WIRE ROPE BASED VIBRATION ISOLATION FIXTURE FOR ROAD TRANSPORTATION OF HEAVY DEFENCE CARGO SANJAY CHAUDHURI* AND BHARAT KUSHWAHA Vehicles Research & Development Establishment (VRDE), Ahmednagar-41400 Maharastra State, India
Abstract. A fixture assembly has been designed for vibration isolation during transportation of heavy extra long cargo by road. The fixture is supported on numbers of heavy-duty metallic wire rope isolators. These isolators are very effective for both vibration and shock isolation and specifically developed for this application. The fixture has been designed based on static, modal and random analysis by finite element method. The strain measurement has been conducted on fixture for specified payload. Vibrations are recorded at various speeds on many locations for determining percentage isolation and system characteristics. The finite element analysis results and measured strain and vibration data are correlated for validation.
Keywords: vibration isolation, wire rope isolators, modal analysis, random vibration, finite element analysis, spectrum analysis, isolation effectiveness
1.
Introduction
Isolation of the road bound shock and vibration are of most important requirement of transportation of defence cargo. The cargo was rested on specially designed and developed vibration isolation fixture and complete assembly was transported on a low bed semi trailer. The requirement of low shock and vibration vis-à-vis transportation of such cargo calls for design and development of special isolation fixture assembly. The restriction on maximum moving dimension (MMD) of vehicle for road transportation, overall low system natural frequencies, dynamic/shock load etc. govern the selection of isolators and
______ *
[email protected]
E. İnan et al. (eds.), Vibration Problems ICOVP-2007, © Springer Science + Business Media B.V. 2008
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structural design of isolator frame. Various types of isolators for e.g. rubber based, laminated rubbers, felts, air bellows, metallic spring type, wired mesh, metallic wire rope etc. are reported in many literatures but selection of right isolators depends on performance characteristics, nature of application and the environmental conditions. Metallic wire rope isolators are found most suitable for this application due to its high payload carrying capacity, compactness, low natural frequency and high deflection under shock. The weight of the frame assembly with cargo is 41T approximately and is supported on total 18 nos. of such isolators. The isolators have 3-D non-linear force-deflection characteristics and capable of isolating in three planes. The natural frequencies are obtained by modal analysis. The prototype isolator fixture assembly has been developed and integrated on semi-trailer along with load for experimental validation. The strains are measured at various locations of fixture and correlated with stress results from FEA. Limited road trails with full load have been conducted for assessment of structural integrity, mobility aspects and vibration characteristics. The vibrations are recorded for various speeds of transportation at different locations on frame before and after isolators. The spectrum analyses of these data are carried out to identify system natural frequencies, performance characteristics and to evaluate isolation effectiveness. 2.
Characteristics of wire rope isolators
Wire rope or cable isolators use multistrand stainless steel cables as flexible elements. The static load-deflection characteristics of these isolators are hardening non-linear at low loads. At higher load the cable elements tends to buckle in a controlled way results in softening non-linear characteristics, which is beneficial for shock absorption. The softening behaviour causes decrease in natural frequency with increase in load. The contact between the cables increases with increase in load in compression and lubricant, if any between the wires, squeezed out and the friction between the wires exhibits characteristics of dry friction. Both stiffness and energy dissipation does not depend on frequency but strongly depends on vibration amplitudes. Under vibratory loading, slippage of wires relative to one another dissipates the energy of motion1. Because of this feature, cable isolators are often used in cases where both vibration and shock protection are required, e.g. for packaging fragile components into containers, cargo sensitive to vibration etc. These isolators have 3-D non-linear forcedeflection characteristics. Fig. 1 shows performance characteristics of the isolator in the vertical direction. Curve fitting of these data yields in third order polynomial of deflection u as given in Fig. 1(a) and load P is represented as function of deflection u in (1). Stiffness K ii and natural frequency ωn , derived from (2) and (3) respectively, depends on u .
Wire Rope Based Vibration Isolation Fixture for Road Transportation
{Pi } = { fi (u)} ;
63
(i = 1, 2,3for three principal directions)
(1)
d (Pi ) = K ii du
(2)
ωn = K ii ∗ g / Pi
(3)
It can be seen from Fig. 1(b) that ωn reduces with increase in deflection. The longitudinal and lateral stiffness ( K 22 , K 33 ) of these isolators are same. The natural frequency of the isolation is 4.4 Hz approx. for the rated static load. 12 10 8
3 2 P= 0.0223 u + 3.0283 u + 296.66 u − 21.774
−60
−50
−40
−30
6000
−20
4
4000 2000
Deflection (mm)
6
4.4
−10 0 −2000 −4000 −8000 −10000 −12000
20
45
40
35
30
25
Energy absorbtion Load (Kg)
−6000
10
( −ve)
Vibration
Shock
Deflection
0
20
1511.3 10
Frequency (Hz)
2
5
−2000 −4000 −6000
Force (−ve)
−8000 −10000
Fig. 1 Performance characteristics of Isolator; (a) curve fitting of vertical Load-deflection data, (b) frequency and load deflection curve.
3.
Finite element analysis of isolation fixture
Solid model of Cargo rested on isolation fixture on trailer platform is shown in Fig. 2. Initially finite element analysis (FEA) of isolation fixture was done by using three dimensional beam elements having six degrees of freedom (three translations and three rotations). The cross members of the frame are joined to the longitudinal members through the nodes. The isolators are also modelled using 3D non-linear spring using load–deflection curve shown in Fig. 1 and joined to the frame through nodes. Generally nodes are positioned at points where members are connected although nodes are also required at load positions and at points where displacements are to be found. The exact position of the node representing a joint is usually the point of intersection of the centroidal axis of the members. Idealisation of this kind makes the joint stiff and has practical limitation due to dimensional differences of various sections. Many
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local openings are provided on the longitudinal and cross members for easy maintenance and accessibility of isolator bolts. Beam element has limitation of accurate modelling of these details. The foregoing discussion brings out the necessity of three-dimensional shell (six degree of freedom) model for the frame that can work accurately and efficiently. The area model of the frame is meshed by shell element. The isolators are modelled in similar way as in beam model. The weight of cargo is modelled as lumped mass at C.G. location and appropriate joints in FE model represent the connection between cargo and fixture. Translation d.o.f. of bottom nodes of spring elements are constrained. Static, modal analysis are carried out by using ABAQUS solvers for both beam and shell model. Mises’ stress for shell model (Fig. 3) is shown for static load.
Fig. 2 Solid model of Fixture with CARGO.
Fig. 3 Mises’ stress plots of FEA.
It is observed from Table 1 that beam model is comparatively stiffer and hence shell model generates more local modes in comparison to beam model. Random response analysis is carried out to find out the spectra of different variables caused by road bound random vibration. Random vibration is usually represented by Power spectral density (PSD) of signal and published in MIL 810-F2 for various modes of road transportation. Common carrier transportation mode, which is typically applicable for paved roadway is considered for this application and PSD values are provided as input (Fig. 4) to FE model at base (where the nodes are constrained). The contribution of vibration above 100 Hz TABLE 1. Comparison of frequencies for beam and shell model. Mode no BEAM Frequency model (Hz) SHELL model
1
2
2.6
4.3
2.5
4.0
3
4
50
60
72
26.8 27.6 31.6 47.5 298
354
455
15.5 15.9 19.3 20.6 28.9 36.6 268
301
350
11.6 18.5 10
5 24
6
7
8
10
Wire Rope Based Vibration Isolation Fixture for Road Transportation
65
is caused by local modes though PSD values are considered up to 350 Hz in analysis. The peak acceleration of cargo is at 4.3Hz . Isolation up to 100Hz on RMS (root mean square) acceleration is observed (Fig. 5) and the increase in vibration from fixture to saddle and to cargo is due to their spatial location. One 40 mm thick rubber pad (not modelled in FEA) is used between cargo and saddle and reduction in vibration on cargo is observed in measurement (Fig. 7). 3
[x10 ]
RMS Accln. (mm/sec2)
PSD ((mm/sec2)2/Hz)
8
10
FIXTURE CARGO INPUT
7
10
6
10
5
10
4
10
3
10
0
10
1
10
2
10
3
10
Frequency(Hz)
Fig. 4 Input and output acceleration PSD.
4.
8.00 6.00 4.00 SADDLE CARGO FIXTURE
2.00 0.00 0 10
1
10
2
10
3
10
Frequency(Hz)
Fig. 5 RMS acceleration spectra from analysis.
Results and experimental validation
After prototype development, all systems are integrated on vehicle and have been subjected to strain, deflection and vibration measurement with full payload to assess structural adequacy, integrity and other performance parameters. Experimental scheme and locations of various sensors is shown in Fig. 6. The
Fig. 6 Experimental scheme and location of strain and vibration sensors.
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strain locations are selected based on results of FEA. Single element strain gauge (S) is used where the direction of stress is known; otherwise strain rosette (R) is used. Environmental and other effect has been taken care appropriately. The measured strains are converted into Von Misses stress for comparison. The comparative stresses on various locations are shown in Table 2. Variation in stress levels is observed due to welding, local reinforcement and inaccessibility to exact location for measurement. Vibrations are measured for three speeds of vehicle in vertical direction only and spectrum analysis of signals is done. Though acceleration increases with increase in speed (Fig. 7), isolation observed on cargo up to 62.2% (Table 3). The effect of speed on vibration and system frequencies measured on cargo is shown in Fig. 8. Peaks are observed at 2.56 Hz , 4.39 Hz , 13.18 Hz etc. caused by tractor and semi-trailer suspension. Peaks at higher frequency are structural modes. TABLE 2. Comparison of stress from measurement and analysis. 2
Stress ( Kg/mm )
FEA Measured
10
S1
S11
S12
S13
9.1-10.0
5.4-6.8
6.7-6.8
8.3-10.6
8.3-10.6
12.53
8.91
8.45
9.84
11.02
0
20 KMPH 30 KMPH 40 KMPH
10
PSD (1x e−05)
g (rms)
A1 A2 A3 A4 A5
R1
−1
101 100 10−1 0
10 20.00
30.00
40 50
Freq 100 150 uen cy (H 200 z) 2500
−2
40.00
Speed (Kmph)
Fig. 7 RMS acceleration vs. frequency plot.
30
eed
300
Sp 350
h) mp
(K
20
Fig. 8 Effect of Speed on vibration.
TABLE 3. Comparison of isolation at various speeds.
Speed (KMPH)
G (RMS) at major locations
Isolation ( % ) w.r.t platform
A3 (Platform)
A2 (Fixture)
A4 (Cargo)
On Fixture
On cargo
20
0.046
0.04
0.021
13
54.3
30
0.053
0.05
0.02
5.7
62.2
40
0.068
0.055
0.028
19.1
58.8
Wire Rope Based Vibration Isolation Fixture for Road Transportation
5.
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Conclusions
It is observed that measured stress values are in close agreement with that of FEA. The contribution of vibration beyond 350 Hz is not observed and hence response analysis using frequency envelope up to 350 Hz is justifiable. The RMS vibration increases with increase in vehicle speed. Wire rope isolators are very effective and yielded isolation up to 62%. Study of interlinking of modes in low frequencies and effect of damping by wire rope isolators on dynamic response needs to be studied as future course of work. The prototype system has been developed and used successfully for its intended application. ACKNOWLEDGEMENT
The authors are indebted to Dr C. L. Dhamejani, Director, VRDE, for his encouragement and Shri Manmohan Singh, Head and other members of VRDE team and team of RCI, Hyderabad for their active efforts and involvement
during measurement.
References 1. M. L. Tinker, M. A. Cutchins, 1992. Damping phenomena in a wire rope vibration isolation system, Journal of Sound and Vibration, 157, 7-18. 2. Military standards handbook MIL-STD-810-F.
