Design example of lockable gas spring

Posted by: harry | on February 14, 2025

Annex H
(informative)
Design example of lockable gas spring

H.1 Example

Design a rigid lockable gas spring in the direction of extension. Requirements: The nominal force of the gas spring F_a = 350 N, nominal force F_b = 416 N, working stroke S₁ = 84 mm, and extended length L = 350 mm.

H.2 Solution

H.2.1 Design calculation of force values

H.2.1.1 Calculation of minimum extension force F₁

According to Table 1: F_a = (F₁+ F₃)/2, F_r = (F₃– F₁)/2, it can be derived that F₁ = F_a– F_r = 350 – 75 = 275 N

NOTE According to Table B.2 of Annex B, when F_a = 350 N, its maximum dynamic friction force F_r = 75 N.

H.2.1.2 Calculation of force ratio α

Calculated by formula (12):

H.2.1.3 Calculation of internal pressure of gas spring

Derived from formula (3):

MPa

NOTE The inner diameter of the hollow piston rod of the lockable gas spring d₀ = 4.3 mm; 7.4.1 requires that the thickness of the hollow piston rod δ₂ should not be less than 2 mm; a hollow piston rod diameter d = 10 mm is therefore selected for this gas spring.

H.2.1.4 Calculation of maximum extension force F₂

Calculated by formula (4):

H.2.1.5 Calculation of minimum compression force F₃

Calculated by formula (5):

H.2.1.6 Calculation of maximum compression force F₄

Calculated by formula (6):

H.2.1.7 Calculation of unlocking force F_kof valve pin

The effective diameter of the valve pin d₁ is selected as 3 mm, and the friction force f_r generated on the valve pin is set as 15 N according to Table 1. This is calculated according to formula (11):

H.2.2 Design of stroke S and extended length L

H.2.2.1 Design of stroke

Working stroke S₁ = 84 mm, based on the requirements of 7.3.2, safe stroke S₂≥ 2 mm, and gas spring safe stroke S₂ = 4 mm.

According to formula (14): S = S₁+ S₂ = 84 + 4 = 88 mm

H.2.2.2 Design of extended length L

The gas spring requires an extended length of 350 mm, and according to formula (15): cylinder length B = 210 mm, design stroke S = 88 mm, rod end length L₁ = 20 mm, cylinder end length L₂ = 32 mm.

L = L₁+ S + B + L₂ = 20 + 88 + 210 + 32 = 350 mm

According to the force ratio α = 1.19 and the working stroke S₁ = 84 mm, this can be derived from formula (12):

Gas chamber length mm

H.2.3 Design of piston rod diameter d and stability verification of piston rod

H.2.3.1 Calculation of piston rod diameter d

The piston rod material is 45# steel, and a hollow piston rod with inner diameter of 4.3 mm is chosen. Calculate according to formula (19):

d = 5.92 mm

According to 7.4.1, the thickness of hollow piston rod δ₂ should not be less than 2 mm, so a 10 mm hollow piston rod is chosen to meet the requirements.

NOTE n = 1.5.

H.2.3.2 Stability verification of piston rod

Calculate the radius of gyration for the piston rod cross-section according to formula (E.4):

Calculate the slenderness ratio according to Annex E.4:

Calculate the moment of inertia of the piston rod cross-section according to formula (E.2):

mm⁴

Calculate the permissible critical force according to formula (E.5):

Calculate the safety factor of the piston rod stability according to formula (E.7):

meets the requirements.

H.2.4 Design thickness of cylinder and verification of cylinder strength

H.2.4.1 Design of cylinder thickness

The cylinder material is 20# steel tube. Calculate according to formula (21):

In order to reduce the force ratio for easier operation, the lockable gas spring is usually chosen a larger cylinder inner diameter. This gas spring’s cylinder inner diameter D₁ = 24 mm and wall thickness δ₁ = 1.25 mm.

H.2.4.2 Verification of cylinder thickness

Calculate the radius ratio according to formula (F.1):

Calculate according to formula (F.2):

MPa

Less than the allowable stress of 20# steel tube, thus meeting the requirements.

H.2.5 Diagram of lockable gas spring

H.2.5.1 Working diagram of lockable gas spring

See Figure H.1 for the working diagram of lockable gas spring.

Unit: mm

Technical Requirements:

1. Materials: the cylinder is made of 20# steel tube, and the piston rod is 45# steel;

2. Extended length L = 350 mm ± 1.8 mm;

3. Design stroke S ≥ 86 mm;

4. Minimum extension force F₁≥ 275 N;

5. The performance of lockable gas spring such as force characteristics, lifespan and corrosion resistance shall be implemented according to GB/T 25750;

6. Manufacturing accuracy is performed in accordance with the standard tolerance value of level IT16 in GB/T 1800.1.

Figure H.1 Working diagram of lockable gas spring

H.2.5.2 Design calculation data

See Table H.1 for design calculation data

Table H.1

No.	Parameter name	Code	Numerical value	Unit	No.	Parameter name	Code	Numerical value	Unit
1	nominal force a	F_a	350	N	13	extended length	L	350	mm
2	nominal force b	F_b	416		14	rod end length	L₁	20
3	minimum extension force	F₁	275		15	cylinder end length	L₂	32
4	maximum extension force	F₂	342		16	gas chamber length	L₃	91
5	minimum compression force	F₃	425		17	cylinder length	B	210
6	maximum compression force	F₄	492		18	piston rod diameter	d	10
7	unlocking force of valve pin	F_k	47		19	inner diameter of hollow piston rod	d₀	4.3
8	force ratio	α	1.19	—	20	cylinder inner diameter	D₁	24
9	pressure within the gas spring	P	4.46	MPa	21	cylinder outer diameter	D₂	26.5
10	design stroke	S	88	mm	22	valve pin diameter	d₁	3
11	working stroke	S₁	84		23	thickness of cylinder	δ₁	1.25
12	safe stroke	S₂	4		—	—	—	—	—