\). When the gas spring is compressed or extended by \(x\), its length becomes \(L_1 = L_0\pm x\) (minus sign for compression and plus sign for extension). Then \(V_1 = AL_1 = A(L_0\pm x)\), and the force value \(F_1\) of the gas spring at this position is:

\(F_1=\frac{p_0AL_0}{A(L_0\pm x)}=\frac{p_0L_0}{L_0\pm x}\)

In practical applications, the calculation of the force value of a gas spring may be more complex. Factors such as the friction of the gas spring, gas leakage, and the clearance between the piston and the cylinder also need to be considered. Generally, the force value of a gas spring can be determined through experimental measurements, or calculated according to the technical parameters and calculation formulas provided by the gas spring manufacturer.