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.

7.5 Design calculation of gas spring cylinder

7.5.1 Calculation of cylinder inner diameter

The cylinder inner diameter of the gas spring should be decided according to GB/T 2348, and it is recommended to adopt the ratio of the cylinder inner diameter D₁ to the piston rod diameter d as approximate D₁/d = 2, or refer to Annex C. It can also be agreed between supplier and vendor.

7.5.2 Calculation of thickness of cylinder

The thickness of cylinder δ₁ is calculated according to formula (21), and is generally not less than 1 mm. The ratio of the cylinder outer diameter D₂ to the inner diameter D₁ is not less than 1.1. The allowable stress of the cylinder material is shown in Table D.2.

       ………………(21)

In the formula, P_max is the maximum internal pressure in the gas spring operating state, where P_max is calculated according to formula (22):

       ………………(22)

7.5.3 Verification of cylinder strength

The strength of the cylinder can be verified as described in Annex F.

7.6 The relationship between the design stroke S, guide length H and cylinder gas chamber length L₃ of the compression gas spring

When designing gas spring, the guide length should be calculated to ensure stability of the movement and a certain anti-deviated load capacity. See Figure 15 for details.

Figure 15 Schematic diagram of design stroke S, guide length H and cylinder gas chamber length L₃ of the compression gas spring

The design stroke S, guide length H and cylinder gas chamber length L₃ should meet the requirements of Table 2.

	Table 2	Unit: mm
Design stroke S	Guide length H	Gas chamber length L3
S ≤ 150	H ≥ 15	L3 ≥ S
150 < S≤ 200	H ≥ 20
200 < S≤ 250	H ≥ 25
250 < S ≤ 300	H ≥ 30
300 < S ≤ 350	H ≥ 35
350 < S ≤ 400	H ≥ 40
S > 400	H ≥ 45

7.7 Example for gas spring design calculation

See Annex G, Annex H, and Annex I for the examples of gas spring design calculation.

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).

7.3 Stroke S and extended length L

7.3.1 Schematic diagram of the overall dimensions of gas spring

See Figure 11 to Figure 14 for the basic dimensions (stroke S, extended length L, etc.) of common gas springs, including compression gas spring, lockable gas spring, chair height adjustment gas spring and stretching gas spring.

Figure 11 Schematic diagram of the dimensions of compression gas spring

Figure 12 Schematic diagram of the dimensions of lockable gas spring

NOTE  In a chair height adjustment gas spring, B refers to the outer tube length.

Figure 13 Schematic diagram of the dimensions of chair height adjustment gas spring

Figure 14  Schematic diagram of the dimensions of stretching gas spring

7.3.2 Design of the gas spring stroke S

When designing the stroke of different types of gas springs, safe stroke should be considered. For details, please refer to the 7.3.1 schematic diagram of the overall dimensions of gas spring (Figure 11 to Figure 14) and calculate according to formula (14):

 ………………(14)

For ordinary compression gas spring and stretching gas spring S₂ ≥ 5 mm; for lockable gas spring and chair height adjustment gas spring S₂ ≥ 2 mm.

7.3.3 Definition of the extended length L

According to the 7.3.1 schematic diagram of the overall dimensions of a gas spring (Figure 11 to Figure 14), the extended length L is calculated according to formula (15):

 ………………(15)

7.4 Design calculation of piston rod

7.4.1 Overview

The diameter of the gas spring piston rod should be decided according to GB/T 2348, and the recommended piston rod diameter d should be 6 mm, 8 mm, 10 mm, 12 mm, 14 mm, 20 mm, or calculated according to 7.4.2 and 7.4.3. The calculation results should refer to Annex C, or be agreed between supplier and vendor. The thickness of hollow rod δ₂ should not be less than 2 mm.

7.4.2 Calculation of solid piston rod

7.4.2.1 The diameter d of the solid piston rod of compression gas spring and chair height adjustment gas spring is generally calculated according to formula (16):

………………(16)

7.4.2.2 When the length of the solid piston rod is less than or equal to 10 times of piston rod diameter d, the diameter d is calculated according to formula (17). While the allowable stress of the gas spring piston rod is decided according to Table D.1 of Annex D:

………………(17)

7.4.2.3 The diameter d of the solid piston rod of a stretching gas spring is calculated according to formula (18):

………………(18)

7.4.3 Calculation of hollow piston rod

7.4.3.1 The piston rod of the lockable gas spring is usually a hollow piston rod, and its diameter d is generally calculated according to formula (19):

………………(19)

7.4.3.2 When the length of the hollow piston rod is less than or equal to 10 times of piston rod diameter d, the diameter d is calculated according to formula (20). While the allowable stress of the gas spring piston rod is decided according to Table D.1:

………………(20)

7.4.4 Verification of piston rod stability

The stability of the piston rod can be verified according to Annex E.

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).

7 Design calculation

7.1 Overview

The design calculation for a gas spring generally involves: force, force ratio, stroke and extended length, piston rod diameter, cylinder inner diameter and wall thickness. The design calculation for the gas spring is based on an ambient temperature of 20°C ± 2°C, and the influence of the ambient temperature should also be considered. For every 1°C change in ambient temperature, the change in nominal force F_a will be approximate 0.37%.

7.2 Force

7.2.1 Schematic diagram of force-displacement curve

The force-displacement curve is shown schematically in Figure 9.

a) Force-displacement curve for compression gas spring

b) Force-displacement curve for stretching gas spring

Figure 9 Force-displacement curve for gas spring

7.2.2 Minimum extension force F₁

For compression gas spring, lockable gas spring, and chair height adjustment gas spring, theoretical calculation of F₁ is according to formula (3). The load-based minimum extension force F₁ of a compression gas spring is calculated according to Annex A. See Annex B for calculating F_r.

………………(3)

7.2.3 Maximum extension force F₂

For compression gas spring, lockable gas spring, and chair height adjustment gas spring, F₂ is calculated according to formula (4):

………………(4)

7.2.4 Minimum compression force F₃

For compression gas spring, lockable gas spring, and chair height adjustment gas spring, F₃ is calculated according to formula (5):

………………(5)

7.2.5 Maximum compression force F₄

For compression gas spring, lockable gas spring, and chair height adjustment gas spring, F₄ is calculated according to formula (6):

………………(6)

7.2.6 Minimum tension force F₅

The minimum tension force F₅ of a stretching gas spring is calculated according to formula (7):

………………(7)

7.2.7 Maximum tension force F₆

The maximum tension force F₆ of a stretching gas spring is calculated according to formula (8):

………………(8)

7.2.8 Minimum resilience force F₇

The minimum resilience force F₇ of a stretching gas spring is calculated according to formula (9):

………………(9)

7.2.9 Maximum resilience force F₈

The maximum resilience force F₈ of a stretching gas spring is calculated according to formula (10):

………………(10)

7.2.10 Unlocking force F_K

See Figure 10 for the inner diameter of hollow piston rod of a gas spring d₀ and the effective diameter of the valve pin d₁.

Figure 10 Schematic diagram of the inner diameter of hollow piston rod d₀ and the effective diameter of the valve pin d₁

The unlocking force of valve pin F_k for lockable gas spring, chair height adjustment gas spring and lockable stretching gas spring is calculated according to formula (11):

………………(11)

7.2.11 Gas spring force ratio α

7.2.11.1 The force ratio of gas spring shall be determined by the load, and is generally calculated according to formula (12):

Or α=F_b/F_a ………………(12)

7.2.11.2 The force ratio of an ordinary stretching gas spring is calculated according to formula (13):

Or α=F_b/F_a ………………(13)

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).

6 Gas Spring Design calculation principle

At constant ambient temperature, the working process of the gas spring can be regarded as an isothermal process, which should follow the gas state formula of Boyle’s law; see formula (1) or formula (2):

PV=C………………(1)

Or

P1V1=P2V2 ………………(2)

where

P  is the pressure (the pressure inside the gas spring in this standard) in megapascals (MPa);

P₁  is the state 1 pressure in megapascals (MPa);

P₂  is the state 2 pressure in megapascals (MPa);

V   is the gas volume in cubic meters (m³);

V₁  is the state 1 gas volume in cubic meters (m³);

V₂  is the state 2 gas volume in cubic meters (m³);

C   is the constant.

NOTE  The common unit of volume is cubic millimeters (mm³).

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).