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2.1 Design and Calculation of Hydraulic Cylinders for Hydraulic Presses
The previous articles in this series discussed the Technical requirements for design and manufacturing of hydraulic cylinders-Barrel tube, hydraulic cylinders-Piston and Piston rod, Cylinder head and cylinder bottom，Guide sleeves, Sealing devices, Buffer, Venting, Anti-loosening，Installation and Connection，Assembly. Today we talk about Design and Calculation of Hydraulic Cylinders for Hydraulic Presses.
A hydraulic press is a machine that uses hydraulic transmission with mineral oil as the transmission medium, transferring energy through the closing of linearly moving molds, and is used for pressure processing (such as deformation or forming) of metallic or non-metallic materials. The hydraulic cylinder is the actuator component of the hydraulic press (hydraulic system), driving the slider (mold) to perform linear reciprocating motion, converting hydraulic energy into mechanical energy.
To better comply with the provisions of the above standards, it is necessary to study the material selection and heat treatment, strength calculation, structural design, and manufacturing precision of hydraulic cylinders used in hydraulic presses (hereinafter referred to as “hydraulic cylinder” or “cylinder”) in order to further improve the safety, reliability, and service life of hydraulic presses.
2.1.1 Types and Uses of Hydraulic Cylinders for Hydraulic Presses
Currently, there are generally three structural types of hydraulic cylinders used in hydraulic presses: single-acting cylinders (such as plunger cylinders), double-acting cylinders (such as piston-single rod cylinders), and differential cylinders (piston rod-double rod cylinders).
According to the definition of a differential cylinder in standard “Fluid Power Systems and Components Vocabulary,” a differential cylinder should be a double-acting cylinder with a piston. However, the differential cylinder in the hydraulic press is a single-acting hydraulic cylinder, and there is no piston inside the cylinder body. The pressure acts directly on the stepped shaft-shaped piston rod. It is neither a differential cylinder as defined where “the effective areas on both sides of the piston are different,” nor is it connected in a “differential circuit”. It is simply a conventional term used in hydraulic presses to refer to a “piston rod-double rod cylinder,” but in essence, it is a plunger cylinder. A more accurate term would be “double-rod plunger cylinder.”
(1) Plunger Cylinder
A plunger cylinder is a single-acting cylinder without a piston inside the cylinder barrel, where the pressure acts directly on the piston rod. This type of hydraulic cylinder is widely used in hydraulic presses, especially water presses, such as for main cylinders, auxiliary cylinders, return cylinders, and balancing cylinders.
Because the plunger cylinder has only one piston rod sealing system and no piston sealing device (system), its structure is simple, easy to manufacture, and low in cost. However, it can only act in one direction and cannot drive the slider (mold) to perform reciprocating linear motion. If gravity cannot ensure the return of the piston rod and the slider (mold) driven by it, a return cylinder is generally needed to achieve cylinder return.
(2) Piston-Single Rod Cylinder
A piston-single rod cylinder is a cylinder where hydraulic pressure can be applied to the piston in two directions, with the piston rod extending from only one end. The piston-single rod cylinder is a double-acting cylinder that can drive the slider (mold) to perform linear reciprocating motion. This type of hydraulic cylinder is widely used in hydraulic presses, especially small and medium-sized hydraulic presses.
(3) Differential Cylinder
The differential cylinder has two piston rods with different outer diameters, and the effective area on which the pressure acts is the difference between the cross-sectional areas of the two rods. Therefore, a differential cylinder must have two sets of piston rod sealing systems.
Because the stepped piston rod is sealed, guided, and supported by the piston rod sealing systems at both ends, this type of hydraulic cylinder has a high operating speed and strong resistance to eccentric loads, and is often used as a return cylinder in hydraulic presses.
In standard “Hydraulic Cylinder and Pneumatic Cylinder Mounting Dimensions and Mounting Type Codes,” the end with the flange on the double piston rod is defined as the front end.
2.1.2 Installation and Connection Types of Hydraulic Cylinders for Hydraulic Presses
In hydraulic presses, some hydraulic cylinders have their cylinder bodies directly mounted on the crossbeam, such as in rubber vulcanizing hydraulic presses. However, most hydraulic cylinders are treated as independent hydraulic components (i.e., independent units) and function as a functional part of the hydraulic transmission system.
Although installing the hydraulic cylinder as an independent unit in the hydraulic press may reduce the strength and rigidity of the crossbeam, it also has its advantages:
① The hydraulic cylinder can be manufactured by specialized factories, and the main machine manufacturer can purchase it externally.
② It reduces the difficulty of processing and manufacturing the hydraulic press frame.
③ The design, manufacturing, testing, acceptance, and maintenance and replacement of the hydraulic cylinder are simple and convenient.
④ It may better meet the standardization, serialization, and modular design requirements of hydraulic presses.
There are various installation types of hydraulic cylinders in hydraulic presses. Although in global standard specifies 64 installation types, it still does not cover all existing hydraulic cylinders.
(1) Cylinder Body Flange and Boss Mounting Types
The front (or rear) flange and boss used for mounting hydraulic cylinders in hydraulic presses are generally directly designed on the cylinder body, rather than on the end cap of the hydraulic cylinder. Although the following description still uses front or rear end flanges and bosses, it differs from general hydraulic cylinders.
Hydraulic cylinder body flanges have three installation types: front end flange, rear end flange, and middle flange; flanges also have three types: round flange, square flange, and rectangular flange; the flange connection holes are generally plain holes, and threaded holes are relatively rare.
① Front end round flange mounting type. The front end flange’s reference point surface is tightly fitted to the inner surface of the crossbeam, and the hydraulic cylinder is fastened to the crossbeam with screws (bolts). During operation, because these fixed joint surfaces are usually compressed against each other, the flange needs to transmit force, so there is stress concentration at the transition between the flange and the cylinder body, which is prone to fatigue failure. Additionally, the presence of connection holes in the flange exacerbates this damage.
There are also designs where the front flange near the reference point surface is tightly fitted against the outer surface of the beam. During operation, this pair of fixed joint surfaces tends to separate, the connecting screws (bolts) experience a significant increase in force, reducing the resistance to eccentric loading, and without improving the stress situation of the cylinder body.
② Rear end circular flange mounting type. The rear flange’s surface far from the reference point is tightly fitted against the inner surface of the beam, and the hydraulic cylinder is fastened to the beam with screws (bolts). During operation, although this pair of fixed joint surfaces usually compresses each other, the flange needs to transmit force, but the direction of force is different from the front flange mounting type. Therefore, the transition between the flange and the cylinder body in the rear flange mounting type generally does not have stress concentration problems, improving the stress situation of the cylinder body. From the perspective of cylinder body stress, it is a viable mounting type, but it also has problems such as a larger maximum equivalent stress on the inner wall of the cylinder, reduced stability of the hydraulic cylinder, and increased frame height.
There are also designs where the rear flange near the reference point surface is tightly fitted against the outer surface of the beam. During operation, this pair of fixed joint surfaces tends to separate, the connecting screws (bolts) experience a significant increase in force, and the stress on the bottom of the rear hydraulic cylinder tends to worsen.
③ Front end boss mounting type. The front end boss’s surface far from the reference point is tightly fitted against the inner surface of the beam. This tight fit is ensured by fixing the boss with a pressure ring, fastening the cylinder body with a large nut at the far end of the reference point, and fastening the pressure ring to the cylinder bottom with screws (bolts) or other methods.
This mounting type is the most common and is widely used in small and medium-sized hydraulic presses.
The stress situation of this mounting type is similar to the front flange mounting type, but because there are no flange connection holes, the stress situation is generally slightly improved, but the stress concentration problem at the transition between the boss and the cylinder body still exists.
(2) Types of Piston Rod and Slider Connections
The term “slider” referring to the main component of a hydraulic press that performs the stroke movement and on which the upper die is mounted. The piston rod connects to the slider, transferring energy to it.
Three types of piston rod threads (one type of internal thread and two types of external threads). In some global standard provides dimensions for piston rod ends with external threads, piston rod ends with wrench flats (with internal threads), piston rod ends with dowel pin holes, piston rod ends with flanges, and piston rod ends with internal threads.
Furthermore, a spherical surface is sometimes machined on the piston rod end. A spherical bearing block is then clamped between the piston rod end and the slider using screws through a central threaded hole, threaded holes on both sides, or a retaining ring, forming a ball joint connection between the piston rod and the slider.
① Rigid connection. The rigid connection between the piston rod and the slider is the most common type of connection. Generally, the piston rod is connected via attachment to the slider.
Due to the different types of piston rod ends and the variety of attachment types, there are many types of connections between the hydraulic press piston rod and the slider. However, safety, reliability, and long service life must be ensured. Any components connected to the hydraulic cylinder should be securely fastened to prevent loosening due to impact and vibration, especially if there is a risk of the slider unexpectedly falling. A risk assessment should be conducted in such cases.
Specific types of rigid connections between the piston rod and the slider:
a. Connection via a threaded flange.
b. Connection consisting of a key and a retaining ring.
c. Connection with direct screw fastening.
d. Connection with a locating sleeve.
In some standard, threaded flanges are also called piston rod flanges.
② Pivoting connection. In connection types such as pin shafts, trunnions, and spherical bearings between the piston rod and the slider, the piston rod and the slider can pivot or rotate. This connection type is also relatively common. However, because general hydraulic presses require high precision and have large nominal forces, the above-mentioned pivoting connection is not widely used in hydraulic presses for metal cold working. However, a spherical joint support connection is commonly used in hydraulic presses.
In this type of spherical joint support connection, the spherical end of the piston rod is generally a concave spherical surface with material removed, and usually has a threaded center hole. The spherical end of the piston rod and the spherical bearing block form a spherical joint, and this spherical joint should be in a compressed state during the working stroke of the hydraulic press. The spherical joint support connection mainly aims to minimize the eccentric force transmitted from the slider to the piston rod, or to accommodate relatively small positional changes of the slider during the working stroke.
There is also a special double spherical joint support connection structure for hydraulic cylinders used in hydraulic presses. Its characteristic is that the piston rod does not directly transmit force to the slider, but uses an intermediate connecting rod. The piston rod transmits force to the intermediate connecting rod through a spherical joint support connection, and the other end of the intermediate connecting rod transmits the force to the slider through a spherical joint support surface. Therefore, there are two (double) spherical joint support connections between the piston rod and the slider. This connection has a better effect in eliminating eccentric forces than a single spherical joint support connection, resulting in a longer service life for the hydraulic cylinder. The ends of the intermediate rod are generally still concave spherical surfaces with material removed, but this hydraulic cylinder structure is relatively complex and difficult to implement in small hydraulic cylinders, and spherical surface lubrication also presents certain difficulties.
According to some references, this double spherical joint support connection hydraulic cylinder works well in large hydraulic presses.
2.1.3 Main Cylinder Part Structure Types, Materials, and Heat Treatment
(1) Piston Rod
Piston rod is A cylinder part that is coaxial with and integrated with the piston, transmitting mechanical force and motion from the piston. A “plunger cylinder” as: “A single-acting cylinder without a piston in the cylinder barrel, where pressure acts directly on the piston rod.” This indicates that the piston rod does not necessarily have to be “coaxial with and integrated with the piston.” In a plunger cylinder, the piston rod can also directly receive pressure and transmit mechanical force and motion to the driven component.
① Materials. Generally, high-quality carbon structural steel such as #45 or #50 steel is used, manufactured by forging or casting. For large-sized piston rods, segmented forging or casting followed by electroslag welding is also used. Small piston rods are sometimes made of chilled cast iron.
Currently, alloy structural steels such as 42CrMo steel are used to manufacture piston rods for hydraulic cylinders in hydraulic presses.
① Structural Types. Piston rods that are coaxial with and integrated with the piston, or piston rods without a piston, can be solid or hollow. However, hollow piston rods should not be designed with the opening facing the cylinder bottom, as this would create an excessively large rodless chamber volume. An excessively large chamber volume is generally detrimental, regardless of its potential impact on hydraulic natural frequency, hydraulic (spring) stiffness, and (step and/or frequency) response characteristics. For example, if the elastic energy accumulated in the cylinder fluid is too large at the end of pressurization, it may cause severe vibration of the hydraulic press and piping during pressure release.
The piston rod end in a plunger cylinder may also have a boss, which abuts against the inner end face of the guide sleeve to limit the cylinder stroke and prevent the piston rod from coming out (or being ejected). This boss may be called the piston rod head, and this type of piston rod may be called a piston rod with a piston rod head.
Some piston rods are designed with a cushioning plunger at the end to slow down the piston (rod) return speed at the bottom of the cylinder, preventing severe impact of the piston against the cylinder bottom.
The piston rod end with external threads, which is flange-connected to the external piston rod, its threads are often designed to only transmit the cylinder return output force and return motion. Therefore, the thread length may be shorter.
③ Heat treatment. The piston rod reciprocates in the guide sleeve and may tilt or wobble under eccentric load, generating lateral thrust on the guide sleeve and sealing device, causing friction and wear. Therefore, the piston rod surface must have sufficiently high hardness and high surface quality (low surface roughness value) to prevent premature wear or the formation of grooves and scratches on the surface.
The surface hardness of the piston rod should generally be no less than 45HRC. The following methods can be used for surface treatment of the piston rod:
a. Quenching and tempering treatment can be used, but the surface hardness often does not meet the requirements.
b. Flame hardening. This method is relatively simple, but sometimes soft spots may form.
c. Induction heating quenching using power frequency, medium frequency, or high frequency.
d. Hard chrome plating. The hardness can reach 800~1000HV, but the plating layer should not be too thick, the maximum thickness is about 0.10mm, and the general thickness should be about 0.05mm.
e. Surface welding with stainless steel. After heat treatment, the hardness can reach above 50HRC.
f. Nitriding of nitriding steel such as 35CrMo, 35CrAlA, 38CrMoAl, etc., can achieve a hardness of over 60HRC. g. Ion soft nitriding treatment of 45 steel piston rods can achieve a surface hardness of up to 64 HRC.
h. For operation under corrosive conditions, stainless steel is often used for piston rods.
There are also other surface treatment methods, such as laser hardening and electroless nickel-phosphorus plating.
(2) Piston
The piston is: “A cylinder part that moves within the cylinder bore and transmits mechanical force and motion by the action of fluid under pressure.” A piston is: “Composed of a piston head and a piston rod, it transmits hydraulic pressure and energy during movement. The piston head is sealed and fitted with the cylinder bore, dividing the cylinder bore into two chambers.”
① Materials: The piston material is generally made of #35 or #45 high-quality carbon structural steel, and also uses gray cast iron, ductile cast iron, and aluminum alloy.
Pistons without support rings (guide rings) can be made of gray cast iron HT200~HT330 or ductile cast iron, aluminum alloy, plastic, etc. Pistons with support rings (guide rings) can be made of #20, #35, #45, or 40Cr steel, etc. Depending on the actual situation or if there are no special requirements, medium carbon steel can generally be considered without heat treatment, but this does not include heat treatment aimed at relieving stress.
② Structural types: Pistons have two structural types: integral and combined. Pistons using V-rings or other seals are of the combined type.
The combined structure is also called the assembled type in standard “Dimensions and Tolerances of Narrow Section Dynamic Sealing Grooves for Hydraulic Cylinder Pistons and Piston Rods”.
(3) Guide Bushing
The guide bushing, is: “a sleeve-shaped part that provides guidance.”
The guide bushing can be manufactured as an integral part of the cylinder head or as a separate component, i.e., the cylinder head type and the bushing type.
① Material. The hydraulic cylinder guide bushing provides support and guidance during the reciprocating motion of the piston rod. Bushing-type guide bushings are generally made by casting and machining wear-resistant and pressure-resistant tin bronze such as ZCuSn6Pb3Zn6 and ZCuSn10P1; some guide bushings are also manufactured using centrifugally cast nylon 6 with molybdenum disulfide, but due to their low resistance to eccentric loads, large thermal expansion, and moisture absorption deformation after processing and assembly, problems such as piston rod oscillation or deflection, piston rod seizure, and body fracture may occur. Currently, gray cast iron and ductile cast iron are the most commonly used materials.
② Structural Design. The length of the guide bushing is generally (0.4~0.8)d; for horizontal plunger cylinders, the guiding length should be increased, and can be (0.8~1.5)d, while for piston cylinders, it can be shorter. Here, d is the piston rod diameter.
The guide bushing is fitted to the inner diameter D of the cylinder barrel. When D ≤ 500mm, H7/k6 or H8/k7 is used; when D > 500mm, H7/g6 or H8/g7 is used; the inner bore of the guide bushing is fitted to the outer diameter of the piston rod with H9/f8 or H9/f9, and the surface roughness value should be less than Ra1.6μm.
Note: The fit between the guide bushing and the inner diameter of the cylinder barrel for hydraulic cylinders used in hydraulic presses is tighter than the H8/f7 used for general hydraulic cylinders.
③ Cylinder Head Material. For cylinder head type guide bushings or cylinder head materials, cast iron can generally be considered when the nominal pressure p ≤ 10MPa; otherwise, #20, #35, and #45 high-quality carbon structural steel can be used. If the cylinder head needs to be welded to the cylinder barrel, #20 or #35 steel is generally used, and stress relief treatment should be performed after welding; for non-welded connections, the cylinder head can be made of 45 steel and heat-treated as needed.
The support ring is the component that directly contacts the piston rod in steel cylinder heads or guide bushings.
(4) Cylinder Body Material
The material for the hydraulic cylinder body can be selected based on the working pressure of the medium and the size of the hydraulic cylinder, offering a wide range of options. For low-pressure, small-sized hydraulic cylinders, gray cast iron can be used, commonly grades HT200 to HT350. For higher requirements, ductile iron can be used, such as QT450-10, QT500-7, and QT600-3. For even higher requirements, cast steel can be used, such as ZG200-400, ZG230-450, ZG270-500, and ZG310-570. For large and medium-sized forging hydraulic presses, 35 or 40 forged steel is commonly used, and sometimes alloy steels such as 20MnMo, 35CrMo, and 38CrMoAl are used to manufacture the hydraulic cylinder body. In some large-tonnage forging or die forging hydraulic presses, the hydraulic cylinder material is sometimes 18MnMoNb alloy steel, and large steel ingots can be directly forged into hydraulic cylinder blanks.
Smaller hydraulic cylinders often use seamless steel pipes as blanks, with materials such as #20, #35, #45, and 27SiMn steel. These offer small machining allowances, good processability, and short production preparation cycles, making them suitable for large-scale production.
Alternatively, commercially available cylinder tubes conforming to standard “Technical Conditions for Hydraulic Cylinder Tubes” can be used. Their inner diameter dimensions (series) conform to standard, and suppliers can be requested to provide heat-treated cylinder tubes.
However, when using cold-drawn high-frequency welded pipes as hydraulic cylinder tubes for hydraulic presses, the mechanical properties of the material and the pressure resistance of the cylinder tube should be agreed upon by both the supplier and the buyer, as there may be certain problems when used for high-pressure and ultra-high-pressure cylinders due to the influence of the material and processing technology of the cold-drawn cylinder tubes.
The structural type, installation and connection type, and the structural type and materials of the main cylinder parts of hydraulic cylinders for hydraulic presses can be found in further Section in this Hydraulic cylinder engineering newsletters.
2.1.4 Stress Analysis and Strength Calculation
A hydraulic cylinder is a sealed, special pressure vessel, often operating under high or ultra-high pressure. The cylinder body is the main part of the hydraulic cylinder. The cylinder body of a hydraulic press is generally a cylindrical component with one end open and the other closed. The structure of the cylinder body is generally divided into three parts: the cylinder bottom, the flange, and the thick-walled cylindrical section (cylinder barrel).
Hydraulic cylinders in hydraulic presses are subjected to heavy loads and frequent operation, and are often prone to premature failure due to improper design, manufacturing, or use.
(1) Failure Locations, Characteristics, and Modes of Hydraulic Cylinders
Most failures of hydraulic cylinders occur in the transition arc section connecting the flange and the cylinder wall, followed by the arc section transitioning from the cylinder wall to the cylinder bottom, especially near the flow channels in this section. A few failures involve cracks in the cylinder barrel wall, and some are caused by severe cavitation. Based on the usage of hydraulic cylinders, failures generally occur after a very high number of working cycles (or 200,000 to 1,500,000 cycles), and the cracks form and propagate gradually, indicating fatigue failure.
① Failure Locations and Characteristics of Hydraulic Cylinders, as follows:
a. Cracks in the cylinder barrel wall generally appear first on the inner wall and gradually develop outwards. The cracks are mostly longitudinally distributed or at a 45° angle to the cylinder wall generatrix.
b. Cracks in the flange section of the cylinder first appear on the outer surface of the transition arc between the cylinder barrel and the flange. The cracks gradually extend to the circumference and the inner wall, eventually penetrating through; or the cracks extend to the bolt holes, causing local detachment of the flange; in some severe cases, the entire flange may crack and detach along the transition arc.
c. Cracks in the cylinder bottom first appear on the inner surface of the transition arc at the cylinder bottom. The cracks (annular) gradually extend to the outer wall, eventually penetrating through.
d. Hydraulic cylinder barrels can also be damaged by cavitation, resulting in honeycomb-like pitting.
② Failure Modes of Hydraulic Cylinders. The failure modes that may occur due to the application of rated fatigue pressure are listed as follows:
a. Structural fracture.
b. Any cracks caused by fatigue under cyclic test pressure.
c. Excessive leakage at the seal due to deformation.
Several failure modes and verification criteria for the rated static pressure of the tested pressure vessel. The failure modes that may occur due to the application of rated static pressure are listed as follows:
a. Structural fracture.
b. Any cracks caused by fatigue under cyclic test pressure.
c. Excessive leakage at the seal due to deformation.
d. Permanent deformation that hinders the normal operation of the pressure vessel.
(2) Analysis of the Causes of Hydraulic Cylinder Damage
① Design-related reasons: The flange is designed too thin; the structural shape of the transition zone from the flange to the cylinder wall is unreasonable; the transition radius from the cylinder bottom to the cylinder wall is too small, etc. The main reasons are insufficient bending strength or stress concentration causing damage.
② Manufacturing-related reasons: Poor surface quality, especially in stress concentration areas, which are very sensitive to surface roughness values. High surface roughness values can reduce fatigue strength, causing fatigue cracks in the transition radius area, leading to damage; the cylinder body, whether forged or cast, may have quality defects; problems with welding quality or improper heat treatment can also cause cylinder body damage; after welding the cylinder body, appropriate measures must be taken to eliminate internal stress and unfavorable crystalline structures. The same treatment should be applied when using repair welding.
③ The joint surface between the flange and the beam should be tightly fitted. After pre-tightening, a 0.05mm feeler gauge should be used for inspection. The insertion depth of the feeler gauge should not be greater than 1/4 of the joint surface, and the cumulative length of the areas where the feeler gauge can be inserted should not be greater than 1/10 of the circumference. Local contact can lead to uneven force distribution, causing premature failure. Loose connecting screws (bolts) can cause cylinder body movement and impact, indenting the joint surface and causing damage.
④ If the working medium is corrosive, it may also reduce the fatigue strength of the cylinder body. Therefore, the hydraulic oil used in the hydraulic press should have good anti-rust properties and be replaced regularly.
(3) Stress Analysis of the Cylinder Body
During operation, high-pressure working fluid enters the cylinder body, acting on the piston or piston rod. The reaction force acts on the cylinder bottom and is transmitted through the cylinder wall to the flange, where it is balanced by the support reaction force on the flange and the beam support surface.
The stress state of the cylinder body can be analyzed in three parts: the cylinder bottom, the flange, and the thick-walled cylindrical section (cylinder barrel).
Both theoretical analysis and stress testing show that only the middle section of the cylinder barrel, at a distance of 0.75D1 from the upper surface of the flange (support surface with a transition radius) and the inner surface of the cylinder bottom (with a transition radius), can be calculated for strength using the thick-walled cylinder formula. The other two sections (parts) cannot be calculated using the general thick-walled cylinder formula because they are affected by the bending moments of the cylinder bottom and the flange.
The same problem exists in the stress analysis of the cylinder bottom. If calculated using the elastic mechanics formula for a peripherally fixed circular thin plate under uniformly distributed load, the calculated stress may be far less than the actual stress because the actual effect and influence of the cylinder wall are not considered, nor is the stress concentration in the transition radius area. Reference [31] proposes a ring shell coupling method that analyzes the cylinder bottom, cylinder wall, and flange as an interconnected whole, also considering the changes in the cross-section of the transition zone. Therefore, the calculation result for the cylinder bottom thickness may be closer to reality.
If the finite element method is used to analyze and calculate the cylinder bottom, the results will likely be more accurate.
(4) Strength Calculation of the Cylinder Body
① Strength and deformation calculation of the cylinder tube. For hydraulic cylinders with front-end circular flange or front-end boss type mounting, the middle section of the cylinder tube, made of ductile materials such as low-carbon steel, non-hardened medium-carbon steel, and annealed ductile cast iron, is analyzed according to the theory of elasticity, using the Von Mises strength criterion, i.e., the fourth strength theory condition. The maximum equivalent stress and strength condition on the inner wall of the cylinder are as follows:
When the cylinder inner diameter D and the allowable stress [σ] of the material are known, the outer diameter D1 of the cylinder can be derived as:
In the formula:
D – inner diameter of the cylinder, mm, D = 2R;
D₁ outer diameter of the cylinder barrel, mm, D₁ = 2R₁;
[σ] – allowable stress of the material, MPa,[σ]=σs/ns
where ns is the safety factor, typically taken as 2-2.5;
p – hydraulic pressure for the pressure resistance test of the cylinder, MPa.
For hydraulic cylinders with a rear-end circular flange mounting, the maximum combined equivalent stress on the inner wall of the cylinder and the corresponding strength condition are given as follows.
The (unilateral) expansion amount is the radial displacement value u1 of the outer surface of the middle section of the hydraulic cylinder barrel under the pressure p of the working medium inside the cylinder, i.e., the radial displacement.
Where:
μ — Poisson’s ratio of the cylinder material;
E — Elastic modulus of the cylinder material;
Other parameters are the same as above.
② Strength calculation of the cylinder bottom. Forged cylinder bodies often have a flat-shaped bottom, rather than a concave shape. The center of the cylinder bottom usually has through-holes for oil inlet/outlet or fluid filling valve installation, as well as non-through-holes for buffer chambers. Therefore, in the stress analysis and strength calculation, it is generally treated as a circular thin plate or disc with fixed or constrained edges. To date, there is still no simple and authoritative formula for calculating the cylinder bottom thickness. The reasons for this include the difficulty in determining the working conditions of the hydraulic cylinder bottom, and the problems with the mechanical models used to derive the strength calculation formulas.
The strength calculation formula currently in common use is:
Where:
σd — calculated stress, MPa;
p — hydraulic cylinder pressure test pressure, MPa;
R — cylinder (inner) radius, mm;
δ — cylinder bottom thickness, mm;
φ — coefficient, related to the radius R of the oil hole in the cylinder bottom,That is
[σ]—Allowable stress of the material, [σ] = σs/ns, where the safety factor ns ranges from 4 to 4.5.
Strength calculation formula:
In the formula, φ is a coefficient, taken as 0.7 to 0.8.
Another strength calculation formula:
All three formulas above are derived from the elastic mechanics solution of a circular thin plate with fixed edges under uniformly distributed load, and the first two formulas consider the effect of the opening in the cylinder bottom using the parameter φ. For cylinder heads and cylinder blocks made of carbon steel and low-alloy steel with full-penetration welded connections at room temperature, and with either no holes or holes in the flat-shaped cylinder head, the following formulas are recommended for strength verification:
Where:
K — Structural characteristic coefficient, K = 0.44δ/δc, where δc is the effective wall thickness of the cylinder, and the value range of K is 0.3 to 0.5;
φ — Welding joint coefficient, taken as φ = 1 for fully penetrated butt welds with complete non-destructive testing, and φ = 0.85 for partial non-destructive testing;
[σ] — Allowable stress of the material at room temperature, MPa;
Other parameters are the same as above.
If the above formula is used for the design of a flat-shaped cylinder bottom, then this flat-shaped cylinder bottom, whether perforated or not, has been strengthened. However, if the cylinder bottom is manufactured directly from rolled plates, additional requirements for resistance to lamellar tearing should be specified for the plate material during the design process.
Cast hemispherical cylinder bottoms can be calculated using the strength formula for internally pressurized spherical shells.
For hemispherical cylinder bottoms made of cast steel, calculated stress and strength condition are as follows:
Where:
R1 — inner radius of the spherical shell, mm;
R 2— outer radius of the spherical shell, mm;
Other parameters are the same as above.
For hemispherical cylinder bottoms made of cast iron (excluding annealed ductile cast iron), the second strength theory is used for the strength condition, and its equivalent calculated stress and strength condition are as follows:
In the formula:
[σ] — the allowable stress of the material, MPa, [σ] = σb/n.
2.1.5 Some Design Guidelines for Hydraulic Cylinders
① The radius of the transition arc from the cylinder bottom to the cylinder wall should generally not be less than D/8, where D is the inner diameter of the cylinder.
② The surface roughness value of the arc surface in the stress concentration area should generally not exceed Ra3.2 μm.
③ The distance between the circumferential weld and the inner surface of the cylinder bottom should be as large as possible, but not less than 0.75D₁, and the distance from the upper surface of the flange should also not be less than (0.75~1.0)D₁, where D₁ is the outer diameter of the cylinder barrel.
④ Let K=D₁/D. When K≤1.15, the cylinder body subjected to internal pressure can be calculated using the thin-walled cylinder formula, meaning that the influence of radial stress can be ignored, and the tangential stress can be considered to be uniformly distributed along the wall thickness.
Where:
M — Bending moment;
δ1 — Wall thickness of the stepped hole;
Others are as above.
Hydraulic presses should have sufficient rigidity and strength, but the rigidity requirement cannot replace the strength requirement, and the same applies to the hydraulic cylinders used in hydraulic presses.
Although the main failure mode of hydraulic cylinders used in hydraulic presses, especially the cylinder body, is fatigue failure, static load failure should absolutely not be ignored.
2.1.6 Technical Requirements for Hydraulic Cylinder Operation
The technical requirements for the trial run and/or operation of hydraulic cylinders vary in different hydraulic cylinder standards. For example, in standard “General Technical Conditions for Marine Reciprocating Hydraulic Cylinders” stipulates that the hydraulic cylinder should operate without jamming at a working medium temperature of -15℃.
In standard “General Technical Conditions for Forging and Pressing Machinery” stipulates that after assembly of moving and rotating parts, the movement should be smooth, flexible, and easy, without any obstruction.
In standard “Technical Conditions for Hydraulic Presses” stipulates that the hydraulically driven hydraulic cylinder should not exhibit vibration, crawling, or stagnation within the specified stroke and speed range (during operation), and there should be no impact phenomena that affect normal operation during reversal and pressure relief.
In standard “Hydraulic Cylinders for Metallurgical Equipment (PN≤25MPa)” stipulates that during no-load and loaded operation, the movement of the piston should be smooth, and there should be no abnormal phenomena such as crawling.
In standard “Technical Conditions for Agricultural Double-Acting Hydraulic Cylinders” stipulates that during the trial run, the piston movement should be uniform, and there should be no abnormal phenomena such as crawling or external leakage.
In standard “Hydraulic Cylinders” stipulates that during the low-pressure test, the hydraulic cylinder should be free from vibration or crawling.
In standard “Large Hydraulic Cylinders” stipulates that the dynamic load test of the hydraulic cylinder should be conducted at the user’s site, and the smoothness and flexibility of the movement should be observed.
In standard “Hydraulic Cylinders for Marine Hatch Covers” stipulates that at the nominal pressure, the tested cylinder (minimum stable speed test) should operate over its full stroke at a speed of 8-10 mm/s for more than two cycles, without any abnormal phenomena such as crawling. According to standard “Servo Hydraulic Cylinders Part 1: Technical Conditions,” when the piston diameter is 500~1000mm, the runout value shall not exceed 0.05mm.
Considering all the above standards, the starting and operating conditions of a qualified hydraulic cylinder should be as described in Table 1-76.
Table 1-76 Description of the starting and operating conditions of a qualified hydraulic cylinder
Note: For hydraulic cylinders requiring specific cushioning performance, the description should also include “there should be no metallic impact sound when the stroke reaches its end.”
★★★Review of selected articles in our hydraulic cylinder engineering newsletters:
- Classification and Structure of Hydraulic Cylinders
- Hydraulic Cylinder Parameters and Parameter Calculation
- Hydraulic Cylinder Parameter Calculation Example
- Technical requirements for design and manufacturing of hydraulic cylinders-Barrel tube
- Technical requirements for Piston and Piston rod
- Technical requirements for Cylinder head and cylinder bottom
- Technical requirements for guide sleeves
- Technical requirements for sealing devices
- Technical Requirements for Buffer, Venting, Anti-loosening, and Other Devices
- Technical Requirements for Installation and Connection
- Several Design Methods for Flow Regeneration Using Differential Circuits
- Design, calculation and processing points of hydraulic cylinders: recommended collection
- Piston rod that is too smooth or too rough will affect the sealing life of the hydraulic cylinder
- Hydraulic Cylinder Assembly Technical Requirements