Truck Handling Stability Simulation and Comparison of Taper-Leaf and Multi-Leaf Spring Suspensions with the Same Vertical Stiﬀness

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Article Truck Handling Stability Simulation and Comparison of Taper-Leaf and Multi-Leaf Spring Suspensions with the Same Vertical Stiﬀness

Leilei Zhao 1, Yunshan Zhang 2, Yuewei Yu 1,*, Changcheng Zhou 1,*, Xiaohan Li 1 and Hongyan Li 3

1 School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo 255000, China; [email protected] (L.Z.); [email protected] (X.L.) 2 Shandong Automobile Spring Factory Zibo Co.,Ltd., Zibo 255000, China; [email protected] 3 State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130022, China; [email protected] * Correspondence: [email protected] (Y.Y.); [email protected] (C.Z.); Tel.: +86-135-7338-7800 (C.Z.)

Received: 16 December 2019; Accepted: 31 January 2020; Published: 14 February 2020

Abstract: The lightweight design of trucks is of great importance to enhance the load capacity and reduce the production cost. As a result, the taper-leaf spring will gradually replace the multi-leaf spring to become the main elastic element of the suspension for trucks. To reveal the changes of the handling stability after the replacement, the simulations and comparison of the taper-leaf and the multi-leaf spring suspensions with the same vertical stiffness for trucks were conducted. Firstly, to ensure the same comfort of the truck before and after the replacement, an analytical method of replacing the multi-leaf spring with the taper-leaf spring was proposed. Secondly, the effectiveness of the method was verified by the stiffness tests based on a case study. Thirdly, the dynamic models of the taper-leaf spring and the multi-leaf spring with the same vertical stiffness are established and validated, respectively. Based on this, the dynamic models of the truck before and after the replacement were established and verified by the steady static circular test, respectively. Lastly, the handling stability indexes for the truck were compared by the simulations of the drift test, the ramp steer test, and the step steer test. The results show that the yaw rate of the truck almost does not change, the steering wheel moment decreases, the vehicle roll angle obviously increases, and the vehicle side slip angle slightly increases after the replacement. Thus, the truck with the taper-leaf spring suspension has better steering portability, however, its handling stability performs worse.

Keywords: trucks; handling stability; lightweight; taper-leaf spring; suspension; step steer

1. Introduction The handling stability is one of the extremely important performances that aﬀect the driving safety of trucks. How to obtain the strong handling stability for improving the driving safety is an important issue in vehicle design [1–3]. The suspension is an important system connecting the truck frame and wheel [4]. The leaf spring is the most widely used elastic element in the suspension system for trucks. Moreover, it plays a crucial role in the handling stability for trucks. At present, the lightweight design of trucks is of great importance to enhance the load capacity and reduce the production cost [5–7]. For leaf springs, the lightweight design of trucks is mainly reﬂected in replacing the multi-leaf spring with the taper-leaf spring, so as to reduce the trucks’ weight, to improve the power performance, and to reduce the fuel consumption and the exhaust pollution [8–10]. In modern society, with the development of people’s living standard, people have higher and higher

Appl. Sci. 2020, 10, 1293; doi:10.3390/app10041293 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 1293 2 of 21 requirements for the handling stability of trucks [11–13]. However, the changes of the handling stability after the replacement have not been revealed. Due to the advantages of light weight and low noise, the taper-leaf spring is more and more used in trucks. At present, scholars mainly focus on its dynamic property, stress, and strain. Moreover, most of the studies of its mechanical properties mainly were conducted by using simulation software packages, such as Ansys, Nastran, Abaqus, and Adams. Duan et al. created the dynamic model of the tandem suspension equipped with the taper leaf spring for trucks based on Adams software [14]. In order to research the stress of a taper leaf spring, Moon et al. established a flexible multi-body dynamic model [15]. Wang et al. proposed a calculation method of the stiffness of the taper-leaf spring based on the combine superposition method and the finite difference method [16]. Zhou et al. analyzed the mechanical properties of the taper leaf spring considering the friction between the leaf springs on the basis of the FE (Finite Element) contact analysis [17]. To improve the kinematics characteristics of a midsize truck, Kim et al. selected the optimal combination parameters based on a vehicle model with a taper leaf spring [18]. Some scholars improved the performance of leaf springs from the perspective of materials. For example, Chandra et al. researched the high-temperature quality of the accelerated spheroidization on SUP9 leaf spring and the machining performance of Sup9 leaf spring can be significantly improved under high temperature [19]. Fragoudakis et al. optimized the development of 56SiCr7 leaf springs and micro-hardness measurements show surface degradation effects [20]. Kumar et al. optimized the key design parameters of EN45A flat leaf spring and the developed leaf spring program can be used to optimize various parameters of the leaf spring quickly and reliably [21]. Jenarthanan proposed carbon/glass epoxy composite as a leaf spring material and analyzed the leaf spring by using Ansys software [22]. Ozmen et al. proposed a new method on the basis of testing and simulation for the durability of leaf springs [23]. In their study, the finite element method and the multi-body simulation were used to calculate the fatigue life. Some scholars researched the fatigue life of leaf springs. For example, Duru¸set al. proposed a method to predict the fatigue life of Z Type leaf spring and created an approach to validate the proposed method [24]. Bakir et al. researched the correlation of simulation, test bench, and rough road testing in terms of strength and fatigue life of a leaf spring [25]. Kong et al. conducted the failure evaluation of a leaf spring eye design under various load cases [26] and this study provides a valuable reference for preventing the failure of leaf spring in engineering design. Bi et al. carried out the fatigue analysis of leaf-spring pivots [27]. Malikoutsakis proposed the design and optimization procedure for parabolic leaf springs and made a multi-disciplinary optimization of the high performance front leaf springs [28]. In addition, some scholars researched the influences of the taper-leaf spring on the vehicle performances. For instance, Liu et al. analyzed the effects of the taper-leaf spring on the vehicle braking property, simulated the motion characteristics of the front less leaf spring suspension system and the motion law of the front axle jumping up with the wheel [29]. Liu et al. researched the main leaf center trajectory of the taper leaf spring and analyzed the suspension kinematics, and unreasonable toe-in angle was solved by optimizing the hard point of the plumbing arm [30]. In addition, some scholars focus on the influence of suspension designs on handling performance. Termous et al. a proposed coordinated control strategy to control the roll dynamics on the basis of active suspension systems [31]. Li et al. applied the hydraulically interconnected suspension to an articulated vehicle and proved that it can effectively improve the vehicle handling performance [32]. In order to improve the handling stability, Zhang et al. carried out the multi-objective optimization design of suspensions for electric vehicles [33]. Bagheri et al. carried out a multi-objective optimization on the double wishbone suspension to improve the vehicle handling stability [34]. A linear mathematical model and MATLAB model which included suspension K and C characteristics parameters were established by Li et al. [35]. Moreover, the accuracy of the mathematical model was validated. Ahmadian et al. discussed an application of magneto-rheological (MR) suspensions about vehicle Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 20 Appl. Sci. 2020, 10, 1293 3 of 21 using MR suspensions can increase the speed at which the onset of hunting occurs as much as 50% handlingto more than stability 300% and [36] their. results show that using MR suspensions can increase the speed at which the onsetThe ofabove hunting-mentioned occurs asstudies much provide as 50% to theoretical more than guidance 300% [36 ].for the application and promotion of theThe taper above-mentioned-leaf spring in studiesvehicles. provide They also theoretical provide guidance a useful forreference the application for the theoretical and promotion research of theof taper-leafthe taper- springleaf spring. in vehicles. They They mainly also focus provide on thea useful mechanical reference properties for the theoretical of the taper research-leaf of itself. the taper-leafThere is no spring. research They focusing mainly on focus the on changes the mechanical of the handling properties stability of the after taper-leaf replacing itself. the There multi is-leaf no researchspring with focusing the on taper the-leaf changes spring of the for handling trucks. The stability study after of replacingthe changes the will multi-leaf help tospring optimize with the the taper-leafdesign of spring the suspension for trucks. system The study and of improve the changes the willhandling help to stability optimize for the trucks. design Thus, of the the suspension changes systemneed to and be further improve researched the handling. stability for trucks. Thus, the changes need to be further researched. TheThe aim aim of of this this paper paper is to is reveal to reveal the changes the changes of the handling of the handling stability after stability replacing after the replacing multi-leaf the springmulti-leaf with spring the taper-leaf with the spring taper- forleaf trucks. spring Thefor trucks. main contributions The main contributions of this paper of are this as paper follows: are (1) as Anfollows: analytical (1) An method analytical of replacing method the of multi-leafreplacing the spring multi with-leaf the spring taper-leaf with springthe taper was-leaf proposed spring andwas validatedproposed by and test. validated (2) The dynamicby test. (2) models The dynamic of the truck models before of and the aftertruck the before spring and replacement after the spring were establishedreplacement and were verified established by tests, and respectively. verified by (3) tests, The changes respectively. of the handling(3) The changes stability of after the replacinghandling thestability multi-leaf after spring replacing with the taper-leaf multi-leaf spring spring were with revealed the taper by- theleaf simulations spring were of the revealed drift test, by the the rampsimulations steer test, of the and drift the steptest, steerthe ramp test. steer test, and the step steer test.

2.2. ModelingModeling ofof thethe Taper-LeafTaper-Leaf and and the the Multi-Leaf Multi-Leaf Spring Spring

2.1.2.1. TheThe MechanicalMechanical ModelModel ofof thethe Multi-LeafMulti-Leaf SpringSpring InIn ourour previousprevious researchresearch [37[37],], thethe mechanical mechanical modelmodel ofof thethe multi-leafmulti-leaf springspring waswas createdcreated andand validatedvalidated by by test, test, as as shown shown in in Figure Figure1 .1. The The half half of of the the multi-leaf multi-leaf spring spring can can be be regarded regarded as as an an elastic elastic beam.beam.It It is is ﬁxed fixed at at one one end. end A. concentratedA concentrated load loadF is appliedF is applied at the at other the other end. Itend is assumed. It is assumed that under that Funder, each pieceF, each does piece not do separatees not from separate each from other each and two other adjacent and two pieces adjacent have the pieces same have deﬂection the same at thedeflection contact at point. the contactw is the point end displacement. w is the end displacement of the multi-leaf of the spring. multin-isleaf the spring number. n is of the slices num forber the of multi-leafslices for spring.the multib is-leaf the widthspring. of b each is the piece. width The of length each parameterspiece. The oflength half ofparameters the spring of pieces half areof Lthe1, Lspring2, L3, ... pieces, Ln–1 , areLn fromL1, L large2, L3, to…, small, Ln–1, respectively.Ln from large Correspondingly, to small, respectively. the thickness Correspondingly, parameters of thethe halfthickness of the springparameters pieces of aretheh half1, h2 of, h 3the, ... spring, hn–1 ,pieceshn, respectively. are h1, h2, h3,…, hn–1, hn, respectively.

F L 1 h1 L 2 h2 L 3 h3

Ln1 hn1

Ln hn

FigureFigure 1. 1.The The mechanicalmechanical modelmodel ofof thethe multi-leafmulti-leaf spring. spring.

BasedBased on on the the mechanical mechanical model model in in Figure Figure1, the1, the sti stiffnessﬀness of theof the half half of theof the multi-leaf multi-leaf spring spring can can be expressedbe expressed as [ 37as]: [37]: bE n ()()()LLLLLLL3   3 3   3 K Xn /[]13 i 1 i3 1L3 1(L 1 L n)3 bE (L1 Li)3(L 31 Li 1) 3 31 31 n 3 3 , (1) K = /[ 4 − h− h − − h+ h  h− − h  h ], (1) 4 i23 + 13 + 2+ 3 i 13 + 13 + 2+ 3 n 1 + n 3 i=2 h1 h2 ... hi 1 h1 h2 ... hn 1 hn where E is the elastic modulus. − − where E is the elastic modulus. 2.2. The Mechanical Model of the Single Taper-Leaf Spring 2.2. The Mechanical Model of the Single Taper-Leaf Spring The half of the single taper-leaf spring is taken as the research object. Its mechanical model is The half of the single taper-leaf spring is taken as the research object. Its mechanical model shown in Figure 2. Similarly, the half of the single taper-leaf spring also can be regarded as an elastic is shown in Figure2. Similarly, the half of the single taper-leaf spring also can be regarded as an beam. It is fixed at one end. A concentrated load F is applied at the other end. The geometric Appl. Sci. 2020, 10, 1293 4 of 21

Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 20 elastic beam. It is ﬁxed at one end. A concentrated load F is applied at the other end. The geometric parametersparameters and and the coordinate coordinate system system are are marked marked in Figure in Figure2. L is 2. theL is half the length half oflength the single of the taper-leaf single taperspring;-leafh spring;is the thicknessh2 is the thickness for x [l , forL]; hx∈is[l the2, L]; thickness h1 is the forthicknessx [0, l for]. h (xx∈) is[0, the l1]. thickness h(x) is the for thicknessx [l , l ]. 2 ∈ 2 1 ∈ 1 ∈ 1 2 forγ isx∈ deﬁned[l1, l2]. γ as is the defined thickness as the ratio thickness and γ = ratioh1/h 2and. γ = h1/h2.

FigureFigure 2. 2. TheThe mechanical mechanical model model of of the the single single taper taper-leaf-leaf spring spring..

BasedBased on on the the model model in FigureFigure2 ,2, when when the the load loadF isF appliedis applied at theat the free free end, end, the samethe same normal normal stress stressat any at positionany position for x for[l1 ,xl∈2][ isl1, [ l92]:] is [9]: ∈ 6Fx σ = (2) x 62Fx( )   bh x x bh2  x (2) From Equation (2), the normal stress σB of Section B for x = l2 can be expressed as:

From Equation (2), the normal stress σB of Section6Fl B for x = l2 can be expressed as: σ = 2 (3) B 6Fl2 bh22  B = 2 (3) bh2 In order to meet the requirements of the equal stress at Section B for x = l2, σx = σB must be satisfied.In order According to meet to the Equations requirements (2) and of (3), theh (equalx) can stress be expressed at Section as: B for x = l2, σx = σB must be satisfied. According to Equations (2) and (3), h(x) can be expressed as: r x h(x) = h2 x (4) l2 h x  h2 (4) l2 According to Equation (4), h1 can be expressed as: According to Equation (4), h1 can be expressed as: r l = 1 h1 h2 l1 (5) hh12 l2 (5) l2 When the load F is applied at the free end, the deformation energy U can be expressed as: When the load F is applied at the free end, the deformation energy U can be expressed as: Z 2 Z l1 2 Z l2 2 Z L 2 (Fx) 2(Fx) 2(Fx 2) 2(Fx) U = Fxdx = l12 Fx dx + l Fx dx + L  Fx dx (6) UL =2EI d x0 2EI1 d x l 2EI d2 x  l 2 dEI x 3 (6) L 0  l1  l 2 12 2EI 2 EI1 2 EI 2 2 EI 3 3 3 bh1 bh (x) I I I I 3 = I3 = I 3 = where 1, 2, 3 are the inertia moments at different thicknesses andbh1 12bh, 2 x 12 ,bh3 3 1   2 wherebh2 I1, I2, I3 are the inertia moments at different thicknesses and I1 = , I2 = , I3 = , 12 , respectively. 12 12 12 respectively.According to the Castigliano Second Theorem [37], the end deformation of the spring can be expressed as: According to the Castigliano Second Theoremh [37], the endi deformation of the spring can be 3 + 3 3 expressed as: ∂U 4F L l2 1 γ y = = − (7) ∂F Ebh3 3 32 3 U 41F L l2     (7) Based on Equation (7), the stiffnessy== of the half of the3 single taper-leaf spring can be expressed as: F Ebh2 3 Based on Equation (7), the stiffness of the half ofEbh the2 single taper-leaf spring can be expressed as: Ks = h i (8) 3 + 3( 3) 4 L l2 13 γ Ebh2 − Ks  (8) 41Ll3 3 3 2  

According to Equation (8), the design formula of the root thickness can be expressed as: Appl. Sci. 2020, 10, 1293 5 of 21

Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 20 According to Equation (8), the design formula of the root thickness can be expressed as: s 3 3 3 h41Ks L l2  i  3 3 3 +3( 3) (9) h 4Ks L l2 1 γ h = 2 Eb− (9) 2 Eb

2.3.2. The3. T Mechanicalhe Mechanical Model Model of theof the Taper-Leaf Taper-Leaf Spring Spring Including Including n Pieces n Pieces TheThe half half of theof the taper-leaf taper-leaf spring spring including includingn pieces n pieces (n = (n2 = or 2 3)or is3) taken is taken as theas the research research object. object Its. Its mechanicalmechanical model model isshown is shown in Figurein Figure3. Similarly, 3. Similarly, the the half h ofalf the of the single single taper-leaf taper-leaf spring spring also also can can be be regardedregarded as anas elastican elastic beam. beam It.is It ﬁxedis fixed at oneat one end. end A. concentratedA concentrated load loadF is F appliedis applied at theat the other other end. end. TheThe geometric geometric parameters parameters and and the coordinatethe coordinate system system are marked are marked in Figure in Fi3gure. The 3. end The displacement end displacement of the taper-leaf spring is y. γ is deﬁned as the thickness ratio and γ = h /h . Moreover, all the design of the taper-leaf spring isi y. γi is defined as the thickness ratio andi γii1 = hi2i1/hi2. Moreover, all the design values of γ are the same in practical engineering application and γ = γ. values ofi γi are the same in practical engineering application andi γi = γ.

FigureFigure 3. The 3. The mechanical mechanical model model of theof the taper-leaf taper-leaf spring spring including includingn pieces. n pieces.

UnderUnder the the load loadF, eachF, each piece piece does do notes not separate separate from from each each other other at theat the free free end. end. The The free free ends end ofs of thethen pieces n pieces for for the the taper-leaf taper-leaf spring spring are are equivalent equivalent to ato whole a whole body body and and the the vertical vertical displacement displacement occursoccurs under under the the load loadF. Thus, F. Th eachus, each piece piece has thehas samethe same vertical vertical displacement displacementy at they at free the end,free thatend, is: that is: yi = y (10) yyi = (10) where yi the displacement of the ith piece at the free end (i = 1, 2 or i = 1, 2, 3). where yi the displacement of the ith piece at the free end (i = 1, 2 or i = 1, 2, 3). According to Equation (7), yi can be expressed as: According to Equation (7), yi can be expressed as: h i 3 3 33 3 4Fi 41LF+ Ll 1 l γ  i 2 −2   yi = y = (11)(11) i Ebh3 3 iEbh2 i2 wherewhereFi is Fi the is the load load shared shared by theby theith i piece.th piece. SubstitutingSubstituting Equation Equation (11) (11) into into Equation Equation (10), (10), obtain obtain the the following: following: FF FFF F1 F2 12Fi inFn F = 3= 3=  = 3 =  3=  3 (12) 3 3 3 3 3 (12) h12··· h 22 hin··· 2 h 2 h e2 h12 h22 hi2 hn2 he2

where he2 is the equivalent thickness. where he2 is the equivalent thickness. AccordingAccording to the to model the model in Figure in 3 F,i thegure sum 3, of the the sum concentrated of the concentrated forces is equal forces to the concentrated is equal to the loadconcentratedF, that is: load F, that is: F1 + F2FFFF++ +Fn= F = (13) 12··· n (13) According to Equations (12) and (13), h can be calculated by: According to Equations (12) and (13),e2 he2 can be calculated by: q 3 3 3 33 33 3 h = he2h + hh 12 + h 22 + h  hn 2 (14)(14) e2 12 22 ··· n2

According to Equation (12), Fi can be calculated by: Appl. Sci. 2020, 10, 1293 6 of 21

According to Equation (12), Fi can be calculated by:

h3 F = i2 F (15) i 3 he2

Under the load F, the maximum normal stress of the ith piece can be expressed as:

6F L σ = i (16) imax 2 bhi2

Substituting Equation (15) into Equation (16), obtain the following:

6FLh σ = i2 (17) imax 3 bhe2

3. Analytical Method of Replacing the Multi-Leaf Spring with the Taper-Leaf Spring This paper mainly research the changes of the handling stability after replacing the multi-leaf spring with the taper-leaf spring for trucks by comparison. Therefore, it is necessary to ensure that the two leaf springs have the same vertical stiﬀness. Only on this premise can the conclusions of the comparison be valuable. In addition, the design of the taper-leaf spring must meet the stress condition. In this section, an analytical method of replacing the multi-leaf spring with the taper-leaf spring under the precondition of the same vertical stiﬀness was proposed.

3.1. The Analytical Design Method of the Taper-Leaf Spring

For the taper-leaf spring, σimax must be not larger than the allowable stress [σ]. Thus, based on σ max [σ] and Equation (17), the root allowable thickness of the ith piece can be expressed as: i ≤ bh3 [σ] [h ] = e2 (18) i2 6FL According to Equation (14), when h = h = = h , obtain the following: 12 22 ··· n2 3 = 3 he2 nhi2 (19)

According to Equation (19), the number n of the spring pieces can be expressed as:

h3 n = e2 (20) h 3 i hi2

Based on Equation (20), rounding up n, obtain the number [n] of the spring pieces meeting stress requirements. Substituting [n] into Equation (20), the design value of the root thickness of the ith piece can be calculated by: he2 hi2 = p (21) 3 [n]

According to Equation (5) and the deﬁnition of the thickness ratio γ, the design value of l1 can be calculated by: 2 l1 = l2γ (22)

According to the deﬁnition of the thickness ratio γ and hi2, hi1 can be designed as:

hi1 = γhi2 (23) Appl. Sci. 2020, 10, 1293 7 of 21

3.2. The Design Flow The design flow of the analytical method of replacing the multi-leaf spring with the taper-leaf spring under the precondition of the same vertical stiffness can be summarized as follows: Step 1. By using Equation (1), calculate the stiffness K of the multi-leaf spring of the original vehicle. Step 2. Let Ks = K and by using Equation (9), calculate the equivalent thickness he2. Appl. StepSci. 2020 3., Substituting10, x FOR PEERh REVIEWe2 into Equation (18), obtain the root allowable thickness [hi2]. 7 of 20 Step 4. Substituting he2 and [hi2] into Equation (20), rounding up n, obtain the number [n] of the spring3.2. The pieces Design meeting Flow stress requirements. Step 5. Based on [n], by using Equation (21), obtain the root thickness hi of the ith piece. The design flow of the analytical method of replacing the multi-leaf spring2 with the taper-leaf Step 6. Based on γ and l , by using Equation (22), obtain the length l of the end segment. spring under the precondition2 of the same vertical stiffness can be summarized1 as follows: Step 7. Based on γ and h , by using Equation (23), obtain the end thickness h of the ith piece. Step 1. By using Equationi2 (1), calculate the stiffness K of the multi-leaf springi1 of the original 3.3.vehicle Case. Study Step 2. Let Ks = K and by using Equation (9), calculate the equivalent thickness he2. A light truck was selected as the research object. Its rear suspension is equipped with the multi-leaf Step 3. Substituting he2 into Equation (18), obtain the root allowable thickness [hi2]. spring. Moreover, the number of slices for the multi-leaf spring is five. The specific parameters are as Step 4. Substituting he2 and [hi2] into Equation (20), rounding up n, obtain the number [n] of the follows: b = 63.0 mm, h = 8.0 mm, L = 525.0 mm, L = 450.0 mm, L = 350.0 mm, L = 250.0 mm, L = spring pieces meeting stress requirements1 . 2 3 4 5 150.0 mm, E = 206 GPa, [σ] = 750.0 Mpa. In order to meet the requirements of the spring installation, l3 Step 5. Based on [n], by using Equation (21), obtain the root thickness hi2 of the ith piece. was designed as 50 mm for the taper-leaf spring. According to l2 = L1 l3, l2 was designed as 475 mm. Step 6. Based on γ and l2, by using Equation (22), obtain the length− l1 of the end segment. Based on the analytical method of replacing the multi-leaf spring with the taper-leaf spring, the other Step 7. Based on γ and hi2, by using Equation (23), obtain the end thickness hi1 of the ith piece. design parameters values were determined. The key design parameters values of the taper-leaf spring are3.3. shown Case Study in Table 1. The prototype of the taper-leaf spring manufactured by Shandong Automobile Spring Factory is shown in Figure4. A light truck was selected as the research object. Its rear suspension is equipped with the multi-leaf spring. Moreover, theTable number 1. The ofdesign slices parameters for the values. multi-leaf spring is five. The specific parameters are as follows: b = 63.0 mm, h = 8.0 mm, L1 = 525.0 mm, L2 = 450.0 mm, L3 = 350.0 mm, L4 = Parameter Value Unit Parameter Value Unit 250.0 mm, L5 = 150.0 mm, E = 206 GPa, [σ] = 750.0 Mpa. In order to meet the requirements of the spring installation, l3 wasn designed 3as 50 mm pieces for the taperh11-leaf spring5.6. According mm to l2 = L1 − l3, l2 was designed as 475 mmσmax. Based on the460.2 analytical MPa method ofh21 replacing5.6 the multi mm-leaf spring with the b 63.0 mm h 5.6 mm taper-leaf spring, the other design parameters values were31 determined. The key design parameters l1 123.5 mm h12 11.0 mm values of the taper-leaf spring are shown in Table 1. The prototype of the taper-leaf spring l2 475.0 mm h22 11.0 mm manufactured by Shandongl3 Automobile50.0 Spring mm Factory ish32 shown in11.0 Figure 4. mm

Figure 4. The prototype of the taper-leaf spring. Figure 4. The prototype of the taper-leaf spring. 4. Dynamic Modeling and Test Verification Table 1. The design parameters values. 4.1. Dynamic Modeling and Verification of Leaf Springs Parameter Value Unit Parameter Value Unit Adams is recognized asn a professional3 softwarepieces for theh11 vehicle dynamics5.6 mm modeling. The dynamic models based on the softwareσmax can truly460.2 reflect theMP dynamica h performance21 5.6 of vehiclesmm [38,39]. Adams/Leaf b 63.0 mm h 5.6 mm tool uses discrete beam elements to simulate leaf springs.31 In other words, each piece of leaf springs is l1 123.5 mm h12 11.0 mm divided into several sections, which are connected by flexible beams without mass. The flexible beam l2 475.0 mm h22 11.0 mm is a kind of flexible connection.l3 The force50.0 and momentmm betweenh32 two11.0 marked mm points of two elements are calculated by the theory of Timoshenko beam [40]. In this study, according to the structural parameters values4. Dynamic of the Modeling multi-leaf springand Test and Verification the taper-leaf spring, the simulation models were established based on Adams/Leaftool software, as shown in Figure5. Because the friction force between the adjacent pieces4.1. Dynamic is very Modeling small [37 and], it Verification is ignored inof Leaf the simulationSprings models. Moreover, the previous tests in [37] Adams is recognized as a professional software for the vehicle dynamics modeling. The dynamic models based on the software can truly reflect the dynamic performance of vehicles [38,39]. Adams/Leaf tool uses discrete beam elements to simulate leaf springs. In other words, each piece of leaf springs is divided into several sections, which are connected by flexible beams without mass. The flexible beam is a kind of flexible connection. The force and moment between two marked points of two elements are calculated by the theory of Timoshenko beam [40]. In this study, according to the structural parameters values of the multi-leaf spring and the taper-leaf spring, the simulation models were established based on Adams/Leaftool software, as shown in Figure 5. Because the friction force between the adjacent pieces is very small [37], it is ignored in the Appl. Sci. 20202020, 10, x 1293 FOR PEER REVIEW 8 of 2120 Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 20 simulation models. Moreover, the previous tests in [37] show that the load-stiffness characteristics simulation models. Moreover, the previous tests in [37] show that the load-stiffness characteristics showfor multi that-leaf the load-stispringsff nessand taper characteristics-leaf spring fors multi-leafare almost springs linear. and Thus, taper-leaf their vertical springs stiffness are almost and linear. the for multi-leaf springs and taper-leaf springs are almost linear. Thus, their vertical stiffness and the Thus,torsional their stiffness vertical are sti ffoftenness used and theto verify torsional the stimodelffness accuracy are often [9] used. to verify the model accuracy [9]. torsional stiffness are often used to verify the model accuracy [9].

(a) (b) (a) (b) Figure 5. The simulation models: (a) The multi-leaf spring; (b) the taper-leaf spring. Figure 5. The simulation models:models: ( a) The multi multi-leaf-leaf spring spring;; ( b) the taper taper-leaf-leaf spring. To verify the accuracy of the models, the vertical and torsional stiffness tests were conducted. ToTo verifyverify thethe accuracy accuracy of of the the models, models the, the vertical vertical and and torsional torsional stiff stiffnessness tests tests were were conducted. conducted The. The test equipment is the TYE-W400I hydraulic testing machine produced by Jinan Shidai Shijin testThe equipment test equipment is the is TYE-W400I the TYE-W400I hydraulic hydraulic testing testing machine machine produced produced by Jinan by Shidai Jinan Shijin Shidai Group, Shijin Group, as shown in Figure 6. It uses the programmable logic controller. It can measure the load and asGroup shown, as inshown Figure in6 F.igure It uses 6. It the uses programmable the programmable logic controller. logic controller It can. It measure can measure the load the load and theand the displacement through sensors. The load was measured by a NS-WL1 tension–compression displacementthe displacement through through sensors. sensors. The loadThe wasload measured was measured by a NS-WL1 by a NS tension–compression-WL1 tension–compression sensor. sensor. The displacement was measured by a SDVG20 displacement sensor. The control system Thesensor. displacement The displacement was measured was measured by a SDVG20 by displacementa SDVG20 displacement sensor. The control sensor.system The control automatically system automatically collected and processed the test force and the deformation of leaf springs, and collectedautomatically and processed collected theand test process forceed and the the test deformation force and ofthe leaf deformation springs, and of directly leaf spring outputs, and the directly output the stiffness value through the microcomputer display screen. For the models in stidirectlyffness outputvalue through the stiffness the microcomputer value through display the micr screen.ocomputer For the display models screen. in Figure For 5 the, the model verticals in Figure 5, the vertical forces were applied to simulate the deformation, respectively. The simulated forcesFigure were 5, the applied vertical to force simulates were the applied deformation, to simulate respectively. the deformation The simulated, respectively. stiffness values The simulated from the stiffness values from the simulation results were calculated. A comparison of the stiffness values is simulationstiffness values results from were the calculated. simulation A results comparison were calculated. of the stiffness A comparison values is shown of the in stiffness Table2. values is shown in Table 2. shown in Table 2.

Figure 6. The test equipment. Figure 6. TheThe test equipment.equipment.

Table 2. A comparison of the stistiffnessﬀness values.values. Table 2. A comparison of the stiffness values. VerticalVertical Torsional Vertical Torsional Type Test Simulation Error Test Simulation Error Type Type Test TestSimulationSimulation ErrorError TestTest SimulationSimulation ErrorError (kN/m) (N/m) (%) (kNm/rad) (kNm/rad) (%) (kN/m)(kN /m) (N/m)(N /m) (%) (%) (kN(kNmm/rad/rad)) ((kNmkNm/rad/rad)) (%)(%) The multi-leaf spring 112.3 109.0 2.9 10.6 10.1 4.7 The multiThe- multi-leafleaf spring spring 112.3 112.3109.0 109.02.9 2.910 10.6.6 10.110.1 4.74.7 The taperThe- taper-leafleaf spring spring 113.1 113.1109.2 109.23.5 3.58.4 8.4 8.28.2 2.42.4 The taper-leaf spring 113.1 109.2 3.5 8.4 8.2 2.4

From Table 2, it can be seen that the vertical stiffness values of the multi-leaf spring and the From TableTable2 2,, it it can can be be seen seen that that the the vertical vertical sti stiffnessffness valuesvalues ofof thethe multi-leafmulti-leaf springspring and the taper-leaf spring are almost the same. The result shows that the taper-leaf spring can equivalently taper-leaftaper-leaf spring are almostalmost thethe same.same. The result shows that the taper-leaftaper-leaf springspring cancan equivalentlyequivalently replace the original multi-leaf spring. From Table 2, it also can be seen that the torsional stiffness of replace the original multi-leafmulti-leaf spring. From From T Tableable 22,, itit alsoalso cancan bebe seenseen thatthat thethe torsionaltorsional stistiffnessffness of the multi-leaf spring is obviously larger than that of taper-leaf spring. Moreover, the test values are the multi-leafmulti-leaf spring is obviously larger than that of taper-leaftaper-leaf spring.spring. Moreover, the test values are close to the simulation values. The results show that the simulation models can effectively reflect close toto thethe simulationsimulation values. values. The The results results show show that that the the simulation simulation models model cans can effectively effectively reflect reflect the the stiffness characteristics of the multi-leaf spring and the taper-leaf spring, respectively. In stitheff ness stiffness characteristics characteristics of the of multi-leaf the multi spring-leaf springand the and taper-leaf the taper spring,-leaf respectively. spring, respectively In addition,. In addition, the experimental results indicate that the weight of the taper-leaf spring is less 13.4% than theaddition, experimental the experimental results indicate results that indicate the weight that the of theweight taper-leaf of the springtaper-leaf is less spring 13.4% is thanless 13.4 that% of than the that of the multi-leaf spring. multi-leafthat of the spring.multi-leaf spring.

Appl. Sci. 2020, 10, 1293 9 of 21 Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 20 4.2. Dynamic Modeling of the Truck 4.2. Dynamic Modeling of the Truck The parameters values of the light truck are shown in Table3. The geometric model of the The parameters values of the light truck are shown in Table 3. The geometric model of the light light truck is shown in Figure7a. The modeling process is as follows: ﬁrstly, the geometric model is truck is shown in Figure 7a. The modeling process is as follows: firstly, the geometric model is imported into Adams through the “parasolid” data format; then, system constraints, loads, and drives imported into Adams through the “parasolid” data format; then, system constraints, loads, and are applied in Adams; ﬁnally, the simulation models of the multi-leaf spring and the taper-leaf spring drives are applied in Adams; finally, the simulation models of the multi-leaf spring and the are imported and assembled to establish the vehicle dynamic models, respectively. The dynamic model taper-leaf spring are imported and assembled to establish the vehicle dynamic models, respectively. of the truck with the multi-leaf spring is shown in Figure7b. The tire adopts the PAC2002 tire model. The dynamic model of the truck with the multi-leaf spring is shown in Figure 7b. The tire adopts This tire model adopts the magic formula, which is suitable for the simulation analysis of stability with the PAC2002 tire model. This tire model adopts the magic formula, which is suitable for the high accuracy [41,42]. The steering system is equipped with rack-and-pinion steering gear and the simulation analysis of stability with high accuracy [41,42]. The steering system is equipped with angular ratio of steering gear is 18.0. rack-and-pinion steering gear and the angular ratio of steering gear is 18.0.

Table 3. The parameters values of the light truck. Table 3. The parameters values of the light truck. Parameter Value Parameter Value Parameter Value Parameter Value The unsprungThe massunsprung for the mass front for wheel the front/(kg) wheel /(kg 46.4) 46.4 The differential The differential ratioratio 4.778 4.778 The front axleThe loadfront/ (kg)axle load /(kg) 884884 The mass The mass of the of drive the drive shaft shaft/(kg)/ (kg)8.3 8.3 The rear axleThe load rear/ (kg)axle load /(kg) 16411641 The arm The length arm length of the of stabilizer the stabilizer /(mm/)(mm) 204 204 The wheelbaseThe /wheelbase/(m)(m) 2.62.6 The bar The length bar length of the of stabilizer the stabilizer /(mm/)(mm) 910 910 The front tread /(m) 1.32 The front wheel radius /(m) 0.297 The front tread /(m) 1.32 The front wheel radius /(m) 0.297 The rear tread /(m) 1.41 The rear wheel radius /(m) 0.297 The rear tread /(m) 1.41 The rear wheel radius /(m) 0.297 The stiffness of the front suspension /(N/mm) 55 The front wheel stiffness /(kNm 1) 383.4 The stiffness of the front suspension /(N/mm) 55 The front wheel stiffness /(kNm−1) −383.4 The unsprung mass for the rear wheel /(kg) 83 The rear wheel stiffness /(kNm 1) 383.4 The unsprung mass for the rear wheel /(kg) 83 The rear wheel stiffness /(kNm−1) −383.4 The angular ratio of steering gear 18.0 The angular ratio of steering gear 18.0

(a) (b)

Figure 7. The light truck models models:: ( a)) The geometric model, ( b) the dynamic model model,, ( c) the sub-modelsub-model of the stabilizer system,system, and (d) the sub-modelsub-model of thethe rear axleaxle withwith dampers.dampers.

4.3. S Steadyteady Static Circular Test VerificationVerification Based on the standard GB GB/T6323.6/T6323.6-1994,-1994, the steady steady static static circular circular tests tests were were conducted. conducted. The specificspecific test method method is is as as follows follows:: firstly, firstly, fix fix the the steering steering wheel wheel angle angle and and the the starting starting circle circle radius radius is 2 1is5.0 15.0 m; m; then, then, accelerate accelerate slowly slowly at at the the longitudinal longitudinal acceleration acceleration below below 0.25 0.25 m/ m/ss2 untiluntil the lateral 2 acceleration reaches 6.5 mm//s2.. Based Based on on the the two two truck truck dynamic model models,s, the the s steadyteady static circular test were carried out,out, respectively.respectively. The simulation settings are the same as the realreal testtest conditions.conditions. A ccomparisonomparison ofof thethe curvescurves ofof thethe body body roll roll angle angle versus versus the the lateral lateral acceleration acceleration is shownis shown in Figurein Figure8. α81. α1 and α2 are the absolute values of the sideslip angles of the front axle and the rear axle, respectively. In order to facilitate the test and analysis, researchers usually choose evaluation Appl. Sci. 2020, 10, 1293 10 of 21 and α are the absolute values of the sideslip angles of the front axle and the rear axle, respectively. In Appl. Sci.2 2020, 10, x FOR PEER REVIEW 10 of 20 orderAppl. Sci. to facilitate2020, 10, x FOR the PEER testand REVIEW analysis, researchers usually choose evaluation indicators to describe10 of 20 and evaluate the steady-state response of the vehicle according to their own habits. α α is one of indicators to describe and evaluate the steady-state response of the vehicle according1 − to2 their own thehabits most. α important1 − α2 is one evaluation of the mostindicators. important If α1 evaluationα2 > 0, the indicators vehicle has. If under-steer α1 − α2 > 0, characteristics; the vehicle has if habits. α1 − α2 is one of the most important −evaluation indicators. If α1 − α2 > 0, the vehicle has αunder1 α2-steer= 0, the characteristics vehicle has;neutral if α1 − α steering2 = 0, the characteristics; vehicle has neutral If α1 steeringα2 < 0, characteristics the vehicle has; If over-steer α1 − α2 < 0, under− -steer characteristics; if α1 − α2 = 0, the vehicle has neutral −steering characteristics; If α1 − α2 < 0, characteristicsthe vehicle has [43 over]. A-steer comparison characteristics of the curves [43]. A of comparisonα1 α2 versus of the the curve laterals of acceleration α1 − α2 versus is shownthe lateral in the vehicle has over-steer characteristics [43]. A comparison− of the curves of α1 − α2 versus the lateral Figure9. From Figure9, it can be seen that the simulation results are close to the test results, which acceleration is shown in Figure 9. From Figure 9, it can be seen that the simulation results are close proves that the two truck models can reproduce the handling dynamic responses. Figure9 also shows to the test results, which proves that the two truck models can reproduce the handling dynamic that the truck has slight over-steer characteristics. responses. Figure 9 also shows that the truck has slight over-steer characteristics.

8 8 8 8

/ (°) /

/ (°) / 6 φ 6

6 φ 6

4 4 4 4

Test 2 Test 2 2 2 Test Simulation Test Simulation Simulation 0 0 Simulation 0 0

Thevehicle roll angle

Thevehicle roll angle -2 -2 -20 1 2 3 4 5 6 -20 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6 2 2 The lateral acceleration a /(m/s2) The lateral acceleratio a /(m/s2) The lateral acceleration ay /(m/s ) The lateral acceleratio ay /(m/s ) y y (a) (b) Figure 8. A comparison of the curves of the body roll angle versus the lateral acceleration for the FigureFigure 8. 8.A A comparison comparison of of the the curves curve ofs theof the body body roll angleroll angle versus versus the lateral the lateral acceleration acceleration for the for truck the truck with: (a) the multi-leaf spring, and (b) the taper-leaf spring. with:truck ( awith:) the multi-leaf(a) the multi spring,-leaf spring, and (b )and the ( taper-leafb) the taper spring.-leaf spring.

0.10 0.10 0.10 0.10 0.05 0.05 0.05 0.05 Test Test 0.00 Test 0.00 Simulation 0.00 Test 0.00 Simulation Simulation -0.05 Simulation -0.05 -0.05 -0.05

/ (°) / (°) /

2 2

/ (°) / (°) /

α α

2 2

- -0.10 - -0.10

α α

1 1

- -0.10 - -0.10

α α

1 1 α -0.15 α -0.15 -0.15 -0.15 -0.20 -0.20 -0.20 -0.20 -0.25 -0.25 -0.250 1 2 3 4 5 6 -0.250 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6 2 2 The lateral acceleration a /(m/s2) The lateral acceleration a /(m/s2) The lateral acceleration ay /(m/s ) The lateral acceleration ay /(m/s ) y y (a) (b)

Figure 9. A comparison of the curves of α1-α2 versus the lateral acceleration for the truck with: (a) FigureFigure 9. 9.A A comparison comparison of of the the curves curve ofs ofα α1-α 2 versus thethe laterallateral accelerationacceleration forfor thethetruck truck with: with:( a(a)) 1 − 2 TheThe multi-leaf multi-leaf spring, spring, and and ( b(b)) the the taper-leaf taper-leaf spring. spring.

5. Handling Stability Simulation and Comparison 5. Handling Stability Simulation and Comparison In general, handling stability tests of vehicles are very dangerous, such as the drift test [43,44]. In In general, handling stability tests of vehicles are very dangerous, such as the drift test [43,44]. order to avoid the potential dangers of handling stability tests, this paper uses simulation methods to In order to avoid the potential dangers of handling stability tests, this paper uses simulation carry out the comparative analysis. The changes of the handling stability after replacing the multi-leaf methods to carry out the comparative analysis. The changes of the handling stability after replacing spring with the taper-leaf spring were revealed by the simulations of the drift test, the ramp steer test, the multi-leaf spring with the taper-leaf spring were revealed by the simulations of the drift test, the and the step steer test. ramp steer test, and the step steer test. 5.1. Simulation and Comparison of the Drift Tests 5.1. Simulation and Comparison of the Drift Tests The drift test is an important method to study the transient responses of vehicles under the limit The drift test is an important method to study the transient responses of vehicles under the operating condition. In the drift simulation, the truck reaches a steady-state condition in the ﬁrst 10.0 s. limit operating condition. In the drift simulation, the truck reaches a steady-state condition in the A steady-state condition is one in which the truck has the desired steer angle 360◦, the initial throttle first 10.0 s. A steady-state condition is one in which the truck has the desired steer angle 360°, the 20.0, and the initial velocity 40 km/h. In 1.0–4.0 s, Adams ramps the steering angle from an initial value initial throttle 20.0, and the initial velocity 40 km/h. In 1.0–4.0 s, Adams ramps the steering angle to the desired value. It then ramps the throttle from 0.0 to the full throttle value 100.0 from 5.0 s to from an initial value to the desired value. It then ramps the throttle from 0.0 to the full throttle value 100.0 from 5.0 s to 10.0 s. Finally, it keeps the throttle fully open from 10.0 s to 15.0 s. The same simulation parameters were set for the two truck models with the multi-leaf spring and the taper-leaf spring, respectively. A comparison of the simulated dynamic responses is shown in Figure 10. Appl. Sci. 2020, 10, 1293 11 of 21

10.0 s. Finally, it keeps the throttle fully open from 10.0 s to 15.0 s. The same simulation parameters were set for the two truck models with the multi-leaf spring and the taper-leaf spring, respectively. A comparisonAppl. Sci. 2020, of10, thex FOR simulated PEER REVIEW dynamic responses is shown in Figure 10. 11 of 20

60.0

50.0

/ (Nm)

40.0

30.0

20.0

10.0

0.0

he steeringhe wheel torque

T −10.0

Time t / (s)

(a)

he yawhe rate / (°/s)

Time t / (s)

(b)

he truckhe sideslip angle / (°)

Time t / (s)

(c)

﹍the taper-leaf spring, ＿the multi-leaf spring

FigureFigure 10.10. AA comparisoncomparison ofof thethe simulatedsimulated dynamicdynamic responsesresponses obtainedobtained fromfrom thethe driftdrift tests:tests: ((aa)) TheThe steeringsteering wheelwheel torque,torque, ((bb)) thethe yawyaw rate,rate, andand ((cc)) thethe trucktruck sideslipsideslip angle.angle.

FromFrom FigureFigure 1010a,a, itit cancan bebe seenseen thatthat forfor thethe samesame input,input, whenwhen thethe steeringsteering angleangle reachesreaches thethe setset value,value, thethe steeringsteering wheelwheel torquetorque ofof thethe trucktruck withwith thethe multi-leafmulti-leaf springspring suspensionsuspension isis signiﬁcantlysignificantly largerlarger thanthan thatthat of of the the truck truck with with the the taper-leaf taper-leaf spring spring suspension. suspension. The The result result shows shows that thethat truck the tru withck with the taper-leaf spring suspension has better steering portability than the truck with the multi-leaf spring suspension. From Figure 10b, it can be seen that the two truck models have almost the same yaw rate. The result shows that replacing the multi-leaf spring with the taper-leaf spring has almost no effect on the yaw rate. From Figure 10c, it can be seen that when the steering wheel angle is increased to the set value, the sideslip angles on the basis of the two truck models are almost the same. With the increase of the throttle opening, the sideslip angles on the basis of the Appl. Sci. 2020, 10, 1293 12 of 21

the taper-leaf spring suspension has better steering portability than the truck with the multi-leaf spring suspension. From Figure 10b, it can be seen that the two truck models have almost the same yaw rate. The result shows that replacing the multi-leaf spring with the taper-leaf spring has almost no effect on the yaw rate. From Figure 10c, it can be seen that when the steering wheel angle is increased to the set Appl.value, Sci. 2020 the, 10 sideslip, x FOR PEER angles REVIEW on the basis of the two truck models are almost the same. With the12 increase of 20 ofAppl. the Sci. throttle 2020, 10 opening,, x FOR PEER the REVIEW sideslip angles on the basis of the two truck models begin to deviate.12The of 20 twosideslip truck models angle of begin the truck to deviate with the. The taper-leaf sideslip spring angle suspension of the truck is obviously with the larger taper than-leaf that spring of the two truck models begin to deviate. The sideslip angle of the truck with the taper-leaf spring suspensiontruck with is the obviously multi-leaf larger spring than suspension. that of the The truck result with shows the thatmulti the-leaf handling spring ofsuspension. the truck with The the suspension is obviously larger than that of the truck with the multi-leaf spring suspension. The resulttaper-leaf shows springthat the suspension handling of is poorerthe truck than with that the of thetaper truck-leaf with spring the suspension multi-leaf spring is poorer suspension. than that The result shows that the handling of the truck with the taper-leaf spring suspension is poorer than that of themain truck reason with should the multi be related-leaf spring to that suspension the torsional. The stiff mainness ofreason the taper-leaf should be spring related is less to that 18.8% the than of the truck with the multi-leaf spring suspension. The main reason should be related to that the torsionalthat of stiffness the multi-leaf of the spring.taper-leaf spring is less 18.8% than that of the multi-leaf spring. torsional stiffness of the taper-leaf spring is less 18.8% than that of the multi-leaf spring. 5.2.5.2. Simulation Simulation and andComparison Comparison of the of theRamp Ramp Steer Steer Tests Tests 5.2. Simulation and Comparison of the Ramp Steer Tests In aIn ramp a ramp-steer-steer analysis, analysis, time time-domain-domain transient transient response response metrics cancan be be obtained obtained [43 [4].3]. The The most In a ramp-steer analysis, time-domain transient response metrics can be obtained [43]. The mostimportant important quantities quantities to beto measuredbe measured are: are: the the steering steering wheel wheel torque, torque, the yawthe yaw rate, rate, the truck the truck sideslip most important quantities to be measured are: the steering wheel torque, the yaw rate, the truck sideslipangle, angle and, theand truck the truck roll angle.roll angle. During During a ramp-steer a ramp-steer analysis, analysis, Adams Adams ramps ramps up up the the steering steering input sideslip angle, and the truck roll angle. During a ramp-steer analysis, Adams ramps up the steering inputfrom from an initialan initial value value at a at specified a specified rate, rate as shown, as shown in Figure in F 11igure. The 11 simulations. The simulations of the rampof the steer ramp tests input from an initial value at a specified rate, as shown in Figure 11. The simulations of the ramp steerwere test conducteds were conducted in Adams in basedAdams on based the two on truckthe two models, truck respectively.models, respectively. The simulation The simulation settings are steer tests were conducted in Adams based on the two truck models, respectively. The simulation settingsas follows: are as thefollows initial: the steer initial value steer= 0 ◦value, the initial = 0°, the velocity initial 40 velocity km/h, the 40 rampkm/h,= thetan( rampθ) = 15.0,= tan( theθ) start= settings are as follows: the initial steer value = 0°, the initial velocity 40 km/h, the ramp = tan(θ) = 15.0,time the= start3.0 s, time and the= 3.0 end s, time and= the15.0 end s. A time comparison = 15.0 s. of A the comparison simulated dynamic of the simulated responses dynamic is shown in 15.0, the start time = 3.0 s, and the end time = 15.0 s. A comparison of the simulated dynamic responseFigures 12is .shown in Figure 12. responses is shown in Figure 12.

Steer value Steer value θ θ Initial value Initial value Time Time Start time Start time End time End time Figure 11. The curve of the input versus the time for the ramp steer test. FigureFigure 11 11.. TheThe curve curve of ofthe the input input versus versus the the time time for for the the ramp ramp steer steer test test..

30.0

30.0 25.0 25.0 20.0 20.0 15.0 15.0 10.0 10.0 5.0 5.0 0.0 0.0

he steeringhe wheel torque / (Nm)

T −5.0

he steeringhe wheel torque / (Nm)

T −5.0 Time t / (s) Time t / (s)

(a) (a)

Figure 12. Cont.

he yawhe rate / (°/s)

Time t / (s) Time t / (s)

(b) (b) Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 20

two truck models begin to deviate. The sideslip angle of the truck with the taper-leaf spring suspension is obviously larger than that of the truck with the multi-leaf spring suspension. The result shows that the handling of the truck with the taper-leaf spring suspension is poorer than that of the truck with the multi-leaf spring suspension. The main reason should be related to that the torsional stiffness of the taper-leaf spring is less 18.8% than that of the multi-leaf spring.

5.2. Simulation and Comparison of the Ramp Steer Tests In a ramp-steer analysis, time-domain transient response metrics can be obtained [43]. The most important quantities to be measured are: the steering wheel torque, the yaw rate, the truck sideslip angle, and the truck roll angle. During a ramp-steer analysis, Adams ramps up the steering input from an initial value at a specified rate, as shown in Figure 11. The simulations of the ramp steer tests were conducted in Adams based on the two truck models, respectively. The simulation settings are as follows: the initial steer value = 0°, the initial velocity 40 km/h, the ramp = tan(θ) = 15.0, the start time = 3.0 s, and the end time = 15.0 s. A comparison of the simulated dynamic responses is shown in Figure 12.

Steer value θ Initial value

Time Start time

End time

Figure 11. The curve of the input versus the time for the ramp steer test.

30.0

25.0

20.0

15.0

10.0

5.0

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he steeringhe wheel torque / (Nm)

T −5.0

Time t / (s) Appl. Sci. 2020, 10, 1293 13 of 21

(a)

he yawhe rate / (°/s)

Time t / (s)

Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 20 (b)

roll angle / (°)

he truckhe

Time t / (s)

(c)

he truckhe sideslip angle / (°)

Time t / (s)

(d)

﹍the taper-leaf spring, ＿the multi-leaf spring

FigureFigure 12.12. AA comparisoncomparison ofof thethe simulatedsimulated dynamicdynamic responsesresponses obtainedobtained fromfrom thethe rampramp steersteer tests:tests: ((aa)) TheThe steeringsteering wheelwheeltorque, torque,( b(b)) the the yaw yaw rate, rate, ( c(c)) the the truck truck roll roll angle, angle, and and ( d(d)) the the truck truck sideslip sideslip angle. angle.

FromFrom FigureFigure 1212a,a, itit cancan bebe seenseen thatthat thethe steeringsteering wheelwheel torquestorques fromfrom thethe twotwo trucktruck modelsmodels areare almostalmost thethe samesame fromfrom thethe beginningbeginning toto aboutabout 10.010.0 s.s. Moreover,Moreover, inin thethe laterlater stage,stage, withwith thethe increasingincreasing ofof the the steersteer angle,angle, the the steering steering wheel wheel torque torque of of the the multi-leaf multi-leaf spring spring trucktruck modelmodel increases increases moremore obviously.obviously. InInother other words, words, when when the the steer steer angle angle is veryis very small, small, the the two two truck truck models models show show almost almost the samethe same steering steering portability. portability However,. However, when thewhen steering the steering angle is angle very large,is very the large, truck the with truck the taper-leaf with the springtaper-leaf suspension spring suspension has better steeringhas better portability. steering portability. From Figure From 12b, Figure it can 1 be2b seen, it can that be the seen two that truck the modelstwo truck show models almost show the samealmost yaw the rate. same The yaw result rate. shows The result that replacingshows that the replacin multi-leafg the spring multi with-leaf spring with the taper-leaf spring has almost no effect on the yaw rate. From Figure 12c, it can be seen that the truck roll angles on the basis of the two truck models are almost the same from 0.0 s to 5.0 s. With the increase of the steer value, the truck roll angles on the basis of the two truck models begin to deviate. The truck roll angle of the truck with the taper-leaf spring suspension is obviously larger than that of the truck with the multi-leaf spring suspension. The results show that the truck with the multi-leaf spring suspension has the stronger stability. From Figure 12d, it can be seen that the two truck models show almost the same sideslip angle. The result shows that replacing the multi-leaf spring with the taper-leaf spring has almost no effect on the truck sideslip angle during the ramp steer test.

5.3. Simulation and Comparison of the Step Steer Tests The purpose of the step steer test is to characterize the transient response behaviors of vehicles [44]. The steering input ramps up from an initial steer value to the maximum steer value, as shown in Figure 13. During the step steer test, the steady state of the truck changes from the straight driving to the circular motion and the transition between the two steady-state movements is the Appl. Sci. 2020, 10, 1293 14 of 21

the taper-leaf spring has almost no eﬀect on the yaw rate. From Figure 12c, it can be seen that the truck roll angles on the basis of the two truck models are almost the same from 0.0 s to 5.0 s. With the increase of the steer value, the truck roll angles on the basis of the two truck models begin to deviate. The truck roll angle of the truck with the taper-leaf spring suspension is obviously larger than that of the truck with the multi-leaf spring suspension. The results show that the truck with the multi-leaf spring suspension has the stronger stability. From Figure 12d, it can be seen that the two truck models show almost the same sideslip angle. The result shows that replacing the multi-leaf spring with the taper-leaf spring has almost no eﬀect on the truck sideslip angle during the ramp steer test.

5.3. Simulation and Comparison of the Step Steer Tests The purpose of the step steer test is to characterize the transient response behaviors of vehicles [44]. The steering input ramps up from an initial steer value to the maximum steer value, as shown in Appl.Appl. Sci. 20Sci.20 20, 1020, ,x 10 FOR, x FOR PEER PEER REVIEW REVIEW 14 of14 20 of 20 Figure 13. During the step steer test, the steady state of the truck changes from the straight driving transienttotransient the circularresponse response motion. The. The simulations and simulations the transition of theof thestep between step steer steer test the tests two weres steady-statewere conducted conducted movementsin Adamsin Adams based is thebased on transient onthe the tworesponse.two truck truck models, Themodels, simulations respectively. respectively. of According the According step steer to Chineseto tests Chinese were GB/T6323.2 conductedGB/T6323.2-94, in- 94,the Adams tsimulahe simula basedtiontion settings on settings the two are are truckas as followsmodels,follows: the: respectively. theinitial initial steer steer value According value = 0 °=, the0 to°, Chinese thestep step start GBstart time/T6323.2-94, time 2.0 2.0s, the s, the theduration simulationduration time time settings6.0 6.0s, the s, are theend as end time follows: time 30.0 30.0the s, andinitials, and the steer thefinal final value steer steer= value0◦ ,value the 100.0 step 100.0° start. A° . c timeAomparison comparison 2.0 s, the of duration theof thesimulated simulated time 6.0 dynamic s, dynamic the end response time response 30.0s is s,s shown andis shown the in ﬁnal in FiguresteerFigure 14 value. 14. 100.0◦. A comparison of the simulated dynamic responses is shown in Figure 14.

SteerSteer value value StepStep start start time time DurationDuration of step of step

FinalFinal value value

InitialInitial value value TimeTime End time End time Figure 13. The curve of the input versus the time for the step steer test. FigureFigure 13.13. The curve of the input versus the timetime forfor thethe stepstep steersteer test.test.

5.5 5.5

4.5 4.5

3.5 3.5

2.5 2.5

1.5 1.5

0.5 0.5

0.0 0.0

he steeringhe wheel torque / (Nm)

T −0.5T −0.5 TimeTime t / (s) t / (s)

(a) (a)

Figure 14. Cont.

he yawhe rate / (°/s)

TimeTime t / (s) t / (s) (b) (b)

angle / (°)

he truckhe roll

TimeTime t / (s) t / (s)

transient response. The simulations of the step steer tests were conducted in Adams based on the two truck models, respectively. According to Chinese GB/T6323.2-94, the simulation settings are as follows: the initial steer value = 0°, the step start time 2.0 s, the duration time 6.0 s, the end time 30.0 s, and the final steer value 100.0°. A comparison of the simulated dynamic responses is shown in Figure 14.

Steer value Step start time Duration of step

Final value

Initial value Time End time Figure 13. The curve of the input versus the time for the step steer test.

5.5

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he steeringhe wheel torque / (Nm) T −0.5 Time t / (s) Appl. Sci. 2020, 10, 1293 15 of 21

(a)

he yawhe rate / (°/s)

Time t / (s) (b)

angle / (°)

he truckhe roll

Time t / (s)

Appl. Sci. 2020, 10, x FOR PEER REVIEW 15 of 20 (c)

he truckhe sideslip angle / (°)

Time t / (s)

(d)

﹍the taper-leaf spring, ＿the multi-leaf spring

FigureFigure 14.14.A A comparisoncomparison ofof thethesimulated simulated dynamicdynamic responsesresponses obtainedobtained fromfrom thethe stepstepsteer steer tests:tests: ((aa)) TheThe steering steering wheel wheel torque, torque, ( b(b)) the the yaw yaw rate, rate, ( c()c) the the truck truck roll roll angle, angle and, and ( d(d)) the the truck truck sideslip sideslip angle. angle.

FromFrom FigureFigure 14 14a,a, itit cancan bebe seenseen thatthat thethe steeringsteering wheelwheel torquestorques fromfrom thethe twotwo trucktruck modelsmodels areare basicallybasically the the same same from from 0.0 0.0 s to s about to about 6.5 s. 6.5 The s. steering The steering wheel torque wheel oftorque the truck of the with truck the taper-leaf with the springtaper-leaf suspension spring is suspension slightly smaller is slightly than thatsmaller of the than truck that with of the themulti-leaf truck with spring the multi suspension-leaf spring from 20.0suspension s to 30.0 from s. Moreover, 20.0 s to the30.0 steering s. Moreover, wheel t torquehe steering of the wheel truck torque with the of taper-leafthe truck springwith the suspension taper-leaf isspring obviously suspension smaller is than obviously that of smaller the truck than with that the of multi-leaf the truck springwith the suspension multi-leaf from spring 6.5 suspension s to 20.0 s. Thefrom results 6.5 s to prove 20.0 thats. The the results truck withprove the that taper-leaf the truck spring with the suspension taper-leaf has spring better suspension steering portability has better duringsteering the portability step steer during test. From the Figurestep steer 14b, test.it can From be seen Figure that the14b, two it can truck be models seen that show the almost two truck the samemodels yaw show rate duringalmost the the step same steer yaw test. rate The during result the further stepshows steer testthat. replacing The result the further multi-leaf shows spring that withreplacing the taper-leaf the multi spring-leaf spring has almost with nothe e ﬀtaperect on-leaf the spring yaw rate. has Fromalmost Figure no effect 14c, on it can the beyaw seen rate. that From the Figure 14c, it can be seen that the truck roll angles on the basis of the two truck models are almost the same from 0.0 s to 3.0 s during the step steer test. With the increase of the steer value, the roll angle of the truck with the taper-leaf spring increases more obviously. The results show that the truck with the taper-leaf spring suspension has the poorer stability. Figure 14d illustrates that the sideslip angle of the truck with the taper-leaf spring suspension is obviously larger than that of the truck with the multi-leaf spring suspension. The result further shows that the truck handing performs worse after replacing the multi-leaf spring with the taper-leaf spring.

5.4. Simulation and Comparison of the Braking-in-Turn Tests The braking-in-turn analysis is one of the most critical analyses encountered in everyday driving. This analysis examines path and directional deviations caused by sudden braking during cornering. Typical results collected from the braking-in-turn analysis include the steering wheel torque, the yaw rate, and the truck sideslip angle [40]. The simulations of the braking-in-turn tests were conducted in Adams based on the two truck models, respectively. According to the international standard ISO7975-85, the simulation settings are as follows: the brake deceleration 6.3 m/s2, the lateral acceleration 5.1 m/s2, the turn radius 30.0 m, the maximum brake duration 5.0 s, the initial straight-line distance 15.0 m. Figure 15 provides the simulation diagram of the braking-in-turn test based on Adams. Figure 16 provides a comparison of the simulated dynamic responses. From Figure 16a, it can be seen that the steering wheel torques from the two truck models are basically the same. Figure 16b depicts that there are almost no differences for the yaw rate. Figure 16c shows that the sideslip angle of the truck with the taper-leaf spring suspension is almost the same as that of the truck with the multi-leaf spring suspension. From Figure 16d, it can be seen that the two truck models show almost the same bushing longitudinal force at the spring eye during the braking-in-turn test. This proves that the replacement of the leaf spring has little impact on the in-train longitudinal forces during braking. Appl. Sci. 2020, 10, 1293 16 of 21 truck roll angles on the basis of the two truck models are almost the same from 0.0 s to 3.0 s during the step steer test. With the increase of the steer value, the roll angle of the truck with the taper-leaf spring increases more obviously. The results show that the truck with the taper-leaf spring suspension has the poorer stability. Figure 14d illustrates that the sideslip angle of the truck with the taper-leaf spring suspension is obviously larger than that of the truck with the multi-leaf spring suspension. The result further shows that the truck handing performs worse after replacing the multi-leaf spring with the taper-leaf spring.

5.4. Simulation and Comparison of the Braking-in-Turn Tests The braking-in-turn analysis is one of the most critical analyses encountered in everyday driving. This analysis examines path and directional deviations caused by sudden braking during cornering. Typical results collected from the braking-in-turn analysis include the steering wheel torque, the yaw rate, and the truck sideslip angle [40]. The simulations of the braking-in-turn tests were conducted in Adams based on the two truck models, respectively. According to the international standard ISO7975-85, the simulation settings are as follows: the brake deceleration 6.3 m/s2, the lateral acceleration 5.1 m/s2, the turn radius 30.0 m, the maximum brake duration 5.0 s, the initial straight-line distance 15.0 m. Figure 15 provides the simulation diagram of the braking-in-turn test based on Adams. Figure 16 provides a comparison of the simulated dynamic responses. From Figure 16a, it can be seen that the steering wheel torques from the two truck models are basically the same. Figure 16b depicts that there are almost no diﬀerences for the yaw rate. Figure 16c shows that the sideslip angle of the truck with the taper-leaf spring suspension is almost the same as that of the truck with the multi-leaf spring suspension. From Figure 16d, it can be seen that the two truck models show almost the same bushing longitudinal force at the spring eye during the braking-in-turn test. This proves that the replacement of the leaf spring has little impact on the in-train longitudinal forces during braking. Appl. Sci. 2020,, 10,, xx FORFOR PEERPEER REVIEWREVIEW 16 of 20

Figure 15. The simulation diagram of the braking-in-turn test based on Adams. Figure 15. The simulation diagram of the braking braking-in-turn-in-turn test based on Adams.Adams.

0.00.0

(Nm) (Nm) −−1.01.0

−−2.02.0

−−3.03.0

−−4.04.0

−−5.05.0

teering wheel torque teering wheel torque −−6.06.0

S S Time tt // (s)(s)

((a))

Figure 16. Cont.

he yawhe rate / (°/s)

Time tt // (s)(s)

((b))

he he truck sideslip angle /

T (°) T (°) Time tt // (s)(s)

((cc)) Appl. Sci. 2020, 10, x FOR PEER REVIEW 16 of 20

Figure 15. The simulation diagram of the braking-in-turn test based on Adams.

0.0

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teering wheel torque −6.0 S Time t / (s) Appl. Sci. 2020, 10, 1293 17 of 21

(a)

he yawhe rate / (°/s)

Time t / (s)

(b)

he he truck sideslip angle / T (°) Time t / (s)

Appl. Sci. 2020, 10, x FOR PEER REVIEW 17 of 20 (c)

6.0

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ushing force /(kN)

2.0 Time t / (s)

(d)

﹍the taper-leaf spring, ＿the multi-leaf spring Figure 16. A comparison of the simulated dynamic responses obtained from the step steer tests: (a) The steering Figure 16. A comparison of the simulated dynamic responses obtained from the step steer tests: (a) The wheel torque, (b) the yaw rate, (c) the truck sideslip angle, and (d) the bushing longitudinal force at the spring steering wheel torque, (b) the yaw rate, (c) the truck sideslip angle, and (d) the bushing longitudinal eye. force at the spring eye.

6.6. Analysis on the Reason of Suspension Performance Differences Differences for the TwoTwo LeafLeaf SpringsSprings In Section Section5 , 5, the the di ff differenceserences of the of the simulated simulated dynamic dynamic responses response for thes for handling the handling stability stability should beshould related be related to that to the that torsional the torsional stiffness stiffness of the of two the leaf two springs. leaf springs To prove. To prove it, the it, influencethe influence of the of stabilizerthe stabilizer bar bar on suspensionon suspension performance performance with with the twothe two leaf leaf springs springs should should be revealed. be revealed Thus,. Thus, the driftthe d simulationrift simulation test wastest was conducted. conducted. The stabilizerThe stabilizer bar stibarffness stiffness is increased is increased by 1.2 by times. 1.2 times The other. The simulationother simula settingstion settings are the are same the as same those as in those Section in 5.1 Section. A comparison 5.1. A comparison of the simulated of the simulated dynamic responsesdynamic response is showns inis shown Figure 17in .Figure From Figure17. From 17a, Figure it can 1 be7a, seen it can that be after seen increasing that after theincreasing stiffness the of stabilizerstiffness of bar, stabilizer the steering bar, wheelthe steering torque wheel for the torque taper-leaf forspring the taper is closer-leaf spring to that foris closer the multi-leaf to that for spring the withmulti the-leaf original spring stabilizer with the bar. original Figure stabilizer 17b shows bar that. Figure the yaw 17 rateb shows for the that taper-leaf the yaw spring rate is for almost the unchangedtaper-leaf spring afterincreasing is almost the unchanged stiffness ofafter stabilizer increasing bar. Figure the stiffness 17c illustrates of stabilizer that the bar truck. Figure sideslip 17c angleillustrates for the that taper-leaf the truck spring sideslip becomes angle smallerfor the taper after increasing-leaf spring the becomes stiffness smaller of stabilizer after bar.increasing Moreover, the afterstiffness increasing of stabilizer the sti barffness. Moreover, of stabilizer after bar, increasing the truck the sideslip stiffness angle of stabilizer for the taper-leaf bar, the springtruck sideslip is more angle for the taper-leaf spring is more consistent with that for the multi-leaf spring with the original stabilizer bar. The comparison results show that the torsional stiffness of the two leaf springs have a certain impact on the handling stability.

60.0

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steering wheel torque / (Nm) 0.0

he he T −10.0 Time t / (s)

(a) Appl. Sci. 2020, 10, x FOR PEER REVIEW 17 of 20

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ushing force /(kN)

2.0 Time t / (s)

(d)

﹍the taper-leaf spring, ＿the multi-leaf spring Figure 16. A comparison of the simulated dynamic responses obtained from the step steer tests: (a) The steering wheel torque, (b) the yaw rate, (c) the truck sideslip angle, and (d) the bushing longitudinal force at the spring eye.

6. Analysis on the Reason of Suspension Performance Differences for the Two Leaf Springs In Section 5, the differences of the simulated dynamic responses for the handling stability should be related to that the torsional stiffness of the two leaf springs. To prove it, the influence of the stabilizer bar on suspension performance with the two leaf springs should be revealed. Thus, the drift simulation test was conducted. The stabilizer bar stiffness is increased by 1.2 times. The other simulation settings are the same as those in Section 5.1. A comparison of the simulated dynamic responses is shown in Figure 17. From Figure 17a, it can be seen that after increasing the stiffness of stabilizer bar, the steering wheel torque for the taper-leaf spring is closer to that for the multi-leaf spring with the original stabilizer bar. Figure 17b shows that the yaw rate for the taper-leaf spring is almost unchanged after increasing the stiffness of stabilizer bar. Figure 17c Appl.illustrates Sci. 2020 ,that10, 1293 the truck sideslip angle for the taper-leaf spring becomes smaller after increasing18 of the 21 stiffness of stabilizer bar. Moreover, after increasing the stiffness of stabilizer bar, the truck sideslip angle for the taper-leaf spring is more consistent with that for the multi-leaf spring with the original consistent with that for the multi-leaf spring with the original stabilizer bar. The comparison results stabilizer bar. The comparison results show that the torsional stiffness of the two leaf springs have a show that the torsional stiﬀness of the two leaf springs have a certain impact on the handling stability. certain impact on the handling stability.

60.0

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steering wheel torque / (Nm) 0.0

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he yawhe rate / (°/s)

Time t / (s)

(b)

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Time t / (s)

(c)

＿the multi-leaf spring with the original stabilizer bar, ﹍the taper-leaf spring with the original stabilizer bar, ﹍the taper-leaf spring with increasing the stabilizer bar stiffness

FigureFigure 17. 17. A Acomparison comparison of ofthe the simulated simulated dynamic dynamic response responsess obtained obtained from from the the drift drift test tests:s: (a) ( aThe) The steeringsteering wheel wheel torque, torque, (b ()b the) the yaw yaw rate rate,, and and (c) ( cthe) the truck truck sideslip sideslip angle angle..

7. Conclusions To reveal the changes of the handling stability after the replacement, the simulations and comparison of the taper-leaf and the multi-leaf spring suspensions with the same vertical stiffness for trucks were conducted. The main innovations and achievements of this paper are as follows: (1) An analytical method of replacing the multi-leaf spring with the taper-leaf spring for trucks was proposed. (2) The dynamic models of the truck before and after the spring replacement were established. (3) The changes of the handling stability after replacing the multi-leaf spring with the taper-leaf spring were revealed by the simulations of the drift test, the ramp steer test, and the step steer test. Both the proposed method and the established model were validated by test. The simulation results show that the yaw rate of the truck almost does not change, the steering wheel moment decreases, the vehicle roll angle obviously increases, and the vehicle side slip angle slightly increases after the replacement. The main reason should be related to that the torsional stiffness of the taper-leaf spring is less than that of the multi-leaf spring. This paper provides a useful reference for the design, modeling, and simulation of the taper-leaf spring suspension system for trucks.

Author Contributions: The corresponding = C.Z. proposed this research, Y.Z. designed the spring experiments; X.L. and Y.Y. performed the truck experiments; H.L. and L.Z analyzed the test data and conducted the simulations; C.Z. reviewed and edited the manuscript; and L.Z. wrote the paper.

Funding: This work was supported by the National Natural Science Foundation of China (51575325), Scientific Research Starting Foundation for Doctors (419067), and the School-Enterprise Cooperation Project (2018-KJ-4). Appl. Sci. 2020, 10, 1293 19 of 21

7. Conclusions To reveal the changes of the handling stability after the replacement, the simulations and comparison of the taper-leaf and the multi-leaf spring suspensions with the same vertical stiﬀness for trucks were conducted. The main innovations and achievements of this paper are as follows: (1) An analytical method of replacing the multi-leaf spring with the taper-leaf spring for trucks was proposed. (2) The dynamic models of the truck before and after the spring replacement were established. (3) The changes of the handling stability after replacing the multi-leaf spring with the taper-leaf spring were revealed by the simulations of the drift test, the ramp steer test, and the step steer test. Both the proposed method and the established model were validated by test. The simulation results show that the yaw rate of the truck almost does not change, the steering wheel moment decreases, the vehicle roll angle obviously increases, and the vehicle side slip angle slightly increases after the replacement. The main reason should be related to that the torsional stiﬀness of the taper-leaf spring is less than that of the multi-leaf spring. This paper provides a useful reference for the design, modeling, and simulation of the taper-leaf spring suspension system for trucks.

Author Contributions: The corresponding author C.Z. proposed this research, Y.Z. designed the spring experiments; X.L. and Y.Y. performed the truck experiments; H.L. and L.Z analyzed the test data and conducted the simulations; C.Z. reviewed and edited the manuscript; and L.Z. wrote the paper. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the National Natural Science Foundation of China (51575325), Scientific Research Starting Foundation for Doctors (419067), and the School-Enterprise Cooperation Project (2018-KJ-4). Conflicts of Interest: The authors declare no conflict of interest.

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