礦山簡(jiǎn)擺顎式破碎機(jī)的設(shè)計(jì),礦山簡(jiǎn)擺顎式破碎機(jī)的設(shè)計(jì),礦山,顎式破碎機(jī),設(shè)計(jì) A R C H I V E S O F M E T A L L U R G Y A N D M A T E R I A L S Volume 58 2013 Issue 3 DOI: 10.2478/amm-2013-0092 S. WOLNY DYNAMIC BEHAVIOUR OF A VIBRATING JAW CRUSHER FOR DISINTEGRATION OF HARD MATERIALS DYNAMIKA WIBRACYJNEJ KRUSZARKI SZCZKOWEJ DO ROZDRABNIANIA MATERIAW TWARDYCH One of the trends in design solutions of crushers ensuring the crushing ratio of about 30 involves the application of the vibratory-impulse action to the material to be crushed. Crushers utilising these effects are referred to as vibratory crushers. During the vibratory crushing the material to be disintegrated is subjected to the action of fast changing shearing forces, which leads to the material being crushed either by applied impulses or by fatigue action, unlike conventional crushers where the structure of the material is damaged by the applied pressure. A dynamic analysis of the vibrating jaw crusher operation is provided and its potential application to crushing hard materials, such as alloy materials containing iron and slag from metallurgical processes are explored. Keywords: crusher, dynamic, disintegration Jednym z kierunkw poszukiwa rozwiza konstrukcji kruszarek w ktrych uzyskuje si stopie rozdrobnienia okoo 30 jest wykorzystanie efektu udarowo wibracyjnego oddziaywania na kruszony materia. Kruszarki wykorzystujce t zasad dziaania nazywa si kruszarkami wibracyjnymi. Zasada wibracyjnego rozdrabniania polega na poddaniu rozdrabnianego materiau dziaania szybko zmiennych si ciskajcych, co w rezultacie powoduje rozdrobnienie materiaw udarem, wzgldzie na zasadzie zmczeniowej, a nie jak w klasycznych kruszarkach, niszczenie struktury materiau zgniotem. W opracowaniu po przedstawieniu analizy dynamicznej pracy kruszarki wibracyjnej wskazano na moliwoci jej wykorzystania do rozdrabniania materiaw trwaych, w tym elastostopw oraz uli metalurgicznych. 1. Introduction Jaw crushers are widely used crushing machines. They are used for disintegration of hard and medium-hard materials to obtain various product size. They are robust, their design and construction is relatively simple, they are easy to oper- ate and maintain. Alongside those obvious advantages, they exhibit a number of drawbacks, too, including: low crushing ratio (of the order of 5), large inertia loading to foundations, large mass. One of the trends in design solutions of crushers ensur- ing the crushing ratio of about 30 involves the application of the vibratory impulse action to the material to be crushed. Crushers utilising these effects are referred to as vibrating crushers. During the vibratory crushing the material to be disintegrated is subjected to the action of fast changing shear- ing forces, which leads to the material being crushed either by applied impulses or by fatigue action, unlike conventional crushers where the structure of the material is damaged by the applied pressure. A dynamic analysis of the vibrating jaw crusher operation is provided and its potential application to crushing hard ma- terials, such as alloy materials containing iron and slag from metallurgical processes are explored. 2. Dynamic analysis of a jaw in a vibrating jaw crusher The analysis of design solutions used in vibrating jaw crushers reveals that in most cases jaw vibrations are induced by two- or four-mass inertia vibrators 2, 3. Vibrating jaw crushers operate mostly below the range of natural frequencies !0/! = 0.6-0.8 (!0 natural frequency of vibrations) so the jaw lead increases with an increase in the jaw vibration fre- quency, in accordance with the first branch of the resonance frequency plot 4 for induced vibrations of a single DOF (degree-of-freedom) system. The jaw in a vibratory jaw crusher (Fig. 1) complete with springs constitutes a vibrating system, which can be approxi- mated by a model of a single DOF system, shown in Fig. 2. The requirement stipulating high frequencies of jaw crushers vibrations encourages the use of steel springs, with a very low damping ratio. Therefore, the damping in the considered vibrating system can be neglected. The equation of motion of a jaw in a vibrating jaw crusher shown schematically in Fig 2 can be written as 2: J0 00 +kz l2 sin = b P0 sin!t (1) where: AGH UNIVERSITY OF SCIENCE AND TECHNOLOGY. FACULTY OF MECHANICAL ENGINEERING AND ROBOTICS. DEPARTMENT OF STRENGTH AND FATIGUE OF MATERIALS AND STRUCTURES, AL. A. MICKIEWICZA 30, 30-059 KRAKW, POLAND Brought to you by | China University of Mining t) t2 a 22 (x;t) x2 = 0 (11) Brought to you by | China University of Mining o) = 0 u(x;t) t jt=0 = 8 : 0 dla x 0 V0 dla x = 0 (12) and the boundary conditions: m 2u (o;t) t2 = AE u (x;t) x jx=0 ; (13a) u (h;t) = 0: (13b) The general solution to equation (11) is given as: u (x;t) = t xa + t + xa : (14) Substituting (14) to the boundary condition (13.b), we obtain: t + ha ! = t ha ! : (15) As t can assume any arbitrary value, it can be thus written: (z) = z 2ha ! ; (16) where the argument z may assume any value. Recalling (16) and (14) and replacing z by relevant argu- ments from (14), we get the displacement formula: u (x;t) = t xa t + xa 2ha ! (17) Substituting (17) into the boundary condition (13a) and rear- ranging, we get: ” (t) + AEma0(t) = ” t 2ha ! AEma0 t 2ha ! : (18) Using the relationship (18) and the initial conditions, the form of the function is gradually defined and, recalling (14), the motion of particular cross-sections of the rod 1 5 can be expressed as: 06t6 2ha u (x;t) = V0EA; 1 e EAma V0t ; (19) (x;t) = E u (t;x)x = aV0e EAma t: (20) To emphasise the qualitative effects of the impulse action, let us briefly analyse the stresses at characteristics points. For t = 0 and x = 0, recalling (17) we get: 0 = aV0: (21) Fig. 3. Geometric diagram of the jaw at the instant it touches the crushed material It appears (see 21) that stress at the moment of applied impulse is not related to the mass of the impacting body. Of major importance is the velocity V0 to which the stress is proportional. It can be concluded, therefore, that there exists some critical impulse velocity Vk at which the yield point of the material gets exceeded. For example, let us calculate Vk for a specified material: a = s E (22) Vk = H a = HpE (23) for t = ha; x = h (the point where the stress wave meets the opposite end) is obtained from formula (20b) 1, yielding: = 2 aV0 The stress experienced by the material next to investigated walls increased two-fold in relation to the initial level. To achieve the required crushing effect, the geometric and operational parameters of the jaw crushers should be con- trolled such that at the instant the jaw hits the material, its peripheral velocity should become V0 = VK. 4. Crushing capacity of vibrating jaw crushers To confirm the adequacy of the applied crushing method, the efficiency of the vibrating jaw crusher was tested in the laboratory set-up (Fig. 4). Brought to you by | China University of Mining 3 32s 1. Such narrow frequency ranges indicate that the effect of the discharge size on the optimal performance is minimal for the frequency range n = 30 31 s 1, at which the optima are registered for the chamotte bricks, the jaw lead dur- ing the idle run would fall in the interval Se = 0,8 0,925 min. Fig. 6. Crusher capacity in the function of jaw vibration frequency for sulphur ore 5. Summing-up The final effect of the research efforts is to determine the capacity of vibratory crushers for the practicable and feasible frequency ranges. For that purpose the dynamic analysis was performed of the crusher jaw behaviour and the necessary con- ditions were defined that would trigger the vibratory-impulse process. These considerations allowed for estimating the re- quired technical parameters of a vibratory jaw crusher, neces- sary to implement the crushing process. The vibratory crusher being designed and fabricated, crushing tests were performed on various materials, including the crushing capacity tests. Results of laboratory testing of operational and construction- al parameters of vibratory jaw crushers required for effective disintegration of various types of materials are provided and crushing capacity can be determined accordingly. REFERENCES 1 S. K a l i s k i, i in., Drgania i fale w ciaach staych. PWN. Warszawa 1966. 2 R. K o b i a k a, Wpyw parametrw dynamicznych i konstrukcyjnych na wydajno wibracyjnych kruszarek szczkowych. Praca doktorska AGH, Krakw 1978. 3 Patent nr 69785 PRL. 4 K. P i s z c z e k, J. W a l c z a k, Drgania w budowie maszyn. PWN Warszawa 1975. 5 S. W o l n y, Dynamic Loading the Pulley Black in a Hoist- ing Installation in Normal Operating Conditions. Archives of Mining Sciences 54, 9, 2, Krakw 2004. This article was first presented at the VI International Conference ”DEVELOPMENT TRENDS IN MECHANIZATION OF FOUNDRY PROCESSES”, Inwad, 5-7.09.2013 Received: 20 January 2013. Brought to you by | China University of Mining & Technology,Beijing Authenticated Download Date | 3/12/18 8:20 AM