Dynamic coefficients in impact mechanics

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For non-sliding conditions a general solution corresponds to the rolling of particles and the equations should be replaced by [ 2 ] v =− kv (8) n , 2 n1 − =− + (9) 2 ( 7 ), vt v 2 t v Rω 1 t1 − =− − (10) 51 ( vt 7 R R ). Ω ω ω 1 The loss of the kinetic energy K is expressed as: ω = + + − + − (11) K 1 m( v v ) 1 I 1 m( v v ) 1 I . Ω 2 2 2 2 2 2 n t n t 1 1 2 2 2 2 2 2 Equation (11) can be rewritten in terms of Eqs. (4), (5) and (6): = + − + − + + (12) 1 2 2 (1 )[1 2 (1 2 )(1 )], K mvn k k fb f λ k 1 where b ( vt R ) v ω = − . 1 n1 The energy loss can be expressed in a more convenient, non-dimensional form by dividing K by the initial kinetic energy of a particle. This normalized energy K is expressed as ∗ K 2 2 1 k b 1 f − f = + − ⎜2 ⎟, 1 b λ + + ⎝ ⎠ 1 b 1 fc fc ∗ ⎛ ⎞ 2 2 (13) + where f c is the maximal value of the coefficient of dynamic friction: f c 1 b = . (14) λ 1 + 1 + k Equation (14) approaches the expression (7) in the case of a solid sphere. For some applications, the coefficients may be determined with an analytical procedure like the dynamic finite element analysis, or experimentally. Therefore the main task of this study is experimental determination of the coefficients of restitution to calculate the particle energy loss or the energy, absorbed by the target material during the impact. 3. EXPERIMENTAL PROCEDURE AND MATERIALS A schema of the test equipment used for the measurements of particle velocities and impact angles is shown in Fig. 2. An Ar-Ion laser beam was used 29
to illuminate the working area [ 5,6 ]. The light area was produced by widening the laser beam with a cylindrical lens. The impact event was recorded with a digital video camera and transferred into a PC. The video images were then decomposed into individual frames with software. A calibration procedure was carried out to eliminate any distortions. Figure 2 shows the particle accelerator, which was specially developed by SIVUS GmbH at Chemnitz University of Technology, Germany, for the determination of dynamic coefficients. The particles leave the feeding system and enter the particle accelerator (a rotating disk). This accelerator permits a precise evaluation of the collision variables. A centrifugal force drives particles through the channels of the accelerating disk that is set in rotation by a circulating belt [ 5,7 ]. Being pushed by the centrifugal force, the particles move towards a target that can be fixed at a corresponding angle onto a bracket of the cover. Therefore the particles outlet has a fixed spatial position and a negligible rotation. Steel and ceramic–metal composites (cermets) of different composition were used as target materials. Composition of the tested materials and hardness ratio of the material and glass particles (HV = 540) are listed in Table 1. Fig. 2. Experimental facility. Table 1. Composition and mechanical properties of materials tested Grade Composition Vickers hardness, HV10 Hardness ratio, HV /HV C20 80wt % Cr 3 C 2 + 20wt %Ni 1140 2.11 W15 85wt % WC + 15wt %Co 1258 2.33 C20S 80wt % Cr 3 C 2 + 20wt %Ni (reaction sintering) 1233 2.28 St 16MnCr5 steel 740 1.37 m p 30
Page 1 and 2: Proc. Estonian Acad. Sci. Eng., 200
Page 3: The appropriate equations are well
Page 7 and 8: where α 1 is the impact angle. The
Page 9 and 10: 0.140 Coefficient of dynamic fricti
Page 11 and 12: This reveals that the energy loss a
Page 13 and 14: velocity restitution, k , and the d

Dynamic coefficients in impact mechanics

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