Flow Measurement and Instrumentation 23 (2012) 26–32

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Flow Measurement and Instrumentation

journal homepage: www.elsevier.com/locate/flowmeasinst

Design and accuracy analysis of pneumatic gauging for form error of spool valveinner holeJun Liu ∗, Xudong Pan, Guanglin Wang, Aoyu ChenSchool of Mechatronics Engineering, Harbin Institute of Technology, Harbin 150001, PR China

a r t i c l e i n f o

Article history:Received 23 September 2011Received in revised form29 December 2011Accepted 30 December 2011

Keywords:Non-contact inspectionPneumatic gaugeForm errorMeasuring uncertaintyInner hole

a b s t r a c t

The inner hole of a spool valve is a slender hole required to have high precision form, and the form error isgenerally not allowed to exceed 1 µm in servo valve production. Aiming at ultra-precision measurementfor the spool valve inner hole in situ, this paper proposes a novel non-contactmeasurementmethod basedon the differential pressure pneumatic measuring principle and develops a form error pneumatic gaugesystem for the spool valve inner hole. The pneumatic measuring circuit, gauge head and precise drivingmechanism have been designed. The factors that influence the accuracy of the pneumatic gauge systemhave been thoroughly analyzed and tested to evaluate the measuring uncertainty. The system calibrationand measurement experiments have been carried out. Results show that the measuring error does notexceed 0.3 µm, which can be further improved by the error separation and compensation technique.

© 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Spool valves, including a valve spool and a valve sleeve,are the key components of the electro-hydraulic servo valve.Their machining quality, especially the radial coupling accuracyof the valve spool and sleeve, directly decides the static anddynamic characteristics of the servo valve, such as sensitivity,resolution, leakage rate, static consumption flow, pressure gain,and so forth [1,2]. There are extremely strict requirements for theprecision of radial clearance coupling between the valve spool andsleeve, and the fit clearance is always only 2–4 µm. High precisionform is required for the inner hole of the valve sleeve to guaranteethe radial coupling accuracy. And the cylindricity error plays amajor role in the form accuracy of the inner hole, which is usuallyless than 1 µm in servo valve production [3].

As shown in Fig. 1, the valve sleeve has many intersection holesand its structure is very complex. The length-to-diameter ratioof the valve sleeve inner hole is so large that its form error isvery difficult to measure in situ with high precision. The accuratemeasured value of the form error cannot be obtained directlyby using the conventional mechanical tools such as electroniccaliper or plug gauge [4]. Universal measurement equipment, suchas coordinate measuring machines (CMMs), is mainly used tomeasure the form error in industrial production [5,6]. However,the probes are usually used to contact the measured surface,which may cause surface damage to some extent [7]. On the

∗ Corresponding author. Tel.: +86 451 86413831; fax: +86 451 86413831.E-mail addresses: liu_hit@yahoo.com.cn, junliu@hit.edu.cn (J. Liu).

0955-5986/$ – see front matter© 2012 Elsevier Ltd. All rights reserved.doi:10.1016/j.flowmeasinst.2011.12.007

other hand, they cannot be used in situ and their low measuringefficiency seriously affects the productivity of the servo valve.Besides, the optical measurement method is sensitive to theeffect of the slender holes and intersection holes, which cause adiffraction effect around themeasured fringe so as to influence themeasurement accuracy.

Pneumatic measurement has many advantages, such as non-contact measurement, small measuring force, self-cleaning func-tion, high sensitivity, high measuring precision, simple structure,convenience for operation and maintenance, so it is widely usedin the industrial production [8,9]. The application of pneumaticgauging is well established and has extensively been practiced inthe industry for a long time [10,11]. Pneumatic measurement ofdisplacement has largely been employed in static or quasi-staticapplications to do with dimensional measurement, assessmentof geometric form such as flatness and conicity, and also in thecharacterization of surface roughness to a limited extent [12,13].Special applications of the principle have been realized in themetrology of biological matter [14] and foodstuff [15].

In this paper, a differential pressure pneumatic measuringprinciple is presented and employed for measuring the form errorof the spool valve inner hole. An automatic pneumatic gaugesystem is developed based on the proposed method. The staticcharacteristics and coefficient of pneumatic gauge are obtainedby the system calibration and measurement experiments. Thenthe errors and the measuring uncertainty of the gauge system areanalyzed and evaluated in detail. Finally, some potential methodsto improve the measuring accuracy are discussed, which are veryimportant and useful to further theoretical and experimentalresearch in pneumatic gauging.

J. Liu et al. / Flow Measurement and Instrumentation 23 (2012) 26–32 27

Fig. 1. Composition and sectional view of a spool valve.

Fig. 2. Principle of the nozzle-flapper type of pneumatic sensor.

2. Proposed technique

2.1. Pneumatic measuring principle

Pneumatic gauge uses the pressured air as the measuringmedium. Its basic principle is that some geometric parameters(dimension, shape or relative position) can be obtained bymeasuring the physical parameters (flow or pressure) of thepressured air which flows through the measured geometric parts.A typical back-pressure pneumatic gauge works as a nozzle-flapper mechanism, and the principle of the nozzle-flapper typeof pneumatic sensor can be explained with reference to Fig. 2. Thepressured air at constant pressure Pg impinges upon the measuredsurface and then enters the atmosphere through an inlet nozzle dw

and a measuring nozzle dp in turn, passing a measuring chamberwith a variable pressure. A change in the slot width s between themeasuring nozzle tip and the measured surface alters the flow ofair as it leaves the nozzle. This is reflected as a highly sensitivechange in the back-pressure Pc in the measuring chamber, whichcan be measured by using a pressure transducer [16].

Assuming the incompressible steady flow, the static character-istics Pc = f (s) of the pneumatic sensor can be approximated usinga simple well-known formula [17],

Pc =Pg

1 + (αBs)2(1)

where α is the flow through coefficient of the pneumatic sensor;B is the construction coefficient and can be calculated by B =

4dp/d2w , in which dp and dw are the diameters of the measuringand inlet nozzle, respectively. Usually, α and B can be regarded asconstant when dp and dw are determined. There is no exact linearrelation between the back-pressure Pc and the slot width s. Fig. 3presents a typical graph of the static characteristics Pc = f (s) ofthe pneumatic sensor, and some part of the graph is proportional,

Fig. 3. Typical graph of the static characteristics Pc = f (s).

Fig. 4. Measuring principle for the form error of the inner hole.

which is marked asWp and can be treated as the measuring range.It is worth noting that the slot width s should be small enough inrelation to the nozzle opening, in order to effectively reduce the airescape area and improve the sensitivity of the pneumatic sensor.

2.2. Pneumatic measuring method for the form error of inner hole

In order to evaluate and calculate the form error of the spoolvalve inner hole, the spatial coordinates of points on the measuredcylindrical surface should be obtained by a sort of samplingstrategies. In the actual measurement, the measured spool valveis fixed by a precision fixture. The gauge head with a measuringnozzle can move along the axial direction in the inner hole ofthe valve sleeve, and several circular sections are chosen to bemeasured. Besides, it can also revolve in the inner hole so that themeasuring nozzle scans the sampling sections. The back-pressurePc of the measuring chamber will change with the measuring slotwidth s, which alters due to the relative normal displacementsbetween the measuring nozzle and the sampling points on thecylindrical surface of the spool valve inner hole. Consequently, thevalue of s can be obtained indirectly by measuring the value ofPc by using a piezoresistive pressure transducer. Meanwhile, therotation angle of the gauge head at eachmeasured circular section,which is called θ , is measured by a high precision rotary encoder.The axial displacement of the gauge head, which is called z, ismeasured by a high precision grating ruler. Then the spatial polarcoordinates of the sampling points from the measured cylindricalsurface are obtained as Pij(r, θ, z), and r = d + s, in which d is aconstant related to the structure of the gauge head. The pneumaticmeasuring principle for the form error of the spool valve inner holeis shown in Fig. 4.

As specified in the ISO/1101 standard, the form error with theminimum zone criterion (MZC) can be obtained byminimizing themaximum deviation of the inspected surface from a fitting feature.As shown in Fig. 5, the MZC evaluation of the cylindricity error

28 J. Liu et al. / Flow Measurement and Instrumentation 23 (2012) 26–32

Fig. 5. Calculating method for the form error of the inner hole.

can be regarded as minimizing the radius difference of two coaxialcylinders that thoroughly enclose the measured cylinder, whichcan be formulated as a nonlinear optimization model with thecomplex constraint conditions. Based on the spatial coordinatesof each sampling point, the evaluation and calculation of thecylindricity error can be solved by using intelligent computationmethods such as a genetic algorithm, particle swarm optimizationalgorithm, ant colony optimization algorithm, and so forth [18–20].

3. Design and calibration of the pneumatic gauge

3.1. Design of the measuring machine

According to the pneumatic measuring method for the formerror of the spool valve inner hole, an automatic pneumatic gaugesystem is developed, which mainly consists of the air supplysystem, pneumatic measuring circuit, precise driving mechanismand clamping fixture for the valve sleeve, transducer and sensorinstrument circuit, and an industrial computer system includingthe form error evaluation software, which is shown in Fig. 6.The precise driving mechanism is the executive machinery ofthe pneumatic gauge system in which the gauge head and themeasured valve are fixed by using the clamping fixture. Then thegauge head can be driven by a linear slide guide with a ball screwwhich is driven by a servomotor, so as to realize the high precisionaxial movement. In addition, the high precision rotary movementof the gauge head relative to the measured inner hole is realizedby a worm gear mechanism which is also driven by a servo motor.Fig. 7 shows the precise driving mechanism and the clampingfixture of the automatic measuring machine.

3.2. Design of the pneumatic measuring circuit

From the principle and formula (1) of the pneumatic nozzle-flapper mechanism, the working pressure Pg of the air supplyshould be a constant in the back-pressure pneumatic gauge systemto guarantee the strict proportional relation between Pc and s.However, in the actual measurement, the working pressure Pgstabilized by a pressure regulator still fluctuates slightly influencedby the pressure and flow characteristics of the pressure regulatorand the measurement environment. To enhance the measuringaccuracy of the form error pneumatic gauge, the fluctuation of theworking pressure Pg must be eliminated.

Table 1Experimental results of the system calibration (kPa).

No. Pt (with inlet nozzle 1,Φ 6.3758 mm)

Pt (with inlet nozzle 2,Φ 6.4278 mm)

1 28.44 7.052 28.42 7.063 28.43 7.074 28.43 7.055 28.44 7.06Average 28.432 7.058

A bridge type of differential pressure air circuit is designedby combining two back-pressure air circuits, which is shown inFig. 8. One is used as themeasuring air circuit,whose back-pressurereflects the value of the measured slot width. The other one isthe regulating air circuit, whose back-pressure keeps stable inthe measuring process. The two air circuits share the same airsupply and pressure regulator. The difference of the back-pressurebetween the two air circuits can be measured by a piezoresistivedifferential pressure transducer, and then it is used to calculate themeasured slot width. Therefore the pressure fluctuation inducedby the air supply and measuring environment is eliminated andthe measuring accuracy of the pneumatic gauge system can beimproved to a great extent.

3.3. System calibration

Pneumatic measurement is a relative measuring approach, andthe pneumatic gauge needs to be calibrated so as to obtain theprecise measured value for the geometrical measurand. Two highprecisionmaster rings with upper and lower tolerance are used forthe adjustment of the gauge system. The radius of the two masterrings is 6.3758 mm and 6.4278 mm with the dimension and formerror less than 0.2 µm, respectively.

In the system calibration experiment, the air source pressureis stabilized at 100 kPa, and the radius of inlet nozzle 1 and 2is 0.4 mm and 0.5 mm, respectively. The experiment indicatesthat the pneumatic gauge system has the higher sensitivity andwider linear range when the reference pressure is 52 kPa and thedifferential pressure Pt is approximately 16.5 kPa by adjusting thethrottle valve in the regulating air circuit. Both of the two masterrings are used to measure five times separately. The measuringresults of the calibration experiment are shown in Table 1. Thenthe calibration coefficient K of the pneumatic gauge system can becalculated as 2.433 µm/kPa.

4. Accuracy analysis for the pneumatic gauge

There aremany uncertain factors affecting themeasuring resultof the pneumatic gauge system for the form error of the spoolvalve inner hole, mainly the air circuit system, drivingmechanism,measuring conditions, gauge head, and so on. The errors arethoroughly analyzed to estimate the measuring uncertainty of thepneumatic gauge. Moreover, the pneumatic gauge can be regardedas a quasi-static measuring system as the moving velocity of thegauge head is relatively low so that the dynamic error can beignored.

4.1. Measuring error caused by the air circuit system δ1

4.1.1. Measuring error caused by the air supply fluctuation δ11In the pneumatic measuring process, the working pressure

of the air supply inevitably generates slight fluctuation affectedby the external environment and air pump. It can be stabilizedas Pg by using a high precision pneumatic pressure regulator.

J. Liu et al. / Flow Measurement and Instrumentation 23 (2012) 26–32 29

Fig. 6. Block diagram of the pneumatic gauge system.

Fig. 7. Diagram of the automatic measuring machine.

Fig. 8. Schematic diagram of the differential air circuit.

30 J. Liu et al. / Flow Measurement and Instrumentation 23 (2012) 26–32

Fig. 9. Schematic diagramof themeasuring error by the linearity of the linear stage.

However, the stabilized accuracy and pressure-flow characteristicof the regulator also result in measuring error for the pneumaticpressure value. In this study, a QGD-200 pneumatic pressureregulator with high accuracy is used. When the pressure of the airsupply changes by 10%, the pressure fluctuation of the regulatordoes not exceed 0.2% of the maximum working pressure of100 kPa. According to the system characteristic by the calibrationexperiment, the measuring error caused by the stabilized accuracyof the pneumatic pressure regulator is about 0.47 µm, and theerror is relatively high for the formerrormeasuremenr. However, itcan be eliminated by using the bridge type of differential pressureair circuit.

On the other hand, with the change of the slot width s,the change and fluctuation of the air flow in the nozzle-flappermechanism causes pressure fluctuation in themeasuring chamber.Actually, it is a system error and can be reflected in the systemcalibration error, so it does not need to be calculated separately.Therefore themeasuring error caused by the air supply fluctuationδ11 can be eliminated and δ11 = 0 when the differential pressureair circuit is developed.

4.1.2. The indication error of the pressure transducer δ12The pneumatic gauge system uses a high precision piezoresis-

tive pressure transducer with the measuring range of 30 kPa. Thecomprehensive error of the pressure transducer does not exceed0.1% FS, including the nonlinearity, non-repeatability and hystere-sis error. According to the system characteristic by the calibrationexperiment, the indication error of the pneumatic gauge systemcaused by the comprehensive error of the pressure transducer isless than 0.07 µm, so that δ12 = 0.07 µm.

4.1.3. The nonlinearity error of the system characteristic δ13According to the pneumatic measuring principle, the system

static characteristic curve of Pc − s is not strictly linear. In actualmeasurement, a linear regression for the measuring range of thecharacteristic curve inevitably results in nonlinearity error, whichis related to the actual measuring range of the characteristiccurve. As is known from the system calibration experiment, thenonlinearity error of the system characteristic δ13 is about 0.04µmwhen the linear measuring range is 52 µm.

4.2. Measuring error caused by the driving mechanism δ2

4.2.1. Linear movement error δ21The linear movement of the gauge head in the spool valve inner

hole is realized by an electric linear stage which consists of alinear slide guide and a ball screw. The positioning accuracy of thelinear stage has a very small influence on the measuring accuracy.However, the straightness error of the linear movement in the

vertical plane directly affects the relative position reference of thegauge head, which can bring error to the pneumatic measuringresults, as shown in Fig. 9. It can be deduced as the following,

δ21 = s′ − s (2)

r = (d + s′) cosα (3)

where α is the straightness error of the electric linear stage inthe full length. After the accuracy test, it can be obtained thatα = 0.006/200 mm. Actually r = d + s, so it can be calculatedas the following,

δ21 =(d + s)(1 − cosα)

cosα. (4)

According to the Taylor expansion,

cosα = 1 −α2

2!+

α4

4!−

α6

6!+ · · · (5)

the high order terms can be ignored, and cosα = 1 −α2

2! . It iscalculated as δ21 = 0.12 µm.

4.2.2. Rotation movement error δ22The rotation of the gauge head is realized by a high precision

electric rotary mechanism and its rotation error does not exceed0.25µmwhich is measured by an accuracy test. For the form errorpneumatic gauge system, the precise drivingmechanism should betaken into consideration adequately, so themeasuring error causedby the rotation movement of the gauge head δ22 can be regardedas 0.25 µm.

4.3. Measuring error caused by the measuring conditions δ3

4.3.1. Calibration error of the gauge system δ31As a kindof relativemeasuringmethod, in the calibration exper-

iment for the pneumatic gauge system, the measuring accuracy ofthe whole system is directly affected by the manufacturing errorof the standard master rings, which is determined by the limitingerror of the master rings. According to the accuracy requirementof the form error measuring, the error of the master rings used forthe formerror pneumatic gauge system is less than0.15µm, there-fore the calibration error of the gauge system can be considered as0.15 µm.

4.3.2. Measuring error caused by the ambient temperature δ32Since the pneumatic gauge is used to measure the form error of

the spool valve inner hole in situ in themachining plant, where theenvironment is bad, the ambient temperature should be taken intoconsideration.

The changes of the ambient temperature have important effectson the mechanical structure of the measured valve, gauge head,air flow, pressure transducer and electric circuit. However, if theambient temperature changes, the measured spool valve, gaugehead andmaster rings also change in the same pattern due to theirsame material, so the measuring error caused by the change ofthe ambient temperature for the test piece is rather small and canbe ignored. Actually, the measuring error caused by the change ofthe ambient temperature for the pressure transducer and electriccircuit has been calculated in the system calibration experimentand analysis, so it does not need to be calculated alone. In addition,the negative effect of the pneumatic pressure change on themeasuring accuracy caused by the temperature change of the airflow can be fairly well controlled by the bridge mechanism of thedifferential pressure air circuit, and the effects can be ignored.Therefore, themeasuring error caused by the ambient temperaturecan be considered as δ32 = 0.

J. Liu et al. / Flow Measurement and Instrumentation 23 (2012) 26–32 31

4.4. Measuring error caused by the measuring head δ4

4.4.1. Measuring error caused by the eccentric fixture of the gaugehead δ41

The gauge head is fixed on a precise driving mechanism bya spring collet, so the fixturing accuracy of the spring collet canalso cause measuring error. However, by many assembling andtesting experiments, the fixturing accuracy of the spring collet canbe guaranteed, and the error caused by the eccentric fixture ofthe gauge head in final pneumatic measuring results is less than0.1 µm.

4.4.2. Measuring error caused by the bend of the gauge head δ42Since the fixed gauge head is similar to a cantilever beam

structure, it will inevitably generate extremely slight flexuraldeformation by itself, which can also bring in measuring error. Theerror can be regarded as similar to the measuring error causedby the linear movement straightness error of the slide guide.Considering that the gauge head is very light and the rigidity ofits fixture is very high, the error caused by the slight bend of thegauge head can be ignored so that δ42 = 0.

4.5. Measuring uncertainty evaluation

Combining the errors of each factor by using the square rootformula, the measuring uncertainty δ of the form error pneumaticgauge system can be evaluated by the general limit error as thefollowing,

δ = ±

δ212 + δ2

13 + δ221 + δ2

22 + δ231 + δ2

41

= ±

0.072

+ 0.042+ 0.122

+ 0.252+ 0.152

+ 0.12

= ±0.34 µm. (6)Actually, the measuring error is less than the value calculated

by formula above on condition that the accurate relative positionbetween themeasured valve and gauge head is strictly guaranteed.Therefore, the measuring accuracy of the form error pneumaticgauge is rather high and the measuring uncertainty error isgenerally less than 0.3 µm.

4.6. Methods to improve the measuring accuracy

According to the accuracy analysis of the pneumatic gaugesystem, the pressure fluctuation of the air supply, drivingmechanism and master rings are the main factors that influencethe measuring accuracy. The measuring error caused by thepressure fluctuation of the air supply can be eliminated bythe optimization of an air circuit using a bridge type ofdifferential pressure air circuit. Actually, the accuracy of the drivingmechanism mainly reflects on the movement of the gauge head.In the form error pneumatic gauge system, the movement errorof the gauge head can be measured by using the pneumaticmeasuring method so that the measuring data of the inner surfacecan be corrected and the movement error can be compensated,which is expected to improve the measuring accuracy to a largeextent. For the calibration accuracy of the pneumatic gauge system,it is mainly decided by the machining accuracy of the masterrings. Linearity is one of the most important characteristics ofthe measurement system. It should be noted that the typical airgauge requires two setting masters in order to determine thebasic points of its characteristics. The form error pneumatic gaugesystem allows linearization based on three or more points. Thisway the linearity error may be reduced, the measuring error of thepneumatic gauge systemmay be reduced and themeasuring rangewidened. However, for that purpose more high accuracy settingmaster rings should be prepared which may greatly increase theexpense.

5. Conclusions

The research presented in this paper has established the proof-of-concept of non-contact pneumatic form error measurement forthe spool valve inner hole. A gauge system has been designedand developed which builds on the principle of differentialpressure pneumatic measuring, and relates the form error of thecylindrical surface to the differential pressure signal acquiredby using a piezoresistive differential pressure transducer. Theaccuracy analysis and experiments for the gauge system have beencarried out in detail and then themeasuring uncertainty evaluated.Results show that the comprehensivemeasuring error of the gaugesystem is less than 0.3 µm, and it is feasible to measure theform error of slender holes in situ with high accuracy. Finally,some potential methods to improve the measuring accuracy havebeen discussed.

The proposed pneumatic measuringmethod and the form errorpneumatic gauge system are simple andmore precise and effectivethan the conventional methods. Moreover, the gauge system iseasy to operate and convenient for automaticmeasurement in situ,so it can promote the measuring accuracy and efficiency for thespool valve to a large extent. And then the measuring methodand gauge system can be extended and applied in measuring thedimension, form and position error for other types of valves orprecision components.

Acknowledgments

The authors would like to acknowledge technical supportprovided by the Lab of Process Automation and Detection, Schoolof Mechatronics Engineering, Harbin Institute of Technology.This project is supported by the Development Program forOutstanding Young Teachers in Harbin Institute of Technology(HITQNJS.2009.009). The anonymous reviewers are appreciatedfor their careful reading of the paper and valuable comments toimprove the quality of this paper.

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