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A COMPARISON OF MATERIAL AND SLIP
DAMPING BY USING A DUAL-MATING
CANTILEVER BEAM MADE OF FERROMAGNETIC
HIGH DAMPING ALLOYS
H. Kawabe
To cite this version:
H. Kawabe.
A COMPARISON OF MATERIAL AND SLIP DAMPING BY USING A
A COMPARISON OF MATERIAL AND SLIP DAMPING BY USING A DUAL-MATING CANTILEVER BEAM MADE OF FERROMAGNETIC HIGH DAMPING ALLOYS
H.
KAWABEDepartment o f Mechanical E n g i n e e r i n g . F a c u l t y o f E n g i n e e r i n g ,
T h e H i r o s h i m a I n s t i t u t e
ofT e c h n o l o g y , I t s u k a i c h i , H i r o s h i m a
7 3 1 - 5 1 , Japan
~ 6 s u m 6
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Comme une approche pour 1'6valuation des amplitudes relatives de/ 1' amortissement des mat6riaux Q-lrn et de 1' amortissement externe Q-le dads la structure d'une machine, les propribtes' d'amortissement pour une poutre encastrbe L une extrgmit6 ont bt6 6tudibes c o m e un param'etre de l'amplitude des efforts &r et de la force de serrage des surfaces de contact P. Dans le systsme mbtal d'amortissement ferromagnbtique SIA, l'amortissement total Q-lt augmente avec Er et prend la valeur la plus &levbe Q-lt (=O. 11)2
Er=l. 4x10-' dans le cas05
P=0.98kN. Dans le systgme d'acier 2 faible amortissement S45C, 1I valeur maximale Q-'t (-Q-le)=0.08 s'obtient 'a +=0. 9 ~ 1 0 - ~ avec PZ0.98kN.Abstract
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As an approach to evaluate the relative magnitudes of material damping Q-lm and external damping Q-le in a machine structure assembly, the damping properties for a dual-mating cantilever beam have been investigated as functions of strain amplitude E, and contact surface clampinf
force
P. In the ferromagnetic damping metal SIA system, the total damping Q- t: Increases with Er, showing the highest Q-lt (=0.11) at ~ ~ = 1 . 4 ~ 1 0 - ~ in the case of P=0.98 kN. In the low damping steel S45C system, the maximum Q-lt(-Q-1e)=0.08 is ob- tained at Er=O. 9 ~ 1 0 - ~ in P=0.98kN.
I
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INTRODUCTIONThe total damping ~-'t of a machine structure assembly can be determined by summing the material damping ~ - l m of its construction members and the external damping ~ - l e re-
sulting from their joint interface slip and other effects. From the viewpoints of pos- itively utilizing the ~ - l m in order to improve the anti-vibration properties of prac- tical machine structures, it has been intended to evaluate the relative magnitudes of
Q-1,
and Q-le by using a structure model made of high and low damping materials. As a more realistic experimental system, such a dual-mating cantilever beam as shown in Fig.l(a) is adopted on the ground that the present system having the oint interface1
slip can easily generate the slip damping Q - ~ S as a representative Q- e, and that a configurational limitation is also required for the extrapolation of a solenoid to control the ferromagnetic damping mechanism of the specimen used. In the present pa- per, therefore, the amplitude-dependent damping and dynamic stiffness of a two-mating beam are investigated as a parameter of the contact surface clamping force(close1y re- lated to the occurrence of Q-'s). There will be, useful comparisons of the Q-'S with the Q-lrn by applying magnetic field.
I1 - EXPERIMENTAL METHODS
As the specimens, a ferromagnetic high damping metal SIA['] and a commercial low damp- ing steel S45C are used to shape the plates of 8x34x500mm3, with their contact sur- faces finished to -0.6vm Rmax(hereafter called SIA(C) and S45C(C), respectively). As shown in Fig.l(a), each of specimens is fixed at the point 405 mm apart from the free end, with their fastening force at the fixed end being 50kN. The clamping force P is adjusted by two small load cells mounted near the free end. The sinusoidal exciting force is applied by a vibrator attached to the free end, the amplitude response of the system being obtained from the strain gauge c r attached near the fixed end.
C10-730
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RESULTS AND DISCUSSIONIn Fig. 2, the resonant diagram for the SIA system is shown for P=13.72kN, as a parameter of exciting force G.C. The resonant frequency fr shifts to the left with increasing G.C. This means the dynamic stiffness f decreases with the vibration amplitude. Such non-linear dynamical properties (lfke a gradually softening spring) can be explained from the AE effect/2/ peculiar to ferromagnetic metals, and from the lowering of the contact stiffness due to the joint interface slip 3,4/. The
i
strain amplitude (E,)-dependent Q-lt and f are shown in Fig. 3. Q- t is obtained from the half width of the resonant diagrazs. ~ - l t increases nearly monotonically with cr, while the stiffness fr2 vs E is characterized with a monotonically decreasing curve bounded below. Whatris noL%worthy here is the very high Q-lt(Q-'th=~.ll) which can be seen at E =1.4x10 at P=0.98kN. Furthermore, with increasing P, Q-lt decreases and ftr correspondingly increases over the whole range of measured cr. This can be due to the decrease in the interface slip.
Figure 4 indicates the E -dependent Q-lt and f in the case where the magnetic field H=15kA/m is applies by the solenoid (thaz is, the magnetomechanical damping mechanism is not operative).
As
compared with Fig. 3 (H=O), there exist distinct differences, i.e. the damping decreases by Q-lt -0.02 and correspondingly f increases. (The recovery rate of elasticity can be taken to be-
7%). Ther difference in the properties acqording to the presence or the absence of H can be basically explained by the change in the domain wall distribution: When the restrictive force H acts on the movement of non-180" domain wall as the magnetic damping origin, fixing domain wall movement or extinguishing domain walls is carried out, accordingly the magneto-mechanical hysteresis-mechanism disappears. Zn fact, such reduction in Q-lt by applying H corresponds to the magneto-mechanical damping Q-lglof thglalloy /5/. Therefore, this means that the dam in differenceP g
A=Q t
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Q m (e.g. A = Q-'th-
Q-lrn = 0.09 at E =1.4x10d ) results mainly from the external dampingQ - ~
e, i .e. the slip damping Q-'sfFigure 5 shows the damped free oscillation curves which are obtained after
resonating by the same sinusoidal applied force (G.C. = 2000 mA), as parameters of the clamping force P and the field H. In Fig. 5(a), (b) and (c), the variation of the damping curves in H=O is shown with the change in P(0.98
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13.72kN). The resonant amplitude (just before freely oscillating) tends to increase with increasing P. This can be explained by the reduction of the total damping Q-It contributed mainly by the Q-~s. On the other hand, Fig. 5(d), (e) and (f) show the transient response waveforms in the absence of the Q-fm effect, that is, the case where there occurs no change in domain wall distribution by H=15kA/m. Making respective comparisons between both side figures according to the presence or the absence of H, it is easily seen that the resonant amplitudes on the right side are larger than on the left side, because of the recovery of elasticity due to the domain wall fixation. Therefore Fig. 5(a) is the most effective resopance-suppressing case due to both damping contributions Q-lm and Q-ls (-Q e), while, to the contrary, Fig. 5(f) shows the case where those damping effects hardly operate. Depending on the size of the damping, there exists a clear difference among the resonant amplitudes under the same vibration force. Furthermore, as shown in Fig.
5(f), from the envelope shape of free decay curves, it can be said that the damping mechanisms are characterized .as follows: (1) large amplitude region(1) featured by an approximately linear high decay curve where the Coulomb type damping mechanism /3/ is dominant; (2) small amplitude region(J.11) featured by a low damped
oscillation curve where the main contribution to Q-lt can be regarded to be the material damping of the beam; (3) intermediate amplitude region(I1) where both damping mechanisms as mentioned above coexist.
Figure 6 indicates the E~-dependent Q-lf and f: in the S45C system. As in the case of SIA, the f 2vs E is characterized with a monotonically-decreasing function bounded below: On $he elher hand, Q-lt vs c repsesents a convex function, which has a maximum Q-lt (- Q sm = 0.08) at E ~ = O . ~ X I O -
.
Such convexivity in Q-lt vs EI
Roughness
-0.6 Urn Rmax
1
(b) Small amplitude state ( 0 ) Large amplitude state
having little joint causing considerable
interface slip. joint interface slip.
Fig.1
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Schematic illustration for (a) a dual- mating cantilever beam system and its dynami-cal behaviors according to (b small or (c)
1
large vibration amplitude. Q- m:Material damp- ing of beams; Q-ls: slip dam ing resulting from
!
the joint interface slip; Q t: total damping of the beam system; P: clamping force between two mating beams.
Fig.2
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Resonant diagram of the SIA system in no field H as a parameter of exciting force G.C.Fig.3
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The Er-dependent Q-lt and fr2 Fig. 4-
The cr-dependent Q-lt and fr2 for the SIA system without field H. for the SIA system with the field H=C10-732
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I H= -0 L H
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15kA/m Fig.5-
Variation of the damped free oscillation curves in the SIA system with clamping force P and field H(un- der the same exciting force).Fig.6
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The &,-dependent Q-lt and fr2 in the S45C system.are freely oscillated after resonating by the constant sinusoidal applied force(G.C.=2000mA), are shown as a function of P. As already dis- cussed for the SIA system, it can be similarly said that large or small P has a great effect on the occurrence of slip damping Q-ls.
It is concluded that the most effective appli- cation of the high damping alloys to a machine structure is to construct its assembly with the mating surfaces or interfaces joined in an opti- mal press fit ~ondition[~] depending on the sur- face roughness and the contact pressure at joint interfaces.
REFERENCES
/I/ Sugimoto, K., J. Iron & Steel Inst. Jap. 60 [I9741 2203.
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/2/ Bozorth, R. M., Ferromagnetism, D. Van Nost- rand Co., New York, [I9651 684.
/ 3 / Masuko, M., Ito, Y. and Yoshida, K., Bull.
Japan Soc. Mech. Eng. 317 [I9731 382. /4/ Kawabe, H., Bull.
J G ~
Soc. Prec. Engg.(to be published).
/5/ Kawabe, H. and Kuwahara, K. Trans. J I M , 2
[ 19811 301.
/6/ Lazan, B. J., Damping
of
MateriaZs and Mem- bers in StructuraZ Mechanics, Pergamon Press,[I9681 23.
