How is stroke length calculated in telescopic cylinders?

In the realm of engineering for fluids, there are few parts that require such precision in geometry, like the telescopic hydraulic cylinders. It is found in dump trucks, floating work platforms for aerials, marine cranes, and industrial lift equipment. Telescopic hydraulic cylinders resolve an essential design challenge that is how to get lengthy working strokes in an extremely compact and retracted unit. But the process of achieving this efficiency is based on one crucial calculation: stroke length.

The wrong stroke length in the telescopic cylinder isn't an unimportant error. It has a direct impact on load capacity, the volume of oil required, system pressure, and the quality of the structural integrity of each stage. This article delves into the mechanics that calculate stroke length stage by stage.

What is a telescopic cylinder?

A telescopic cylinder is comprised of multiple tubular stages, typically between two and five, which extend in a sequence to create an overall stroke that is much greater than the length of the cylinder. In contrast to a single-stage cylinder, where stroke equals the distance a piston rod is moving, a cylinder's effective stroke is the total of stage extensions.

There are two main configurations:

• Single-acting telescopic cylinders that are extended using hydraulic pressure and retracted by gravity or the weight of the load. Common in dump truck bodies.
• Double-acting telescopic cylinders—both retraction and extension are powered by hydraulics. They are used when controlled retraction is required, like in marine and refuse vehicle applications.

The distinction is crucial in stroke calculation since dual-acting design requires more intricate geometric calculations for annular area and rod volume across each stage.

The basic formula is of the total stroke

The stroke total of a telescopic cylinder is the sum of all stage strokes:

Total Stroke (S_total) = S1 + S2 + S3 + ... + Sn

Each Si represents the total travel distance of the stage that is in relation to the stage that surrounds it.

However, the calculation of each stage stroke separately requires careful consideration of geometry, particularly the lengths of overlap, which must be maintained between stages with full extension in order to protect the structural integrity of the structure and avoid stage separation.

Stage overlap: The most important design factor

Each stage of a telescopic cylinder should have the minimum amount of overlap with the barrel enclosing it at full extension. The overlap serves two functions to keep the stage level (preventing deflection due to side loading) and also ensures that the sealing surface is engaged.

The minimal overlap is usually defined as a function of the stage's internal diameter:

Minimum Overlap (Lo) = k x Di

Where:

• Di is the diameter of the inner part of the barrel's outer diameter of the stage.
• K is an empirical variable that is typically found within the range 1.0 to 1.5, dependent on the use conditions, side-loading, and the manufacturer's standards.

For mobiles that are heavy-duty and that are subject to lateral loads like tipper cylinders -- the k ranges in the range of 1.2 up to 1.5 are common. In vertical-lift applications with good guidance, K = 1.0 is a reasonable number.

Calculating the individual stage stroke

Each stage's usable stroke is calculated from the stage's total length without the overlap allowance, as well as wall thickness adjustments:

Si = Li - Loi - Di

Where:

• Li = length total of stage (i.e., the physically tube's length the sleeves)
• The Loi is the minimum amount of overlap that must be present for stage I
• Di refers to structural deviations that include the thickness of the end cap and depth of the bearing/gland housing and the wiper seal housing

The designer has to be able to iteratively solve the geometry; the length of each stage determines its stroke. However, its stroke determines how the length of the collapse is distributed throughout the whole assembly.

The stroke ratio and length of the stroke are both reduced.

One of the key performance metrics for a telescopic cylinder is the stroke-to-collapsed-length ratio—often called the extension ratio. In the case of an n-stage cylinder:

Extension Ratio = S_total / L_collapsed

A properly designed two-stage telescopic cylinder generally has extension ratios between 1.6:1 and 1.9:1. Three-stage designs are able to reach 2.2:1 to 2.6:1, and five-stage assemblies are common in large-capacity tipper trucks and can reach ratios that exceed 3.5:1.

The length of the stage that has been collapsed is not just the longest length on the stage with the longest length. It encompasses the base arrangement for mounting and the geometry of the port hydraulic and any fittings for the plunger nose that all take up axial space and do not contribute to stroke.

Pressure and load considerations throughout different stages

Stroke length calculations cannot be done in isolation from analysis of force. In a telescopic cylinder, every time a stage expands, the area of the piston shrinks due to the fact that the size of the bores for each stage is less than the preceding one. This means that the force output decreases with each stage change at the same pressure.

For a telescopic cylinder that is single-acting under load F, at the pressure of supply P:

Ai = p/4 x Di²

F = P x Ai

The design should ensure that the stage with the smallest bore—that is, the last to expand and usually has the biggest moment arm—can be able to generate enough force when operating at the system's pressure. This is often the reason for the choice of the stage's diameters, not the reverse.

Oil volume per stage

Another direct result of the calculation of stroke length is the volume of oil needed for each stage to be filled:

Vi = Ai x Si

In which case the AI refers to the annular space of the stage I (bore area) minus the cross-sectional area of the inside of the stage or the plunger it surrounds.

The total volume of system oil is the total of all the stage volumes as well as the line and plumbing volume. This is a crucial figure for the sizing of hydraulic reservoirs as well as pump flow rate determination and estimation of cycle time. The under-sizing of the reservoir or pump in relation to the telescopic's total demand for oil is the most common cause of underperformance on field-based installations.

A practical example: Single-acting three-stage Cylinder

Think about a three-stage single-acting telescopic cylinder that has the following stage diameters (barrel): Stage 1 (barrel) - 200 millimeters, Stage 2 (barrel) - 160 millimeters, and Stage 3 (plunger) - 120 millimeters. Consider a wall thickness of 8 mm all over the three stages; the k value is 1.2 for all stages, and bearing/gland reductions of 40 millimeters per stage.

Stage 1 bore = 200 2(8) = 184 mm. Stage 2 bore = 200 2(8) = 184 millimeters - overlap = 1.2 2021 mm. Stage 2 bore = 161 x 2(8) = 140 mm - overlap = 1.2 x 173 mm stage 3 (plunger) (plunger) -- No enclosure stage, stroke limit by the geometry of the Stage 2 bore.

If each tube measures 900 mm, the strokes usable would be:

• S1 = 900 - 221 - 40 = 639 mm
• S2 = 900 - 173 - 40 = 687 mm
• S3 = 90 + 40 = 860 mm (plunger that is limited in Stage 2's extension depth to full extent)

Total stroke of 2,186 millimeters from an approximate collapsed length of 1000-950 mm. This is an extension ratio of close to 2.2:1.

Common design pitfalls

Inadequately estimating overlap requirements when under lateral loads—side forces can reduce overlap, leading to wear and tear on the bearing's lands and may result in stage seizure or premature failure of the seal.

By ignoring the plunger's length, the fitting of the nose to the point of the final stage is dead length but is not a part of the stroke.

If stage lengths are equal in well-designed designs, lengths of the stage are typically separated to balance stroke contribution and reduce length collapse.

Inadvertently ignoring thermal expansion when working in high-cycle or high-temperature applications, the expansion of thermal energy in tube stages must be incorporated into overlap margins in order to avoid locking at the operating temperature.

The calculation of stroke length in telescopic cylinders is a multi-variable engineering task that incorporates geometry forces analysis, overlap mechanics, and accounting for fluid volume. The basic formula that calculates all strokes as the product of each stage's strokes, minus structural and overlap—it is quite simple in the sense of. In the real world it requires a meticulous focus on each stage's dimensional stack-up as well as the load it needs to support.

When designing or specifying engineers for telescopic cylinders, the calculation of stroke is the base on which pressure selection for the system as well as pump sizing and structural analysis rest. Making it perfect from the beginning is much more affordable than fixing it later on in the field.