9th WSEAS Int. Conf. on ACOUSTICS & MUSIC: THEORY & APPLICATIONS (AMTA '08), Bucharest, Romania, June 24-26, 2008
Design of a New Base Isolation System for Forging Hammer ANA-MARIA MITU, TUDOR SIRETEANU, DANIEL CĂTĂLIN BALDOVIN Institute of Solid Mechanics Romanian Academy C-tin Mille Street no 15, 010141, Bucharest ROMANIA
[email protected],
[email protected] ,
[email protected] Abstract: Generally, the tensions caused by mechanical shocks and vibrations have negative effects upon the mechanic structures, given the fact that these structures are exposed to additional dynamic stresses. The aim of the paper is to employ the modeling of SERB hysteretic dissipative devices used for reducing the transfer of vibrations or shocks generated by forging hammers. Methods of linear equivalence of the dissipative component of the hysteretic type characteristics based on energy considerations will be applied. Key-Words: - shocks, vibrations, base isolation system, forging hammer, SERB-BC devices Therefore the shock isolation problems can be dividing into two major classifications: 1. Mitigation of effects of foundation motion; 2. Mitigation of effects of force generated by equipment The forging hammer shock belongs to second class. For this class is necessary as the transmissibility of shock forces to the foundation should be minimum. From this condition results the approximate value of the critical damping fraction for the foundation isolator (an isolator having a linear spring and viscous damping): ζ ≅ 0.25 . For an isolator having a linear spring and viscous damping the transmissibility ratio increases as a function of the fraction of critical damping ζ as ζ is increased beyond or decreased under 0.25.
1 Introduction All strengths imposed by shocks and vibrations, generally, have got unpleasant effects upon the mechanic structures, because the additional stresses of dynamic type to which they were subdued. Such shocks and vibrations affect the proper operation of the technological installation, systems and components, damage the building where structures they are installed in and generate waves and noises that propagate to the environment, affecting the foundations of sensitive installations and equipment, and also a discomfort for the operation personnel and for the occupants of buildings is created. Also, a very great danger in respect of the uncontrolled radiologic contamination of the environment is represented by the demage of nuclear objectives, distroy resulted from missiles and plane crashes. Function of their generating source, shocks and vibrations evidence strong different dynamic characteristics and the elimination or reduction of their effects may be obtained only by special solutions applicable to each individual case after having analyzed excitation kinetic characteristics. In this paper is study the foundations supporting hammers and presses which have to withstand powerful short-period impact loads. Two classes of shock are considered. In the first is the shock characterized by motion of a support or foundation where a shock isolator reduces the severity of the shock experienced by equipment mounted on the support and the second is the shock characterized by forces applied to or originating within a machine where a shock isolator reduces the severity of shock experienced by the machine support.
ISBN: 978-960-6766-74-9
2 Presentation of shock source The source of shocks is one CM 1250 forging hammer. The hammer construction is frame type, the bed plate as common part with the hammer. The assembly weight is approximately 36 t and maximum striking power is 36 kJ. For this forging hammer the prescripted natural frequency is about 11 Hz. Due to the fact that the level of vibrations in an apartment building generated by the operations of the CM 1250 hammer placed at approximately 250 m from the building was exceeding the maxim permissible level (coincident with the DIN 4150 prescriptions the velocity maximum admitted values is 5 mm/s for f ≤ 10 Hz and for all directions) a new isolated method was imposed. Figure 1 shows the vibrations recorded in the apartment block, at 4th floor, simultaneously on two
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ISSN 1790-5095
9th WSEAS Int. Conf. on ACOUSTICS & MUSIC: THEORY & APPLICATIONS (AMTA '08), Bucharest, Romania, June 24-26, 2008
perpendicular directions - on vertical direction and a horizontal direction approximately on the propagation direction of the vibrations generated by the forging hammer. In this figure it is worthy noting that the vibrations recorded in apartment building at 4th floor denote a „rocking” movement of the building. Presumably, this movement results from the repeatable impact of building foundation with the shock waves generated by the activity forging hammer stands by the old foundation.
suspended by the isolation frame at a value equal with the maximum hammer blow frequency multiply with 2 ÷ 2.5. In order to achieve these objectives, devices with stiffness and dissipative proprieties (especially SERB-BC devices (Fig.2) can be used to support impact-producing equipment.
Fig. 1. Wave shape for vibrations recorded in apartment building (- - - vertical direction; ___ horizontal direction).
Fig.2.The SERB-BC type support
These supports are new types of adjustable controlled elasticity and damping mechanical devices, capable to adapt their stiffness and damping function to the load level, providing a good control on the structure behavior.
The old solution for isolation system of forging hammer foundation (the building vibrations source) consist of an inertial mass (rigid block made of concrete having the weight of 126 t), attached to the forging hammer, which is then supported by an isolation frame made of the linear springs and viscous dampers. Because the loading of the viscous dampers of the old solution isolation system was bigger this dampers had been tear off. In these conditions, beyond the hammer blow, the forging hammer with rigid block is undamped moving (the transmissibility ratio is 1.0).
3 The new solution for hammer isolation When designing these foundations, there are several requirements to take into account. The vibration amplitudes and the forces transmitted to the supporting piles or soil medium must be reduced to meet serviceability and stability requirements and to minimize any disturbance to the neighborhood and surroundings. Considering the characteristics of activity with the forging hammer, is adequate to adjust the natural frequency of the forging hammer
ISBN: 978-960-6766-74-9
Fig.3. Constructive scheme for SERB-BC type support
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ISSN 1790-5095
9th WSEAS Int. Conf. on ACOUSTICS & MUSIC: THEORY & APPLICATIONS (AMTA '08), Bucharest, Romania, June 24-26, 2008
Methods of linear equivalence of the dissipative component of the hysteretic type characteristics based on energy considerations can be applied. Such methods are efficient in cases when the study encompasses the dynamic component of the excited structures in the resonance range , in the rated speed operation requires or due to structure is characterized by frequency spectra having a dominant component. This paper will employ a method of linear equivalence of the hysteretic dissipative component considering that, in case of reducing the transfer of vibrations or shocks generated by industrial equipment operation, such regimes show the highest practical interest.
SERB-BC devices are made up of elastic blade packages made from high strength austenitic stainless steel thin plates, bound as a sandwich type assembly (fig. 3). The forging hammer bed plate is in direct contact with isolation frame made of the new supports as is shown in Fig. 4
4 Analytical model The dynamical response of the forging hammer, placed on base isolation devices with hysteretic characteristics, can be analyzed by considering single degree of freedom system (Fig. 6), whose equation of motion and initial condition are:
Fig. 4. The new solution for isolation system
The SERB-BC devices have hysteretic characteristic with stiffness characteristics displaying geometric nonlinearity (as shown in Fig.5) 100
Edisp=54.5J Edisp=98.2J Edisp=138.7J
90
Force [kN]
80 70 60 50
Fig. 6: Mechanical model of the forging hammer with base isolation system
40 30 20 -12
-10
-8
-6
-4
-2
0
2
4
6
Md&& + F (d , d& ) = P (t ) d (0) = d& (0) = 0
8
Displacement [mm]
(1)
where M is the total mass of the equipment, d ( t ) Fig. 5. Laboratory test diagrams of SERB-BC
is vertical displacement of the equipment exciting by
The dissipative component is characterized by hysteretic loop aria, is high dependent of motion amplitude and less dependent of motion frequency.
hammer’s action , F (d , d& ) is the hysteretic characteristic of the base isolation system, and P (t )
ISBN: 978-960-6766-74-9
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ISSN 1790-5095
9th WSEAS Int. Conf. on ACOUSTICS & MUSIC: THEORY & APPLICATIONS (AMTA '08), Bucharest, Romania, June 24-26, 2008
corresponding to the same values of displacement (quasistatical tests fig 7. and dynamical tests fig 8.) The elastic blade packages are subject to normal deformations on their contact surfaces by means of stiff deflective disks with an adequate geometry required by the desired force – deflection ratio. The destruction of shock energy is accomplished by friction to contact surfaces of elastic blades.
is the impact load time variation necessary for forging process. Generally, the impact force time variation is hard to measure. If the impact load time value versus system’s fundamental period is very short, the dynamical response of the system will be almost independent of the shock’s shape, in condition that impulse value remains the same. Moreover, in these hypotheses, forced vibration analysis described by (1) is dynamically equivalent with free vibration analysis described by the following Cauchy problem:
Md&& + F (d , d& ) = 0 d (0) = 0; d& (0) = v
(2)
0
where v0 is the initial velocity of the suspended mass due to the shock. The hysteretic characteristic is analytical modeled by:
(
)
F d , d& = F ( d ) + cd&
(3)
where F (d ) is the stiffness characteristic of the base isolation system with hysteretic characteristic and c the equivalent damping characteristic, determined from experimental hysteretic curves (Fig. 5).
Fig. 7. The hysteresis loops for 1500 daN preload (cvasistatical test conditions).
5 Experimental data The experimental tests have been performed on a SHENCK-type hydropuls stand capable of producing dynamic forces of up to 100 kN within a frequency range that covers the field of frequencies which present a practical interest for passive antiseismic or anti-vibratory protection systems. Experimental measures consisted in simultaneous record of the displacements imposed between the points where the devices are joined to the hydropuls, and of the forces developed on the devices. If d (t ) and Fdisp (t ) represent the variations in time
Fig. 8. The hysteresis loops for 1500 daN preload (dynamical test conditions – frequency = 0.5 Hz )
of the displacement and force signals simultaneously recorded, by removing the time variable one gets a hysteretic loop Fdisp (t ) , which provides information
For dynamic cyclic strains on the amplitudes, frequencies and forces that stand below the maximal working limits of the hydropuls, we could approximate the imposed displacement rather accurately by means of a periodical function with the form:
concerning both the stiffness feature of the tested device and its ability to dissipate the energy of vibrations. On the basis of the hysteretic curve settled experimentally for a single device subject to a quasistatic compression - decompression loading (see Fig. 7), could be found out its stiffness characteristic by means of averaging the values of the force
ISBN: 978-960-6766-74-9
d ( t ) = D0 + Dcos2πft
(4)
where D, f stands for the amplitude and, respectively, frequency of the cyclic displacement imposed between the points of fastening of the
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ISSN 1790-5095
9th WSEAS Int. Conf. on ACOUSTICS & MUSIC: THEORY & APPLICATIONS (AMTA '08), Bucharest, Romania, June 24-26, 2008
Fdisp (d ) = −2259 + 9.305 ⋅106 d +
device on the hydropuls, D0 being the initial displacement by which we get the static preload. The energy dissipated per cycle by the device may be evaluated taking into account the area of limited field of the hysteretic loop experimentally obtained:
Edisp ( D, f ) =
∫ F ( d ) ⋅ dd disp
50k
(5)
40k
The energy dissipated by a device with linear viscous damping while being subjected to the cyclic strain described by the function (4) has the expression:
20k
(6)
where c( D, f ) represent the damping coefficient. Setting the condition that for the same cyclic strain the Edisp ( D) energy, dissipated by the device with
1 Edisp ( D, f ) 2π ⋅ f ⋅ D 2 2
Bound
10k 0 -10k
Rebound
-20k -30k -40k
the hysteretic feature experimentally ascertained, should be equal with the energy by an (equivalent) Elin ( D, f ) dissipated corresponding device with visco-linear damping one obtains the value
c ( D, f ) =
experimental analytic approximation
30k
Force [N]
Elin ( D, f ) = 2π2 ⋅ f ⋅ D 2 ⋅ c ( D, f )
-50k -0.0050
-0.0025
0.0000
0.0025
0.0050
Displacement [m]
Fig. 10:The experimental stiffness characteristic of a device and its analytic approximation
(7)
We are concerned with the movement of the equipment for displacements on this and on the other side of the static balance position for −0.005m ≤ d ≤ 0.005m . One of the laboratory test diagram is presented in Fig 9.
Linear local rigidity of the base isolation system (around the static balance position) and the natural frequency of the small oscillations of the equipment are given by the equations (9).
k = 6kdisp = 6
120.0k 100.0k
(8)
+7.046 ⋅108 d 2 + 3.077 ⋅1010 d 3
1 fn = 2π
Hysteretic loop Elastic characteristic
dFdisp dd
= 55.83 ⋅106 N/m d =0
(9)
k = 6.3Hz M
Force [N]
80.0k
Using the values of the energy dissipated per cycle by a device, which we acquire by calculating the areas closed inside the hysteretic loops in the figure 5, we could find out the coefficient of the equivalent viscous linear damping of the base isolation system, by averaging these values and multiplying the result with the number of devices. The relation of energetic equivalation applies also for f = f n , that is for the fundamental frequency of the free vibrations of the equipment caused by the hammer’s impact.
60.0k 40.0k 20.0k 0.0 0.000 0.002 0.004 0.006 0.008 0.010 0.012
Displacement [m]
Fig. 9. Laboratory test diagrams of SERB-BC
4 Comparison of experimental results
In the figure 10 it is represented the stiffness characteristic of the device, alongside its analytic approximation, given by:
ISBN: 978-960-6766-74-9
analytical
and
By numerical integration of equation 2 are obtained the variation of spring mass acceleration.
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ISSN 1790-5095
9th WSEAS Int. Conf. on ACOUSTICS & MUSIC: THEORY & APPLICATIONS (AMTA '08), Bucharest, Romania, June 24-26, 2008
analytic expressions of certain corresponding viscose-elastic characteristics with the same rigidity and having an equivalent damping in the operation range of the machine. Methods of linear equivalence of the dissipative component of the hysteretic type characteristics based on energy considerations are efficient in cases when the study encompasses the dynamic component of the excited structures in the resonance range , in the rated speed operation requires or due to structure is characterized by frequency spectra having a dominant component. Such an equivalent facilitates the analysis by numerical simulation of the equipment’s response to the shocks caused by the hammer blows. The non-linear stiffness characteristics of the devices potentially restrain the occurrence of resonance regimes in the structures located in the neighborhood of the equipment, to which, unavoidably are produced free vibrations caused by the running forge hammer.
In figures 11 and 12 are presented the acceleration time history measured in situ on the sprung mass of the forging hammer placed on the base isolation system (for two consecutive shocks) and the analytical results (for one shock). It can be seen that the difference between the predicted and experimental data is at an acceptable level. Thus, this method of linear equivalence of the hysteretic dissipative component is an efficient one.
References: [1] Abdul Ghafar Chehab, M. Hesham El Naggar Design of efficient base isolation for hammers and presses, Soil Dynamics and Earthquake Engineering, 2003, pg. 127-141 [2] Viorel Serban, Gheorghe Ghita, Florin Mailat, Ana-Maria Mitu, A new vibration isolation method of forging hammer, The Annual Symposium of the Inst. of Solid Mechanics, SISOM-2004, Bucharest, 20-21 may 2004 [3] V.Serban, T.Sireteanu, A.M.Mitu, F.Mailat, D.Stancioiu, Experimental assessment of a new base isolation system for buildings, The Annual Symposium of the Inst. of Solid Mechanics 2003, Bucharest, 15-16 may, pp.101- 108 [4] M. Hesham El Naggar and Abdul Ghafar Chehab Vibration barriers for shock-producing equipment , Canada Geotech. J. Vol. 42, 2005 , pp 297–306, [5] Gh. Ghita, V. Serban, Ana-Maria Mitu, An efficient shock isolation system for forging hammer, Advanced Engineering in Applied Mechanics, editors: L. Vladareanu, T. Sireteanu, Editura Academiei, Bucuresti, 2007, cap. 6.
Fig 11 Measured data 6
acceleration [m/s2]
4 2 0
-2 -4 -6 0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
time[s] Fig 12 Analytical data
5 Conclusion On the ground of hysteretic type characteristics, experimentally measured for the SERB-BC devices, employed for the base isolation system of the forging hammer equipment, we can determine the
ISBN: 978-960-6766-74-9
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