Documentation

Cylinder Cushion

Cushion in hydraulic cylinders

Library

Hydraulic Cylinders

Description

The Cylinder Cushion block models a hydraulic cylinder cushion, the device that decelerates the cylinder rod near the end of the stroke by restricting the flow rate leaving the cylinder chamber. The figure shows a typical design of a cylinder cushion [1].

As the piston moves toward the cap (to the left in the figure), the cushioning bush enters the chamber in the cap and creates an additional resistance to the fluid leaving the chamber. The bush profile determines the desired deceleration. Near the end of the stroke, the fluid flows through the gap between the bush and the cap and through the cushioning valve with constant cross-sectional area. The check valve located between the chambers allows free flow to the piston chamber to ease the piston breakaway from the end position.

The block is implemented as a structural model that replicates a cushioning device, as shown in this diagram.

The Variable Orifice block represents a variable gap between the bush and the cavity machined in the end cap. The lookup table of the Variable Orifice block implements the relationship between the orifice area and the piston displacement. The Fixed Orifice and the Check Valve blocks simulate the cushioning valve and the check valve installed between chambers. The Translational Hydro-Mechanical Converter represents a plunger created by the bush and the cavity. The Ideal Translational Motion Sensor block monitors the piston displacement and conveys it (with the initial piston position accounted) to the Variable Orifice block. The names assigned to the nested blocks in the model are shown in parentheses.

The block develops a cushioning effect for the flow rate from port B to port A. The check valve in the block is oriented from port A to port B.

You can use this block with any of the cylinder blocks in the library to model a single-acting or double-acting cylinder with cushion. The following diagram shows the model of a double-sided hydraulic cylinder with cushion built from a Double-Acting Hydraulic Cylinder block and two Cylinder Cushion blocks.

You can adjust the cushioning effect by changing the area of the fixed orifice and the profile of the cushioning bush (variable orifice). Specify the profile using the one-dimensional lookup table of the orifice area versus piston displacement. The next figure shows a typical configuration of a double-acting cylinder with the double-sided cushioning, similar to the model shown in the block diagram above.

To ensure cushioning on both sides of the stroke, set the variable orifice area of the left cushion (AL) and the right cushion (AR) similar to the profile shown in the figure. The origin of the plot is located at the position where the piston touches the cap. If the cylinder acts in the negative direction, the piston displacements are negative, and you must make the profile specification in the fourth quadrant.

The following figure shows a typical motion diagram of a cylinder with the double-sided cushioning.

The cushions are set to provide deceleration at ~10 mm before the end of the stroke. The stroke of the cylinder is 10 cm, and the initial position of the piston is 0.04 m. The plot shows the velocity (yellow line) and motion (magenta line) profiles.

Connections A and B are hydraulic conserving ports associated with the device hydraulic inlet and outlet. Connection R is a mechanical translational conserving port that connects to the cylinder rod. Connection C is a mechanical translational conserving port that connects to the cylinder clamping structure.

Parameters

Cushion Piston Tab

Cushion piston area

Addition of the cushion to a cylinder converts the respective cylinder into two cylinders, rigidly connected and acting in parallel, with the total effective area equal to the piston area before addition. This parameter sets the area of the cushion piston, which is the face area of the cushion bush. The default value is 1e-4 m^2.

Piston initial displacement

The distance between the cylinder piston and cap A at the start of simulation. The default value is 0, which corresponds to the fully retracted position of the piston.

Piston orientation

Piston orientation with respect to the globally assigned positive direction. Since the cushion piston is part of the cylinder piston, its orientation must be the same as the orientation of the cylinder piston at the side the cushion is attached to. Similar to a cylinder model, if pressure applied at port A exerts force in the negative direction, set the parameter to Acts in negative direction. The default value is Acts in positive direction.

Fixed Orifice Tab

Fixed orifice area

The area of the fixed orifice installed between cushion chambers. The default value is 1e-6 m^2.

Fixed orifice flow discharge coefficient

Semi-empirical coefficient that is used in the computation of flow rate through the fixed orifice. The default value is 0.7.

Fixed orifice critical Reynolds number

The maximum Reynolds number for laminar flow through the fixed orifice. The transition from laminar to turbulent regime is supposed to take place when the Reynolds number reaches this value. The value of the parameter depends on the orifice geometrical profile. You can find the recommendations on the parameter value in hydraulic textbooks. The default value is 10.

Variable Orifice Tab

Tabulated piston displacements

Vector of input values for piston displacements, specified as a one-dimensional array. The input values vector must be strictly increasing. The values can be nonuniformly spaced. The minimum number of values depends on the interpolation method: you must provide at least two values for linear interpolation, at least three values for smooth interpolation. The Tabulated piston displacements values are used together with Tabulated orifice area values for one-dimensional table lookup. Due to the nature of the cylinder hard stops, the piston can move below zero and above the stroke value. It is good practice to account for piston deformation and provide piston displacements beyond the ideal stroke range to avoid extrapolation. The default values, in mm, are [-2, 10, 11, 89, 90, 102].

Tabulated orifice area

Vector of orifice areas, specified as a one-dimensional array. The vector must be the same size as the piston displacements vector. All the values must be positive. The default values, in cm^2, are [0.004, 0.006, 9, 9, 9, 9].

Variable orifice interpolation method

Select one of the following interpolation methods for approximating the output value when the input value is between two consecutive grid points:

  • Linear — Select this option to get the best performance.

  • Smooth — Select this option to produce a continuous curve with continuous first-order derivatives.

For more information on interpolation algorithms, see the PS Lookup Table (1D) block reference page.

Variable orifice extrapolation method

Select one of the following extrapolation methods for determining the output value when the input value is outside the range specified in the argument list:

  • Linear — Select this option to produce a curve with continuous first-order derivatives in the extrapolation region and at the boundary with the interpolation region.

  • Nearest — Select this option to produce an extrapolation that does not go above the highest point in the data or below the lowest point in the data.

For more information on extrapolation algorithms, see the PS Lookup Table (1D) block reference page.

Variable orifice flow discharge coefficient

Semi-empirical coefficient that is used in the computation of flow rate through the variable orifice. The default value is 0.7.

Variable orifice critical Reynolds number

The maximum Reynolds number for laminar flow through the variable orifice. The transition from laminar to turbulent regime is assumed to take place when the Reynolds number reaches this value. The value of the parameter depends on the orifice geometrical profile. You can find recommendations on the parameter value in hydraulics textbooks. The default value is 10.

Variable orifice leakage area

The total area of possible leaks in the completely closed orifice. The main purpose of the parameter is to maintain numerical integrity of the circuit by preventing a portion of the system from getting isolated after the valve is completely closed. The parameter value must be greater than 0. The default value is 1e-12 m^2.

Check Valve Tab

Check valve maximum area

Valve passage maximum cross-sectional area. The default value is 1e-4 m^2.

Check valve cracking pressure

Pressure level at which the orifice of the valve starts to open. The default value is 0.5e5 Pa.

Check valve full opening pressure

Pressure differential across the valve needed to fully open the valve. Its value must be higher than the cracking pressure. The default value is 1.5e5 Pa.

Check valve flow discharge coefficient

Semi-empirical coefficient that is used in the computation of flow rate through the check valve. The default value is 0.7.

Check valve critical Reynolds number

The maximum Reynolds number for laminar flow through the check valve. The transition from laminar to turbulent regime is assumed to take place when the Reynolds number reaches this value. The default value is 10.

Check valve leakage area

The total area of possible leaks in the completely closed valve. The main purpose of the parameter is to maintain numerical integrity of the circuit by preventing a portion of the system from getting isolated after the valve is completely closed. The parameter value must be greater than 0. The default value is 1e-12 m^2.

 Restricted Parameters

Global Parameters

Parameters determined by the type of working fluid:

  • Fluid density

  • Fluid kinematic viscosity

Use the Hydraulic Fluid block or the Custom Hydraulic Fluid block to specify the fluid properties.

Ports

The block has the following ports:

A

Hydraulic conserving port connected to the cylinder inlet.

B

Hydraulic conserving port connected to the cylinder outlet.

R

Mechanical translational conserving port connected to the cylinder rod.

C

Mechanical translational conserving port connected to the cylinder clamping structure.

References

[1] Rohner, P. Industrial Hydraulic Control. Fourth edition. Brisbane : John Wiley & Sons, 1995.

Introduced in R2013b

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