基于有限元比亞迪F3制動(dòng)器的設(shè)計(jì)【鼓式制動(dòng)器】【說明書+CAD+PROE】

基于有限元比亞迪F3制動(dòng)器的設(shè)計(jì)【鼓式制動(dòng)器】【說明書+CAD+PROE】,鼓式制動(dòng)器,說明書+CAD+PROE,基于有限元比亞迪F3制動(dòng)器的設(shè)計(jì)【鼓式制動(dòng)器】【說明書+CAD+PROE】,基于,有限元,f3,制動(dòng)器,設(shè)計(jì),說明書,仿單,cad,proe field Chen Hoist the heat the temperature C211 2008 Elsevier Ltd. All rights reserved. is a process energy hoist situation on 13,6,10,11 is fixed tion of temperature perturbations in multi-disk clutches and brakes during operation. Naji 12 established one-dimensional mathematical model to describe the thermal behavior of a brake system. Yevtushenko and Ivanyk 13 deduced the transient tem- perature field for an axi-symmetrical heat conductivity problem with 2-D coordinates. It is difficult for these models to reflect the real temperature field of brake shoe with 3-D geometry. 2. Theoretical analysis 2.1. Theoretical model Fig. 1 shows the schematic of hoists braking friction pair. In or- der to analyze brake shoes 3-D temperature field, the cylindrical coordinates (r,u,z) is adopted to describe the geometric structure shown in Fig. 2, where r is the distance between a point of brake shoe and the rotation axis of brake disc; u is the central angle; z * Corresponding author. Tel.: +86 13805209649; fax: +86 516 83590708. Applied Thermal Engineering 29 (2009) 932937 Contents lists available E-mail address: (Y.-x. Peng). emergency braking, so there is more intense temperature rise in brake shoe. The brake shoe is kind of composite material, and the temperature rise resulting from frictional heat energy is the most important factor affecting tribological behavior of brake shoe and the braking safety performance 510. Therefore, it is necessary to investigate the brake shoes temperature field with respect to investigating brake pads. Current theoretical models of brake shoes temperature field are based on one dimension or two. Afferrante 11 built a two-dimen- sional (2-D) multilayered model to estimate the transient evolu- method is an analytic solution method, it is difficult to solve the equation of heat conduction with complicated boundaries. There- fore, the analytic solution called integral-transform method is adopted 19, because it is suitable for solving the problem of non-homogeneous transient heat conduction. In order to master the change rules of brake shoes temperature fieldduringhoistsemergencybrakingandimprovethesafereliabil- ity of braking, a 3-D transient temperature field of the brake shoe was studied based on integral-transform method, and the validity is proved by numerical simulation and experimental research. 1. Introduction The hoists emergency braking mechanical energy into frictional heat emergency braking process of mining of high speed and heavy load, and this ing condition of vehicle, train and so work focused on the brake pads temperature Especially, because the brake shoe 1359-4311/$ - see front matter C211 2008 Elsevier Ltd. All doi:10.1016/j.applthermaleng.2008.04.022 of transforming of brake pair. The has the characteristic is worse than brak- . The previous field 14,10,12,13. during the process of The methods solving brake pads 3-D transient temperature field concentrated on finite element method 13,1417, approx- imate integration method 4,18, Greens function method 12 and Laplace transformation method 9,13, etc. The former three methods are numerical solution methods and are of low relative accuracy. For example, finite element method can solve the com- plicate heat conduction problem, but the accuracy of computa- tional solution is relatively low, which is affected by mesh density, step length and so on. Though the Laplace transformation Integral-transform method Emergency braking with experimental data, that the 3-D transient temperature field model of brake shoe is valid and prac- tical, and analytic solution solved by integral-transform method is correct. Three-dimensional transient temperature emergency braking Zhen-cai Zhu, Yu-xing Peng * , Zhi-yuan Shi, Guo-an College of Mechanical and Electrical Engineering, China University of Mining and Technology, article info Article history: Received 22 November 2007 Accepted 27 April 2008 Available online 6 May 2008 Keywords: Brake shoe Three-dimensional Transient temperature field abstract In order to exactly master braking, the theoretical model according to the theory of operating condition of mining deduced by adopting integral-transform field were carried out and ent were obtained. At the same for measuring brake shoes Applied Thermal journal homepage: www.elsevi rights reserved. of brake shoe during hoists Xuzhou 221116, China change rules of brake shoes temperature field during hoists emergency of three-dimensional (3-D) transient temperature field was established conduction, the law of energy transformation and distribution, and the hoists emergency braking. An analytic solution of temperature field was method. Furthermore, simulation experiments of temperature variation regularities of temperature field and internal temperature gradi- time, by simulating hoists emergency braking condition, the experiments were also conducted. It is found, by comparing simulation results at ScienceDirect Engineering is the distance between a point of brake shoe and the friction sur- face. As for the geometric structure and parameters shown in Fig. 2, its seen that a6r6 b,06u6u 0 ,06z6l. It is clear that the brake shoes temperature T is the function of the cylindrical coor- dinates (r,u,z) and the time (t). According to the theory of heat conduction, the differential equation of 3-D transient heat conduc- tion is gained as follows: o 2 T or 2 1 r oT or 1 r 2 o 2 T ou 2 o 2 T oz 2 1 a oT ot ; 1 wherea is the thermal diffusivity,a = k /(qC1 c); k is the thermal con- ductivity; q is the density; c is the specific heat capacity. 2.2. Boundary condition 2.2.1. Heat-flow and its distribution coefficient It is difficult for friction heat generated during emergency brak- ing to emanate in a short time, so it is almost totally absorbed by brake pair. As the brake shoe is fixed, the temperature of the fric- tion surface rises much sharply, and this eventually affects its tri- bological behavior more seriously. In order to master the real temperature field of the brake shoe during emergency braking, the heat-flow and its distribution coefficient of friction surface must be determined with accuracy. According to the operating condition of emergency braking, suppose that the velocity of brake disc decreased linearly with time, the heat-flow is obtained with the form q s r;tk C1lC1 pC1 v 0 C11C0 t=t 0 k C1lC1 p C1 w 0 C1 r:1C0 t=t 0 ; 2 where q is the heat-flow of friction surface; p is the specific pressure betweenbrakepair;v 0 andw 0 istheinitiallinearandangularvelocity ofthebrakedisc;listhefrictioncoefficientbetweenbrakepair;t 0 is the whole braking time, k is the distribution coefficient of heat-flow. Suppose the frictional heat is totally transferred to the brake shoe and brake disk, and the distribution coefficient of heat-flow is obtained according to the analysis of one-dimensional heat con- duction. Fig. 3 shows the contact schematic of two half-planes. Under the condition of one-dimensional transient heat conduc- tion, the temperature rise of friction surface (z = 0) is obtained with the form DT q k p p 4at p q pqck p 4t p ; 3 where q is the heat-flow absorbed by half-plane. And the heat-flow is gained from Eq. (3) p p respectively. According to Eq. (5), the distribution coefficient of Z.-c. Zhu et al./Applied Thermal Engineering 29 (2009) 932937 933 Fig. 1. Schematic of hoists braking friction pair. Fig. 2. 3-D geometrical model of brake shoe. heat-flow entering brake shoe is obtained with the form k q s q a q s q s q d 1C0 q d q s q d 1 C0 1 q s q d 1 1 C0 1 1 q s csks q d c d k d C16C171 2 : 6 2.2.2. Coefficient of convective heat transfer on the boundary With regard to the lateral surface and the top surface of the brake shoe, their coefficients of convective heat transfer are ob- tained, respectively, according to the natural heat convection boundary condition of upright plate and horizontal plate h l 1:42DT l =L l 1 4 ; 7a h u 0:59DT u =L u 1 4 ; 7b q pqckDT= 4t: 4 Suppose the two half-planes has the same temperature rise on the friction surface, and then the ratio of heat-flow entering the two half-planes is given as q s q d pq s c s k s p DT= 4t p pq d c d k d p DT= 4t p q s c s k s p q d c d k d p ; 5 where the subscript s and d mean the brake shoe and brake disc, Fig. 3. Contact schematic of two half-planes. Engineering where the subscript l and u represent the lateral surface and the top surface, respectively; h is the coefficient of convective heat transfer on the boundary, DT is the temperature difference between the boundary and the ambient, L is the shorter dimension of the boundary. 2.2.3. Initial and boundary condition Contact surface between brake shoe and brake disc is subjected to continuous heat-flow q s during emergency braking process. Brake shoes boundaries are of natural convection with the air. The boundary and initial condition can be represented by C0k oT or h 1 T h 1 T 0 f 1 t; r a; t P0; 0 6u6u 0 ; 0 6 z 6 l; 8a k oT or h 2 T h 2 T 0 f 2 t; r b; t P0; 0 6u6u 0 ; 0 6 z 6 l; 8b C0k oT oz h 3 T q s h 3 T 0 f 3 t; z 0; t P0; 0 6u6u 0 ; a 6 r 6 b; 8c k oT oz h 4 T h 4 T 0 f 4 t; z l; t P0; 0 6u6u 0 ; a 6 r 6 b; 8d C0k 1 r oT ou h 5 T h 5 T 0 f 5 t; u 0; t P0; 0 6 z 6 l; a 6 r 6 b; 8e k 1 r oT ou h 6 T h 6 T 0 f 6 t; u u 0 ; t P0; 0 6 z 6 l; a 6 r 6 b; 8f Tr;u;z;tT 0 ; t 0; a 6 r 6 b; 0 6u6u 0 ; 0 6 z 6 l; 8g where T 0 is the initial temperature of the brake shoe at t =0. 2.3. Integral-transform solving method Integral-transform method has two steps for solving the prob- lem. Firstly, only by making suitable integral-transform for space variable, the original equation of heat conduction could be simpli- fied as the ordinary differential equation with regard to the time variable t. Then, by taking inverse transform with regard to the solution of the ordinary differential equation, the analytic solution of the temperature field with regard to the space and time vari- ables could be obtained. Integral-transform method is applied to solve Eq. (1) with boundary condition Eq. (8). By integral-transform with regard to the space variables (z,u,r) in turn, their partial differential could be eliminated”. Writing formulas to represent the operation of taking the inverse transform and the integral-transform with re- gard to z, these are defined by Tr;u;z;t X 1 m1 Zb m ;z Nb m Tr;u;b m ;t; 9 Tr;u;b m ;t Z l 0 Zb m ;z 0 C1Tr;u;z 0 ;tdz 0 ; 10 934 Z.-c. Zhu et al./Applied Thermal where Tr;u;b m ;t is the integral-transform of T(r,u,z,t) with regard to z; Z(b m ,z) is the characteristic function, Z(b m ,z)= cosb m (l C0 z); b m is the characteristic value, b m tanb m l = H 3 , and H 3 h 3 k ; N(b m ) is the norm, 1 Nb m 2 b 2 m H 2 3 lb 2 m H 2 3 H 3 . Submit Eq. (10) into Eqs. (1) and (8), the following equations is obtained: o 2 T or 2 1 r oT or 1 r 2 o 2 T ou 2 f 3 k cosl C1 b m C0b 2 m C1 Tr;u;b m ;t 1 a oTr;u;b m ;t ot ; 11a C0k oT or h 1 T C22 f 1 t; r a; t P0; 0 6u6u 0 ; 11b k oT or h 2 T C22 f 2 t; r b; t P0; 0 6u6u 0 ; 11c C0k 1 r oT ou h 5 T C22 f 5 t; u 0; t P0; a 6 r 6 b; 11d k 1 r oT ou h 6 T C22 f 6 t; u u 0 ; t P0; a 6 r 6 b; 11e Tr;u;b m ;t Z l 0 Zb m ;z 0 C1T 0 dz 0 ; t 0; a 6 r 6 b; 0 6u6u 0 : 11f In the same way, the inverse transform and the integral-transform with regard to u and r are defined by Tr;u;b m ;t X 1 n1 Uv n ;u Nv n e Tr;v n ;b m ;t; 12 e Tr;v n ;b m ;t Z u 0 0 u 0 C1Uv n ;u 0 C1Tr;u 0 ;b m ;tdu 0 ; 13 where e Tr;v n ;b m ;t is the integral-transform of Tr;u;b m ;t with re- gard to u; U(v n ,u) is the characteristic function, U(v n ,u)=v n C1 cosv n u + H 5 C1 sinv n u; v n is the characteristic value, tanv n u 0 vnH 5 H 6 v 2 n C0H 5 H 6 H 5 h 5 k ;H 6 h 6 k ; N(v n ) is the norm, 1 Nvn 2 v 2 n H 2 5 C1 u 0 H 6 v 2 n H 2 6 C16C17 H 5 hi C01 . e Tr;v n ;b m ;t X 1 i1 R v c i ;r Nc i e T v c i ;v n ;b m ;t; 14 e T v c i ;v n ;b m ;t Z b a R v c i ;r 0 C1 e Tr 0 ;v n ;b m ;tdr 0 ; 15 where e T v c i ;v n ;b m ;t is the integral-transform of e Tr;v n ;b m ;t with regard to r; R v (c i ,r) is the characteristic function, R v (c i ,r)=S v C1 J v (c i C1 r) C0 V v C1 Y v (c i C1 r), J v (c i C1 r) and Y v (c i C1 r) are the Bessel functions of the first and second kind with order v, where S v c i C1Y 0 v c i C1bH 2 C1Y v c i C1b; U v c i C1J 0 v c i C1aC0H 1 C1J v c i C1a; V v c i C1J 0 v c i C1bH 2 C1J v c i C1b; W v c i C1Y 0 v c i C1aC0H 1 C1Y v c i C1a; c i is the characteristic value which satisfies the equation U v C1 S v C0 W v C1 V v =0; N(c i ) is the norm, 1 Nc i p 2 2 c 2 i U 2 v B 2 C1U 2 v C0B 1 C1V 2 v , where B 1 H 2 1 c 2 i 1 C0v=c i a 2 C138 and B 2 H 2 2 c 2 i 1 C0v=c i b 2 C138. Finally, according to the above integral-transform, Eqs. (1) and (8) can be simplified as follows: d e T v dt ab 2 m c 2 i e T v Ac i ;v n ;b m ;t; t 0; 16a v v 29 (2009) 932937 e Tc i ;v n ;b m ;t e T 0 ; t 0; 16b where A(c i ,v n ,b m ,t)=g 1 + g 2 + g 3 , g 1 aC1 b C1 R v c i ;b k C1 e C22 f 2 a C1 R v c i ;a k C1 e C22 f 1 C18C19 ; g 2 Z b a v k C1 C22 f 5 C1 r 2 C1 R v c i ;rdr Z b a v C1cosv n u 0 H 5 C1sinv n u 0 k C1 C22 f 6 C1 r 2 C1 R v c i ;rdr; g 3 Z b a f 3 k C1 cosl C1b m C1 sinv n b m H 5 v 1C0 cosv n b m C20C21 C1 r C1 R v c i ;rdr: The solution e T v c i ;v n ;b m ;t can be gained by solving the Eq. (16).By taking the inverse transform with regard to e T v c i ;v n ;b m ;t according to Eqs. (9), (12) and (14), the analytic solution of brake shoes 3-D transient temperature field is obtained Tr;u;z;t X 1 m1 X 1 n1 X 1 i1 Zb m ;z Nb m Uv n ;u Nv n R v c i ;r Nc i e C0ab 2 m c 2 i t C1 e T v 0 Z t 0 e C0ab 2 m t 0 Ac i ;v n ;b m ;tdt 0 2 4 3 5 : 17 field is carried out with t 0 = 7.23 s. The change rules of temperature field and internal temperature gradient are analyzed. Whats shown in Figs. 59 are partial simulation results. What is shown in Fig. 5 is brake shoes 3-D temperature field when time is 7.23 s. It is seen from Fig. 5 that the highest temper- ature of the brake shoe is 396.534 K after braking, and its lowest temperature is 293 K. And the heat energy is mainly concentrated Fig. 5. 3-D temperature field of brake shoe (t = 7.23 s). Fig. 6. The change of temperature on friction surface with time t. Z.-c. Zhu et al./Applied Thermal Engineering 29 (2009) 932937 935 Fig. 4. Half section view of brake shoes sample. Table 1 Basic parameters of brake pair and the emergency braking condition q (kg m C03 ) c (J kg C01 K C01 ) k (W m C01 K C01 ) T 0 (K) v 0 (m s C01 ) p (MPa) l 3. Simulation and experiment Fig. 4 shows the half section view of brake shoe sample. Line c and d are the center line and bottom line of the cross section, respectively. The sample dimension is: a = 137.5 mm, b = 162.5 mm, u 0 = 1/6 rad, l = 6 mm. The material of brake shoe and brake disc are asbestos-free and 16Mn, respectively. Their parameters and the condition of emergency braking are shown in Table 1. Suppose that the friction coefficient and the specific pressure are constant during emergency braking process. Based on the above analytic model, simulation of brake shoes 3-D temperature Brake shoe 2206 2530 0.295 293 10 1.38 0.4 Brake disc 7866 473 53.2 12.5 1.58 Fig. 7. The change of temperature on line d with time t. creases all the time when zP0.0006 m. Once the z is up to 0.002 m, the difference in temperature during brake is less than 3 K. It indicates that the heat energy focuses on the thermal effect layer, and its thickness is about 0.002 m. In order to prove the analytic model, experiments were carried out on the friction tester in Fig. 10. The experimental principle is as follows: when the brake begins, two brake shoes are pushed to brake the disc with certain pressure p and the temperature of point e on the friction surface is measured by thermocouple. Because the specimen thickness is too thin and the structure of the friction tes- ter is limited, it is difficult to fix the thermocouple in the brake shoe. Therefore, the thermocouple is fixed directly on the brake disc which is closed to point e shown in Fig. 10. Fig. 11 shows the temperatures change rules at point e under two situations of emergency braking. From Fig. 11, it is observed that the temperature at point e in- at first, then decreases; the highest temperature by simula- is lower than and also lags behind the experimental data. In 11a, the simulation temperature reaches the maximum K at 3.6 s while the experimental data comes up to the 435.65 K at 3.8 s. In Fig. 11b, the simulation result the maximum 469.55 K at 4.5 s while the experimental comes up to 479.68 K at 5 s. It is seen from Fig. 11, the temper- measured by experiment is lower than simulation results at Engineering 29 (2009) 932937 Fig. 8. The change of temperature gradient on line c with time t. 936 Z.-c. Zhu et al./Applied Thermal on the layer of friction surface (named thermal effect layer), which indicates the thermal diffusibility of the brake shoe is poor. In or- der to mater the temperature change rules of friction surface dur- ing emergency braking process, the variation of friction surfaces temperature with time t is simulated. What is shown in Fig. 6 re- veals that the temperature of friction surface increases firstly, then decreases. This is because that the speed of brake disc is high in the beginning and this results in large heat-flow while the coefficient of convective heat transfer is low on the boundary at the moment, so the temperature increases; at the late stage of brake the heat- flow decreases with the speed while the coefficient of convective heat transfer is high due to large difference in temperature on the boundary, which leads to decreasing in temperature. Figs. 6 and 7 reflect the temperature change rules in the radial dimension: the temperature at the outside of brake shoe is higher than that in- side, and the outside temperature changes more greatly. Fig. 8 demonstrates the change rules of the temperature gradi- ent along the direction z. The highest temperature gradient of the friction layer is up to 3.739 C2 10 5 K/m and decreases sharply along the direction z. The lowest value is only 4.597 C2 10 C011 K/m. In the beginning the temperature gradient of thermal effect layer is the highest while the temperature is close to the surrounding temper- ature. As the brake goes on, the temperature gradient decreases gradually until the end. Fig. 9 shows the change of temperature at different depth on the line c with time t. The temperature de- creases sharply with the increasing z, and the boundary condition has litter influence on the inner temperature. The temperature in- then it inverses. This is because the thermocouple itself ab- heat energy from the brake shoe in the beginning, then re- to the brake shoe when the temperature decreases. on between the experimental data and the simulation re- indicates that the simulation shows good agreement with the nt, and the errors of their highest temperature are 1.99% Fig. 9. The change of temperature at different depth on the line c with time t. Fig. 10. Schematic of friction tester. creases tion Fig. 427.14 maximum reaches data ature first, sorbs leases Comparis sults experime Fig. 11a. Temperatures change rules at point e with time t (p = 1.38 MPa, v 0 =1- 0 m/s). beginning the temperature gradient of thermal effect layer change rules of brake shoes 3-D transient temperature field during emergency braking. Acknowledgements This project is supported by the Key Project of Chinese Ministry of Education (Grant No. 107054) and Program for New Century Excellent Talents in University (Grant No. NCET-04-0488). Z.-c. Zhu et al./Applied Thermal Engineering 29 (2009) 932937 937 was the highest, the temperature increased swiftly; as the braking process going on, the temperature gradient decreased while the temperature increased; the boundary and 2.16%, respectively. It indicates that the analytic solution of 3- D transient temperature field is correct. 4. Conclusion (1) The theoretical model of 3-D transient temperature field was established acco