Active vibration damping in hydraulic construction machinery

Active Vibration Damping in Hydraulic Construction Machinery Procedia Engineering 176 ( 2017 ) 514 – 528 1877 7058 © 2017 The Authors Published by Elsevier Ltd This is an open access article under the[.]

Procedia Engineering 176 ( 2017 ) 514 – 528

1877-7058 © 2017 The Authors Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license

( http://creativecommons.org/licenses/by-nc-nd/4.0/ ).

Peer-review under responsibility of the organizing committee of the international conference on Dynamics and Vibroacoustics of Machines

doi: 10.1016/j.proeng.2017.02.351

ScienceDirect

Dynamics and Vibroacoustics of Machines (DVM2016)

Active vibration damping in hydraulic construction machinery

Addison Alexandera,*, Andrea Vaccaa, Davide Cristoforib

a Purdue University, 610 Purdue Mall, West Lafayette, IN 47907, USA

b CNH Industrial, Strada di Settimo 323, San Mauro Torinese 10099, Italy

Abstract

Hydromechanical systems are prone to significant oscillations, due to the ability of hydraulic oil to store potential energy This is extremely important when considering mobile hydraulic machinery, especially those machines which handle large loads Oscillations can negatively affect the stability of the payload, the comfort of the operator, and the overall safety of the system For the particular case of earthmoving machines, several systems have been designed in order to alleviate these oscillations and increase machine operability These systems include both passive and active designs which attempt to utilize the motion of the payload in such a way as to cancel out the effect of machine vibrations

This paper seeks to assess the potential advantages of active oscillation control strategies with respect to current state of art passive strategies A reference case vehicle (wheel loader) is presented and analyzed in order to determine its typical vibrational behavior A simulation model for the reference machine is developed and used in assessing machine performance The effectiveness of the current passive vibration damping approach with respect to reducing the vibrations perceived by the operator

in the cabin, as well as those affecting the payload, is presented Then, an active (electrohydraulic) control structure is presented using both acceleration and pressure feedback, including an adaptive controller constructed using an extremum-seeking algorithm To quantitatively compare the relative performances of these various systems, an appropriate objective function is defined Simulation results are presented for each of the considered control strategies, and their performances are compared The simulation indicates a performance of active vibration control systems roughly equivalent to that of currently implemented passive control strategies In some cases, the active control performance is actually two to three times as effective as the passive control

©2016 The Authors Published by Elsevier Ltd

Peer-review under responsibility of organizing committee of the Dynamics and Vibroacoustics of Machines (DVM2016)

Keywords:Vibration control; extremum seeking; hydraulics; construction machinery; electrohydraulic control; oscillation damping

* Corresponding author Tel.: +1-765-477-1609; fax: +1-765-448-1860

E-mail address: addisonalexander@purdue.edu

© 2017 The Authors Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license

( http://creativecommons.org/licenses/by-nc-nd/4.0/ ).

Peer-review under responsibility of the organizing committee of the international conference on Dynamics and Vibroacoustics of Machines

1 Introduction

One of the prevalent issues related to the operation of mobile hydraulic construction machinery is the propensity

of these systems to generate oscillations while traveling Conditions such as driving on uneven surfaces introduce vibrations into the machine, which can excite certain oscillatory modes, often causing strong low-frequency motion

of the system This can have several negative effects, including decreasing implement and/or load stability, causing discomfort for the operator, and reducing the overall safety of the system Without an adequate system for reducing machine vibrations, productivity, safety, and machine life can all suffer

Several solutions have been proposed in the past to address this issue, with varying degrees of success In general, these solutions fall into two different categories The first category is that of “passive” vibration damping These designs take advantage of the behavior of hydraulic systems, often incorporating specialized components or adding capacitive and/or resistive elements into the existing circuitry [1,2] Passive damping is typically effective in cancelling vibrations, but only in a very limited range of operating conditions Furthermore, by modifying the hydraulic circuit, the response dynamics of the system are often negatively impacted Also, the additional required hydraulic elements represent an added cost for the system

Fig 1 Two-body system showing chassis and implement

These and other limitations of passive vibration damping systems inspired the development of “active” vibration control methods The term active refers to the fact that these systems utilize electrohydraulic setups that actively monitor various system parameters and generate electronic signals to control the motion of the hydraulic components

in such a way that the machine oscillations are cancelled out [3] One of the main advantages of active control is that it often can be implemented in such a way that modifications to the basic layout of hydraulic system the reference machine are not required Such control strategies have previously been applied to several prototype machines in controlled environments, including those utilizing displacement-control architectures [4,5] This work,

on the other hand, focuses on a more conventional hydraulic architecture for controlling actuators through hydraulic control valves The schemes presented in this paper use either machine acceleration or hydraulic pressure to synthesize the control signal

The active ride control method put forth in this work utilizes a simple, non-model-based controller to damp the machine vibrations This simple control structure has several benefits, in that it can be transferrable from one system

to another and the theory behind it is well understood However, this also means that the controller relies heavily on

an online optimization method in order to work properly for any given system To verify the feasibility of the the proposed controller, and to gain an understanding of the system behavior, a simulation model was created

A basic schematic of this system model is shown in Fig 1 It includes considerations for rigid body motion and hydraulic system dynamics, as well as a simple tire deflection model Oscillations are introduced into the system through vibrations represented as vertical motion of the tire/road interface The tires themselves are modeled as a spring-damper connection between the road surface and the axle of the machine

Using the simulation model, the effectiveness of the current passive vibration damping approach is analyzed The existing passive system is based on the addition of a capacitive element (accumulator) and a resistive element (4/4

spool valve) into the hydraulic circuit These elements work together in a way similar to the shock absorbers on an automobile suspension The resistive component damps the transmitted vibrations between the implement and the chassis, while the capacitive component can reduce both the amplitude and frequency of the transmitted vibrations

In order for it to effectively optimize the controller parameters, a numerical objective function was defined which allows different controller performances to be compared This objective function attempts to quantify the oscillations in the system over a given period of time A well-defined objective function is also necessary for implementing the non-model-based adaptive controller

Nomenclature

Variables

A area

a gain of sinusoidal perturbation

C H hydraulic capacitance

c damping rate of tire

F force

f function describing dynamic system

h high-pass filter pole location

J moment of inertia

k spring rate of tire, extremum-seeking algorithm integrator gain

M moment

m mass

p pressure

Q net flow into control volume

t time

x displacement in the x-direction

y displacement in the y-direction, output of dynamic system

z measured quantity

α hydraulic cylinderchamber area ratio

β wheel loader boom angle

γ isentropic exponent of a gas

Δ change in parameter

θ rotational displacement, parameter estimate

ξ damping ratio of second-order system

τ time constant of first-order system

ω frequency of sinusoidal perturbation

ω n natural frequency of second-order system

Subscripts

A related to the cylinder chamber of the hydraulic piston

atm atmospheric pressure

acc related to the hydraulic accumulator

B related to the piston chamber of the hydraulic piston

command the value sent into a dynamic system as a command

ext external to current system

gas related to the gas in the hydraulic accumulator

i related to component i

net the net value of a term (in minus out)

oil related to the hydraulic oil in the system

PRC related to the passive ride control (PRC) system

pilot related to the pilot line of a valve

pre related to the pre-charge pressure of the hydraulic accumulator

pump occurring at the hydraulic pump

raise related to the raising action of the hydraulic piston

rod related to the rod of the hydraulic piston

W related to the wheels of the wheel loader

x occurring in or about the x-direction

y occurring in or about the y-direction

z occurring in or about the z-direction

0 initial value

2 Reference Machine

For the purposes of determining the performance of the active vibration damping method used in this paper, a reference machine was needed which could be a representative case for describing the behavior of mobile construction equipment.The reference machine used for this work is a Case 621F wheel loader This is a twelve-metric ton wheel loader with articulated steering and a loading bucket capable of holding 1.9 m3 of material It has a four-speed transmission with a maximum speed of 38.6 km/h

This research is primarily focused on the hydraulic actuation of the wheel loader implement (boom and bucket with linkages) Therefore, no considerations are given to the other actuators on the machine or the transmission system The hydraulic circuit controlling the implement motion is a post-compensated load-sensing (LS) system, in which the LS supply pump serves the boom and bucket as users

Fig 2 Boom control system schematic, including passive ride control (PRC)

The reference machine is also equipped with a passive ride control (PRC) setup capable of damping vibrations under certain operating conditions The actual hydraulic schematic of this system is shown in Fig 2 In this case, the oscillation reduction is accomplished by the addition of a hydraulic capacitance and a hydraulic resistance into the existing circuit which controls the position and motion of the boom This capacitance takes the form of an accumulator (labeled as #13 in Fig 2) connected to the boom control circuit via a pilot-operated 4/4 spool valve The inclusion of the accumulator and valve has a significant effect on the dynamic behavior of the system For instance, the system now includes the pressurized gas within the accumulator, which has a much higher compressibility than the hydraulic oil This allows fluid to flow in and out of the accumulator as the changing pressure causes the volume of the gas to expand and contract This flow means that the system with the PRC

enabled is more pliable; that is, it allows a wider range of relative motion between the wheel loader frame and the implement By adjusting the orifice (#10) on the pilot line of the 4/4 spool valve (#9), the dynamics of this flow, and hence the dynamics of the moving implement, can be modified even further (i.e to achieve a desirable behavior)

The primary effect of allowing a greater motion of the boom is that the wheel loader no longer behaves in theory

as a single rigid body but rather as two separate masses (implement and chassis) connected to each other through a hydraulic circuit which behaves in many respects like a spring-damper connection (see Fig 1) The motion of the wheel loader implement now produces its own forces which are reacted by the chassis of the wheel loader and which counteract the forces that cause the undesired oscillations in the machine

By tuning the accumulator and valve parameters, the equivalent spring-damper connection between the chassis and the implement can be adjusted in order to reduce the machine oscillations within a wide range of operating conditions Once the parameters for the PRC have been set, this circuit can work well at the specified operating condition, but its performance will suffer when the system is very far from the design point To overcome this limitation of the PRC, an active ride control (ARC) system is desired A well-designed active control system should not be susceptible to the performance issues mentioned when the PRC is being used far from its design point, because the active control can generate different control signals for different operating conditions

3 Machine Model

The first step in assessing the machine behavior and the effect of the various oscillation reduction methods is the generation of a suitable simulation model for the system This model has several different objectives, but its main goals are as follows First, the model needs to include the rigid body dynamics of both the chassis and the implement of the reference machine Second, it must account for the effect of the tires, as they are the only contact points between the machine and the driving surface Finally, the model must incorporate the dynamics of the hydraulic system used to control the position of the boom, as the motion of this system will play a large role in the performance of the vibration control strategies

3.1 Vehicle Dynamics Model

To generate the simulation model for the entire machine, it must be analyzed from a vehicle dynamics standpoint

As mentioned in the discussion of the reference machine, when a vibration control strategy has been activated, the implement and chassis of the wheel loader are able to move relative to each other Therefore, this system is treated

as two decoupled masses, a chassis and an implement, which are linked together via pin connections and a hydraulic cylinder

Figure 1shows the full system with the implement portion of the machine circled Since they are treated as

separate bodies, the chassis and the implement are represented as having distinct centers of gravity (labeled as CG1

and CG2, respectively) For the purposes of this research, each of these machine sections is treated as a rigid body Therefore, in terms of dynamics, each body is described by its own force balance

Equations (1) through (3) are standard free-body motion equations which have been incorporated into the model

to describe the motion of the system components In these equations, F x and F y represent the forces acting body i in the x- and y-directions, respectively (these directions are labeled in Fig 1), M z represents the moments acting about

the z-axis (extending out of the page), m i and J i ¬ are the mass and moment of inertia of body i The linear accelerations of body i in the x- and y-directions are shown as ẍ i and as ÿ i, respectively, and the rotational

acceleration about the z-axis is represented by θ̈ z,i By combining these equations with the appropriate kinematic constraints for the system (as done in [4]), this system reduces from a six degree-of-freedom model to one with only four degrees of freedom

The forces and moments in (1)-(3) include both those exterior to the machine as well as reaction forces from one body to another Also considered is the force from the hydraulic cylinders (two acting in parallel) which connect the boom (implement) to the chassis It is this force which is used to counteract the machine oscillations, so its value is closely tied to the oscillation reduction strategy being used The model describing the cylinder force is described in detail in the next subsection of this paper

To analyze the system behavior, an appropriate input for the system model must be determined In the case of this research, it was decided that the model input would be the height of the roadover time with respect to its starting height This is a reasonable analog to what the real-world system actually sees as an input, and in conjunction with the tire model described below, it translates well to a force input which will cause the dynamics model to behave appropriately Figure 3shows a typical road profile acquired from actual measurements on the reference machine, which begins with the machine remaining stationary for the first five seconds and then traveling over terrain

Fig 3 Representative road profile used as a model input (normalized)

For this research, it was decided that an appropriate model for the tire dynamics is a spring-damper model This approach is widely used in literature due to its relatively simple construction and reasonable results [4,5,7] In this model formulation, the tire is treated as a spring-damper connection between the ground and the machine The road profile controls the lower side of the vertical spring-damper connection shown in Fig 1, so the motion of the center point of the wheel W is a function of the forces generated by the spring-damper tire model

In this model, the tire is assumed to only exert a vertical force onto the machine This is because the primary input affecting the system vibrations is the height profile of the road Thus, the horizontal forces generated by the tire are neglected, as they do not contribute in an important way to the vibrations being considered

Using this simplified tire dynamics model, then, the force acting on the machine at each axle due to the tire is as follows:

where k y and c y are the equivalent (vertical) spring and damping rates for the tire, respectively, and Δy W and ẏ W are the change in relative vertical displacement and velocity of the wheel center with respect to the road surface, respectively It can be seen that when the distance between the wheel center and the road surface decreases (or is

decreasing), the vertical force acting on the machine at W increases, and it decreases in the opposite case

3.2 Boom Cylinder Hydraulic System Model

One aspect of the machine simulation model which must be represented with a high degree of accuracy is the hydraulic circuit which controls the motion of the boom of the wheel loader implement It is integral to properly simulating the machine dynamics This system is shown in Fig 2

Time [s]

-1 -0.5 0 0.5

Front axle Rear axle

The motion of the boom itself relative to the chassis of the machine is directly controlled by the position of the cylinders on each side of it These cylinders are linked hydraulically, so their motion can be considered equal A typical dual-acting single-rod cylinder, like those used on the reference machine, is shown in Fig 4 The motion of this cylinder is defined by a simple force balance equation

In equation (5), m rod represents the mass of the cylinder rod, ẍrod is the acceleration of the cylinder rod, p A and p B

are the pressures in the two cylinder chambers, A A is the area of the piston, α is the area ratio between the piston face

in the rod-side cylinder chamber and the full piston face in chamber A, and F ext includes all external forces acting on the piston, including the inertial forces of the masses connected to the rod This force includes all inertias and motion effects from the chassis and implement which are connected to the cylinder It should also be noted that friction forces are neglected in this model, as the primary forces being considered are much larger

Fig 4 Schematic of hydraulic cylinder model

It can be seen from (5) that the pressures in cylinder chambers A and B are perhaps the most important factors in determining the motion of the boom in terms of cancelling out vibrations Therefore, the pressure in each chamber needs to be defined for the model

𝑝̇ =

𝑝̇ =

In these equations, p i represents the pressure in chamber i, C H,i is the hydraulic capacitance (volume of fluid

divided by its bulk modulus) of the fluid in chamber i, Q i is the net fluid flow into chamber i, and ẋ rod is the velocity

of the cylinder rod All other variables are the same as above In general, the hydraulic capacitance C H,i is a function of the cylinder stroke (as it changes with fluid volume) Therefore, these equations are valid only at a certain cylinder position Nevertheless, because they consider not only the piston chambers but the connected transmission lines (which also have a relatively high compliance), the volumes dealt with here are so large, it isreasonable to assumethat the capacitances are constant

As this system does not have significant leakage flows, (7) can be further simplified to:

𝑝̇ =

where α is the same area ratio used in (5) above

When giving a command to the valve that raises and lowers the boom, the flow into the cylinder is fairly well defined It can be modeled using a simple orifice equation and an appropriate dynamic equation for the spool

displacement y

where for orifice i: Q i is the flow through the orifice, B i is the valve constant, y i and y 0,i are the current displacement

and initial position of the spool, and Δp i is the pressure difference across the orifice This is a very standard way of calculating the flow through a given valve However, in the case of this research, the valve pressure-flow characteristics were mapped based on experimental data available for the reference valve

Because the circuit under consideration is a load-sensing hydraulic system, the pump is designed to give a proper amount of flow so that the pressure in the supply line is always at a constant offset above the pressure of the boom

cylinder circuit Thus, Δp across the valve is more or less constant, and the flow through the valve is primarily a

function of spool displacement To model the dynamics of the spool in the valve, a second-order dynamic is given

In this equation, Y i (s) is the Laplace transform of the spool position y i , I(s) is the Laplace transform of the input command current to the spool, ω n is the natural frequency of the system, and ζ is the damping ratio of the system

This transfer function gives a second-order dynamic for the spool given a certain command current

One final consideration for this system is that while the pump flow is controlled by a load-sensing circuit, it is not capable of changing flow instantaneously To model this dynamic, a first-order time constant has been modeled for the pump flow

where Q pump (s) is the Laplace transform of the actual flow given by the pump, Q command (s) is the commanded flow from the load-sensing circuit, and τ pump is the time constant for this system In actual implementation, this is split into two different time constants, one for “stroking” and one for “de-stroking,” since the pump dynamics can be different depending on whether the commanded flow is increasing or decreasing

3.3 Passive Ride Control System Model

The final aspect of the complete system model which needs to be simulated is the passive ride control (PRC) structure For the sake of elaborating on the system structure, a schematic of the PRC system is shown in Fig 2 When in normal operation (with the 3/2 enabling valve #11 in the on position rather than as shown and accumulator #13 above its precharge pressure and below its maximum pressure), it can be seen that the 4/4 stabilizing spool valve (#9) controls the flow between the boom cylinders and the PRC system accumulator Therefore, the motion of this valve is an important component to the system dynamics When it is at the first stage (on the left), the PRC system is fully connected to the boom control cylinders The other three stages work to ensure that the PRC accumulator (#13) maintains the appropriate pressure The orifice to the left of the stabilizing valve (#10) is meant to control the dynamics of the spool in the valve; therefore, the pressure seen by the pilot line entering the left side of the valve is described by a first-order transfer function

where P pilot and P raise are the Laplace-transformed functions of pressure at the pilot line of the valve and in the line

connected to the raise chamber of the boom cylinder, respectively, and τ PRC is the time constant associated with the orifice connecting those two lines The stabilizing valve’s spool displacement is therefore related to the pressure difference between the pilots on either side of the valve The flow through the valve, then, can be calculated using the same orifice equation (9) which is used for determining the flow into the cylinder

Having determined all of these model expressions, the final component needed to model the behavior of the PRC system is the pressure in the PRC accumulator, as this pressure affects the flow through the stabilizing valve and therefore, the motion of the machine implement In general operation for the machine (line pressure above

accumulator precharge but below maximum system pressure), the pressure of the oil in the line is equal to the pressure of the gas in the accumulator

Since the pressure of the gas in the accumulator is known, the volume of that gas can also be determined using the isentropic relationship for an ideal gas

where V acc,gas and V acc,pre are the current volume and precharge volume of the gas in the accumulator, respectively,

p acc,pre and p acc,gas are the precharge and current pressures of the gas, and γ is the isentropic exponent for the gas

Knowing the volume of the gas and the volume of the accumulator, the flows into and out of the accumulator can

be determined The net flow into the accumulator Q acc,net can then be used in the pressure build-up equation of the accumulator to determine the oil pressure

𝑝 , = 𝛾 ∫ ,

Typically, the solution comes from a numerical integration, since the time evolution ofp acc.oil depends on the

instantaneous value of the p acc,oil, which affects the bulk modulus For other operating conditions (i.e above the max system pressure or below the accumulator precharge), these expressions do not hold But those conditions are not within the normal operation of the machine, so they fall outside the scope of this paper

4 Proposed Control Structure

Active ride control (ARC) works by generating an appropriate signal for the valve that controls the motion of the boom cylinder on the machine Due to this fact, the active control system consumes more system energy than the passive control, which does not demand any current for controlling valves That being said, the ARC system uses the standard hydraulic system for the wheel loader (i.e no hardware modifications are required) Thus, it is easily implementable on production machines such as the reference machine

To synthesize a proper control signal for commanding the boom valve, information about the current state of the system must be available to the controller This feedback control setup is pivotal to the design of the ARC, and selecting the correct feedback signal is of utmost importance Using an improper feedback signal could cause the controller to underperform or even to have a negative impact on the system

Fig 5 ARC schematic with (a) acceleration feedback (ARC a ) and (b) pressure feedback (ARC p )

For the current system, two potential feedback signals were identified The first signal, and perhaps the most intuitive, is the acceleration of the cab or boom of the machine This should be an acceptable feedback signal because the vibrations in the cab and implement of the wheel loader are essentially accelerations, and they are exactly the phenomena which the system is actually attempting to control From a controls perspective, it makes sense to directly measure the system state that is being targeted by the controller

As discussed in Section 2, the complete machine can be considered as two separate bodies which have their own dynamic behaviors Therefore, there are two different locations where the acceleration can be measured to attain different information about the system Because of this, there are two different configurations for ARC using acceleration feedback (shortened to ARCa): using the acceleration in the wheel loader cab (chassis) and using the acceleration of the boom (implement) Figure 5a shows a simplified schematic of this setup

The second feedback signal considered is the pressure in the raise side of the boom actuation cylinder A similar sensor configuration has been previously investigated for load-handling machines [8] The pressure in this line provides a different indicator of the forces acting on the machine Therefore, by examining the pressure in this line,

it should be possible to generate a motion which can counteract the forces causing vibrations in the machine A simplified schematic of the ARC using pressure feedback (denoted ARCp elsewhere in this paper) is shown inFig 5b

It is important to note that both the pressure- and acceleration-based ARC structures also include sensors which

monitor the angle of the boom (denoted by β) Due to the difference in resistive loads between raising and lowering

the boom, as well as other factors, the boom has a tendency to drift from the desired angle during operation of the ARC system Therefore, the angle of the boom is treated as a feedback signal so that the controller can correct for drift and maintain the correct boom angle when it is not attempting to counteract vibrations

Fig 6 Basic control structure for ARC p setup

Using the feedback of either pressure or acceleration signals, many different traditional control structures for the ARC can be used For the case of this paper, the control scheme considered is a simple proportional-derivative (PD) controller The PD control structure is a simple and well-understood control scheme, and it is well suited to the application at hand As the proportional control attempts to drive the current error to zero, the derivative component strives to cut down on the response time of the controller This is important for dynamic systems such as the reference machine, where the idea is to attenuate machine oscillations as rapidly as possible While stability analysis for this system is outside the scope of this paper, similar control strategies have previously been shown to

be stable under comparable operating conditions [9] Therefore, it should lend itself well to a fairly aggressive optimization scheme

Figure 6 shows what this basic structure looks like for ARC using pressure feedback From this figure, it can be seen that the proportional and derivative gains (KP and KD) are determined by a gain scheduler, which is capable of modifying them in real-time based on the operating condition at hand As shown in the figure, the operating condition is determined using the operator command and the feedback signal The inclusion of the operating condition identification is one of the primary facets which sets the ARC apart from the PRC ARC can be adapted