COMBINED VIBRATION ISOLATOR OF DISC SPRINGS FOR CLOSED HIGH-SPEEDPRECISION PRESS: DESIGN AND EXPERIMENTS

F. Jia1 and F.Y. Xu21School of Mechanical Engineering, Southeast University, Nanjing 210096, China

2School of Automation, Nanjing University of Posts and Telecommunication, Nanjing 210003, ChinaE-mail: jfang@seu.edu.cn, xufengyu598@163.com

Received August 2013, Accepted June 2014No. 13-CSME-157, E.I.C. Accession Number 3615

ABSTRACTThe structure, strength, and stiffness of disc springs are analyzed or investigated. Based on the previousstudies, two finite element models of combined disc springs are established and their loading and unloadingdeformation patterns are analyzed to determine the optimal combination of disc springs for a desirablevibration isolator of high-speed press. The structural parameters and loading data of JF75G-200 high-speedpress are used for simulation and other experiments. The dynamic working points of disc springs in differentcombinations are drawn, and complete test data are collected. Results show that combined vibration isolator,an isolator with nonlinearly combined disc springs functioning as a whole for vibration isolation, is the bestchoice. Results from both simulation and tests confirm the feasibility and validity of the proposed isolator.The isolator can efficiently minimize the vibration of the high-speed press.

Keywords: vibration isolator; nonlinearly combined disc springs; closed high-speed precision press.

ISOLATEUR DE VIBRATION COMPOSÉ DE RESSORTS À DISQUE POUR LES PRESSES DEPRÉCISION À HAUT DÉBIT FERMÉES: CONCEPTION ET TESTS

RÉSUMÉLa structure, la force et la rigidité d’un ressort à disque sont étudiés et analysés. Pour déterminer la combinai-son optimale de ressorts à disque pour un isolateur de vibrations désiré d’une presse à haut débit, plusieursmodèles à éléments finis sont construits pour analyser les déformations de charge et de décharge des res-sorts à disque. Les paramètres de structure et les données de charge d’une presse à haut débit JF75G-200sont utilisés pour la simulation et les tests. Les points de travail dynamique de différentes combinaisons deressorts à disque sont affichés, et la totalité des données de test sont collectées. Ensuite, en nous basant surnotre analyse, l’isolateur de vibration composé est proposé. C’est un isolateur basé sur une combinaisonnon linéaire de ressorts à disque fonctionnant ensemble pour l’isolation des vibrations. Les résultats, tantdes simulations que des tests, ont montré la faisabilité et la validité de l’isolateur proposé pour l’isolationefficace des vibrations d’une presse à haut débit.

Mots-clés : isolateur de vibration; ressorts à disque non linéaires; presse à haut débit fermée de précision.

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1. INTRODUCTION

Vibration isolation is crucial to the dynamic accuracy and reliability of high-speed precision press. Mini-mizing the vibration of the press or guiding it outward is necessary to realize high-precision stamping.

Productive research has focused on reducing vibration and noise in stamping. In the last decade, numer-ous scholars conducted extensive investigations on vibration isolation. Novak [1, 2] studied the dynamicsof a hammer system equipped with a vibration isolator, focusing mainly on the modeling of the foundationsystem. In 1985, Kushida [3] established a dynamic model of the vibration isolation system of high-speedpress. He employed a rubber vibration isolator bearing a high stiffness to construct the vibration isolationsystem for press. Moreover, he analyzed and compared the responses of the dynamic model before and aftervibration isolation stiffness adjustment. In 1993 to 1995, Yoshimuto et al. [4, 5] studied the vibration andnoise reduction of C-structure turret punch press in depth. Through finite element analysis (FEA) and exper-iments, they introduced an “acoustic modal theory between punch load action point and structure responsepoint” and designed a “vibration-free” punch structure. Vibration was greatly reduced in their structure. Co-operating with Tokyo Institute of Technology, Park [6] of Korea Ocean University analyzed punch vibrationcharacteristics and completed a dynamic optimization design. Chehab et al. [7, 8] investigated the design ofthe isolation foundation of forging equipment. Basing on the fundamental characteristics of soil mechanics,they analyzed the efficiency of different vibration reduction combination structures and optimized the designparameters.

Zhu [9] investigated a two-degree-of-freedom (2-DOF) nonlinear vibration system with variable stiffnessand damping and pointed out that vibration could be reduced by adjusting the parameters of the vibrationsystem and excitation frequency. Lang et al. [10] analyzed the effects of nonlinear viscous damping on thevibration isolation of 1-DOF systems and established the output frequency response function between theparameter of viscous damping and transmissibility of the isolator. In connection with multiple dimensionalvibration isolation, a 3-D human body model with 1-DOF in each direction was established by Coe et al.[11]. This model was combined with a simple seat model into a simplified 3-D human body-seat interactionmodel for naval architects to investigate the integrated interaction system when subjected to ship motions.Their experiment results have proven the theoretical model to be a simplified valid approach to high-speedcraft seat design for reducing the shock and vibration level experienced by the crew. Li [12] proposed ahybrid manipulator applied to the vibration isolation of manufacturing systems. As the translations androtations of the manipulator are decoupled, the proposed isolator can isolate vibrations at a wide range offrequency. Yang et al. [13] developed a mathematical model for a complex nonlinear coupling isolator thatcouples quadratic damping, viscous damping, Coulomb damping, and nonlinear spring force; the dynamictransmissibility of this model under deterministic excitation is deduced. Elastomeric isolators are commonlyapplied between the electronic device and the equipment bay structure in the aerospace fields to preventelectronic devices from severe shock and vibration loads. A new type of isolator named pseudoelastichybrid mesh isolator was proposed [14]. The isolator promises better isolation performance throughoutfrequency range than conventional isolators.

Vibration reduction can be realized by improving press structure. Vibration isolation and buffer can alsobe achieved by mounting a vibration isolator in engineering. Most presses adopt the equal-stiffness linearvibration isolator with metal spiral springs as its vibration isolation component. This type of vibrationisolator, although working well in low-frequency vibration isolation, is prone to propagating high frequencyvibration because of its narrow effective frequency range and large vibration amplitude.

Disc springs have gained considerable attention in the fields of aerospace, automotive, construction, ma-chinery, etc. because of their variable stiffness, compact installation space, and self-friction damping. Discsprings can bear very large load under very small deformation. Such springs can effectively isolate thetransmission of impact vibration to the ground because their loading and unloading curves do not coincide.

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Therefore, disc springs can meet the requirements of high-speed press: on the action of impulsive load,vibration isolation and impact reduction on the ground can be achieved. Since 2006, our research teamhas been engaged in the research of the vibration characteristics of closed high-speed press [15–17]. Wehave designed several nonlinear isolators, including rubber combination vibration isolator and disc-springvibration isolator, to isolate vibration [18, 19].

The present study proposes a nonlinear combined vibration isolator using disc springs as the key com-ponent on the basis of previous research on high-speed precision press and its vibration. The isolator isdesigned to improve the peak response and attenuation speed, as well as minimize the vibration of the high-speed press. The remainder of this paper is structured as follows. The structure of a single disc spring isintroduced, and its theoretical calculation is shown. A finite element model (FEM) of disc spring combina-tion is established, and the stiffness of combined disc springs is examined. A type of nonlinear combinedvibration isolator with disc springs as the key component is proposed, and a field test on high-speed press isconducted to determine the vibration isolation effect of the isolator. Test results are analyzed, and conclu-sions are drawn.

2. STRUCTURE AND THEORETICAL CALCULATION OF SINGLE DISC SPRINGS

2.1. Structure and Combination of Disc SpringsDisc springs are characterized by small volume, large bearing capacity, even pressure, strong buffering, andvibration reduction. The deformation characteristic curves of nonlinear, incremental, zero, and negativestiffness can be acquired under different loads and different combinations, e.g., in overlay or opposite form.Disc springs have quasi-zero stiffness; therefore, when impact load increases to a certain point, the stiffnessof disc springs rapidly decreases but reverts to the initial state as the load impact diminishes. Moreover, theloading and unloading curves of disc springs do not coincide. Corresponding combinations of disc springscan be designed and applied on the basis of impact load for the wide-frequency vibration isolation of theimpact load of large-tonnage and high-speed press.

Disc springs fall into the supporting surface and supporting surface-free types. Disc springs with thicknesst < 3 mm are machined into the supporting surface-free type because of the small load (Fig. 1a). In the figure,d is the inner diameter of disc spring, D is the outer diameter, h0 is the inner cone height, t is the springthickness, and f is the deformation when load P is added on the outer circumference of the inner circle.However, the inner and outer circumferential end surfaces of disc springs with thickness of t > 3 mm aremachined into supporting surfaces for large load bearing. As shown in Fig. 1(b), the supporting surfacewidth b is 1/150 times of the disc spring diameter D.

The main characteristics of disc spring can be generalized as follows:

(a) As shown in Fig. 2, the load deformation characteristic curve of disc springs is nonlinear [21, 22].When the material, inner diameter d, outer diameter D, and thickness t are fixed, the curve onlyrelates to and is greatly affected by h0/t.

When h0/t < 0.5, linear changes occur; when 0.5 < h0/t <√

2, only nonlinear variations are observ-able. Moreover, stiffness diminishes with increasing deformation. When h0/t =

√2, the disc spring

stiffness is zero if deformation f = h0; when√

2 < h0/t < 2√

2 and load increases to a certain value,a negative stiffness region is observable. Deformation increases constantly with the reduction of load.The work condition of disc springs is unstable in his situation.

(b) Disc springs can bear large load with small deformation and can be applied in a compact axial spacebecause of their small size in load direction (axial direction), large size in radial direction (horizontaldirection), and flat shape.

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(a) Supporting surface-free

(b) Supporting surface

Fig. 1. Supporting forms of disc spring.

(c) Disc springs feature strong vibration absorption capability. Thus, in overlay form, part of the i mpactenergy can be absorbed by the large damping created by the friction between disc springs. Thedamping characteristics are important to the vibration isolation of high-speed press.

Generally, the deformation and load of a single disc spring cannot meet the requirements of the vibrationisolation of high-speed press. Therefore, disc spring combinations are often employed (Fig. 3).

1. Overlay form. This combination is composed of n disc springs of the same direction and specifica-tion (Fig. 3a). The number of overlay disc springs is determined by the magnitude of load bearing.Regardless of friction, we obtain

Pz = nPfz = fHz = H +(n−1)t

(1)

where P is the load of single disc spring, Pz is the load of overlay disc springs, f is the deformation ofa single disc spring, H is the free height of a single disc spring, and Hz is the free height of disc springcongruence.

2. Opposite form. This combination is composed of i disc springs of the same specification (Fig. 3b).The number of disc springs is determined by the total deformation required. Regardless of friction,we obtain

Pz = Pfz = i fHz = iH

(2)

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Fig. 2. Load deformation characteristic curve of disc springs.

(a) Overlay form (b) Opposite form

(c) Composite form

Fig. 3. Typical disc spring combinations.

3. Composite form. This combination is composed of overlay and opposite disc springs (Fig. 3c). n andi are determined by the load and total deformation. Regardless of friction, we obtain

Pz = nPfz = i fHz = i[H +(n−1)t]

(3)

The load-displacement characteristic curve of the typical composite disc spring forms are presented inFig. 4.

2.2. Theoretical Calculation of Single Disc SpringTheoretical calculation of disc spring was executed on the basis of the following hypotheses: (a) After loadis added to disc spring, the cross-section in the axial direction of disc spring remains rectangular (i.e., nodistortion occurs). This cross-section rotates around a neutral point. That is, radial stress can be neglected.(b) External load and reactive force on the supporting surface distribute uniformly along the inner and outercircumferences. (c) The material is completely elastic (i.e., no plastic deformation). (d) Friction on the

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Fig. 4. Composite formation of n congruent disc springs and i disc springs.

contacting surface is negligible. (e) The stresses generated in the quenching, shot peening, and prestressingof disc springs are negligible.

2.2.1. Relationship between Load and DeformationAccording to the parameters described in Fig. 1, the relationship between disc spring load and deformationis [20]

P =f t3

αD2

[(h0

tft

)(h0

t−0.5

ft

)+1]

(4)

where

α =1π

(C−1C

)2

C+1C−1 −

2lnC

1−µ2

4E, C =

Dd

where µ is the Poisson ratio of material. According to the definition of stiffness, the stiffness of disc springscan be obtained by Eq. (4).

Kν =dPd f

=t3

αD2

[(h0

t

)2

−3h0

tft+

32

(ft

)2

+1

](5)

2.2.2. Strength DesignThe strength of disc springs under static load is determined by the stress σ1 on point I. The strength of adisc spring at any point (x,y) can be calculated as [20]

σi(x,y) =−4E f

(1−µ2)(D−d)2(C− x)

[x(

h0−f2

)+

2yD−d

]. (6)

The maximum stress of disc spring, observable at points I, II, III, and IV of the upper and lower ends ofinner and outer circumferences, can be calculated as

σI =−f t

αD2

[β

(h0

t−0.5

ft

)+ γ

], (7)

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σII =−f t

αD2

[−β

(h0

t−0.5

ft

)+ γ

], (8)

σIII =f t

αD21C

[(2γ−β )

(h0

t−0.5

ft

)+ γ

](9)

σIV =f t

αD21C

[(2γ−β )

(h0

t−0.5

ft

)− γ

](10)

where

C =Dd, β =

1π

6lnC

(C−1lnC

−1), γ =

1π

6lnC

C−12

As P, f ,h0 in Eqs. (7) to (10) to are replaced by P′, η f , ηh0 for the disc spring with supporting surface, thecalculation formula of disc spring isolator with supporting surface was obtained. η was calculated accordingto the following formula [20]:

η =D−d

D∗−d∗=

11− 4

κ

CC−1

κ, κ =Db

(11)

3. FINITE ELEMENT MODELING AND ANALYSIS OF DISC SPRING COMBINATIONS

The theoretical calculation of disc spring combinations is complex and prone to error because of thesesprings have geometric and contact nonlinearity. In this study, was employed to model, simulate, and ana-lyze the disc spring combinations. Suitable types of disc springs and their combinations were determinedaccording to the actual working condition of high-speed press.

3.1. Selection of Disc SpringAs shown in Fig. 2, disc springs with different h0/t may possess different load-deformation characteristiccurves and different stiffness characteristics. As a component of vibration isolation, a disc spring mustpossess quasi-zero stiffness and nonlinear stiffness. When 1.3≤ h0/t <

√2, disc-spring quasi-zero stiffness

is observed, i.e., the curve becomes softer with increasing load. If applied to the vibration isolation of press,this type of disc spring can bear large pressure in a low range of static deformation. Moreover, its gradualsoftening feature meets the stiffness requirement of a vibration isolator. According to the national standard,the three standard value h0/t can be 0.4, 0.75, and 1.3. Therefore, springs of the third series h0/t = 1.3 wereselected by the China Standard, which satisfies the characteristic of quasi-zero stiffness.

Under the gravity of press, a disc spring generates a certain pre-pressing deformation f . Moreover, thedisc spring used for press vibration isolation bears periodic fluctuating load. Generally, it is expected tocombine more disc springs in overlaying to improve disc spring damping. However, this condition results inheat production on the friction surface because of the overlaying of many springs; in addition, the producedheat is hard to dissipate. Thus, the combination of more than four disc springs is unallowable.

The closed high-speed press is supported by four feet, each of them packed with a vibration isolator.Its quality parameters are as follows: upper part mass, m1 = 13300 kg; lower part mass, m2 = 11583 kg;crank-connect rod slider mechanism, mslider = 4300 kg; and press total mass, mwhole = 29183 kg.

As a component of vibration isolation, disc spring is under the action of variable impact load. Accordingto the handbook of mechanical design, these characteristics will be satisfied when f = 0.75h0 [21]. Thegravity that can be borne by each vibration isolator is approximately 7500 kg. Disc springs of 160× 82×4.3× 9.9 (hereinafter called type I) and (type II) were selected by the standard of f = 0.75h0. The innercone heights of these disc springs are 5.6 and 7.1 mm, respectively.

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Fig. 5. Type I FEM of four overlaying disc springs.

According to Eq. (4), E = 2.06× 1011 pa, µ = 0.3. For the type I spring, D = 160 mm, d = 82 mm,t = 4.3 mm, and h0 = 9.9 mm; therefore

PI =f t3

αD2

[(h0

t− f

t

)(h0

t−0.5

ft

)+1]= 21800 N

For the type II spring, D = 225 mm, d = 112 mm, t = 6.5 mm, h0 = 13.6 mm, PII = 44600 N. Therefore,the loads of types I and II are 21800 N, respectively. The disc springs were placed in congruence in two orfour each set. Then, two or more sets of overlaying disc springs were involuted together as the main bodyof vibration isolator.

3.2. Characteristics of Different Disc Spring CombinationsThe isolator was designed using a composite form of the overlaying combined with the opposite (Fig. 3). Inoverlaying disc springs, deformation increases proportionally with the number of overlaying sets. However,the influence of the opposite is small enough to be negligible. Thus, only one set of overlaying disc springsneeds to be modeled and calculated in numerical analysis.

3.2.1. FEMThe axisymmetric model of disc spring was built using the 2D unit plane42. This unit is composed of fournodes, which can degenerate into three, each of which has translational degrees of freedom in the x and ydirections. The plane42 unit is equipped with plasticity, creep, stress stiffening, large strain, etc.

To facilitate theoretical calculation, the contact frictions between disc spring and supporting plate andbetween disc springs are often ignored as being nonlinear. According to the material and process charac-teristics of disc springs, we set the static friction coefficient to 0.15 and the dynamic to 0.1 in analysis. Inthe combined vibration isolator, disc springs were placed on a metal bottom plate. The inner hole of eachdisc spring was installed with a guide sleeve. A gap was left between the guide sleeve and the disc springinside the hole. The bottom plate and guide sleeve constitute a rigid body. The elastic modulus of materialproperties was set far higher than that of disc spring. The disc springs were divided using a dense grid; theguide sleeve and metal bottom plate were divided by a coarse grid. Finally, FEM was built (Figs. 5 and 6).

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Fig. 6. Type II FEM of two overlaying disc springs.

Fig. 7. Contour plot of radial displacement ( f = 5.5 mm).

3.2.2. FEA resultsTheoretical calculation and previous simulation analysis indicated that the disc spring bottom is fully con-strained [20]. However, in the present study, full displacement constriction was only applied to the nodesbelow the bottom plate. The disc spring and bottom plate were connected by contact pairs. This way, theactual motion state could be simulated to its maximum degree. Vertical load was imposed on the disc springat the top.

Figure 7 shows the radial displacement contour plot of four congruent disc springs of type I pressed to5.5 mm The spring bottom moved outward by 0.49 mm and the top moved inward by 0.51 mm in the radicaldirection. This result suggests that the spring slides on the support bottom plate. Then, when two overlaying

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Fig. 8. Friction sliding distance between disc springs ( f = 5.5 mm).

disc springs of type II were pressed to 7 mm, the spring bottom moved outward by 0.67 mm and the topmoved inward by 0.68 mm in the radical direction.

Figure 8 shows the friction sliding distance between the four congruent disc springs of type I pressed to5.5 mm. The maximum sliding distance can be observed on both ends of disc spring, namely, on the conetop and bottom. The middle part had no dislocation displacement, and the maximum sliding displacementwas 0.65 mm.

When two overlaying disc springs of type II were pressed to 7 mm, the maximum friction sliding distanceis 0.9 mm. The loading curve is not in line with the unloading curve because of the presence of Coulombfriction between disc springs. Thus, a hysteresis area is produced near the working site of the disc springs.Figure 9 shows the loading-unloading curves of the congruent disc springs of two types and numbers.

Loading and unloading stiffness of the curves can be obtained by means of central difference method withthe precision of order as follows:

y′i =−yi+2 +8yi+1−8yi−1 = yi−2

12∆t(12)

Substituting load and displacement into Eq. (12) yields the loading and unloading stiffness of four over-laying disc springs of type I. As demonstrated by Fig. 10, the loading stiffness basically coincides withthe unloading stiffness. Unloading begins when the press reaches the maximum, followed by a change infriction direction and a suddenly drop in disc spring stiffness. The stiffness of overlaying disc springsof type I (h0 = 5.6 mm) Koverlaying = 5.4× 106 N/m when f = 0.75h0 = 4.2 mm. A single vibration

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Fig. 9. Loading/unloading curves of congruent disc springs of two types and numbers.

Fig. 10. Stiffness characteristic curves of four overlaying disc springs of type I.

isolator is composed of three opposite sets of overlaying disc springs, with a corresponding vibration-isolation stiffness of Ksingle = Koverlaying/3 = 1.8× 106 N/m. The total stiffness of four vibration isolatorsKtotal = 4×Ksingle = 7.2× 106 N/m. The stiffness of the overlaying disc springs exhibits a steady declinewith increasing load.

The loading and unloading stiffness of two overlaying disc springs of type II can be calculated in thesame way. As shown in Fig. 11, their curves appear similar to those of four overlaying disc springs oftype I. The stiffness of the overlaying disc springs of type II (h0 = 7.1 mm) Koverlaying = 5.54× 106N/mwhen f = 0.75h0 = 5.33 mm. A single vibration isolator is composed of three opposite sets of overlaying

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Fig. 11. Stiffness characteristic curves of two overlaying disc springs of type II.

Fig. 12. Loading stiffness curves of overlaying disc springs of two types.

disc springs, with a corresponding vibration-isolation stiffness of Ksingle = Koverlaying/3 = 1.85× 106 N/m.The total stiffness of four vibration isolators Ktotal = 4×Ksingle = 7.4×106 N/m. The stiffness of combineddisc springs exhibits on a steady decline with increasing load.

Figure 12 compares the loading stiffness characteristic curves of overlaying disc springs of the two types.Similar nonlinearity is observable between the curves. The stiffness of the combined disc springs declineswith increasing load.

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(a) Working point of composite disc springs (b) Magnified working point of composite disc springs

Fig. 13. Working point of three sets of two overlaying type-II disc springs.

3.3. Hysteretic Characteristics of Disc-Spring Working PointWhen the high-speed press is placed on the disc-spring vibration isolator, the disc springs generate staticdeformation with the compression f0 termed as the working point of the isolator.

As the springs mentioned above are selected by calculating the compression, i.e., the working point ( f0 =0.75h0), they need to be verified again in terms of the actual mass of press, which, as calculated before, ismwhole = 29183 kg. That is, the weight on each isolator is 7.5×104 N. The deformation at the working pointof two congruent type-II disc springs f = 4.18 mm, the stiffness at this point Koverlaying = 7.70×106 N/m,and that of three congruent disc-spring sets Ksingle = Koverlaying/3 = 2.57×106 N/m. Thus, the total stiffnessof four sets of vibration isolators Ktotal = 4×Ksingle = 10.28×106 N/m.

The isolator was designed in accordance with the amplitude range of 0.9 mm of high-speed press. Thus,each overlaying set of the three opposite disc-spring sets vibrates within the range of -0.15 mm to 0.15 mmat the working point. A hysteresis region is formed between the loading and unloading curves becauseof the presence of Coulomb friction between disc springs. Figure 15 displays the working point of thecombined disc springs by involution of three sets of two overlaying type-II disc springs. In static state, thepress is placed on vibration isolators. Disc springs produce initial compression by the gravity of press. Thehysteresis loop in Fig. 13(a) presents that the disc spring shows soft characteristics. When the compressionis increased to f = 4.18 mm, the disc spring deformation terminates and the disc spring enters the quasi-zerostiffness working area. In working state, disc spring compression fluctuates at approximately f = 4.18 mmbecause of the press impact and vibration on the vibration isolator. As a result, a hysteresis area is formed.The hysteresis curve obtained by calculation is shown in Fig. 13.

3.4. Experimental VerificationTo verify the correctness of the FEM results, the characteristic curves of disc springs combined in differentoverlaying forms were tested at the professional testing center of disc spring manufacturers. The results aredemonstrated in Fig. 14.

As shown in Fig. 14, the FEA curves significantly differ from the test curves in the initial phase ofdeformation. The differences are gradually narrowed with increasing deformation because of errors in theassembly process of disc springs. During the load process, when disc spring deformation f = 4.4 mm,

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Fig. 14. Force-displacement curves of two overlaying type-II disc springs.

the bearing load obtained by test is 76.35 KN and that by FEA is 77.298 KN, an error of approximately1.2%. During the unloading process, the load obtained by test is 71.62 KN and that obtained by FEAis 76.3493 KN, an error of approximately 6.6%. The results show that the gradual softening of the discsprings is significant in FEM analysis. This result is caused by the disc manufacturing error and the discspring friction error in FEA. As indicated in the figure, the FEA results are close to the test results, and theformer can be fairly supposed to be a reliable basis for designing the vibration isolator of combined discsprings.

4. STRUCTURAL DESIGN OF VIBRATION ISOLATOR OF NONLINEAR DISC SPRING COM-BINATION

Generally, a single vibration isolation component cannot work satisfactorily unless in combination withothers. Given its stiffness nonlinearity, the disc spring at work gives no obvious resonance peak unlike themetal spiral spring. Moreover, the displacement between disc springs can provide friction damping, andit slightly varies with the rapid increase in impact load. As a result, a large amount of impact energy isabsorbed and good buffer effect is achieved.

Therefore, two types of disc springs were used in this study. Assuming f = 0.75h0, two sets of vibrationisolators were designed. The first set is composed of three sets of four overlaying type-I disc springs, here-inafter referred to as composite vibration isolator; the other set is composed of three sets of two overlayingtype-II disc springs, hereinafter referred to as vibration isolator.

Both DS I and DS II vibration isolators use disc spring as main isolator component and rubber isolationpad as supporting component. The rubber pad has an excellent isolation effect on high-frequency vibrationand can upgrade the work reliability of press because of its antiskid function. Figure 15 presents the designof a nonlinear-combination vibration isolator composed of three sets of overlaying disc springs in involution.The guide of middle hole is realized through guide pillar to prevent the deviation of disc springs in vibration.Polyurethane pads are placed between the overlaying disc springs to adjust friction damping. Both sides ofthe isolator are assisted with friction dampers to increase damping.

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Fig. 15. Structure of nonlinear-combination vibration isolator.

Fig. 16. Press with metal-spring damping vibration isolator.

5. TEST OF ISOLATOR

5.1. Test SystemThe effect of the DS II vibration isolator is better than that of the DS I vibration isolator. Thus, only theDS II vibration isolator is tested in this part. To indicate the loading/unloading curves of disc spring withdifferent types and numbers, the analysis of DS I is also carried out earlier in this article.

The metal-spring damping vibration isolator specially designed for this test and the vibration isolator wereplaced on the four feet of press.

Figures 16 and 17 show the high-speed press installed with metal-spring damping vibration isolator andthat installed with the type disc-spring nonlinear vibration isolator, respectively. Figure 18 shows the pressfeet and the typical test points on ground where acceleration sensors were placed. A pile force of 120 ton wasprovided to the two isolators. The vibration isolation effects of the two isolators were tested and comparedat the spindle speeds of 200, 240, 270, and 300 rpm.

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Fig. 17. Press with nonlinear vibration isolator.

Table 1. Acceleration peak at foot and corresponding ground test point of press with metal-spring damping vibrationisolator.

Spindle speed (rpm) Foot (m/s2) Ground (m/s2) Vibration isolationtransmissibility (%)

200 94.94 2.00 97.89240 130.17 3.58 97.25270 139.75 3.57 97.45300 256.72 5.33 97.92

The test was focused on the vibration acceleration of typical positions, including multiple test points onthe upper beam and lower beams, typical test points on the press feet, and four test points on the ground30 cm away from the isolator. Test results show that the vibration acceleration at the press feet is of similarvariation to that at the corresponding test points on the ground. This section discusses the acceleration valuesmeasured at No. 1 foot (i.e. the foot on the right side of flywheel) and its corresponding ground test point.

5.2. Test Results and Discussion5.2.1. Vibration isolation transmissibilityTable 1 displays the acceleration-peak variations of the vibrations with spindle speed under different im-pacting frequencies at the No. 1 foot and corresponding ground test point of the press installed with themetal-spring damping vibration isolator.

With the metal-spring damping vibration isolator installed, the acceleration at the press foot and cor-responding ground test point increases with increasing spindle speed (Table 1). The vibration isolationtransmissibility exceeds above 97%. The vibration isolation transmissibility increases with increasing spin-dle speed. At 300 rpm, the acceleration at the foot reaches 256.72 m/s2, whereas that at the ground test pointis only 5.33 m/s2, with a vibration isolation transmissibility of 97.92 %. Thus, the metal-spring isolator has

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(a) Acceleration sensors at press feet

(a) Acceleration sensors on ground

Fig. 18. Acceleration sensors at typical test points.

Table 2. Acceleration peak at foot and corresponding ground test point of press with the DS II vibration isolator.Spindle speed (rpm) Foot (m/s2) Ground (m/s2) Vibration isolation

transmissibility (%)200 83.06 1.67 97.99240 100.84 1.97 98.05270 151.42 2.53 98.33300 217.81 3.12 98.57

good vibration-isolation transmissibility.Table 2 displays the acceleration-peak variations of the vibrations with spindle speed under different

impacting frequencies at the No. 1 foot and corresponding ground test point of the press installed with theDS II vibration isolator.

As illustrated in Table 2, the corresponding ground test point grows with increasing spindle speed withthe DS II vibration isolator installed at the press foot. The vibration isolation transmissibility continuesto at 98% and above. The vibration isolation transmissibility increases with increasing spindle speed. At300 rpm, the acceleration at the foot reaches 217.81 m/s2, whereas that at the ground test point is only3.12 m/s2, with a vibration isolation transmissibility of 98.57%. The results show that the DS II vibrationisolator has good vibration-isolation transmissibility.

Figures 19 and 20 show the acceleration variation curves of the No. 1 press foot and correspondingground test point under different impact frequencies and with different isolators. Figure 21 illustrates the

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Fig. 19. Acceleration peaks at press foot with different vibration isolators installed.

Fig. 20. Acceleration peaks at ground test point with different vibration isolators installed.

comparison of vibration isolation transmissibility at different spindle speeds between the two isolators. Asshown in Fig. 19, the acceleration peak at the press foot rises with increasing spindle speed in both isolators.However, the former is higher than the latter. At 300 rpm, the peak at the foot of press with the metal-springisolator reaches approximately 257 m/s2, whereas that with DS II is only 218 m/s2, a difference of 40 m/s2.This result verifies that DS II has good performance in vibration isolation for high-speed press.

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Fig. 21. Transmissibility comparison between vibration isolators.

5.2.2. Frequency domain of ground vibration accelerationFigure 22 presents the frequency domain of ground vibration acceleration. With the metal-spring isolator,an obvious vibration peak appears at approximately 190 Hz, with a response value of 0.08 m/s2. Apparentresonances are also observable within the high frequency range of 1000 to 2000 Hz. However, with the DS IIisolator, only a low response peak is observed around the inherent frequency (maximum of approximately0.04 m/s2). Moreover, no resonance occurs, and minimal response is present at above 1000 Hz.

In summary, the nonlinear disc-spring isolator promises much better vibration-isolation performance thanthe linear metal-spring isolator. It can greatly weaken the vibration of high-speed press and improve itsinternal dynamic stress distribution in high-speed stamping, thereby enhancing stamping precision, pro-longing the service life of the press and die, and allowing resonant-free vibration isolation. Moreover, thedisc-spring isolator enables the high-frequency stress cycle of the press to decay rapidly with no delay, al-lowing the high-frequency amplitude on the foundation and the surrounding environment to dwindle by agreat deal.

6. CONCLUSION

The structure, strength, and stiffness of disc springs were initially discussed and explored. Two types of discsprings (DS I and DS II) were selected to realize the nonlinear variable stiffness of vibration isolator withcombined disc springs. FEMs of disc spring combinations in involution or congruence were established.The loading and unloading data of DS I and DS II in different overlaying forms were obtained. The optimalcombination form of disc springs was determined in terms of the spring static-load work-point stiffness.The hysteretic characteristics of the dynamic-load working points of combined disc springs used for directelastic support of the high-speed press were studied as well. The high-speed press, JF75G-200 was used totest the proposed combined isolator. The results were compared with those from the test on the metal-springdamping vibration isolator. The comparison suggests that the proposed vibration isolator of nonlinearlycombined disc springs promises much better vibration-isolation performance than the linear metal-spring

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Fig. 22. Frequency domain of ground vibration acceleration.

isolator. It can greatly weaken the vibration of high-speed press and improve its internal dynamic stressdistribution in high-speed stamping, thereby enabling the high-frequency stress cycle of the press to decayrapidly with no delay.

The combined vibration isolator was applied in Xuzhou Metal Forming Machine (Group) Co., Ltd. Thevibration of the press is reduced when stamping machine part. The service life of the press and die isprolonged; therefore, resonant-free vibration isolation is realized.

DS II vibration isolator, which allows simple and low-cost manufacturing, is expected to gain wide appli-cation in the field of vibration isolation for bulky mechanical devices with impacting load, such as pressesand forging hammers. However, further research on this isolator must still be conducted.

ACKNOWLEDGEMENTS

This project is supported by the Jiangsu Special Fund for Transformation of Technological Achievementsunder grant No. BA2008030. The authors especially wish to thank the engineers from Xuzhou Metal Form-ing Machine (Group) Co., Ltd. for precious suggestions on experiments and helping to design plan ofvibration isolator.

REFERENCES

1. Novak, M., “Foundations of shock-producing machines”, Canadian Geotechnical Journal, Vol. 20, No. 1,pp. 141–158, 1983.

2. Novak, M. and Hifnawy, L.E., “Vibration of hammer foundations”, Soil Dynamics and Earthquake Engineering,Vol. 2, No. 1, pp. 43–53, 1983.

3. Hiroshi, K., Dynamic Absorbers for High-speed Big Press Machines, Takenaka Technical Research Report,pp. 1–7, 1985.

4. Yoshimura, M., Kobayashi, H., Momose, A., Adachi, M. and Tsutsumi, M., “Evaluation for vibration restrictionof punch oress by CAE”, JSME Part C, Vol. 59, No. 568, pp. 3954–3961, 1993.

5. Yamamoto, Y. and Tsutsumi, M., “Vibration and noise reduction of C-frame Turret punch press using impactmass damper”, JSME Part C., Vol. 61, No. 589, pp. 3467–3473, 1995.

6. Park, S.C., Ishii, T., Honda, S. and Nagamatsu, A., “Vibration analysis and optimum design of press machine”,JSME Part C, Vol. 56, No. 524, pp. 872–879, 1990.

7. Chehab, A.G. and Naggar, M.H., “Design of efficient base isolation for hammers and presses”, Soil Dynamics &Earthquake Engineering, Vol. 23, No. 2, pp. 127–141, 2003.

8. Chehab, A.G. and Naggar, M.H., “Response of block foundations to impact loads”, Journal of Sound and Vibra-tion, No. 276, No. 1–2, pp. 293–310, 2004.

484 Transactions of the Canadian Society for Mechanical Engineering, Vol. 38, No. 4, 2014

9. Zhu, S.J., Zheng, Y.F. and Fu, Y.M., “Analysis of non-linear dynamics of a two-degree-of-freedom vibrationsystem with non-linear damping and non-linear spring”, Journal of Sound and Vibration, Vol. 271, No. 1–2,pp. 15–24, 2004.

10. Lang, Z.Q., Jing, X.J., Billings, S.A., Tomlinson, G.R. and Peng, Z.K., “Theoretical study of the effects ofnonlinear viscous damping on vibration isolation of SDOF systems”, Journal of Sound and Vibration, Vol. 323,No. 1–2, pp. 352–356, 2009.

11. Coe, T.E., Xing, J.T., Shenoi, R.A. and Taunton, D., “A simplified 3-D human body-seat interaction model and itsapplications to the vibration isolation design of high-speed marine craft”, Ocean Engineering, Vol. 36, No. 9–10,pp. 732–746, 2009.

12. Li, B., Zhao, W. and Deng, Z.G., “Modeling and analysis of a multi-dimensional vibration isolator based on theparallel mechanism”, SME Journal of Manufacturing Systems, Vol. 31, No. 1, pp. 2011.

13. Yang, P., Yang, J.M. et al., “Dynamic transmissibility of a complex nonlinear coupling isolator”, TsinghuaScience and Technology, Vol. 11, No. 5, pp. 538–542, 2006.

14. Han, J.H., Youn, S.H., Jeong, H.K. and Jang, Y.S., “Enhanced shock and vibration isolator for the attenuationof low-frequency vibration and high-frequency pyroshock loads”, in Third International Conference on SmartMaterials and Nanotechnology in Engineering, Vol. 8409, April 2, 2012.

15. Jia, F., Chen, S.J., Zang, D.F., et al., “A study on kinematics accuracy reliability for high speed pressmechanisms”, in Proceedings of the 2009 IEEE International Conference on Mechatronics and Automation,Changchun, China, August 9–12, pp. 2923–2927, IEEE, 2009.

16. Jia, F., Zheng, E.L. and Jiang, S., “He Chen. Theoretical study and kinematic simulation of working perfor-mance for press based on non-circular belt transmission”, in Proceedings of the 11th International Workshop onAdvanced Motion Control (AMC 2010-Nagaoka), Nagaoka, Japan, IEEE, 2010.

17. Zheng, E.L., Jia, F., Zhang, Z.S., et al., “Dynamic modelling and response analysis of closed high-speed presssystem”, Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics,Vol. 226, No. 4, pp. 315–330, 2013.

18. Zheng, E.L., Jia, F., Zhang, Z.S., et al., “Modelling and simulation of nonlinear combination disc-spring vibrationisolator for high-speed press”, Advanced Materials Research, Vol. 211, No. 212, pp. 40–47, 2011.

19. Jia, F. and Xu, F.Y., “Dynamic analysis of closed high-speed precision press: Modeling, simulation and exper-iments”, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical EngineeringScience, doi: 10.1177/0954406213517093.

20. Carrella, A. and Brennan, M.J., “On the design of a high-static-low-dynamic stiffness isolator using linear me-chanical and magnets”, Journal of Sound and Vibration, Vol. 301, pp. 678–689, 2007.

21. Lu, W.S., Design and Manufacture of Calculation of Disc Spring, Fudan University Press, Shanghai, 1990 [inChinese].

22. Zhang, Y.H., Lui, H.H. and Wang, D.C., Spring Design Manual, Chinese Machinery Industry Press, Beijing,2008 [in Chinese].

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