Annex I
(informative)
Design example of ordinary tension gas spring

I.1 Example

Design requirements of ordinary tension gas spring: using horizontally, the fully extended length is 334 mm, the working stroke is 55 mm, the force ratio α is 1.52, the minimum tension force is 147 N, and the piston rod diameter is 8 mm. See Figure I.1 for the design example of tension (stretching) gas spring.

Figure I.1 Design example of tension gas spring

I.2 Solution

I.2.1 Design of ordinary tension gas spring stroke, cylinder length and gas chamber length

I.2.1.1 Design of stroke

According to 7.3.2, the general tension gas spring safe stroke S₂ ≥ 5 mm, the gas spring safe stroke is set to 5 mm, and the design stroke S = S₁ + S₂ = 55 + 5 = 60 mm.

I.2.1.2 Design of cylinder length L

Calculate the cylinder length according to formula (15):

B = L- S – L₁ – L₂ = 334 – 20 – 60 – 20 = 234 mm

NOTE  The rod end length of the gas spring L₁ = 20 mm, and the cylinder end length of the gas spring L₂ = 20 mm.

I.2.1.3 Design of gas chamber length

Derived from formula (I3):

mm

I.2.2 Design of cylinder inner diameter D₁

According to 7.5.1 and Annex C, when the piston rod diameter d = 8 mm, the cylinder inner diameter D₁ is 16 mm.

I.2.3 Design calculation of gas spring force

L.2.3.1 Design of minimum tension force F₅

According to I.1, the minimum tension force F₅ = 147 N.

I.2.3.2 Calculation of internal pressure in gas spring

Derived from formula (7):

MPa

According to Table B.1 of Annex B, the dynamic friction force of the gas spring F_r = 20 N.

I.2.3.3 Calculation of maximum tension force F₆

Calculated by formula (8):

N

I.2.3.4 Calculation of minimum resilience force F₇

Calculated by formula (9):

N

I.2.3.5 Calculation of maximum resilience force F₈

Calculated by formula (10):

N

I.2.3.6 Calculation of nominal force a and nominal force b

Calculate according to Table 1:

N

N

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

I.2.4.1 Calculation of cylinder thickness

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

mm

According to 7.5.2, a cylinder thickness of δ₁ = 1 mm is selected for this gas spring.

I.2.4.2 Verification of cylinder strength

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

Calculated by formula (F.2):

MPa

This is less than the allowable stress 130 MPa for 20# steel tube, in line with the requirements.

I.2.5 Diagram of tension gas spring

L.2.5.1 Working diagram of tension gas spring

See Figure I.2 for the working diagram of tension (stretching) gas spring.

Unit: mm

Technical Requirements:

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

2. Extended length L = 334 mm ± 1.8 mm;

3.Design stroke S ≥ 60 mm;

4. Minimum tension force F₅ ≥ 147 N;

5. Manufacturing accuracy corresponds to the standard tolerance value of level IT16 in GB/T 1800.1.

Figure I.2 Working diagram of stretching gas spring

I.2.5.2 Design calculation data

The design calculation data are shown in Table I.1.

Table I.1

No.	Parameter name	Code	Numerical value	Unit	No.	Parameter name	Code	Numerical value	Unit
1	nominal force a	Fa	127	N	11	safe stroke	S2	5	mm
2	nominal force b	Fb	192.5		12	extended length	L	334
3	minimum tension force	F5	147		13	rod end length	L1	20
4	maximum tension force	F6	212		14	cylinder end length	L2	20
5	minimum resilience force	F7	107		15	gas chamber length	L3	161
6	maximum resilience force	F8	173		16	cylinder length	B	234
7	force ratio	α	1.52		17	piston rod diameter	d	8	mm
8	pressure within the gas spring	P	0.84	MPa	18	cylinder inner diameter	D1	16
9	design stroke	S	60	mm	19	cylinder outer diameter	D2	18
10	working stroke	S1	55		20	thickness of cylinder	δ1	1

Bibliography

[1] Cen JunJian. (2008). Non-standard Design Manual (Volume 1). National Defence Industry Press. 

[2] Authors panel of Gas Spring Design Calculation. (1987). Mechanical Design Manual (2nd Edition). Chemical Industry Press.

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).

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):

N

H.2.1.5 Calculation of minimum compression force F₃

Calculated by formula (5):

N

H.2.1.6 Calculation of maximum compression force F₄

Calculated by formula (6):

N

H.2.1.7 Calculation of unlocking force F_k of 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):

N

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):

mm

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):

mm

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):

mm

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	Fa	350	N	13	extended length	L	350	mm
2	nominal force b	Fb	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	Fk	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		—	—	—	—	—

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).

Annex F
(normative)
Verification of cylinder strength

F.1 Radius ratio

The radius ratio is calculated according to formula (F.1):

       ………………(F.1)

F.2 Cylinder strength of gas spring

The cylinder strength of a gas spring can be verified according to formula (F.2):

         ………………(F.2)

Annex G

(informative)

Design example of compression gas spring

G.1 Example

As shown in Figure G.1, it is known that the gravity (G) of a hatch door is 392 N, its height is 800 mm, and the opening angle is required to be 110°. Please design and calculate a compression gas spring that meets these requirements.

Unit: mm

Figure G.1 Design example for compression gas spring

G.2 Solution

G.2.1 Design calculation of force values

G.2.1.1 Calculation of minimum extension force F₁

Calculated by formula (A.1):

N

NOTE  In Figure G.1, it is determined that l is 400 mm, b is 162 mm, o is l.1, and i is 2.

G.2.1.2 Calculation of maximum extension force F₂

Derived from formula (3) and formula (4):

N

NOTE  According to Table B.1 of Annex B, the maximum dynamic friction force F_r is 60 N when F₁ = 532 N.

Under normal circumstances, the force ratio of the compression gas spring is not more than 1.5, and the current force ratio is set to 1.22.

G.2.1.3 Calculation of minimum compression force F₃

Derived from formula (3) and formula (5):

N

G.2.1.4 Calculation of maximum compression force F₄

Derived from formula (3) and formula (6):

N

G.2.1.5 Calculation of nominal forces a and b

Calculate the nominal forces F_a and F_b according to Table 1:

F_a=（F₁+F₃）/2=（532+652）/2=592 N

F_b=（F₂+F₄）/2=（662+782）/2=722 N

G.2.2 Design calculation of stroke and extended length

G.2.2.1 Design calculation of stroke

According to Figure G.1, the working stroke S₁ = 620 – 422 = 198 mm.

According to 7.3.2, the safe stroke of general compression gas spring is S₂ ≥ 5 mm. The safe stroke in the example is set to 12 mm, therefore the stroke design S = S₁ + S₂ = 198 + 12 = 210 mm.

G.2.2.2 Design calculation of extended length and cylinder length

According to Figure G.1, the extended length of this gas spring L = 620 mm.

Calculate the cylinder length B according to formula (15):

B = L – L₁ – L₂ – S = 620 – 20 – 20 – 210 = 370 mm

NOTE  The rod end length of the gas spring L1 = 20 mm, and the cylinder end length L2 = 20 mm.

G.2.2.3 Guide length of gas spring

To ensure stability of the movement and a certain anti-deviated load capacity, the guide length H should be formulated according to the stroke S, while meeting the provisions of Table 2, i.e. H ≥ 25 mm. In this example, the guide length of the compression gas spring is H = 38 mm, meeting the requirements.

G.2.3 Design calculation of piston rod

The piston rod material is 45# steel, and the piston rod diameter d is calculated according to formula (16):

When n = 1.4, d²  = 64.36  d = 8.02 mm

When n = 2,   d² = 76.92  d = 8.77 mm

According to the recommendation of 7.4.1 and the calculation above, upon comprehensive consideration, a piston rod diameter of d = 10 mm is selected.

G.2.4 Design calculation of cylinder

G.2.4.1 Design of cylinder inner diameter D₁

According to 7.5.1 and Annex C, when the piston rod diameter d = 10 mm, the cylinder inner diameter D₁ is 20 mm.

G.2.4.2 Calculation of internal pressure of gas spring

Derived from formula (3):

MPa

G.2.4.3 Calculation of cylinder thickness

The cylinder material is 20# steel tube. The allowable stress of the material is shown in Table D.2 of Annex D, and calculation is according to formula (21):

mm

The cylinder thickness can be δ₁ ≥ 1 mm.

G.2.5 Calculation of the force ratio of gas spring

Calculated by formula (12):

This is basically the same as the set force ratio α = 1.22.

NOTE  L₃ = 370-35-50 = 285 mm, where 50 mm is the length of the axial space occupied by the parts in the cylinder, and 35 mm is the length of the axial space occupied by the damping oil.

G.2.6 Stability verification of piston rod

Calculate radius of gyration for the piston rod’s cross-section, according to formula (E.3):

mm

Calculate slenderness ratio according to Annex E.4:

Calculate moment of inertia of the piston rod’s cross-section, according to formula (E.1):

mm⁴

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

 N

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

 consistent with the requirements.

G.2.7 Strength verification of cylinder thickness

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

Verify the cylinder strength according to formula (F.2):

MPa

Less than the allowable stress of 130 MPa for 20# steel tube, in line with the requirements.

G.2.8 Drawing diagrams for compression gas spring

G.2.8.1 Working diagram of compression gas spring

The working diagram of compression gas spring is shown in Figure G.2.

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 = 620 mm ± 1.8 mm;

3. Design stroke S ≥ 203 mm;

4. F₁ ≥ 532N;

5. Performance of the compression gas spring, including force characteristics, lifespan and corrosion resistance, shall be implemented according to GB/T 25751;

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

Figure G.2 Working diagram of compression gas spring

G.2.8.2 Design calculation data

The design calculation data is shown in Table G.1.

Table G.1

No.	Parameter name	Code	Numerical value	Unit	No.	Parameter name	Code	Numerical value	Unit
1	nominal force a	Fa	592	N	12	extended length	L	620	mm
2	nominal force b	Fb	722		13	rod end length	L1	20
3	minimum extension force	F1	532		14	cylinder end length	L2	20
4	maximum extension force	F2	662		15	gas chamber length	L3	285
5	minimum compression force	F3	652		16	guide length	H	38
6	maximum compression force	F4	782		17	cylinder length	B	370
7	force ratio	α	1.21		18	piston rod diameter	d	10	mm
8	pressure within the gas spring	P	7.54	MPa	19	cylinder inner diameter	D1	20
9	design stroke	S	210	mm	20	cylinder outer diameter	D2	22
10	working stroke	S1	198		21	thickness of cylinder	δ1	1
11	safe stroke	S2	12		—	—	—	—	—

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).

Annex E
(normative)
Verification of piston rod stability

E.1 Calculation of moment of inertia for piston rod cross-section

The moment of inertia of a solid piston rod’s cross-section is calculated according to formula (E.1):

      ………………(E.1)

The moment of inertia of a hollow piston rod’s cross-section is calculated according to formula (E.2):

     ………………(E.2)

E.2 Calculation of the radius of gyration of a piston rod cross-section

The radius of gyration of a solid piston rod’s cross-section is calculated according to formula (E.3):

      ………………(E.3)

The radius of gyration of a hollow piston rod’s cross-section is calculated according to formula (E.4):

      ………………(E.4)

E.3 Design of installation method and installation coefficient m

The installation coefficient m is determined according to the installation method described in Table E.1.

Table E.1

Installation method	Diagram	Installation coefficient m	Description
Hinge – hinge		1	Suitable for most gas springs
Fixed – free		1/4	Suitable for chair height adjustment gas spring
Fixed – hinge		2	Suitable for special situations

E.4 Calculation of permissible critical force

When the slenderness ratio is , the permissible critical force F_L is calculated according to formula (E.5):

   ………………(E.5)

When the slenderness ratio is , the permissible critical force F_L is calculated according to formula (E.6):

   ………………(E.6)

E.5 Verification of piston rod stability

The safety factor n of a piston rod stability is calculated according to formula (E.7):

       ………………(E.7)

The stability check of the gas spring piston rod is mainly to ensure that during the operation of the gas spring, the piston rod will not experience instability, thus guaranteeing the normal operation and safety of the gas spring. The above are the general steps for the stability check of the gas spring piston rod. In practical applications, factors such as the working environment of the gas spring, dynamic loads, and impact loads on the stability of the piston rod also need to be considered. If necessary, a safety factor can be introduced for a more accurate check.

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).

Annex B

(informative)

Selection range for dynamic friction force F_r

B.1 Dynamic friction force for compression gas spring and stretching gas spring

See Table B.1 for the selection range of dynamic friction force of compression gas spring and stretching gas spring.

	Table B.1		Unit: N
Specified force		Maximum dynamic friction force
≤100		25
>100 — 200		30
>200 — 400		40
>400 — 600		60
>600 — 800		80
>800 — 1000		100
>1000 — 1200		130
>1200		150

B.2 Dynamic friction force of lockable gas spring

See Table B.2 for the selection range of the dynamic friction force of lockable gas spring.

	Table B.2		Unit: N
Specified force		Maximum dynamic friction force
≤200		50
>200 — 400		75
>400 — 600		90
>600 — 800		110
>800 — 1000		130
>1000		150

B.3 Dynamic friction force of chair height adjustment gas spring

See Table B.3 for the selection range of the dynamic friction force of chair height adjustment gas spring.

	Table B.3		Unit: N
Specified force		Maximum dynamic friction force
≤350		60
>350 — 650		80

Annex C

(informative)

Selection range of piston rod diameter, cylinder inner diameter and nominal force of gas spring

See Table C.1 for the piston rod diameter, cylinder inner diameter, nominal force and design stoke of gas spring.

Table C.1

No.	Piston rod diametermm	Recommended nominal force FaN	Recommended design strokemm	Recommended cylinder inner diametermm	Recommended maximum pressure within the gas springMPa
1	6	50 — 300	≤ 150	12 — 14	≤ 13
2	8	200 — 550	≤ 200	16 — 20
3	10	300 — 850	≤ 300	20 — 24
4	12	450 — 1200	≤ 400	22 — 26
5	14	600 — 1600	≤ 450	24 — 28
6	16	800 — 2100	≤ 500	28 — 32
7	18	1000 — 2700	≤ 600	32 — 36
8	20	1250 — 3300	≤ 800	36 — 40

Annex D

(informative)

Allowable stress of gas spring piston rod and cylinder

D.1 Allowable stress of piston rod

See Table D.1 for the allowable stress of piston rod.

	Table D.1		Unit: MPa
Material		Allowable stress
35		125
45		145

D.2 Allowable stress of cylinder

See Table D.2 for the allowable stress of cylinder.

	Table D.2		Unit: MPa
Material		Allowable stress
10		110
20		130

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).