Ingenieurwesen - Hidromec

Ein Hydraulikzylinder (auch unter dem Namen hydraulischer Linearmotor) bekannt is ist eine mechanische Vorrichtungen zur Erzeugung einer geradlinigen Bewegung in eine Richtung. Er wird bei zahleichen Anwendungen eingesetzt, vor allem bei mechanischen Geräten und bei der Konstruktion von Fahrzeugen, Industriemaschinen und Anwendungen im Bauingenieurwesen.

Hidromec ist Dank des Know-how ihrer Mitarbeiter in der Lage Zylinder für Ihre speziellen Anwendungen zu erfinden, zu entwerfen und zu bauen, sowie zu warten und zu verbessern.

Engineering bedeutet die Technik der Durchführung und Kontrolle der Konformität, ein Ziel, das nicht einfach zu erreichen ist. Ein getestetes und ISO9001 zertifiziertes Modell muss mehrere Phasen durchlaufen: Von der Überprüfung und Kontrolle der Materialien jedes einzelnen Bestandteils über die Analyse der Oberflächenbeschichtung bis hin zum Reverse Engineering der Teilkomponenten. All das um die beste Qualität und Konformität des Produkts und seiner einzelnen Bestandteile zu garantieren und eine Konformitäts-Datenbank zu erstellen.

Buckling

Buckling without side loading

Special problems to do with stability occur when cylinders with long stroke lengths are used. For the purpose of calculation these cases are divided into areas:

Non elastic buckling loads (Tetmajer’s calculation) and n
Elastic or Hook’s buckling loads (its critical limiting load is determined
by Euler’s equation) n

In hydraulic cylinder Euler’s calculation is basically the calculation used, as the piston rod may
usually be considered to be a slender strut (negligible diameter).

Buckling load and operation load are then calculated as follows:

Buckling load K= ………In N (1) i.e. the rod buckles under this load
Max. operating load F = K/S In N (2)
Sk = free buckling length in mm
E = modulus of elasticity (2.1 x 10 * for steel ) in N/mm
J = moment of inertia for circular cross-section in mm* …..
S = safety factor (3.5)

The length to be used as the free buckling length may be determined from the Euler loading cases (see table 4). In order to simplify the calculation the stiffening due to the
cylinder tube is ignored. This provides the required safety margin in standard cylinders, the installation position of which is usually not known, in order to cater for any superimposed bending loads.

Table 4: Euler’s loading cases

Euler’s loading case	Case 1 One end free, one end rigidly connected.	Case 2 (Basis case) Two ends pivoted.	Case 3 One end pivoted, one end rigidly connected.	Case 4 Two ends rigidly connected.
Illustration
Free buckling length
Installation position for cylinder Note	Mounting type FA,FB,LA,LB, MF3, ME7,MF4,ME8,MS2	Mounting type TA,TC,CA,CB,MP3,MP1, MT4	Mounting typeFA,FB,LA,LB,MF3,ME7, MF4,ME8,MS2 Load must be carefully guided, or else possible bracing.	Mounting type FA,FB,LA,LB,MF3,ME7, MF4,ME8,MS2 Not suitable, as bracing is to be expected.

Force

Hydraulic force - area formulas and calculator

The force produced by a double acting hydraulic piston on the rod side can be expressed as

F₁ = (π (d₂² - d₁²) / 4) P₁ (1)
where
F₁ = rod pull force (lb, N)
d₁ = rod diameter (in, m)
d₂ = piston diameter (in, m)
P₁ = pressure in the cylinder (rod side) (lf_f/in²(psi), N/m² (Pa))

The force produced opposite the rod can be expressed as

F₂ = (π d₂²/ 4) P₂ (2)
where
F₂ = rod push force (lb, N)
P₂ = pressure in the cylinder (opposite rod) (lf_f/in²(psi), N/m² (Pa))

Push Diagram

Rod pushing force for hydraulic cylinders are indicated below:

1 psi (lb/in²) = 144 psf (lb_f/ft²) = 6,894.8 Pa (N/m²) = 6.895x10^-3 N/mm² = 6.895x10^-2 bar
1 N/m² = 1 Pa = 1.4504x10^-4 lb/in² = 1x10^-5 bar = 4.03x10^-3 in water = 0.336x10^-3 ft water = 0.1024 mm water = 0.295x10^-3 in mercury = 7.55x10^-3 mm mercury = 0.1024 kg/m² = 0.993x10^-5 atm
1 lb_f (Pound force) = 4.44822 N = 0.4536 kp
1 N (Newton) = 0.1020 kp = 7.233 pdl = 7.233/32.174 lb_f = 0.2248 lb_f = 1 (kg m)/s² = 10⁵ dyne = 1/9.80665 kg_f
1 in (inch) = 25.4 mm
1 m (meter) = 39.37 in = 100 cm = 1000 mm

Pull Diagram

Rod pulling force for hydraulic cylinders are indicated below:

Rod

Piston Rod Size Selection

The selection of a piston rod for thrust (push) conditions requires the following steps to be carried out:

1. Determine the type of cylinder mounting style and rod end connection to be used. Consult the Stroke Factor table and determine which factor corresponds to the application.
2. Using this stroke factor, determine basic length from the equation:
Basic Length = Net Stroke x Stroke Factor
( The Piston Rod Selection Chart, below, is prepared for standard rod extensions beyond the face of the gland retainer. For rod extensions greater than standard’ add the increase to the stroke to arrive at the basic length’)
3. Find the load imposed for the thrust application by multiplying the full bore area fo the cylinder by the system pressure, or by referring to the Push and Pull Force charts.
4. Using the Piston Rod Selection Chart below, look along the values of ‘ basic length ’ and ‘ thrust ‘ as found in 2. and 3. above, and note the point of intersection.

The correct piston rod size is read from the diagonally curved line labeled ‘Rod Diameter‘ above the point of intersection.

Long Stroke and Stop Tubes

When considering the use of long stroke cylinders, the piston rod should be of sufficient diameter to provide the necessary column strength.
For tensile(pull)loads, the rod size is selected by specifying standard cylinders with standard rod diameters and using them at or below the rated pressure.

For long stroke cylinders under compressive loads, the use of stop tubes should be considered, to reduce bearing stress. Selection of a stop tube is described.

Size

CALCULATION OF CYLINDER DIAMETER

Given that the load and operating pressure of the system are known, and that a piston rod size has been estimated taking account of whether the rod is in tension(pull) or compression (push), then the cylinder bore can be selected.
If the piston rod is in compression, use the ‘Push Force’ table below.

Identify the operating pressure closest to that required;
In the same column, identify the force required to move the load (always rounding up);
In the same row, lock along to the cylinder bore required.

If the cylinder envelope dimensions are too large for your application increase the operating pressure, if possible, and repeat the exercise.

Push Force

Bore φ ㎜	Cylinder Bore Area ㎟	Cylinder Push Force in kN
Bore φ ㎜	Cylinder Bore Area ㎟	10 Bar	40 Bar	63 Bar	100 Bar	125 Bar	160 Bar
40	1257	1.3	5.0	7.9	12.6	15.7	20.1
50	1964	2.0	7.9	12.4	19.6	24.6	31.4
63	3118	3.1	12.5	19.6	31.2	39.0	49.9
80	5027	5.0	20.1	31.7	50.3	62.8	80.4
100	7855	7.9	31.4	49.5	78.6	98.2	126
125	12272	12.3	49.1	77.3	123	15.3	196
160	20106	20.1	80.4	127	201	251	322
200	31426	31.4	126	198	314	393	503
250	49087	49.1	196	309	491	614	785
320	80425	80.4	322	507	804	1005	1287

If the piston rod is in tension, use the ‘Deduction for Pull Force’ table. The procedure is the same but, due to the reduced piston surface area resulting from the piston rod, the force available on the ‘pull’ stroke will be smaller, To determine the pull force.

Follow the procedure given for ‘push’ applications as described above.
Using the ‘Deduction for Pull Force’ table below, establish the force indicated according to the rod diameter and pressure selected.
Deduct this from the original ‘Push’ force. The resultant is the net force available to move the load.

If this force is not large enough, go through the process again but increase the system operating pressure or cylinder diameter if possible. If in doubt, Our design engineers will be pleased to assist.

Deduction for Pull Force

Piston Rod φ ㎜	Piston Rod Area ㎟	Reduction in Force
Piston Rod φ ㎜	Piston Rod Area ㎟	10 Bar	40 Bar	63 Bar	100 Bar	125 Bar	160 Bar
22	380	0.4	1.5	2.4	3.8	4.8	6.1
28	616	0.6	2.5	3.9	6.2	7.7	9.9
36	1018	1.0	4.1	6.4	10.2	12.7	16.3
45	1590	1.6	6.4	10.0	15.9	19.9	25.5
56	2463	2.5	9.9	15.6	24.6	30.8	39.4
70	3848	3.8	15.4	24.2	38.5	48.1	61.6
90	6362	6.4	25.5	40.1	63.6	79.6	102
110	9503	9.5	38.0	59.9	95.1	119	152
140	15394	15.4	61.6	97.0	154	193	246
180	25447	25.4	102	160	254	318	407
220	38013	38.0	152	240	380	475	608