Effect of Control Measures on Wheel/Rail Noise When the Vehicle Curves

applied sciences

Article Effect of Control Measures on Wheel/Rail Noise When the Vehicle Curves

Jian Han 1, Yuanpeng He 1, Xinbiao Xiao 1,*, Xiaozhen Sheng 1,*, Guotang Zhao 1,2 and Xuesong Jin 1 1 State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, China; [email protected] (J.H.); [email protected] (Y.H.) [email protected] (G.Z.); [email protected] (X.J.) 2 China Railway Corporation, Beijing 100844, China * Correspondence: [email protected] (X.X.); [email protected] (X.S.); Tel.: +86-135-4079-1500 (X.X.); +86-180-3069-0757 (X.S.)

Received: 12 October 2017; Accepted: 3 November 2017; Published: 6 November 2017

Abstract: This paper developed a time domain simplified model to study the effect of control measures on wheel/rail noise when the vehicle curves. The time domain model consists of two parts, one being a vehicle-track coupling dynamic model for wheel/rail interaction, the other being a transient finite element and boundary element domain model for vibration and sound radiation. Wheel/rail noise under wheel/rail lateral creep force is predicted for a narrowly curved section of a conventional underground railway, and compared with measurement. Based on the developed model, the effect of wheel/rail friction modification on squeal noise is investigated. In addition, effectiveness of resilient wheel and embedded track to control curve squeal noise are also assessed.

Keywords: wheel/rail noise; vehicle/track dynamic model; wheel/rail friction modiﬁcation; resilient wheel; embedded track

1. Introduction Railway squeal noise is difficult to study because of its mechanism, wheel/rail interaction and random acoustic behaviour. Squeal generates as a railway vehicle negotiates a narrow curve, producing a tonal noise of high amplitude. Typically, the noise is radiated from the wheels and has most of its energy between 400 Hz and 10 kHz (in the frequency band where human beings are most sensitive to noise). In the process of curving, a series of railway wheel modes (particularly the wheel’s axial modes) are easy to be excited, which may lead to curve squeal [1–3]. Known practical solutions for railway squeal in a particular curve include friction modification [4,5] and wheel damping treatments [6–9]. These solutions can reduce the occurrence of squeal for some special circumstance. Curve squeal noise has received increased attention by means of simulations and tests. Most previous research considered that the mechanism of railway curve squeal is mainly a kind of self-excited vibration due to the nonlinear creep forces [1,3,10–19]. Rudd [1] found that the main excitation mechanisms of squeal were related to lateral direction stick-slip phenomena which introduced unstable wheel/rail forces and vibrations. Slope of the creep force-creepage curve becomes negative instead of a constant value when the creepages reach a high level. Many models to simulate curve squeal were developed based on Rudd’s squeal theory. Most of the models begin with a characteristic of the creepage-dependent friction coefficient. Van Ruiten [10], for example, applied Rudd’s model to trams. In a review article, Remington [11] described the state of the art of railway curve squeal up to 1985. He suggested that this model should include finite element models of railway wheel dynamics, numerical models for the dynamics of bogies in curves and details of the friction coefficient versus creepage. Since then, Schneider et al. [12] developed a modal model for the wheel and calculated its

Appl. Sci. 2017, 7, 1144; doi:10.3390/app7111144 www.mdpi.com/journal/applsci Appl. Sci. 2017, 7, 1144 2 of 20 self-excited vibrations in the time domain through introducing Kraft’s formula for the falling friction coefficient in the sliding region. Fingberg [13] included a finite element model of the wheelset and a modal model of the rail. The creep force formula is derived from Kalker’s theory [20] of rolling contact, extended to include a falling regime based on Kraft’s formula to resemble experimental findings more closely at large creepages. Fingberg’s work has been extended further by Périard [14] who included vehicle dynamics simulations in a time-domain curve squeal calculation. Xie [21] introduced a simplified friction law into SIMPACK using a modified FASTSIM for curve squeal calculations based on Fingberg’s work and TWINS. Heckl [16] developed an annular disc model and analyzed its vibration response in time domain. Heckl’s work made a contribution to understanding of the disc vibration and its modal shapes when squeal noise occurs due to lateral creepage. In order to consider railway wheel geometry, Heckl’s model needs to be improved. De Beer et al. [16] also presented a curve squeal model considering lateral creepages. The difference was that his model was developed in frequency domain. Noise radiation was predicted using the standard components of the TWINS software [22]. The model of de Beer was extended by Monk-Steel and Thompson [17] by including the case of wheel flange contact, which usually occurred at the leading wheel at high rail. Chiello et al. [18] presented a curve squeal model including not only tangential dynamics (friction force) but also normal dynamics on the wheel/rail contact zone. The model can predict the unstable wheel modes and the corresponding squeal level and spectrum. Huang [23] reviewed the curve squeal models, and developed a curve squeal model including a self-excited loop and relationship between wheel/rail motions and contact forces. A number of authors have proposed an alternative mechanism based on ‘mode coupling’, which has been explained in a simplified form by Hoffmann et al. [24,25], see also [26]. More recently Thompson comprehensively reviewed two mechanisms (‘falling friction’ and ‘mode coupling’), experimental and theoretical work in the field of curve squeal and discussed mitigation measures in terms of these two mechanisms [27]. This paper developed a time domain simplified model to study the effect of control measures on wheel/rail noise when the vehicle curves. This model, different from the self-excited vibration model, mainly analyzed the wheel/rail noise characteristic under lateral excitation. Wheel/track vibration and sound pressure can approximate predicted for a vehicle negotiating a narrow curve. The effects of lubricant between wheel/rail interface, elastic wheel, and embedded track on wheel/rail noise reduction under lateral excitation are investigated.

2. The Time Domain Model for Predicting Wheel/Rail Noise under Lateral Excitation

2.1. Vehicle/Track Interaction Model with Falling Friction Coefﬁcients Figure1 shows a three-dimensional dynamic model of a metro vehicle which coupled with a conventional ballastless track which can predict the curve squeal when a vehicle negotiates narrow curves. The dynamic model is based on the classical dynamic theory, which was also successfully applied to many research topics in rail transit ﬁeld [28–33]. In this paper, the car-body and two bogies are modelled as rigid bodies. The primary and secondary suspensions are modelled as spring-damp elements. The track system is a triple-layers model as demonstrated in [30], in which the couple of rails are modelled as Timoshenko beams. The explicit integration method in [34] is used to solve dynamic equations. Appl. Sci. 2017, 7, 1144 2 of 20 falling friction coefficient in the sliding region. Fingberg [13] included a finite element model of the wheelset and a modal model of the rail. The creep force formula is derived from Kalker’s theory [20] of rolling contact, extended to include a falling regime based on Kraft’s formula to resemble experimental findings more closely at large creepages. Fingberg’s work has been extended further by Périard [14] who included vehicle dynamics simulations in a time-domain curve squeal calculation. Xie [21] introduced a simplified friction law into SIMPACK using a modified FASTSIM for curve squeal calculations based on Fingberg’s work and TWINS. Heckl [16] developed an annular disc model and analyzed its vibration response in time domain. Heckl’s work made a contribution to understanding of the disc vibration and its modal shapes when squeal noise occurs due to lateral creepage. In order to consider railway wheel geometry, Heckl’s model needs to be improved. De Beer et al. [16] also presented a curve squeal model considering lateral creepages. The difference was that his model was developed in frequency domain. Noise radiation was predicted using the standard components of the TWINS software [22]. The model of de Beer was extended by Monk-Steel and Thompson [17] by including the case of wheel flange contact, which usually occurred at the leading wheel at high rail. Chiello et al. [18] presented a curve squeal model including not only tangential dynamics (friction force) but also normal dynamics on the wheel/rail contact zone. The model can predict the unstable wheel modes and the corresponding squeal level and spectrum. Huang [23] reviewed the curve squeal models, and developed a curve squeal model including a self-excited loop and relationship between wheel/rail motions and contact forces. A number of authors have proposed an alternative mechanism based on ‘mode coupling’, which has been explained in a simplified form by Hoffmann et al. [24,25], see also [26]. More recently Thompson comprehensively reviewed two mechanisms (‘falling friction’ and ‘mode coupling’), experimental and theoretical work in the field of curve squeal and discussed mitigation measures in terms of these two mechanisms [27]. This paper developed a time domain simplified model to study the effect of control measures on wheel/rail noise when the vehicle curves. This model, different from the self-excited vibration model, mainly analyzed the wheel/rail noise characteristic under lateral excitation. Wheel/track vibration and sound pressure can approximate predicted for a vehicle negotiating a narrow curve. The effects of lubricant between wheel/rail interface, elastic wheel, and embedded track on wheel/rail noise reduction under lateral excitation are investigated.

2. The Time Domain Model for Predicting Wheel/Rail Noise under Lateral Excitation

2.1. Vehicle/Track Interaction Model with Falling Friction Coefficients Figure 1 shows a three-dimensional dynamic model of a metro vehicle which coupled with a conventional ballastless track which can predict the curve squeal when a vehicle negotiates narrow curves. The dynamic model is based on the classical dynamic theory, which was also successfully applied to many research topics in rail transit field [28–33]. In this paper, the car-body and two bogies are modelled as rigid bodies. The primary and secondary suspensions are modelled as spring-damp elements. The track system is a triple-layers model as demonstrated in [30], in which the couple of rails are modelled as Timoshenko beams. The explicit integration method in [34] is used to solve Appl. Sci. 2017, 7, 1144 3 of 20 dynamic equations.

Appl. Sci. 2017, 7, 1144 3 of 20

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FigureFigure 1.1.Coupling Coupling dynamic dynamic model model of a of metro a metro vehicle vehicle and a conventionaland a conventional ballastless ballastless track: (a) Elevation;track: (a) (Elevation;b) End view. (b) End view.

Wheel-rail normal force is calculated based on non-linear Hertzian contact theory. Non-linear Wheel-rail normal force is calculated based on non-linear Hertzian contact theory. Non-linear Hertzian contact force is simulated by Equation (1). The normal force depends on the relationship Hertzian contact force is simulated by Equation (1). The normal force depends on the relationship between normal loading and wheel, rail deformation if the normal compression at the wheel/rail between normal loading and wheel, rail deformation if the normal compression at the wheel/rail contact point is larger than zero when wheel and rail are in contact. The normal force is zero if the contact point is larger than zero when wheel and rail are in contact. The normal force is zero if normal compression at the wheel/rail contact point is not larger than zero when the wheel and rail the normal compression at the wheel/rail contact point is not larger than zero when the wheel and separates. rail separates. ( 1 3/2 [ 1 Zwrnc(t)] 32, Zwrnc(t) > 0 N(t) = G[()],()0Hertz Zt Zt> (1) =  wrnc wrnc Nt() 0, GHertz Zwrnc(t) ≤ 0 (1)  ≤ 0,Zt2/3wrnc ( ) 0 where GHertz is the contact constant of wheel and rail (m/N ). For LM wheel tread proﬁle and CN60 −0.115 × −8 rail,whereGHertz GHertz= is 3.86 theR contact constant10 . R isof thewheel wheel and rolling rail (m/N radius.2/3). ForZwrnc LM(t )wheel is the tread normal profile compression and CN60 at therail, wheel/rail GHertz = 3.86 contact R−0.115 point.× 10−8. R is the wheel rolling radius. Zwrnc (t) is the normal compression at the wheel/railThe tangential contact point. creep forces of wheel and rail are calculated based on Kalker’s simpliﬁed creep theory,The in tangential which the creep falling forces down of friction wheel lawand [rail13] isare introduced. calculated Thebased contact on Kalker’s area is simplified discretized creep and thetheory, tangential in which wheel-rail the falling creep down force friction is solved law through[13] is introduced. iteration from The thecontact leading area part is discretized of the contact and areathe tangential to its trailing wheel-rail part. Thus, creep the forc tangentiale is solved wheel-rail through creep iteration forces from can the be writtenleading aspart follows: of the contact area to its trailing part. Thus, the tangential whee l-rail creep forces can be written as follows: ξx ξzyi  pxi = px(i−1) − L − L ∆x 1 3 (2)  ξξξy yξz(xi+0.5∆x)  pyi=−−Δ= py(i−1) − xziL − L ∆x  ppxi x(1) i− 2 x3 LL13  (2) ξ ξ (0.5)xx+Δ  pp=−−y zi Δ x  yi y(1) i−   LL23 where pxi and pyi are longitudinal and lateral tangential wheel-rail creep force. ξx, ξy, ξz are longitudinal, lateral and spin creepage, respectively. Δx is the longitudinal width of discrete grid. L1, L2, L3 are flexibility coefficients and can be written as follows:

88aaπ aab ===，， LL12 L 3 (3) 33GC11 GC 22 4 GC 23 where a and b are the lengths of longitudinal and lateral semi-axis, respectively. G is the shear modulus of wheel/rail. Cij is the coefficient calculated by Kalker in 1967 [20].

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where pxi and pyi are longitudinal and lateral tangential wheel-rail creep force. ξx, ξy, ξz are longitudinal, lateral and spin creepage, respectively. ∆x is the longitudinal width of discrete grid. L1, L2, L3 are flexibility coefficients and can be written as follows: √ 8a 8a πa a/b L1 = , L2 = , L3 = (3) 3GC11 3GC22 4GC23 where a and b are the lengths of longitudinal and lateral semi-axis, respectively. G is the shear modulus of wheel/rail. Cij is the coefficient calculated by Kalker in 1967 [20]. The tangential wheel-rail creep forces at any point of contact area can be written as follows: q pti = pxi + pyi (4)

If pti ≤ µpn(x, y) (5) where µ is the wheel/rail friction coefﬁcient, and p is the distribution of wheel/rail normal force, the particle in contact area is in an adhesion state. The tangential wheel-rail creep forces can be calculated by Equation (2). If pti > µpn(x, y) (6) the particle in contact area is in a slide state. The tangential wheel-rail creep forces can be reduced to Equation (7):  µp (x,y)  p = p n xi xi pti µp (x,y) (7)  p = p n yi yi pti The wheel/rail friction coefficient µ can be modeled by a constant [35], Fingberg law (Equation (8)) [13] or piecewise friction coefﬁcient (Equation (9)) [21].

50 0.1 µ(x, y) = µs[ + ] (8) 100 + |v(x, y)|2 0.2 + |v(x, y)| where v(x, y) is the slip velocity between rail and wheel, µs is the static friction coefficient.  µ if |v(x, y)| = 0  s µs−µd µ(x, y) = µs − v · |v(x, y)| if 0 < |v(x, y)| ≤ vc (9)  c  µd if |v(x, y)| > vc where µd is the sliding friction coefficient, vc the critical sliding velocity, and v(x, y) is the slip velocity in the local coordinate system. Figure2 gives the relationship of Creep force and Creepage based on three kinds of friction coefficients. The Fingberg model and piecewise model both consider the falling down friction coefficient. The piecewise friction coefficient is simplified from Fingberg model. The falling friction coefficient needs to be taken into account in the process of curve squeal simulation. This study used the Fingberg’ model. In this study, a special type of track, i.e., embedded track, is investigated. Figure3 shows the dynamic model of filling material (including elastomer and rail pad) in the groove. The filling material is glued to the rail and slab, and it provides elastic support and damping. There is no relative motion between filling material and rail/slab. In the dynamic simulation of embedded track, the filling material of the embedded track is approximately simulated as mass-spring-damping system. Compared with the spring-damping simulation, the effects of the inertia of elastomer can be considered Appl. Sci. 2017, 7, 1144 5 of 20

in the mass-spring-damping system in this paper. The slab of the embedded track is simulated by 3D Appl. Sci. 2017, 7, 1144 5 of 20 Appl.Appl.ﬁnite Sci.Sci. element 20172017,, 77,, 11441144 in the vehicle-track coupling dynamic model. 55 ofof 2020

20 2020 Constant μ ConstantConstant μμ 18 Fingberg μ 1818 FingbergFingberg μμ μ 16 Piecewise μμ 1616 Piecewise 14 1414 12 1212

1010 8 Creep force (kN) force Creep 88 Creep force (kN) force Creep Creep force (kN) force Creep 6 66 4 44 2 22 0 00.0000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.0000.000 0.002 0.002 0.004 0.004 0.006 0.006 0.008 0.008 0.010 0.010 0.012 0.012 0.014 0.014 0.016 0.016 Creepage CreepageCreepage Figure 2. Creep force-Creepage relationship based on three kinds of friction coefficients. FigureFigureFigure 2.2. 2. CreepCreepCreep force-Creepageforce-Creepage force-Creepage relationshiprelationship basedbased onon threethree kindskinds of of friction friction coefficients. coefﬁcients.coefficients.

Figure 3. Dynamic model of filling material in groove. FigureFigure 3.3. DynamicDynamicDynamic modelmodel ofof fillingfilling ﬁlling materialmaterial inin groove.groove.

Figure 4 shows the force diagram of elastomer of filling material (the mass in Figure 3). The FigureFigure 4 44 shows showsshows the thethe force forceforce diagram diagramdiagram of elastomerofof elastomerelastomer of filling ofof fillingfilling material materialmaterial (the mass(the(the mass inmass Figure inin Figure3Figure). The 3). lateral3). TheThe lateral and vertical motions of elastomer of filling material on left side and right side of the one rail laterallateraland vertical andand verticalvertical motions motionsmotions of elastomer ofof elastomerelastomer of filling ofof material fillingfilling ma onmaterial leftterial side onon and leftleft rightsideside and sideand ri ofrightght the sideside one of railof thethe are oneone written railrail are written in Equations (10)–(13). The stiffness (Kph and Kfill_v) and damping (Cph and Cfill_v) are arearein Equations writtenwritten inin (10)–(13). EquationsEquations The (10)–(13).(10)–(13). stiffness TheThe (K stiffnessstiffnessand K ((KK)phph and andand damping KKfill_vfill_v)) andand (C dampingdampingand C ((CC)phph are andand including CCfill_vfill_v)) areare in including in forces in Figure 4. ph fill_v ph fill_v includingincludingforces in Figure inin forcesforces4. inin FigureFigure 4.4.

Figure 4. Dynamic model of elastomer in groove. Figure 4. Dynamic model of in groove. FigureFigure 4.4. DynamicDynamic modelmodel ofof elastomerelastomer inin groove.groove.

LateralLateral motionmotion equationequation ofof elastomerelastomer onon thethe leftleft sideside  =+ Myfilli lfLRi(,)=+=+ F sfhLRi (,) F frhLRi (,) (10) Myffilliilli lfLRi lfLRi(,)(,) F sfhLRi sfhLRi (,) (,) F frhLRi frhLRi (,) (,) (10)(10)

Appl. Sci. 2017, 7, x; doi: www.mdpi.com/journal/applsci Appl.Appl. Sci.Sci. 20172017,, 77,, x;x; doi:doi: www.mdpi.c www.mdpi.com/journal/applsciom/journal/applsci Appl. Sci. 2017, 7, 1144 6 of 20

Lateral motion equation of elastomer on the left side

.. M f illiyl f (L,R)i = Fs f h(L,R)i + Ff rh(L,R)i (10)

Vertical motion equation of elastomer on the left side

.. M f illizl f (L,R)i = −Fl f rv(L,R)i − Fl f sv(L,R)i + Fl f f (L,R)i + Fl f r(L,R)i (11)

Lateral motion equation of elastomer on the right side

.. M f illiyr f (L,R)i = Ff sh(L,R)i + Fr f h(L,R)i (12)

Vertical motion equation of elastomer on the right side

.. M f illizr f (L,R)i = −Fr f rv(L,R)i − Fr f sv(L,R)i + Fr f f (L,R)i + Fr f r(L,R)i (13)

.. .. where Mﬁlli is the mass of the i-th elastomer on one side (left or right) of the rail. zl f (L,R)i and zr f (L,R)i are .. .. vertical accelerations of the i-th elastomer on the left and right sides of the rail. yl f (L,R)i and yr f (L,R)i are lateral accelerations of the i-th elastomer on the left and right sides of the rail. Fs f h(L,R)i (Ff sh(L,R)i) and Ff rh(L,R)i (Fr f h(L,R)i) are lateral force between slab and elastomer, and lateral force between elastomer and rail. Fl f rv(L,R)i, Fl f sv(L,R)i, Fl f f (L,R)i and Fl f r(L,R)i are vertical force between elastomer and rail, vertical force between elastomer and slab, vertical force between the i-th and the (i − 1)-th elastomers, and vertical force between the i-th and the (i + 1)-th elastomers on the left side. Fr f rv(L,R)i, Fr f sv(L,R)i, Fr f f (L,R)i and Fr f r(L,R)i are vertical force between elastomer and rail, vertical force between elastomer and slab, vertical force between the i-th and the (i − 1)-th elastomers, and vertical force between the i-th and the (i + 1)-th elastomers on the right side. In addition to the embedded track, the resilient wheel is also examined. Figure5 shows the dynamic model of resilient wheel. The lateral and vertical motions of resilient wheel are written in Equations (14)–(19).

.. V2 .. Mw1[Y1wL,Ri + + Rφsewi] = −FeyL,Ri + FwryL,Ri + Mw1gφsewi (14) Rwi

.. .. V2 Mw1[Z1wL,Ri − a0φsewi − φsewi] = FezL,Ri − FwrzL,Ri + Mw1g (15) Rwi .. V2 .. Mw2[Y2wi + + Rφsewi] = −FfyLi − FfyRi + FeyLi + FeyRi + Mw2gφsewi (16) Rwi .. .. V2 Mw2[Z2wi − a0φsewi − φsewi] = FfzLi + FfzRi − FezLi − FezRi + Mw2g (17) Rwi . . FezL,Ri = Kez(Z1wL,Ri − Z2wi) + Cez(Z1wL,Ri − Z2wi) (18) . . FeyL,Ri = Key(Y1wL,Ri − Y2wi) + Cey(Y1wL,Ri − Y2wi) (19) where Mw1 and Mw2 are the mass of the rim and the rest parts of the wheelset as shown in Figure5...... Y1wL,Ri, Y2wi, Z1wL,Ri, and Z2wi are accelerations of rim and the rest parts of the wheelset. Y indicates . . . . lateral response, and Z indicates vertical response. Y1wL,Ri, Y2wi, Z1wL,Ri and Z2wi are velocities of rim and the rest parts of the wheelset. Y1wL,Ri, Y2wi, Z1wL,Ri and Z2wi are displacements of rim and the rest parts of the wheelset. V is the running speed. R is the curve radii of i-th wheel. a is the half of the wi .. 0 distance between left and right nominal rolling circles. φsewi and φsewi are the angular acceleration and angular of super-elevation. FeyL,Ri, FwryL,Ri, and FfyL,Ri are lateral forces due to the stiffness and damping of rubber, due to wheel/rail interaction, and due to primary suspension system. FezL,Ri, Appl. Sci. 2017, 7, 1144 6 of 20

Vertical motion equation of elastomer on the left side =− − + + Mzfilli lf(,) L R i F lfrv (,) L R i F lfsv (,) L R i F lff (,) L R i F lfr (,) L R i (11)

Lateral motion equation of elastomer on the right side =+ Myfilli rf(,) L R i F fsh (,) L R i F rfh (,) L R i (12)

Vertical motion equation of elastomer on the right side =− − + + Mzfilli rf(,) L R i F rfrv (,) L R i F rfsv (,) L R i F rff (,) L R i F rfr (,) L R i (13) where Mfilli is the mass of the i-th elastomer on one side (left or right) of the rail. zlf(,) L R i and zrf(,) L R i are vertical accelerations of the i-th elastomer on the left and right sides of the rail. ylf(,) L R i and

yrf(,) L R i are lateral accelerations of the i-th elastomer on the left and right sides of the rail. Fsfh(,) L R i

( Ffsh(,) L R i ) and Ffrh(,) L R i (Frfh(,) L R i ) are lateral force between slab and elastomer, and lateral force between elastomer and rail. Flfrv(,) L R i , Flfsv(,) L R i , Flff(,) L R i and Flfr(,) L R i are vertical force between elastomer and rail, vertical force between elastomer and slab, vertical force between the i-th and the (i − 1)-th elastomers, and vertical force between the i-th and the (i + 1)-th elastomers on the left side.

Frfrv(,) L R i , Frfsv(,) L R i , Frff(,) L R i and Frfr(,) L R i are vertical force between elastomer and rail, vertical force between elastomer and slab, vertical force between the i-th and the (i − 1)-th elastomers, and Appl. Sci. 2017, 7, 1144 7 of 20 Appl.vertical Sci. 2017force, 7 ,between 1144 the i-th and the (i + 1)-th elastomers on the right side. 7 of 20 In addition to the embedded track, the resilient wheel is also examined. Figure 5 shows the 2 dynamic model of resilient wheel.++V Theφφ lateral =−− and vertical + motions + of + resilient wheel are written in F i, and F areMYw2 vertical[] 2wiiiiyiyii forces R due sew to the F fyL stiffness F fyR and F e L damping F e R Mg of w2 rubber, sew due to wheel/rail(16) wrzL,R fzL,Ri R interaction,Equations (14)–(19). and due to primary suspensionwi system.

2  −−φφ V =+−−+ MZw2[] 2wii a 0 sew sew iiizizi F fzL F fzR F e L F e R Mg w2 (17) Rwi

−+ − FKZZCZZezL,Rieziiezii=( 1wL,R 2w ) ( 1wL,R 2w ) (18)

−+ − FKYYCYYeyL,Rie=( y 1wL,R i 2w i ) e y ( 1wL,R i 2w i ) (19) where Mw1 and Mw2 are the mass of the rim and the rest parts of the wheelset as shown in Figure 5.     Y1wL,Ri , Y2wi , Z1wL,Ri , and Z2wi are accelerations of rim and the rest parts of the wheelset. Y indicates     lateral response, and Z indicates vertical response. Y1wL,Ri , Y2wi , Z1wL,Ri and Z2wi are velocities of rim and the rest parts of the wheelset. Y1wL,Ri , Y2wi , Z1wL,Ri and Z2wi are displacements of rim and the rest parts of the wheelset. V is the running speed. Rwi is the curve radii of i-th wheel. a0 is the half of the φ φ distance between left and right nominal rolling circles. sewi and sewi are the angular acceleration and angular of super-elevation. FeyL,Ri , FwryL,Ri , and FfyL,Ri are lateral forces due to the stiffness and damping of rubber, due to wheel/rail interaction, and due to primary suspension system. FezL,Ri ,

FwrzL,Ri , and FfzL,Ri are vertical forces due to the stiffness and damping of rubber, due to wheel/rail Figure 5. Dynamic model of resilient wheel. interaction, and due to primary suspension system.

2.2. The Transient Finite and Boundary Element2 Model for Wheel/Rail Vibration and Sound Radiation 2.2. The Transient Finite and Boundary ++V Elementφφ Model =−+ for Wheel/Rail Vibrat +ion and Sound Radiation MYw1[] 1wL,Ri R sew i F e yi L,R F wr yi L,R Mg w1 sew i (14) R Three-dimensional (3D)(3D) ﬁnite finite element welementi (FE) (FE) models models of a standard of a standard metro wheel metro and awheel conventional and a slab track were developed to obtain the vibrations (Figure6). In the model, the normal forces and conventional slab track were developed to obtain2 the vibrations (Figure 6). In the model, the normal lateral creep forces obtained by the−− vehicle/trackφφ V interaction =− dynamic model + in Section 2.1 are applied forces and lateral creep Mforcesw1[]Za1wL,R obtainedii 0 by sew the vehicle/track sew izizi FFMg e L,R interaction wr L,R dynamic w1 model in Section(15) 2.1 R areto theapplied tread to of the wheelset tread of and wheelset rail head. and Figure rail whead.i6 also Figure shows 6 thealso FE shows models the ofFE resilient models wheelof resilient and wheelembedded and trackembedded to analyze track their to effectanalyze on wheel/railtheir effect noiseon wheel/rail attenuation noise under attenuation lateral excitation. under Thelateral FE excitation.model was The developed FE model in commercialwas developed software in commercial ANSYS. software ANSYS.

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FigureFigure 6. DynamicDynamic model model of of resilient resilient wheel and embedded rail.

Once the vibrations of the wheel and track are determined using by 3D FE model, sound Once the vibrations of the wheel and track are determined using by 3D FE model, sound radiations radiations from the wheel and track can be evaluated using an appropriate vibro-acoustic prediction from the wheel and track can be evaluated using an appropriate vibro-acoustic prediction method.

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There are three radiators: the wheels, the rails and the slabs. Equation (20) shows the 3D acoustic integral equation [36] for a sound ﬁeld of frequency ω.

Z ∂G(R) p(x, y, z) = − p(x0, y0, z0) + iρωG(R)v (x0, y0, z0) dS (20) ∂n n S

0 0 0 where p(x, y, z) denotes sound pressure amplitude in the acoustic domain, vn(x , y , z ) denotes air particle velocity amplitude in the normal direction of the domain boundary (the unit normal vector of the boundary, denoted by n, is pointing out of the domain, and ﬁnally,

e−ikR q G(R) = , R = (x − x0)2 + (y − y0)2 + (z − z0)2 (21) 4πR is the Green’s function with the source at (x, y, z) and observer at (x0, y0, z0), and k is the wavenumber. Equation (20) is solved by 3D boundary element method (BEM). Discrete boundary surface into several sub boundary elements Ωae. In this way, the distribution of sound pressure p and normal velocity vn on the boundary surface is approximated to the sound pressure pˆ and normal velocity vˆn in a series of sub boundary elements. Then, the sound pressure p and normal velocity vn can be written as: ne 0 0 0 0 0 0 e 0 0 0 0 0 0 p(x , y , z ) ≈ pˆ(x , y , z ) = ∑ Ni (x , y , z ) · api, (x , y , z ) ∈ Ωae (22) i=1

ne 0 0 0 0 0 0 e 0 0 0 0 0 0 vn(x , y , z ) ≈ vˆn(x , y , z ) = ∑ Ni (x , y , z ) · avi, (x , y , z ) ∈ Ωae (23) i=1 e e The Ni is the shape function of node i. Defined that Ni is one at the node i, and zero at other nodes. api and avi are the sound pressure and normal velocity of the node i. e Defined that [N] is the (1 × na) matrix of shape function Ni . {pî} is the (na × 1) matrix of sound pressure api. {vˆni} is the (na × 1) matrix of normal velocity avi. Here na is the total number of nodes. 0 0 0 0 0 0 pˆ(x , y , z ) and vˆn(x , y , z ) can be further written as:

0 0 0 0 0 0 pˆ(x , y , z ) = [N] · {pˆi}, (x , y , z ) ∈ Ωa (24)

0 0 0 0 0 0 vˆn(x , y , z ) = [N] · {vˆni}, (x , y , z ) ∈ Ωa (25)

To use (24) and (25) solving Equation (20), the relationship of pˆi and vˆni needs to be determined. The relationship of them can be written as:

[Ab]{pˆi} = jρ0ω[Bb]{vˆni} (26)

The ith column element Abi in the coefﬁcient matrix [Ab] can be expressed as:

Z Z 1 ∂ 1 0 0 0 ∂G(Rb) Abi = δbi · [1 + ( )dΩa] − [ Ni(x , y , z )( )dΩa] (27) 4π ∂n |Rb| ∂n Ωa Ωa

The ith column element Bbi in the coefﬁcient matrix [Bb] can be expressed as: Z 0 0 0 Bbi = Ni(x , y , z )G(Rb)dΩa (28)

Ωa

q 2 2 2 where Rb = (x b − x0) + (y b − y0) + (z b − z0) . δbi. is Kronecker symbol. If b = i, δbi = 1, If b 6= i, δbi = 0. Appl. Sci. 2017, 7, 1144 9 of 20

Considering boundary conditions, Equation (26) can be solved. Now the sound pressure of any point (x, y, z) in sound ﬁeld can be determined by the sound pressure and normal velocity on the boundary surface. p(x, y, z) = [C]{pˆi} + [D]{vˆni} (29)

The ith column element Ci in the coefﬁcient matrix [C] can be expressed as:

Z 0 0 0 ∂G(R) Ci = Ni x , y , z dΩa (30) Ωa ∂n

The ith column element Di in the coefﬁcient matrix [D]. can be expressed as: Z 0 0 0 Di = jρoω Ni x , y , z G(R)dΩa (31) Ωa

For the BE model of wheel, the hole left in the wheel hub is closed to model the effect of axle. For the BE model of track, sound radiation only considers rail and slab surface. For a railway on the ground surface, the acoustic domain may be approximated to be a half-space. It has two acoustically hard boundaries (the sound absorption effect of the ground surface will not be considered in this paper). They are the horizontal plane beyond the top surface of the slabs. Other boundaries of the acoustic domain are radiating, including the top surface of the slabs and the surfaces of the rails. Connections between the rails and the slabs are ignored, leaving a uniform gap between the rails and the slabs. The effect of the presence of a train on the sound ﬁeld will not be considered in the current paper. Thus, the acoustic domain is uniform in the track direction.

3. Results and Discussions

3.1. Wheel/Rail Noise Prediction and Preliminary Validation This section gives the wheel/rail force, acceleration and sound pressure level of the wheels under the wheel/rail force excitation with and without squealing phenomenon in a sharp curve. When a vehicle curves, the leading wheel (front wheel) has a potential to produce squeal and the trailing wheel (rear wheel) should not produce squeal. Figure7 gives the lateral creep force of the leading wheelset when a vehicle runs from a tangent line to a narrow circular curve at the speed of 45 km/h. The curve radius is 250 m, and the track cant is 96 mm. The main physical parameters of the metro vehicle used in the simulations are given in Table1.

Table 1. Main parameters of metro vehicle.

Notations Parameters Values (End) M/I Body inertia 4 Mc Car body mass (kg) 2.16 × 10 3 Mb Bogie mass (kg) 4.00 × 10 3 Mw Wheelset mass (kg) 1.86 × 10 2 4 Icx Car body roll moment of inertia (kg·m ) 3.11 × 10 2 5 Icy Car body pitch moment of inertia (kg·m ) 8.61 × 10 2 5 Icz Car body yaw moment of inertia (kg·m ) 8.56 × 10 2 3 Ibx Bogie roll moment of inertia (kg·m ) 1.19 × 10 2 2 Iby Bogie pitch moment of inertia (kg·m ) 8.76 × 10 2 3 Ibz Bogie yaw moment of inertia (kg·m ) 2.10 × 10 2 3 Iwx Wheelset roll moment of inertia (kg·m ) 1.04 × 10 2 2 Iwy Wheelset pitch moment of inertia (kg·m ) 1.37 × 10 2 3 Iwz Wheelset yaw moment of inertia (kg·m ) 1.04 × 10 Appl. Sci. 2017, 7, 1144 10 of 20

Table 1. Cont.

Notations Parameters Values (End)

Appl. Sci. 2017, 7, 1144K/C Primary suspension 10 of 20 Kpx Longitudinal stiffness (MN/m) 17.62 KpyCpz VerticalLateral damping stiffness coefficient (MN/m) (kN·s/m) 13.00 9.62 KpzK/C VerticalSecondary stiffness suspension (MN/m) 0.60 Cpz Vertical damping coefficient (kN·s/m) 13.00 Ksx Longitudinal stiffness (MN/m) 0.16 K/C Secondary suspension Ksy Lateral stiffness (MN/m) 0.16 Ksx Longitudinal stiffness (MN/m) 0.16 Ksz Vertical stiffness (MN/m) 1.39 Ksy Lateral stiffness (MN/m) 0.16 Csy Lateral damping coefficient (kN·s/m) 23.00 Ksz Vertical stiffness (MN/m) 1.39 CsyCsz VerticalLateral dampingdamping coefficientcoefficient (kN(kN·s/m)·s/m) 25.00 23.00 CLsz/D/H Vertical dampingDimension coefficient (kN·s/m) 25.00 L/D/HRw WheelDimension radius (m) 0.42 v RwL VehicleWheel radiuslength (m)(m) 19.5 0.42 LvLb Distance betweenVehicle two length axles (m) of a bogie (m) 2.3 19.5 LbLc Distance Distance between between two two axles bogie of centers a bogie (m) (m) 12.6 2.3 LcDps LateralDistance span between of primary two bogie suspensions centers (m) 2.01 12.6 DpsDss LateralLateral span span of of secondary primary suspensions suspensions (m) (m) 1.9 2.01 DHss bw HeightLateral of bogie span ofcentre secondary from wheelset suspensions centre (m) (m) 0.069 1.9 H Height of bogie centre from wheelset centre (m) 0.069 bwHcb Height of car body centre from bogie centre (m) 1.37 Hcb Height of car body centre from bogie centre (m) 1.37

Figure 7. Lateral creep force of the leading wheelset when a vehicle negotiates a narrow curve Figure 7. Lateral creep force of the leading wheelset when a vehicle negotiates a narrow curve (simulation results). (simulation results).

It can be seen from Figure7 7 that that thethe laterallateral creepcreep forceforce isis veryvery stablestable atat tangenttangent line.line. InIn addition,addition, the fluctuation ﬂuctuation of of lateral lateral creep creep force force increases increases gradua graduallylly from from transition transition curve curve to circular to circular curve, curve, and andreaches reaches maximum maximum when when the thevehicle vehicle negotiates negotiates the the circular circular curve. curve. Figure Figure 88 showsshows the lateral creepcreep forces of leading and trailing wheels. It can be seen that the the fluctuation ﬂuctuation of lateral creep force of leading wheel is larger thanthan trailingtrailing wheel.wheel. Figure 9a,b give the acceleration of leading inner wheel and trailing inner wheel in time domain and frequency domain. It can be seen that the acceleration of the leading inner wheel with squeal is much larger than that of trailing inner wheel without squeal. In addition, highest peaks occur at modal frequencies corresponding to axial modes with zero-nodal-circle, showing that these modes are easy to be excited during curving. The axial mode shapes of wheel are expressed as (m, n). m represents number of nodal circle. n represents number of nodal diameter. For example, (0, 1) represents zero-nodal-circle with one-nodal-diameter. Thus, the frequencies and corresponding axle mode shapes are 265 Hz (0, 1), 353 Hz (0, 0), 468 Hz (0, 2), 1167 Hz (0, 3), and 2008 Hz (0, 4). These

Appl. Sci. 2017, 7, x; doi: www.mdpi.com/journal/applsci Appl. Sci. 2017, 7, 1144 11 of 20

Appl.frequencies Sci. 2017, by7, 1144 simulation in this paper have a good agreement with the FRF test in the semi-anechoic11 of 20 room [8].

-2 Leading wheel Trailing wheel -4

-6

-8 Lateral creep force (kN)

-10

Appl. Sci. 2017, 7, 1144 11 of 20

-12 frequencies by simulation8 in this 9 paper 10 have a11 good agreement 12 13 with 14 the FRF 15 test in 16 the semi-anechoic room [8]. Time (s) -2 Figure 8. LateralLateral creep force of Leading leading wheel wheel and trailing wheel (simulation results). Trailing wheel 600 Figure9a,b give the acceleration-4 of leading inner wheel and trailing inner wheel in time domain Leading wheel and frequency domain.400 It can be seen that the acceleration of the Trailing leading wheel inner wheel with squeal is ) much larger than that2 of trailing-6 inner wheel without squeal. In addition, highest peaks occur at modal frequencies corresponding to axial modes with zero-nodal-circle, showing that these modes are easy 200 to be excited during curving. The axial mode shapes of wheel are expressed as (m, n). m represents -8 number of nodal circle. n represents number of nodal diameter. For example, (0, 1) represents 0 zero-nodal-circle with one-nodal-diameter.Lateral creep force (kN) Thus, the frequencies and corresponding axle mode shapes are 265 Hz (0, 1), 353 Hz (0,-10 0), 468 Hz (0, 2), 1167 Hz (0, 3), and 2008 Hz (0, 4). These frequencies by simulation in this paper-200 have a good agreement with the FRF test in the semi-anechoic room [8]. Acceleration of Rim (m/s Figure 10a,b give the sound pressure level (SPL) (at the point which is 30 cm away from the -12 outside of wheel tyre)-400 of leading8 wheel 9 10 and trailing 11 12 wheel 13 in time 14 domain 15 16 and frequency domain. It can be seen that the SPL of the leading wheel withTime squeal (s) is much higher than that of trailing wheel at frequencies ofFigure axial -6008. modes. Lateral creep force of leading wheel and trailing wheel (simulation results). 0.2 0.3 0.4 0.5 0.6 600 Time (s) (a) Leading wheel 400 Trailing wheel ) 2

200

-200 Acceleration of Rim (m/s

-400

-600 0.2 0.3 0.4 0.5 0.6 Time (s) (a) (b) Figure 9. Cont.

Appl. Sci. 2017, 7, x; doi: www.mdpi.com/journal/applsci

(b)

Appl. Sci. 2017, 7, x; doi: www.mdpi.com/journal/applsci Appl. Sci. 2017, 7, 1144 11 of 20 frequencies by simulation in this paper have a good agreement with the FRF test in the semi-anechoic room [8].

-2 Leading wheel Trailing wheel -4

-6

-8 Lateral creep force (kN)

-10

-12 8 9 10 11 12 13 14 15 16 Time (s) Figure 8. Lateral creep force of leading wheel and trailing wheel (simulation results).

600

Leading wheel 400 Trailing wheel ) 2

200

-200 Acceleration of Rim (m/s

-400

-600 0.2 0.3 0.4 0.5 0.6 Appl. Sci. 2017, 7, 1144 12 of 20 Time (s) (a)

Appl. Sci. 2017, 7, 1144 12 of 20

Figure 9. Acceleration of leading wheel and trailing wheel in (a) time domain and (b) frequency domain (simulation results).

Figure 10a,b give the sound pressure level ((SPLb) ) (at the point which is 30 cm away from the outside of wheel tyre) of leading wheel and trailing wheel in time domain and frequency domain. It Figure 9. Acceleration of leading wheel and trailing wheel in (a) time domain and (b) frequency Appl. Sci.can 2017 be seen, 7, x; doi:that the SPL of the leading wheel with squeal is much higher than www.mdpi.c that of trailingom/journal/applsci wheel domain (simulation results). at frequencies of axial modes.

60 Leading wheel 40 Trailing wheel

Sound pressure (Pa) -20

-40

-60 0.20.30.40.50.6 Time (s) (a) 120

Leading wheel 100 Trailing wheel

Sound pressure level (dB re 2e-5Pa) 20

0 1000 2000 3000 4000 5000 Frequency (Hz) (b)

Figure 10. SPLs at a distance of 30 cm from the leading and trailing wheels in (a) time domain and (b) Figure 10. SPLs at a distance of 30 cm from the leading and trailing wheels in (a) time domain and (b) frequency domain (simulation results). frequency domain (simulation results). Wheel/rail noise is also tested near a wheel (860 mm diameter) used in metro when the vehicle passes a sharp curve (radius = 250 m) at the speed of 45 km/h. The microphone is arranged in the outside of the leading wheel with the distance of 30 cm, which is shown in Figure 11. In the process of field test, squealing noise can be heard clearly. Figure 12 gives comparison between simulation and experimental results of SPL of the leading wheel with the same curve radius and running speed.

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Wheel/rail noise is also tested near a wheel (860 mm diameter) used in metro when the vehicle passes a sharp curve (radius = 250 m) at the speed of 45 km/h. The microphone is arranged in the outside of the leading wheel with the distance of 30 cm, which is shown in Figure 11. In the process of ﬁeld test, squealing noise can be heard clearly. Figure 12 gives comparison between simulation and experimentalAppl. Sci. 2017, results7, 1144 of SPL of the leading wheel with the same curve radius and running speed.13 of 20 Appl. Sci. 2017, 7, 1144 13 of 20

Microphone Microphon

Figure 11. Microphone arrangement. FigureFigure 11.11. Microphone arrangement. arrangement. 120 120 265~468 Hz 265~468 Hz 1167 Hz Simulation 100 1167 Hz SimulationExperiment 100 Experiment 2008 Hz 80 2008 Hz 80

60 60

40 40

Sound pressure level (dB re re 2e-5Pa) (dB level pressure Sound 20

0 0 0 400 800 1200 1600 2000 2400 2800 3200 0 400 800 1200 1600 2000 2400 2800 3200 Frequency (Hz) Frequency (Hz) Figure 12. Comparison between simulation and experimental results of SPL of the leading wheel. Figure 12. Comparison between simulation and experimental results of SPL of the leading wheel. Figure 12. Comparison between simulation and experimental results of SPL of the leading wheel. Figure 12 shows that the SPL at the frequencies of 265–468 Hz, 1167 Hz, 2008 Hz are significant for bothFigure simulation 12 shows and that experimental the SPL at the results. frequencies These of frequencies 265–468 Hz, have 1167 a Hz, good 2008 agreement Hz are significant with the Figure 12 shows that the SPL at the frequencies of 265–468, 1167, 2008 Hz are signiﬁcant for forzero-nodal-circle both simulation and and n-nodal-diameter experimental results. axial wheel These modes frequencies for simulation have a goodand experimental agreement with results. the both simulation and experimental results. These frequencies have a good agreement with the zero-nodal-circleAmplitude difference and n-nodal-diameterpercentages between axial simulation wheel modes and forexperiment simulation of 265–468and experimental Hz, 1167 Hz, results. and zero-nodal-circleAmplitude2008 Hz are difference 3%, and 7%, n-nodal-diameter andpercentages 6.5% of betweentheir axialcorresponding simulation wheel modes and peaks, experiment for respectively. simulation of 265–468 andThe experimentaldifferences Hz, 1167 Hz, mainly results.and Amplitude2008come Hz from are difference the 3%, simplification 7%, percentages and 6.5% and of between assumptiontheir corresponding simulation of the actual and peaks,experiment situation respectively. from of 265–468,the The simulation differences 1167, andmodel. mainly 2008 In Hz arecomeother 3%, 7%,fromwords, and the the 6.5%simplification current of their model corresponding and assumptioncan predict peaks, ofall the squeal respectively.actual frequencies situation The from and differences thegive simulation relatively mainly model. comeaccurate fromIn theotheramplitudes simpliﬁcation words, of thethem. and current Thus, assumption modelthis simplified ofcan the predict actual model all situation ca squealn be used fromfrequencies for the regular simulation and investigation give model. relatively on In otherwheel/rail accurate words, theamplitudesnoise current when model ofthe them. vehicle can Thus, predict curves. this all simplified squeal frequencies model can and be used give for relatively regular accurateinvestigation amplitudes on wheel/rail of them. noise when the vehicle curves. 3.2. Effect of Wheel/Rail Friction Coefficients on Wheel/Rail Noise under Lateral Excitation 3.2. Effect of Wheel/Rail Friction Coefficients on Wheel/Rail Noise under Lateral Excitation This section investigates the effect of friction coefficient between wheel and rail on vibration and wheel/railThis section noise underinvestigates lateral the excita effecttion. of frictionThe friction coefficient coefficient between of 0.012–0.3 wheel and are rail chosen on vibration for analysis and wheel/railbecause they noise cover under the rangelateral of excita commontion. Thefriction friction coef ficients.coefficient The of value 0.012–0.3 of 0.3 are represents chosen fordry analysis friction because they cover the range of common friction coefficients. The value of 0.3 represents dry friction Appl. Sci. 2017, 7, x; doi: www.mdpi.com/journal/applsci Appl. Sci. 2017, 7, x; doi: www.mdpi.com/journal/applsci Appl. Sci. 2017, 7, 1144 14 of 20

Thus, this simpliﬁed model can be used for regular investigation on wheel/rail noise when the vehicle curves.

3.2. Effect of Wheel/Rail Friction Coefficients on Wheel/Rail Noise under Lateral Excitation This section investigates the effect of friction coefficient between wheel and rail on vibration and wheel/rail noise under lateral excitation. The friction coefficient of 0.012–0.3 are chosen for analysis because they cover the range of common friction coefficients. The value of 0.3 represents dry friction Appl. Sci. 2017, 7, 1144 14 of 20 coefficient. The value of 0.012 represents the friction coefficient considering the third medium—oil betweencoefficient. wheel/rail The value interface. of 0.012 The represents values ofthe 0.1 friction and 0.05coefficient represent considering friction the coefficients third medium—oil between dry statusbetween and oil wheel/rail status. interface. The values of 0.1 and 0.05 represent friction coefficients between dry Figurestatus and 13 a,boil status. give the lateral accelerations of leading wheel with different friction coefficients in time domainFigure 13a,b and give frequency the lateral domain. accelerations It can of be leading seen thatwheel the with acceleration different friction decreases coefficients obviously in at curvetime squeal domain frequencies and frequency as the domain. friction Itcoefficient can be seen increase.that the acceleration Figure 14 a,bdecr giveeases the obviously SPLs with at curve different frictionsqueal coefficients frequencies in as time the domainfriction coefficient and frequency increase domain.. Figure 14a,b It can give be the seen SPLs that with SPLs different alsohave friction a good reductioncoefficients in significant in time domain peaks and after frequency reducing domain. the frictionIt can be coefficient.seen that SPLs The also sound have a good reduction reduction (SPL) of in significant peaks after reducing the friction coefficient. The sound reduction (SPL) of wheel wheel considering lubricant can reduce 10–25 dB corresponding to the friction coefficient of 0.012–0.05, considering lubricant can reduce 10–25 dB corresponding to the friction coefficient of 0.012–0.05, comparedcompared with with the the SPL SPL of of friction friction coefficient coefficient ofof 0.3.0.3. Therefore, Therefore, it itsuggests suggests that that proper proper lubrication lubrication betweenbetween the wheelthe wheel and and rail rail interface interface can can reduce reduce squealsqueal noise noise effectively. effectively.

500 Friction coefficient 0.3 400 Friction coefficient 0.1 Friction coefficient 0.05 300

) Friction coefficient 0.012 2 200

100

-100

-200 Acceleration of Rim (m/s Rim of Acceleration -300

-400

-500 0.2 0.3 0.4 0.5 0.6 Time (s) (a) 1000 Friction coefficient 0.3 100 Friction coefficient 0.1 Friction coefficient 0.05 Friction coefficient 0.012 )

2 10

0.1

0.01 Acceleration of Rim (m/s Rim of Acceleration 1E-3

1E-4 1000 2000 3000 4000 5000 Frequency (Hz) (b)

Figure 13. Accelerations with different friction coefficients in (a) time domain and (b) frequency Figure 13. Accelerations with different friction coefﬁcients in (a) time domain and (b) frequency domain (simulation results). domain (simulation results).

Appl. Sci. 2017, 7, x; doi: www.mdpi.com/journal/applsci Appl. Sci. 2017, 7, 1144 15 of 20 Appl. Sci. 2017, 7, 1144 15 of 20

60 Friction coefficient 0.3 Friction coefficient 0.1 40 Friction coefficient 0.05 Friction coefficient 0.012

-20 Sound pressure (Pa)

-40

-60 0.2 0.3 0.4 0.5 0.6 Time (s) (a) 120 Friction coefficient 0.3 Friction coefficient 0.1 100 Friction coefficient 0.05 Friction coefficient 0.012 80

20 Sound pressure level (dB re 2e-5Pa) (dB level pressure Sound

0 1000 2000 3000 4000 5000 Frequency (Hz) (b)

Figure 14. SPLs with different friction coefficients in (a) time domain and (b) frequency domain Figure 14. SPLs with different friction coefﬁcients in (a) time domain and (b) frequency domain (simulation results). (simulation results). 3.3. Effect of Embedded Track on Wheel/Rail Noise under Lateral Excitation 3.3. Effect of Embedded Track on Wheel/Rail Noise under Lateral Excitation This section investigates the effect of embedded track on wheel/rail noise under lateral This section investigates the effect of embedded track on wheel/rail noise under lateral excitation. excitation. The SPL of embedded track is calculated based on the embedded track dynamic model The SPL of embedded track is calculated based on the embedded track dynamic model and transit BEM and transit BEM model in Sections 2.1 and 2.2. Figure 15 shows the SPLs of track comparison between model in Sections 2.1 and 2.2. Figure 15 shows the SPLs of track comparison between conventional conventional slab track and embedded track. It can be seen that the SPL of embedded track without slab track and embedded track. It can be seen that the SPL of embedded track without considering considering wheel has a very good reduction in broad bands due to its damping of the elastic material wheel has a very good reduction in broad bands due to its damping of the elastic material around the around the rail absorbs vibration and then resulting in a low noise. rail absorbs vibration and then resulting in a low noise. Figure 16 gives the total SPLs considering standard metro wheels coupled with the conventional Figure 16 gives the total SPLs considering standard metro wheels coupled with the conventional slab track and embedded track respectively. It can be seen that when the embedded track coupled slab track and embedded track respectively. It can be seen that when the embedded track coupled with a squealing wheel, the reduction of sound is limited (about 2–3 dB) because the wheel is the with a squealing wheel, the reduction of sound is limited (about 2–3 dB) because the wheel is the main main sound radiation source when squeal occurs, as is shown in Figure 17. In Figure 7, the SPL of a sound radiation source when squeal occurs, as is shown in Figure 17. In Figure7, the SPL of a standard standard metro wheel is compared with the embedded track because the contribution of wheel/rail metro wheel is compared with the embedded track because the contribution of wheel/rail noise must noise must be clear. The SPL of the standard metro wheel is larger than that of track in a wide be clear. The SPL of the standard metro wheel is larger than that of track in a wide frequency domain frequency domain which contributes significantly to the total value of wheel-rail noise. Although the

Appl. Sci. 2017, 7, x; doi: www.mdpi.com/journal/applsci Appl. Sci. 2017, 7, 1144 16 of 20 Appl. Sci. 2017, 7, 1144 16 of 20 Appl. Sci. 2017, 7, 1144 16 of 20 embeddedwhich contributestrack is not signiﬁcantly significant to on the the total reduction value of of wheel-rail wheel/rail noise. noise Although in the thecurve, embedded it may trackhave is more embeddednot signiﬁcant track is on not the significant reduction ofon wheel/rail the reduction noise of in wheel/rail the curve, it noise may havein the more curve, effect it onmay reducing have more effect on reducing rolling noise [37,38]. effectrolling on reducing noise [37 rolling,38]. noise [37,38]. 120 120 Conventional slab track Conventional slab track 100 Embedded track 100 Embedded track

80 80

60 60

40 40

20 Sound pressure level (dB re 2e-5Pa) 20 Sound pressure level (dB re 2e-5Pa)

0 0 1000 2000 3000 4000 5000 1000 2000 3000 4000 5000 Frequency (Hz) Frequency (Hz) Figure 15. SPLs of track comparison between conventional slab track and embedded track (simulation Figure 15. SPLs of track comparison between conventional slab track and embedded track (simulation results).Figure 15. SPLs of track comparison between conventional slab track and embedded track (simulation results). results). 120 120 Standard metro wheel-conventional slab track StandardStandard metrometro wheel-embeddedwheel-conventional track slab track 100 Standard metro wheel-embedded track 100

80 80

60 60

Sound pressurelevel (dB re2e-5Pa) 40

20 20 1000 2000 3000 4000 5000 1000 2000Frequency (Hz) 3000 4000 5000 Frequency (Hz) FigureFigure 16. Total 16. Total SPLs SPLs considering considering standard metro metro wheels wheel coupleds coupled with with the conventional the conventional slab track slab and track Figure 16. Total SPLs considering standard metro wheels coupled with the conventional slab track and embedded track track (simulation (simulation results). results). and embedded track (simulation results). 120 120 Standard metro wheel Standard metro wheel 100 Embedded track 100 Embedded track

80 80

60 60

40 40

Sound pressurelevel (dB re 2e-5Pa) 20 Sound pressurelevel (dB re 2e-5Pa) 0 0 1000 2000 3000 4000 5000 1000 2000 3000 4000 5000 Frequency (Hz) Frequency (Hz) Figure 17. SPL compare between standard metro wheel and embedded track (simulation results). Figure 17. SPL compare between standard metro wheel and embedded track (simulation results). Appl. Sci. 2017, 7, x; doi: www.mdpi.com/journal/applsci Appl. Sci. 2017, 7, x; doi: www.mdpi.com/journal/applsci Appl. Sci. 2017, 7, 1144 16 of 20 embedded track is not significant on the reduction of wheel/rail noise in the curve, it may have more effect on reducing rolling noise [37,38].

120 Conventional slab track 100 Embedded track

20 Sound pressure level (dB re 2e-5Pa)

0 1000 2000 3000 4000 5000 Frequency (Hz) Figure 15. SPLs of track comparison between conventional slab track and embedded track (simulation results).

120 Standard metro wheel-conventional slab track Standard metro wheel-embedded track 100

Sound pressurelevel (dB re2e-5Pa) 40

20 1000 2000 3000 4000 5000 Frequency (Hz)

Appl. Sci.Figure2017 ,16.7, 1144Total SPLs considering standard metro wheels coupled with the conventional slab track17 of 20 and embedded track (simulation results).

120 Standard metro wheel 100 Embedded track

20 Sound pressurelevel (dB re 2e-5Pa)

0 1000 2000 3000 4000 5000 Frequency (Hz) Figure 17. SPL compare between standard metro wheel and embedded track (simulation results). Figure 17. SPL compare between standard metro wheel and embedded track (simulation results). Appl. Sci. 2017, 7, 1144 17 of 20 Appl. Sci. 2017, 7, x; doi: www.mdpi.com/journal/applsci 3.4. Effect of Resilient Wheel on Wh Wheel/Raileel/Rail Noise under Lateral Excitation This section investigates the effect of resilient wheel on wheel/rail noise noise under under lateral lateral excitation. excitation. The SPL of resilient wheel is calculated based on the resilient wheel dynamic model and transit BEM model in Sections 2.1 and 2.22.2.. Figure 18 shows the SPLs of wheel comparison between the standard wheel andand thethe resilient resilient wheel. wheel. It It can can be be seen seen that that the the resilient resilient wheel wheel has ahas very a very good good reduction reduction in sharp in peaks,sharp peaks, especially especially for the for peaks the peaks of squeal of squeal frequencies, frequencies, due to due high to high damping damping in the in resilient the resilient wheel wheel and anddecoupling decoupling of the of rimthe andrim web.and web.

120 Standard metro wheel 100 Resilient wheel

20 Sound pressure level (dBre 2e-5Pa)

0 1000 2000 3000 4000 5000 Frequency (Hz)

Figure 18. SPLSPL compare compare between standard metro wheel and elastic wheel (simulation results).

Figure 19 gives the total SPLs of conventional slab track coupled with the standard metro wheel Figure 19 gives the total SPLs of conventional slab track coupled with the standard metro wheel and resilient wheel respectively. It can be seen that when the resilient wheel coupled with the and resilient wheel respectively. It can be seen that when the resilient wheel coupled with the conventional slab track, the reduction of sound is significant (about 5–6 dB) because the resilient conventional slab track, the reduction of sound is signiﬁcant (about 5–6 dB) because the resilient wheel wheel can reduce squeal noise of wheel, which is main source for squeal noise, namely the main can reduce squeal noise of wheel, which is main source for squeal noise, namely the main sound source sound source is controlled. Thus, the total SPLs is reduced by using resilient wheel. is controlled. Thus, the total SPLs is reduced by using resilient wheel. 120 Standard metro wheel-conventional slab track Resilient wheel-conventional slab track 100

40 Sound pressure level (dB re 2e-5Pa) pressure Sound

20 1000 2000 3000 4000 5000 Frequency (Hz) Figure 19. SPLs of common slab track coupled with the standard metro wheel and elastic wheel (simulation results).

Appl. Sci. 2017, 7, x; doi: www.mdpi.com/journal/applsci Appl. Sci. 2017, 7, 1144 17 of 20

3.4. Effect of Resilient Wheel on Wheel/Rail Noise under Lateral Excitation This section investigates the effect of resilient wheel on wheel/rail noise under lateral excitation. The SPL of resilient wheel is calculated based on the resilient wheel dynamic model and transit BEM model in Sections 2.1 and 2.2. Figure 18 shows the SPLs of wheel comparison between the standard wheel and the resilient wheel. It can be seen that the resilient wheel has a very good reduction in sharp peaks, especially for the peaks of squeal frequencies, due to high damping in the resilient wheel and decoupling of the rim and web.

120 Standard metro wheel 100 Resilient wheel

20 Sound pressure level (dBre 2e-5Pa)

0 1000 2000 3000 4000 5000 Frequency (Hz) Figure 18. SPL compare between standard metro wheel and elastic wheel (simulation results).

Figure 19 gives the total SPLs of conventional slab track coupled with the standard metro wheel and resilient wheel respectively. It can be seen that when the resilient wheel coupled with the conventional slab track, the reduction of sound is significant (about 5–6 dB) because the resilient wheelAppl. Sci. can2017 reduce, 7, 1144 squeal noise of wheel, which is main source for squeal noise, namely the18 main of 20 sound source is controlled. Thus, the total SPLs is reduced by using resilient wheel.

120 Standard metro wheel-conventional slab track Resilient wheel-conventional slab track 100

40 Sound pressure level (dB re 2e-5Pa) pressure Sound

20 1000 2000 3000 4000 5000 Frequency (Hz)

Figure 19. SPLsSPLs of of common common slab slab track track coupled coupled with with the standard metro wheel and elastic wheel (simulation results).

4. Conclusions A vehicle-track coupling dynamic model considering the falling wheel/rail friction coefﬁcients was built to study the wheel/rail contact in narrow curve. In addition, a transient ﬁnite element and Appl. Sci. 2017, 7, x; doi: www.mdpi.com/journal/applsci boundary element time domain models of vibration and sound were developed for sound radiation evaluation. Wheel/track vibration and sound pressure response are presented for a vehicle negotiating a narrow curve. The following conclusions can be drawn:

(1) Different wheels have different levels of wheel/rail noise when the vehicle curves. The wheel/rail noise of the leading wheel is 20 dB larger than that of the trailing wheel. (2) Proper lubrication in wheel/rail interface can effectively reduce wheel/rail noise when the vehicle curves. The sound reduction of wheel considering lubricant (friction coefﬁcient: 0.012~0.1) can reduce 10~25 dB compared to that of friction coefﬁcient 0.3. (3) The application of vibration and noise control measures on wheels is better than that on track when the vehicle curves. The total sound reduction of the embedded track coupled with a squealing wheel is about only 2–3 dB. However, the total sound reduction of the elastic wheel coupled with the conventional slab track is about 5–6 dB.

Acknowledgments: This study was supported by the National Key R & D Program of China (2016YFB1200503-02, 2015BAG13B01-03) and the National Natural Science Foundation of China (U1134202, 51305360, 51475390). Author Contributions: Guotang Zhao and Xuesong Jin conceived and designed the simulations and experiments; Jian Han, Yuanpeng He, and Xinbiao Xiao performed the numerical simulations and experiments; Jian Han and Xiaozhen Sheng analyzed the data; Jian Han wrote the paper. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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