What is Multi Stage Hydraulic Cylinder and Why Do We Use Them?

Multistage hydraulic cylinders have become prevalent in various industries, including cranes, trucks, and factories in Fig. 1. In contrast to traditional two-stage hydraulic cylinders, these multistage variants feature an expanded working space, which can lead to substantial bending. To ensure a stable operating environment, it is crucial to consider this bending behaviour during the design process of the cylinder.

Link to EOOE

To calculate the bending behaviour of multistage hydraulic cylinders, the buckling loading should be less than the critical load to avoid a large deflection. Ramasamy and Basha simplified multistage cylinders into one bar with varying cross-sections to estimate the critical load and researched the internal clearance effect of the buckling of multistage cylinders1, which also affects the vibration problem of hydraulic cylinders2. Yoshihiko and Otomo proposed a new concept of partial effective slenderness ratio to advance the buckling calculation3 and provided a buckling test for a six-meter-long telescopic cylinder for comparison with the theoretical mode considering the effective slenderness ratio; the deflection results agreed well with the theoretical mode under the buckling load4. The composite material for a multistage hydraulic cylinder can advance the critical load valve5. Uzny suggested that a high mounting stiffness of the end-rod eye parts can advance the critical load valve6. However, significant buckling behaviour of multistage hydraulic cylinder occurs because the primary load forces are divided into the horizontal and vertical directions. The horizontal load, which is influenced by the critical buckling load, significantly increases the deflection. Conversely, when this factor is unaffected, its impact is minimal. The vertical load is affected by the multi-stage hydraulic cylinder mass, which commonly depends on task requirements, and protector boxes may be used to maintain the smooth surface of the cylinder in working environments without dust and chips, such as cranes7,8,9. The use of protector boxes leads to significant deflections. However, the large buckling behaviour resulting from the mass of the cylinder may lead to a sealing problem which can cause multistage cylinder system failure even if the value of the horizontal buckling load does not exceed the critical load.

Since the introduction of the first elastomer in , it has been widely applied in hydraulic systems10. Selecting an appropriate elastomer seal is crucial; it ensures optimal sealing efficiency for a multistage cylinder while enhancing the overall lifespan of the hydraulic system. The performance of these seals, particularly in terms of contact pressure and their capability to regain their original form, is significantly influenced by their cross-sectional configuration, particularly when subjected to internal working pressures11. In assessing the theoretical leakage criterion, the O-ring seal design stipulates a compression of over 20% from its uncompressed state, which is essential for generating the required sealing force and contact pressure12. Nikas et al. proposed that the contact pressure of a rectangular ring seal should exceed the internal working pressure to prevent leakage13. This leakage criterion is also applicable to reciprocating metal seals14,15. To achieve an optimal sealing performance, it is crucial to select a seal with an appropriate cross-sectional shape.

This study investigated the deflection calculations for a horizontally oriented five-stage hydraulic cylinder operating at its maximum position, confirming that significant deflection adversely impacts the sealing performance. The accuracy of the employed singularity function was validated through finite element analysis. To minimise the deflection in the hydraulic cylinder, the mounting orientations of the rod eye were adjusted, and various installation strategies for the protector box were analysed based on the ANSYS finite element analysis outcomes. Furthermore, sealing performance tests were conducted for different types of seals used in the hydraulic cylinder. The results demonstrated that the U-lip seal offered superior sealing performance compared to the O-rings.

Figure 2 illustrates the structure of a multi-stage hydraulic cylinder, highlighting the main components and their respective positions:

1. 1.

   Housing: The diagram shows four main housing sections, each enclosing a piston cylinder. These are integral parts of the hydraulic system structure, securing the cylinders in place.

2. 2.

   Cylinder: Each piston cylinder is mounted within its corresponding housing. The illustration includes five piston cylinders, indicating this is a five-stage hydraulic system. Multi-stage designs are commonly used in machinery and industrial applications for enhanced output force or stroke.

3. 3.

   Cap: Each piston cylinder is sealed at one end with an end cap, which helps maintain the hydraulic oil’s seal and pressure and prevents contamination.

4. 4.

   Hydraulic Seal: Hydraulic seals are placed at each junction and between the pistons and cylinder walls to prevent hydraulic oil leakage, ensuring the hydraulic system’s efficient operation and responsiveness.

The multistage hydraulic cylinder in this study was modelled as a five-stage cylinder with each end simply supported. Gravity was applied at a position where a vertical force is typically applied using hinge mounting as shown in Fig. 3.

When the cylinder is extended to its maximum working distance, the model resembles a five-stage column with varying cross-sections, as illustrated in Fig. 3 (refer to Appendix). In this simplified five-stage cylinder model, the identified reaction forces are denoted as \(\:{\text{R}}_{1}\)and \(\:{\text{R}}_{2}\). By employing singularity functions and focusing on point B, while disregarding \(\:{\text{R}}_{2}\), the moment equation can be expressed as follows:

$$\begin{aligned}{M}_{B}&={R}_{1}x-mg{\langle x-{x}_{\text{c}enter}\rangle}^{1}\:{+q}_{1}{\langle x-{x}_{1}\rangle}^{0}+{q}_{2}{\langle x-{x}_{2}\rangle}^{0}\\ & \quad +{q}_{3}{\langle x-{x}_{3}\rangle}^{0}+{q}_{4}{\langle x-{x}_{4}\rangle}^{0}+{p}_{1}{\langle x-{x}_{1}\rangle}^{1}+{p}_{2}{\langle x-{x}_{2}\rangle}^{1}\\ & \quad +{p}_{3}{\langle x-{x}_{3}\rangle}^{1}+{p}_{4}{\langle x-{x}_{center}\rangle}^{1}+{p}_{5}{\langle x-{x}_{4}\rangle}^{1}\end{aligned}$$ (1)

Brackets are replaced with parentheses when the arguments are positive at the parallel position. The second area moment for each step of the cylinder is expressed as follows:

$$\:I=\frac{\pi\:}{64}{\left({\varnothing}\right)}^{4}\:$$ (2)

A plot of \(\:M/I\) is shown in Fig. 3. The singularity function step (\(\:bc,\:de,fg\:and\:ij\)) change are shown in Eq. 3.

$$\begin{gathered} {q_1}={\left( {\frac{M}{I}} \right)_b} - {\left( {\frac{M}{I}} \right)_c},~{q_2}={\left( {\frac{M}{I}} \right)_e} - {\left( {\frac{M}{I}} \right)_d}~ \hfill \\ {q_3}={\left( {\frac{M}{I}} \right)_g} - {\left( {\frac{M}{I}} \right)_f},~{q_4}={\left( {\frac{M}{I}} \right)_j} - {\left( {\frac{M}{I}} \right)_{i~~}} \hfill \\ \end{gathered}$$ (3)

The singularity function slopes for \(\:ab\) and \(\:cd\), \(\:cd\) and \(\:ef\), \(\:ef\) and \(\:gh\), \(\:gh\) and \(\:hi\), and \(\:hi\) and \(\:jk\) change by Eq. 4.

$$\begin{gathered} {p_1}=\frac{{{M_2} - {M_1}}}{{{I_2}\left( {{x_2} - {x_1}} \right)}} - \frac{{{M_1} - {M_0}}}{{{I_1}\left( {{x_1} - 0} \right)}}~ \hfill \\ {p_2}=\frac{{{M_3} - {M_2}}}{{{I_3}\left( {{x_3} - {x_2}} \right)}} - \frac{{{M_2} - {M_1}}}{{{I_2}\left( {{x_2} - {x_1}} \right)}}~~ \hfill \\ {p_3}=\frac{{{M_{center}} - {M_3}}}{{{I_4}\left( {{x_{center}} - {x_3}} \right)}} - \frac{{{M_3} - {M_2}}}{{{I_3}\left( {{x_3} - {x_2}} \right)}} \hfill \\ ~{p_4}=\frac{{{M_4} - {M_{center}}}}{{{I_4}\left( {{x_4} - {x_{center}}} \right)}} - \frac{{{M_{center}} - {M_3}}}{{{I_3}\left( {{x_{center}} - {x_3}} \right)}} \hfill \\ {p_5}=\frac{{{M_5} - {M_4}}}{{{I_5}\left( {{x_5} - {x_4}} \right)}} - \frac{{{M_4} - {M_3}}}{{{I_4}\left( {{x_4} - {x_{center}}} \right)}} \hfill \\ \end{gathered}$$ (4)

Substituting the singularity function steps in Eq. (3) and slopes from Eq. (4) into Eq. (1), the total moment equation for a five-section stage cylinder is given as follows:

$$\begin{aligned}\frac{{M}_{B}}{I}&=\frac{{R}_{1}}{{I}_{1}}x-\frac{mg}{{I}_{4}}{\langle x-{x}_{center}\rangle}^{1}+{q}_{1}{\langle x-{x}_{1}\rangle}^{0}+{q}_{2}{\langle x-{x}_{2}\rangle}^{0}\\ & \quad +{q}_{3}{\langle x-{x}_{3}\rangle}^{0}+{q}_{4}{\langle x-{x}_{4}\rangle}^{0}+{p}_{1}{\langle x-{x}_{1}\rangle}^{1}+{p}_{2}{\langle x-{x}_{2}\rangle}^{1}\\ & \quad +{p}_{3}{\langle x-{x}_{3}\rangle}^{1}+{p}_{4}{\langle x-{x}_{center}\rangle}^{1}+{p}_{5}{\langle x-{x}_{4}\rangle}^{1}\end{aligned}$$ (5)

The Eq. (5) has a relationship with deflection function as follows:

$$\:\frac{{M}_{B}}{I}=E\frac{{d}^{2}y}{{dx}^{2}}\:$$ (6)

When the integration of moment equation Eq. (6) two twice, the deflection equation is established using singularity functions. The \(\:E\) is the Young’s Modulus and the\(\:\:C1\) and \(\:C2\) are constants, as illustrated in Eq. (7).

$$\begin{aligned}Ey&=\frac{{R}_{1}}{6\:{I}_{1}}{x}^{3}-\frac{mg}{6\:{I}_{4}}{\langle x-{x}_{center}\rangle}^{3}+{q}_{1}{\langle x-{x}_{1}\rangle}^{2}+{q}_{2}{\langle x-{x}_{2}\rangle}^{2}\\ & \quad +\:{q}_{3}{\langle x-{x}_{3}\rangle}^{2}+{q}_{4}{\langle x-{x}_{4}\rangle}^{2}+\frac{1}{2}{p}_{1}{\langle x-{x}_{1}\rangle}^{3}+{\frac{1}{2}p}_{2}{\langle x-{x}_{2}\rangle}^{3\:}\\ & \quad +\frac{1}{2}{p}_{3}{\langle x-{x}_{3}\rangle}^{3}+\frac{1}{2}{p}_{4}{\langle x-{x}_{center}\rangle}^{3}+\frac{1}{2}{p}_{1}{\langle x-{x}_{4}\rangle}^{3}+C1x\:+C2\end{aligned}$$ (7)

At x = 0, y = 0. This gives \(\:C2\) = 0, and the singularity functions do not exist until the argument is positive. At x =\(\:{x}_{5}\), y = 0, and \(\:C1\) is as follows:

$$\begin{aligned}C1&=\frac{mg}{6{\:x}_{5}\:{I}_{4}}{\langle {\:x}_{5}-{x}_{center}\rangle}^{3}-\frac{{R}_{1}}{6\:{\:x}_{5}\:{I}_{1}}{{\:x}_{5}}^{3}\\ & \quad -\frac{1}{2}{q}_{1}{\langle {x}_{5}-{x}_{1}\rangle}^{2} -\frac{1}{2}{q}_{2}{\langle {x}_{5}-{x}_{2}\rangle}^{2}-\frac{1}{2}{q}_{3}{\langle {x}_{5}-{x}_{3}\rangle}^{2}-\frac{1}{2}{q}_{4}{\langle {x}_{5}-{x}_{4}\rangle}^{2}\\ & \quad-\frac{1}{6}{p}_{1}{\langle {x}_{5}-{x}_{1}\rangle}^{3}+{\frac{1}{6}p}_{2}{\langle {x}_{5}-{x}_{2}\rangle}^{3}+\frac{1}{6}{p}_{3}{\langle {x}_{5}-{x}_{3}\rangle}^{3}\:+\frac{1}{6}{p}_{4}{\langle {x}_{5}-{x}_{center}\rangle}^{3}+\frac{1}{6}{p}_{5}{\langle {x}_{5}-{x}_{4}\rangle}^{3}\end{aligned}$$ (8)

The deflection values of the five-stage cylinder, along with their respective scope distances, were determined using Eqs. (8)–(13) follow equations:

$$~{y_1}=\frac{1}{E}\left( {\frac{{{R_1}}}{{6{I_1}}}{x^3}+C1x} \right) \quad\,\,0 \leqslant x \leqslant {x_1}$$ (9) $${y_2}=\frac{1}{E}~(\frac{{{R_1}}}{{6{I_1}}}{x^3}+C1x+\frac{1}{2}{q_1}{\left( {x - {x_1}} \right)^2}+\frac{1}{6}{p_1}{\left( {x - {x_1}} \right)^3}{\text{~~~~~~}}{x_1} \leqslant x \leqslant {x_2}$$ (10) $$\begin{aligned} y_{3} = \frac{1}{E}~(\frac{{R_{1} }}{{6I_{1} }}x^{3} + C1x + \frac{1}{2}q_{1} \left( {x - x_{1} } \right)^{2} + \frac{1}{6}p_{1} \left( {x - x_{1} } \right)^{3} \\ \quad \quad + \frac{1}{2}q_{2} \left( {x - x_{2} } \right)^{2} + \frac{1}{6}p_{2} \left( {x - x_{2} } \right)^{3} ){\text{~~~~~~~~}}x_{2} \le x \le x_{3} \\ \end{aligned}$$ (11) $$\begin{gathered} {y_4}=\frac{1}{E}~(\frac{{{R_1}}}{{6{I_1}}}{x^3}+C1x+\frac{1}{2}{q_1}{\left( {x - {x_1}} \right)^2}+\frac{1}{6}{p_1}{\left( {x - {x_1}} \right)^3}+\frac{1}{2}{q_2}{\left( {x - {x_2}} \right)^2} \hfill \\ \quad \quad +\frac{1}{6}{p_2}{\left( {x - {x_2}} \right)^3}+\frac{1}{2}{q_3}{\left( {x - {x_3}} \right)^2}+\frac{1}{6}{p_3}{\left( {x - {x_3}} \right)^3})~~~~~~{x_3} \leqslant x \leqslant {x_{{\text{center~~~}}}} \hfill \\ \end{gathered}$$ (12) $$\begin{gathered} {y_5}=\frac{1}{E}~(\frac{{{R_1}}}{{6{I_1}}}{x^3}+C1x+\frac{1}{2}{q_1}{\left( {x - {x_1}} \right)^2}+\frac{1}{6}{p_1}{\left( {x - {x_1}} \right)^3}+\frac{1}{2}{q_2}{\left( {x - {x_2}} \right)^2} \hfill \\ \quad \quad +\frac{1}{6}{p_2}{\left( {x - {x_2}} \right)^3}+\frac{1}{2}{q_3}{\left( {x - {x_3}} \right)^2}+\frac{1}{6}{p_3}{\left( {x - {x_3}} \right)^3}+\frac{1}{6}{p_4}{\left( {x - {x_{center}}} \right)^3} \hfill \\ ~\quad \quad - \frac{{mg}}{{6~{I_4}}}{\left( {x - {x_{center}}} \right)^3})~~~~~~{x_{{\text{center}}}} \leqslant x \leqslant {x_4} \hfill \\ \end{gathered}$$ (13) $$\begin{gathered} {y_6}=\frac{1}{E}~(\frac{{{R_1}}}{{6{I_1}}}{x^3}+C1x+\frac{1}{2}{q_1}{\left( {x - {x_1}} \right)^2}+\frac{1}{6}{p_1}{\left( {x - {x_1}} \right)^3}+\frac{1}{2}{q_2}{\left( {x - {x_2}} \right)^2} \hfill \\ \quad \quad +\frac{1}{6}{p_2}{\left( {x - {x_2}} \right)^3}+\frac{1}{2}{q_3}{\left( {x - {x_3}} \right)^2}+\frac{1}{6}{p_3}{\left( {x - {x_3}} \right)^3}+\frac{1}{6}{p_4}{\left( {x - {x_{center}}} \right)^3} \hfill \\ \quad \quad +\frac{1}{2}{q_4}{\left( {x - {x_4}} \right)^2} - \frac{{mg}}{{6~{I_4}}}{\left( {x - {x_{center}}} \right)^3}+\frac{1}{6}{p_5}{\left( {x - {x_4}} \right)^3})~~~~~~{x_4} \leqslant x \leqslant {x_5} \hfill \\ \end{gathered}$$ (14)

The total deflection of multistage hydraulic cylinder during the Eq. (9)~(14) as follow:

$$\:y={y}_{1}+{y}_{2}+{y}_{3}+{y}_{4}+{y}_{5}+{y}_{6}\:\:\:\:\:\:0\le\:x\le\:{x}_{5}$$ (15)

FEM structural analysis

The ANSYS Workbench program was utilised to conduct an FEA to predict the buckling deflection in a five-stage hydraulic cylinder. Figure 6 shows the assembly of the hydraulic cylinder, highlighting its various components.

3D model and mechanical properties of a five-stage hydraulic cylinder

The dimensions and materials of the hydraulic cylinder from the company were determined according to the field specifications, and are detailed in Tables 2, 3, 4 and 5. The five-stage hydraulic cylinder consists of several components, including a cylinder, cap, rod, boom, pad, and plank. When fully extended to its maximum working length, it measures 13,602 mm.

Design of protector box installation for hydraulic cylinder

The seal provides sealing performance for hydraulic systems; however, when replacement is necessary, it requires the removal of the entire boom encasing the cylinder. To simplify this process, this paper proposes two installation methods: the fully bolted and single-sided diagonal bolt methods. fully bolted and single-sided diagonal bolted, as shown in Fig. 7: single-sided diagonal bolt installation and fully bolted installation. However, disassembling repairs from an internal cylinder is more difficult. The single-sided diagonal bolt installation and the fully bolted installation methods, featuring an L-shaped Tube and bolts as a complete assembly, are the quickest to disassemble.

In the design of a hydraulic cylinder, the orientation of the rod-eye mounting method plays a critical role in operational efficiency and structural integrity. The mounting direction significantly affects the deflection characteristics of the cylinder. In this study, horizontal and vertical mounting methods were used (Fig. 8).

Boundary condition of analysis

To approach the working environment, the hydraulic cylinder introduces a fixed condition at the bottom of the left-end bracket and a constraint condition at the bottom of the right-end bracket such that it can move only along the axis direction. The settings were based on gravity (9.806 m/s²) and friction coefficients of each part (0.1). The last working temperature (100° C) was entered as the boundary condition; all the boundary conditions are shown in Fig. 9(a).

The simulation of a multi-stage cylinder comprises the Booms, Cylinders, Caps, Pads, Planks, and Bolts. The connections between each component has two types, bonded contacts were applied between all Caps with Cylinders, Caps with Planks, as well as Plank and Boom, to prevent relative movement at the joints, thereby enhancing the structural stability. The frictional contacts were applied between Cylinder1 and Cylinder5, Boom1-pad1, Boom2-pad2, Boom3-pad3, and Boom4-Pad4, as well as Boom2–Pad1, Boom3–Pad2, Boom4–Pad3, and Boom5–Pad4, while the remaining interfaces were structure with sliding capability with a friction coefficient of 0.1, to simulate the sliding friction behavior generated during the telescopic extension and retraction of the multi-stage structure shown in Fig. 9(b).

A pretension force of 42,000 N was applied to each Bolt to reflect the actual stress distribution under assembly conditions and enhance the reliability of the joint regions.

The element size for all components was uniformly set to 6 mm, resulting in a total of 5,073,543 nodes and 1,291,258 elements. A hybrid meshing strategy was adopted, whereby different regions were assigned various element types based on their geometric characteristics. The mesh primarily consists of Tet20 (hexahedral) elements, with a smaller number of Hex10 (tetrahedral), Wed15 (wedge), Tri6 (triangular), and Quad8 (quadrilateral) elements, allowing the mesh to accommodate complex geometries and boundary conditions effectively shown in Fig. 9(c).

The mesh quality was evaluated using the skewness method, the majority of mesh elements have skewness values concentrated in the 0–0.13 range, accounting for approximately 68% of the total, which further validates the high quality of the mesh. The minimum skewness was 0.13 the maximum was 0.98, and the average was 0.22. According to ANSYS standards, an average skewness below 0.25 is considered indicative of high-quality meshing, confirming that the overall mesh quality of this model is excellent shown in Fig. 9(d).

Result of analysis

Table 6 lists the maximum deflection results of the boom installation methods (fully bolted and single-sided diagonal bolted) and two rod eye-mounting directions (horizontal and vertical).

The company utilized the boom fully bolt installation method with horizontal-horizontal (H-H) mounting direction, and a significant deflection of 192.9 mm was observed at the second stage of the five-stage hydraulic cylinder at its maximum extension (Fig. 10).

The deflection results of the single-sided diagonal-bolted boom installation method are shown in Fig. 11. When the five-cylinder reaches its maximum position, a large deflection occurs at the second stage with a deflection value of 29.7 mm.

If you want to learn more, please visit our website Multi Stage Hydraulic Cylinder.

Additional reading:
5 Things to Know Before Buying rotary tablet press machine
How to Maximize the Benefits of Hammer Mills: A Complete Guide

Figure 12 presents the deflection results for the two installation methods applied to the five protector boxes, alongside two rod eye mounting directions (H-H and V-V), when the five-stage cylinder is at its maximum working position. The vertical-vertical (V-V) rod eye mounting direction results in significantly less deflection than the H-H direction. In the V-V configuration, the deflections measure 29.7 and 32.5 mm with the single-sided diagonal-bolted and fully bolted boom installation methods, respectively. The single-sided diagonal-bolted boom method is suggested for use in five-stage hydraulic cylinders owing to its cost-effectiveness and rapid disassembly capabilities compared to the full boom bolt installation method.

The equivalent stress was used to assess the structural safety of the system. This study focused on the single-sided diagonal bolted with the V-V direction, which demonstrated the minimum deflection, and a safety evaluation was conducted in this case. Figure 13 shows the equivalent stress results for the hydraulic cylinder and protector box.

The maximum stress in the boom component is 134.9 MPa, which occurs in the second stage at the top of the boom. For the hydraulic cylinder, the maximum stress is 251.6 MPa (yield strength: 343 MPa) and is located at the rod-eye section. Because the equivalent stress does not exceed the yield strength (343 MPa), the hydraulic cylinder remains within safe limits.

The O-ring was initially used in hydraulic systems to provide sealing preference and address the leakage problem. After designing the hydraulic cylinder, a sealing test for the hydraulic cylinder was required to ensure that the system was safe without leakage. This study compares the contact pressure of seals using two different designs: a key design in the V-V direction with a boom single-sided diagonal bolted installation method, and an initial key design from the company in the H-H mounting direction with the fully bolted boom installation method. A comparison was conducted through simulations, and the effectiveness of both designs was verified using FEA.

Test modelling and material

A section radius of 5.15 mm and the radius of the O-ring seal were designed to hold a good seal between the hydraulic cylinders. The seal exhibited an interference of 0.3 mm with the cylindrical part, as shown in Fig. 14.

The mechanical properties of the seal made from a fluoroelastomer (FKM rubber) were determined using Yeoh’s hyperplastic model equations. This mathematical model is a well-known method in materials science for characterising the nonlinear elastic behaviour of elastomers. In this study, the Yeoh third-order modelling was used as described below.

$$\:W={C}_{10}\left({I}_{1}^{{\prime\:}}-3\right)+{{C}_{20}\left({I}_{1}^{{\prime\:}}-3\right)}^{2}+{{C}_{30}\left({I}_{1}^{{\prime\:}}-3\right)}^{3}$$

where \(\:{C}_{10}\), \(\:{C}_{20}\) and \(\:{C}_{30}\) are the hyperplastic material parameters, \(\:{I}_{1}^{{\prime\:}}\) is the first principal invariant, and \(\:W\) is the strain energy density function.

The hyperplastic material parameters (\(\:{C}_{10}\), \(\:{C}_{20}\)and \(\:{C}_{30}\)) were determined through various experiments, including uniaxial tensile, planar shear, and biaxial tensile tests. Table 7 presents the hyperplastic material parameters (\(\:{C}_{10}\), \(\:{C}_{20}\)and \(\:{C}_{30}\)) of both the unaged and aged FKM17. In this study, only the unaged FKM was used, and the hyperplastic material parameters (\(\:{C}_{10}\), \(\:{C}_{20}\), and \(\:{C}_{30}\)) given by \(\:50\)MPa,\(\:\:-66.43\)MPa, and \(\:88.96\) MPa, respectively, were input into the ANSYS program to fit the stress–strain curve of the FKM, as shown in Fig. 15. When the stress–strain curve is fitted, the nonlinear elastic behaviour of the FKM can be simulated using the ANSYS program.

Sealing tests were performed in two cases, which defined the initial design (thickness 6 mm with single-sided diagonal bolted and horizontal mounting method) and the reduced deflection plans suggested in this paper as the best design (thickness 6 mm with single-sided diagonal bolted and vertical mounting method). An elastomeric seal is considered effective in preventing leakage problems if the working pressure does not exceed the contact pressure at the macroscale18,19.

Influence of Deflection on sealing performance

When the hydraulic cylinder reaches its maximum extension position, the large deflection with bending behaviour leads to two contact features between the upper and lower parts of the cylinder surface. When the pressure pushes the seal at the upper groove, the seal at upper groove has more “compression”, implying that more contact pressure is produced at the contact point to provide the fluid leakage. Conversely, the seal at the lower groove has more “tension”, which leads to contact pressure produced at the contact point, contributing to the leakage problem in their region, as depicted in Fig. 16. Points A and D and points B and C indicate the contact points of the upper and lower cap grooves with a seal, respectively.

Discussion and result

The sealing test results of the field’s five-stage hydraulic cylinder design, which uses a boom fully bolted installation method in the H-H mounting direction with a deflection of 192.9 mm, revealed that contact pressure values were 16.45 MPa and 17.2 MPa at A and B contact points, and 13.3 MPa and 12.68 MPa at C and D contact points, respectively. Leakage occurred at contact points C and D at pressures lower than the working pressure (13.7 MPa), indicating leakage in the cylinder system as shown in Fig. 17.

The sealing test results of a five-stage hydraulic cylinder, using the single-sided diagonal-bolt boom installation in the V-V mounting direction, with a deflection of 29.7 mm showed that the contact pressure values were 15.75 MPa and 16.7 MPa at A and B contact points, and 14 MPa and 14.06 MPa at C and D contact points, respectively. No leakage was observed in the cylinder system, as shown in Fig. 18.

The contact pressure results are listed in Table 8. These results confirm that deflection affects the leakage of the hydraulic cylinder.

Design of U-lip seals for the hydraulic cylinder

O-rings, rectangular rings, and U-seals are commonly utilised sealing components in hydraulic systems20. Research has shown that under high contact pressure and high rod speed conditions, O-rings used as reciprocating seals in five-stage hydraulic cylinders are prone to cracking, extrusion, wear, and distortion21, ultimately leading to cylinder leakage22, and also the frictional force is twice compared with U-lip seal at same size23 Additionally, high contact pressure accelerates the wear of the seals. Therefore, to reduce wear and cracking while providing reliable sealing performance, this study conducted detailed tests on these three different shapes of seals. The materials used included fluorocarbon rubber (FKM) and hydrogenated nitrile butadiene rubber (HNBR)24, with all tests, carried out under the same working conditions and dimensions (10.3 mm) with 0.3 mm interference to ensure the accuracy and comparability of the experimental results. The test modelling is shown in Fig. 19.

The results for the maximum contact forces of O-rings, rectangular rings, and U-seals made from two different materials, FKM and HNBR, are displayed in Fig. 20. For FKM material, the maximum contact forces are 17.3 MPa for O-rings, 14.4 MPa for rectangular rings, and 13.6 MPa for U-seals; for HNBR material, the corresponding forces are 0.469 MPa, 0.387 MPa, and 0.374 MPa respectively. The study reveals that U-seals exhibit the lowest contact pressure of all tested seals irrespective of the material used. This finding confirms that U-seals experience the least sliding wear under identical operating conditions, significantly extending their service lifespan. Additionally, the study assessed the ageing performance of seals made from FKM under cyclic pressure and temperature variations and compared the performance differences among the three different shapes of seals. Detailed data on the aged FKM material are shown in Table 7. These results provide crucial guidance for optimising seal design and enhancing the reliability and efficiency of systems.

The contact pressure results from Unaged and aged FKM materials are shown in the Fig. 21. For O-rings, rectangular rings, and U-seals made from FKM material, the maximum contact pressures decreased from 17.3 MPa, 14.4 MPa, and 13.6 MPa to 14.9 MPa, 12.4 MPa, and 11.74 MPa, respectively, before and after aging. Specifically, the contact pressure for O-rings was reduced by 2.4 MPa, for rectangular rings by 2 MPa, and for U-seals by 1.89 MPa. These results indicate that despite using the same material, U-seals are least affected by aging among all tested seals, showing minimal impact on their sealing performance compared to other types of seals. This finding suggests that using U-seals in future applications may help reduce leakage problems caused by material aging, thereby enhancing the overall reliability and sealing performance of the system. This is particularly important for designing hydraulic systems with long service lives and high reliability.

To optimise for reduced contact pressure in the U-lip seal, Fig. 22 illustrates the key parameters: ‘a’ represents the thickness of the seal lip, while ‘b’ denotes the length of the seal lip. The thickness parameter ‘a’ was varied between 1.5 to 3 mm, and the length parameter ‘b’ was adjusted between 3 and 7 mm. This range was strategically chosen to explore the effects of these dimensions on the seal’s performance.

The contact pressure results of the U-lip seal are shown in Fig. 23. All results indicate that increasing the parameter ‘b’ leads to reduced contact pressure. When ‘a’ is set at 1.5 mm, the contact points A to D exhibit lower pressures compared to other cases; however, leakage occurs when ‘a’ exceeds 5 mm. The optimal configuration in this scenario is observed by 1.5 mm for ‘a’ at and 5 mm for ‘b’. For selections of ‘a’ at 2, 2.5 and 3 mm, the contact pressure is higher than that at 1.5 mm, respectively, leading to accelerated seal wear.

The contact pressure tests of the U-lip seal revealed that the best performance observed at a = 1.5 mm and b = 5 mm showed two contact circular regions exceeded. Circular contact region 1 (B to C) had pressures ranging from 16.7 to 14 MPa, whereas circular contact region 2 (A to D) had pressures ranging from 13.75 to 14.06 MPa. All circular contact regions exceeded the working pressure of 13.7 MPa, as shown in Fig. 24.

In this study, a U-lip seal with ‘a’ and ‘b’ as 1.5 and 5 mm, respectively, was selected for further tests. Compared with the above-tested O-ring, the U-lip seal exhibited the same interference of 0.3 mm, and its dimensions were 10.3 mm in length and width, as shown in Fig. 25. This design aimed to minimise the excited contact pressure at the contact points, thereby reducing unnecessary wear on the cylindrical components.

Table 9 shows the result of tested contact pressure comparing the O-ring and U-seal, all the contact pressure points (A, B, C, and D) of the U-seal were lower than those of the O-ring seal and the average contact pressure decreased by 8,02%, indicating that the U-lip seal experienced less wear than the O-ring seal. Therefore, a U-lip seal is recommended for use in hydraulic cylinders owing to its lower wear.

This study conducted simulation tests on the seal states at different positions under the maximum working distance of an extended hydraulic cylinder, supplementing factors of the hydraulic cylinder under deflection states that were not addressed in previous 2D simulations25,26,27, especially for multiple-stage hydraulic cylinder for structural safety and sealing analysis. Furthermore, the study analyses the differences in contact pressures produced by different seals at various positions under large deflection states and found through FEA simulation comparison that U-seals are more suitable for hydraulic cylinder applications.

There are many different types of hydraulic cylinders each with its unique functionality. One of the main advantages of using the telescopic hydraulic cylinder variety is the fact that it has a longer stroke compared with other cylinder designs. This cylinder variety is typically used to enhance the functions of process operations.

If you have operations that are designed to be carried out in a limited or confined space, telescopic hydraulic cylinders are a great option for you. They are also beneficial in places where a longer stroke length is required. But what about hydraulic cylinder repair?

What Is the Telescopic Hydraulic Cylinder?

Telescopic cylinders are also referred to as multi-stage cylinders. They are a variety of linear actuator that consists of tubular rods referred to as sleeves. There are usually four or five sleeves that decrease in diameter and nest inside one another. As soon as hydraulic pressure is exposed to the cylinder, the largest sleeve (called the barrel or main) extends. As soon as the barrel reaches its maximum stroke, the next sleeve (called a stage) starts to extend. This is an ongoing process until the cylinder reaches the final stage that’s referred to as the plunger.

The two types of telescopic hydraulic cylinders include single-acting cylinders and double-acting cylinders. The most common type is single acting which works by using gravity or other external forces to retract the cylinder stages. Once pressure is released, the load’s force pushes oil out of the system and the cylinder retracts.

Benefits

Just like other types of cylinders, there are benefits to using telescopic hydraulic cylinders. We’ve outlined a few of them below.

#1. Telescopic Hydraulic Cylinders Take Less Space

One of the main benefits is the fact that these cylinders can be used effectively in small, compact spaces. If your operations are confined and require compact equipment, consider a telescopic hydraulic cylinder that can extend significantly longer than the collapsed length. This is the most logical option if you have limited mounting space and require a long stroke.

#2. Telescopic Cylinders Can Meet Specific Angle Requirements

Using this cylinder variety is the most practical in vehicles that feature a hydraulic-powered bed such as a dump truck. There are specific angles that are required to gradually release the materials at the required range, requiring a 60-degree angle to empty the contents of the bed. As well as raising the bed, telescoping cylinders are beneficial in collapsing and returning the bed to a horizontal position.

#3. Can be Made as a Constant Thrust / Constant Speed Application

Special telescopic cylinders are known as constant-thrust/constant-speed cylinders. They are configured so that all moving stages extend simultaneously to provide a constant speed and force while it is extending or retracting. This variety of telescopic hydraulic cylinders is often used to drive drill heads in underground mining where performance parameters are necessary. Due to its more complicated design, this type of hydraulic cylinder accomplished the necessary action by internally trapping oil, limiting the number of moving stages, and matching retract and extend areas.

#4. Can be Made as a Double or Single Acting

Another noteworthy advantage is that telescopic hydraulic cylinders can be made as single-acting, double acting, or a combination of the two. If you opt for the combination of single-acting and double-acting telescopic cylinders, you’ll also receive the benefits of a double-acting cylinder combined with the ease of operation and cost-effectiveness of a single-acting hydraulic cylinder.

#5. Telescopic Cylinders Have a Longer Stroke

The stroke length of this cylinder variety is longer than others. The typical collapsed length of a telescopic hydraulic cylinder is roughly 20-40 percent of its fully extended length. This is considered an extra-long stroke that cannot be achieved with other types of cylinder types, making it one of the biggest unique selling points of this variety.

The company is the world’s best dual hydraulic cylinder supplier. We are your one-stop shop for all needs. Our staff are highly-specialized and will help you find the product you need.

Conclusion