曲軸連桿活塞機(jī)構(gòu)及使用鍵合圖法的萬(wàn)向聯(lián)軸器的動(dòng)力學(xué)仿真建模-外文翻譯

1、modeling and simulation of the dynamics of crankshaft-connecting rod-piston-cylinder mechanism and a universaljoint using the bond graph approachabstractthis paper deals with modeling and simulation of the dynamics of two commonly used mechanisms, (1) the crankshaft - connecting rod - piston - cylin

2、der system,and (2)the universal joint system, using the bond graph approach. this alternative method of for mulation of system dynamics, using bond graphs, offers a rich set of features that include, pictorial representation of the dynamics of translation and rotation for each link of the mechanism

3、in the inertial frame, representation and handling of constraints at joints, depiction of causality,obtaining dynamic reaction forces and moments at various locations in the mechanism, algorithmic derivation of system equations in the first order state-space or cause and effect form, coding for simu

4、lation directly from the bond graph without deriving system equations,and so on.keywords: bond graph, modeling, simulation, mechanisms.1 modelingdynamics of two commonly used mechanisms, (1) the crankshaft - connecting rod - piston - cylinder system,and (2) the universal joint system, are modeled an

5、d simulated using the bond graph approach. this alternative method of formulation of system dynamics, using bond graphs, offers a rich set of features 1, 2. these include, pictorial representation of the dynamics of translation and rotation for each link of the mechanism in the inertial frame, depic

6、tion of cause and effect relationship,representation and handling of constraints at joints, obtaining the dynamic reaction forces and moments at various locations in the mechanism, derivation of system equations in the first order state-space or cause and effect form, coding for simulation directly

7、from the bond graph without deriving system equations.usually the links of mechanisms are modeled as rigid bodies.in this work, we develop and apply a multibond graph model representing both translation and rotation of a rigid body for each link. the links are then coupled at joints based on the nat

8、ure of constraint 3-5. both translational and rotational couplings for joints are developed and integrated with the dynamics of the connectinglinks. a problem of differential causality at link joints arises while modeling. this is rectified using additional stiffness and damping elements. it makes t

9、he model more realistic, bringing in effects of compliance and dissipation at joints, within definable tolerance limits.multibond graph models for the crankshaft 一 connecting rod 一piston 一 cylinder system, and, the universal joint system 6, are developed using the bondgraph approach. reference frame

10、s are fixed on each rigid link of the mechanisms using the denavit-hartenberg convention |7j. the translational effect is concentrated at the center of mass for each rigid link.rotational effect is considered in the inertial frame itself,by considering the inertia tensor for each link about its resp

11、ective center of mass, and expressed in the inertial frame. the multibond graph is then causaled and codingin matlab, for simulation, is carried out directly from the bond graph a sketch of the crankshaft mechanism is shown in fig. 1, and its multibond graph model is shown in fig.2. a sketch of the

12、universal joint system is shown in fig.3, and its multibond graph model is shown in fig.4. results obtained from simulation of the dynamics of these mechanisms are then presented.! crankshaft connecting rod piston-cylinder mechanism left side of the bond graph shows the rotational part and right par

13、t shows the translational part. we restrict any motion between the origin of inertial frame o and point on the link 1 that is 01 by applying source of flow sf as zero. similarly we restrict any relative motion at point a, distinguished by al on link 1 and a2 on link 2, by applying source of flow sf

14、as zero. the piston which is link 3, is constrained to translate only along the xo direction. translation along yo and zo direction is constrained by applying source of flow sf as zero for these components- differential causality is eliminated by making the k(1 j) element of the stiffness matrix k b

15、etween link 2 and link 3 as zero.fig. 1 shows thecylinder system. ”sketch of the “ crankshaft - connectingrod 一 piston甘2fig. 1: crankshaft-connecting rod-piston-cylinder mechanism.the individual components are considered as rigid links,connected at joints. the first moving link is the crank,the seco

16、nd link is the connecting rod and the third link is the piston. a frame is fixed on each link. thus frame 1 is fixed on link 1, frame 2 on link 2, and frame 3 on link 3. a fixed inertial frame 0, whose origin coincides with frame 1, is chosen. however, it will neither rotate nor translate. cl, c2 an

17、d c3 are centres of mass of respective links. the frames are fixed on respective links using the denavit-hartenberg convention 4.dynamics of the system of fig. 1 is modeled in the multibond graph shown in fig. 2. the model depicts rotation as well as translation for each link in the system. theaddit

18、ional stiffness and damping elements used for eliminating differential causality make the model more realistic, bringing in effects of compliance and dissipation at joints, within definable tolerance limits. these viscoelastic elements are represented in the bond graph by using c and r elements.we h

19、ave a source of effort se at link 3, which is the pressure force acting on the piston, although this force is also acting only in x direction.fig. 2: multibond graph model for the crankshaft - connecting rod - piston 一 cylinder system of fig. 1.1.2 universal joint mechanismthe fig. 3 shows the sketc

20、h of the " universal joint" mechanism.fig. 3: universal joint mechanism.it has three rigid links, two are yokes which are attached to rotating shafts and the middle one is the cross connecting the two yokes. the inertial frame is numbered o.and it is fixed. frame 1 is on link 1, frame 2 on

21、 the cross which is link 2, and frame 3 on the right yoke which is link 3- origin of the inertial frame coincides with that of frame 1 of link 1. the links 1 and 2 are connected with each other at two coincident end points points a - al on link 1 and a2 on link 2, and b - bl on link 1 and b2 on link

22、 2. similarly links 2 and 3 are connected at two points d d2 on link 2 and d3 on link 3, and e e2 on link 2 and e3 on link 3.link 1 rotates about z axis with respect to the inertial frame. the frame 2 is located at the centre of mass of the link 2. link 2 rotates with respect to the link 1 in direct

23、ion z2 as shown in fig. 3. frame 3 also coincides with frame 2 but it is located on the link 2. the frame 3 on link 3 rotates with respect to the link 2, about z3, as shown in fig. 3. the bond graph for this system is shown in fig. 4.fig. 4: multibond graph for the universal joint system of fig.the

24、issue of differential causality arises for this mechanism also. it is eliminated using additional stiffness and damping elements. as discussed earlier, this makes the model more realistic, bringing in effects of compliance and dissipation at joints, within definable tolerance limits. the relative mo

25、tion between the links at joints, along certain directions, is restrained by applying the source of flow sf as zero. the constraint relaxation is tuned by changing the values of stiffness and damping at corresponding joints. here we restrict the motion of the link 3 in two directions y and z, and al

26、low motion in x direction by resolving the source of flow in three parts and by putting sf as zero in y and z directions only. for the simulation, an excitation torque is applied to link 1 about the z direction2 simulationthe results of computer simulation for the crankshaft mechanism of fig. 1 are

27、discussed first. the initial position of the crankshaft is at 1 。= 60o with the xo axis. it is then released under the effect of gravity. the force of gravity also acts on the connecting rod. no force due to gas pressure is considered for the simulation as it is not the main issue under focus for th

28、is pape匚 the upper row in fig. 5 shows the displacement of the centre of mass cl, as observed and expressed in frame 0. it moves in a circular arc about the z0 axis. the first figure in the lower row of fig. 5 shows the oscillation of the crankshaftabout the z0 axis through change in orientation of

29、the unit vectors of frame 1. the second figure in the second row shows the oscillation of the centre of mass cl with time. this could perhaps be ascribed to the nonlinearity imposed due to coupling with the connecting rod.simulation results for the universal joint system are presented in fig. 8. a c

30、onstant torque is applied to the driving shaft about its axis. the driven shaft makes an angle of 5° with the axis of the driving shaft. the first row shows the response of the driving shaft which is the first link. the component of angular momentum of the driving shaft about its axis increases

31、 linearly, which is as expected. the first two figures of the second row show the change in orientation of the cross, which is link 2. angular motion about all three axes is clearly visible. the driven shaft follows the motion of the driver shaft as is clear from the third row in fig. 8.fig 5 respon

32、se m oti on of the crankshaftfig 6 response motion of the connecting rodfig 7: response motion of the pi st on3 conclusionsthe bond graph approach is used to model dynamics of two commonly used mechanisms, (1) the crankshaft - connecting rod - piston - cylinder system, and (2) the universal joint sy

33、stem. pictorial representation of the dynamics of translation and rotation for each link of the mechanism in the inertial frame,representation and handling of constraints at joints, depiction of cause and effect relationships, coding for simulation directly from the bond graph without deriving syste

34、m equations, have been explained in this work. matlab based simulations have been presented and interpreted for both the systems.ifilg toe f8 simulation results for the universal joint system曲軸連桿活塞機(jī)構(gòu)及使用鍵合圖法的萬(wàn)向聯(lián)軸器的動(dòng)力學(xué)仿真建模摘要木文論述了與常用的兩種機(jī)制的動(dòng)力學(xué)仿真模型，(1)曲軸連桿活塞-缸系 統(tǒng)，及(2)萬(wàn)向接頭系統(tǒng)，使用的鍵合圖方法。這種替代方法的系統(tǒng)動(dòng)力學(xué)仿 真，采用鍵合圖

35、，提供了豐富的功能集，包括，對(duì)慣性系的機(jī)構(gòu)的各個(gè)環(huán)節(jié)的平 移和旋轉(zhuǎn)的動(dòng)態(tài)圖形表示，表示和約束節(jié)點(diǎn)處理，描述的因果關(guān)系，在不同的位 置獲取動(dòng)態(tài)反應(yīng)的機(jī)理力和力矩，算法的系統(tǒng)方程的推導(dǎo)在第一階狀態(tài)空間或因 果形式編碼進(jìn)行了仿真，直接從鍵合圖沒(méi)有導(dǎo)出系統(tǒng)方程，等等。關(guān)鍵詞：鍵合圖，建模，仿真，機(jī)制。1建模常用的兩種機(jī)制的動(dòng)態(tài)，(1)曲軸連桿活塞 缸系統(tǒng)，及(2)萬(wàn)向 接頭系統(tǒng)，進(jìn)行了建模和模擬使用的鍵合圖方法。這個(gè)系統(tǒng)的動(dòng)力學(xué)方程的替代 方法，采用鍵合圖，提供了豐富的功能集1, 2。這些措施包括，對(duì)慣性系的 機(jī)構(gòu)的各個(gè)環(huán)節(jié)的平移和旋轉(zhuǎn)的動(dòng)態(tài)圖形表示，因果關(guān)系，描述表示和約束縫隙 處理，在不同的位置獲

36、取機(jī)制動(dòng)態(tài)反應(yīng)力和力矩，系統(tǒng)方程的推導(dǎo)在第一階段狀 態(tài)對(duì)空間或原因形式及影響編碼進(jìn)行了仿真，沒(méi)有直接從鍵合圖導(dǎo)出系統(tǒng)方程。 通常機(jī)制的鏈接被建模為剛性體。在這項(xiàng)工作中，我們開(kāi)發(fā)和應(yīng)用一個(gè)多元圖模型的每一個(gè)環(huán)節(jié)都要翻譯 和剛體的轉(zhuǎn)動(dòng)。環(huán)節(jié)進(jìn)行耦合基于約束3-5 b然關(guān)節(jié)。平移和旋轉(zhuǎn)接頭的開(kāi)發(fā) 和集成的動(dòng)態(tài)連接。在建模的時(shí)候連接接頭是一個(gè)問(wèn)題。這能糾正使用附加的剛 度和阻尼元件。它使模型更逼真，使合規(guī)和耗散在關(guān)節(jié)的影響，定義在公差范圍 內(nèi)。多元圖模型的曲軸連桿活塞缸系統(tǒng)，和萬(wàn)向接頭系統(tǒng)6 ,采用鍵 合圖方法。每一剛性連接的機(jī)制參考框架固定在采用denavi thartenberg公約 7 。翻譯的

37、影響主要集中在質(zhì)量屮心的每個(gè)剛性連接。旋轉(zhuǎn)效應(yīng)是慣性框架 本身考慮，通過(guò)考慮每個(gè)環(huán)節(jié)對(duì)各自質(zhì)心慣性張量，并在慣性坐標(biāo)系的表達(dá)。然 后使多元圖的編碼在matlab中，仿真，進(jìn)行直接從鍵合圖。種曲軸機(jī)構(gòu)示意 圖如圖所示，其多元圖模型如圖2所示。一種萬(wàn)向接頭系統(tǒng)示意圖如圖3所示, 其多元圖模型如圖4所示。從這些機(jī)制的動(dòng)力學(xué)仿真得到的結(jié)果。1.1曲軸-連桿-活塞缸機(jī)構(gòu)圖1顯示了 “曲軸連桿活塞 缸系統(tǒng)示意。”單個(gè)組件被視為剛性連接，連接的接頭。第一個(gè)移動(dòng)連接曲柄，第二連桿是 連桿、第三連桿是活塞。一架固定在每一個(gè)壞節(jié)。因此，框架1固定鏈接1,框架 2和框架3上連接2,連接3。一個(gè)固定的慣性坐標(biāo)系0,其

38、起源與1幀被選擇。然而， 它%不旋轉(zhuǎn)也沒(méi)有翻譯。cl, c2和c3是各環(huán)節(jié)質(zhì)量中心。該框架固定在各自的鏈 接采用denavi thartenberg公約4 。圖1的系統(tǒng)動(dòng)力學(xué)是在圖2所示的多元圖模型。該模型描述了旋轉(zhuǎn)以及在系統(tǒng) 中的每個(gè)環(huán)節(jié)的翻譯。鍵合圖的左邊顯示的轉(zhuǎn)動(dòng)部分和右側(cè)部分顯示平移部分。 我們限制任何運(yùn)動(dòng)的慣性幀0點(diǎn)起源之間的鏈路上的流量是1, 01 sf應(yīng)用源為零。 同樣，我們限制在任何點(diǎn)的相對(duì)運(yùn)動(dòng)，由a1和a2鏈接1鏈接2,通過(guò)流量sf應(yīng)用源 為零?；钊擎溄?,是約束沿x0方向。這些組件沿y0和z0方向翻譯是受流sf應(yīng) 用源為零。微分因果關(guān)系是使k消除（1,1）的剛度矩陣kz間的聯(lián)系2和鏈接3 元為零。附加的剛度和阻尼元件用于消除微分因果關(guān)系，使模型更逼真，使合規(guī)和耗 散在關(guān)節(jié)的影響，定義的公差范圍內(nèi)。這些粘彈性元件中的鍵合圖用c和r元素。我們有一個(gè)硒在鏈接3源，這是作用在活塞的壓力，盡管這力量也只有在x 方向。sf：o圖2：為曲軸連桿活塞 缸液壓系統(tǒng)圖1多元圖模型。1.2萬(wàn)向節(jié)機(jī)構(gòu)圖3顯示了素描的“萬(wàn)向節(jié)”機(jī)制。它有三個(gè)剛性連接，兩個(gè)線圈被連接到兩個(gè)覘，旋轉(zhuǎn)軸與中間一個(gè)是交叉連接。 慣