0中期情況檢查表學院名稱： 檢查日期： 學生姓名 專 業(yè) 指導教 師 設計（論文）題目 20米自動伸縮門設計已經對自動伸縮門的總體結構有了一定的了解，對減速器的傳動方案做出選擇并進行了設計計算，采用了二級圓錐-圓柱齒輪減速器實現傳動?？刂葡到y(tǒng)已選擇為單片機控制系統(tǒng)，現正在對其原理圖進行設計并對對減速器設計進行驗證。工作進度情況是否符合任務書要求進度 是 能否按期完成任務 能 工作態(tài)度情況(態(tài)度、紀律、出勤、主動接受指導等)對待畢業(yè)設計的態(tài)度較認真，按時完成每周任務，有問題及時向老師請教，與老師進行交流，并虛心接受老師的建議，遵守紀律，按時出勤。質量評價(針對已完成的部分)完成的畢業(yè)設計包括論文及圖紙，設計計算過程均為自己獨立完成。雖然存在一些小問題，但總體來說，設計質量還是可以的，確實認真做了工作。存在問題和解決辦法對圖紙的一些規(guī)定還不熟悉，存在一些問題，但通過一些制圖參考文件的參考能進行改進。對用單片機進行系統(tǒng)控制還無思路，可以去查閱相關資料來自我啟發(fā)。檢查人簽名 教學院長簽名 任 務 書學 院（系）： 專 業(yè) ： 學 生 姓 名： 學 號： 設計(設計) 題目：20米自動伸縮門設計起 迄 日 期 : 指 導 教 師 : 教 研 室 主 任 : 發(fā)任務書日期: 1任 務 書1．設計的背景：本設計所設計的是 20 米自動伸縮門，隨著科技的提高與經濟的發(fā)展，各大、中、小型企事業(yè)單位（包括企業(yè)、研究單位、學校等）的大門口都用上了自動伸縮門。其樣式新穎、美觀、操作方便和功能更多（防盜、在上面顯示通告、遇故自動停止等）。目前，自動門設備大部分依靠進口，國內企業(yè)也開始試制自動門的機電梁系統(tǒng)。1994 年中國建設部 JG/T 3015.1、2—94《推拉自動門》、《平開自動門》發(fā)布，對規(guī)范自動門市場起到了一定的作用。隨著改革開放的加速和國際貿易的擴大，到目前包括日本、歐美等直接進口在內，已有近 70 個品牌的自動門機電梁設備進入中國市場。除推拉門和平開門外，弧形門和旋轉門等各種型號的自動門數量也日益增大，目前年需求量約有 3 萬臺，而且每年以 30%的幅度遞增。2．設計(設計)的內容和要求：內容：1）完成自動伸縮門減速器的設計，確定電動機的類型，計算傳動裝置的運動、動力參數，根據各參數，對各零件做強度校核。確定減速器類型。2）完成鏈傳動設計，確定傳動方案，完成傳動的設計。要求：1) 有關文獻研讀2) 設計說明書 1 份，20000 字，打印裝訂成冊3) 譯文 5000 字4) 利用 AutoCAD 畫圖，圖紙數量折合成零號圖不少于 3 張。3．主要參考文獻：[1] 陳秀寧.主編 .機械設計課程設計，浙江大學出版社，2007[2] 杜白石.機械設計課程設計，西北農業(yè)大學，1993[3] 龔桂義.機械設計課程設計指導書，高等教育出版社 1992[4] 邱宣懷.主編 .機械設計(第四版) ，高等教育出版社，1997[5] 廖林清等 .機械設計方法學，重慶大學出版社，1996.824．設計(設計)進度計劃(以周為單位)：1 周 設計調研2 周 設計調研3 周 總體方案設計4 周 運動動力參數計算5 周 零部件設計計算6 周 總裝配圖繪制7 周 總裝配圖繪制8 周 零部件圖繪制9 周 零部件圖繪制10 周 控制電路設計11 周 外文翻譯12 周 撰寫設計13 周 撰寫設計、準備答辯教研室審查意見：室主任簽名： 2014 年 2 月 21 日學院審查意見：教學院長簽名： 年 月 日 外文翻譯Artificial hip joint學 生 姓 名 班 級 學 院 名 稱 專 業(yè) 名 稱 指 導 教 師 11. IntroductionIt has been recognised by a good number of researchers that the computation of the pressure distribution and contact area of artificial hip joints during daily activities can play a key role in predicting prosthetic implant wear [1], [2], [3] and [4]. The Hertzian contact theory has been considered to evaluate the contact parameters, namely the maximum contact pressure and contact area by using the finite element method [1] and [2]. Mak and his co-workers [1] studied the contact mechanics in ceramic-on-ceramic (CoC) hip implants subjected to micro-separation and it was shown that contact stress increased due to edge loading and it was mainly dependent on the magnitude of cup-liner separation, the radial clearance and the cup inclination angle [3] and [4]. In fact, Hertzian contact theory can captured slope and curvature trends associated with contact patch geometry subjected to the applied load to predict the contact dimensions accurately in edge-loaded ceramic-on-ceramic hips [5]. Although the finite element analysis is a popular approach for investigating contact mechanics, discrete element technique has also been employed to predict contact pressure in hip joints [6]. As computational instability can occur when the contact nodes move near the edges of the contact elements, a contact smoothing approach by applying Gregory patches was suggested [7]. Moreover, the contributions of individual muscles and the effect of different gait patterns on hip contact forces are of interest, which can be determined by using optimisation techniques and inverse dynamic analyses [8] and [9]. In addition, contact stress and local temperature at the contact region of dry-sliding couples during wear tests of CoC femoral heads can experimentally be assessed by applying fluorescence microprobe spectroscopy [10]. The contact pressure distribution on the joint bearing surfaces can be used to determine the heat generated by friction and the volumetric wear of artificial hip joints [11] and [12]. Artificial hip joint moment due to friction and the kinetics of hip implant components may cause prosthetic implant components to loosen, which is one of the main causes of failure of hip replacements. Knee and hip joints' moment values during stair up and sit-to-stand motions can be evaluated computationally [13]. The 2effect of both body-weight-support level and walking speed was investigated on mean peak internal joint moments at ankle, knee and hip [14]. However, in-vivo study of the friction moments acting on the hip demands more research in order to assess whether those findings could be generalised was carried out [15].The hypothesis of the present study is that friction-induced vibration and stick/slip friction could affect maximum contact pressure and moment of artificial hip joints. This desideratum is achieved by developing a multibody dynamic model that is able to cope with the usual difficulties of available models due to the presence of muscles, tendons and ligaments, proposing a simple dynamic body diagram of hip implant. For this purpose, a cross section through the interface of ball, stem and lateral soft and stiff tissues is considered to provide the free body diagram of the hip joint. In this approach, the ball is moving, while the cup is considered to be stationary. Furthermore, the multibody dynamic motion of the ball is formulated, taking the friction-induced vibration and the contact forces developed during the interaction with cup surface. In this study, the model utilises available information of forces acting at the ball centre, as well as angular rotation of the ball as functions of time during a normal walking cycle. Since the rotation angle of the femoral head and their first and second derivatives are known, the equation of angular momentum could be solved to compute external joint moment acting at the ball centre. The nonlinear governing equations of motion are solved by employing the adaptive Runge–Kutta–Fehlberg method, which allows for the discretisation of the time interval of interest. The influence of initial position of ball with respect to cup centre on both maximum contact pressure and the corresponding ball trajectory of hip implants during a normal walking cycle are investigated. Moreover, the effects of clearance size, initial conditions and friction on the system dynamic response are analysed and discussed throughout this work.2. Multibody dynamic model of the artificial hip jointThe multibody dynamic model originaly proposed by Askari et al. [16] has been considered here to address the problem of evaluating the contact pressure and moment of hip implants. A cross section A-A of a generic configuration of a hip joint is depicted in the diagram of in Fig. 1, which represents a total hip replacement. Fig. 1 also shows the head and cup placed inside of the pelvis and separated from stem and 3neck. The forces developed along the interface of the ball and stem are considered to act in such a way that leads to a reaction moment, M. This moment can be determined by satisfying the angular motion of the ball centre during a walking cycle. The available data reported by Bergmann et al. [17] is used to define the forces that act at the ball centre. This data was experimentally obtained by employing a force transducer located inside the hip neck of a live patient. The information provided deals with the angular rotation and forces developed at the hip joint. Thus, the necessary angular velocities and accelerations can be obtained by time differentiating the angular rotation. Besides the 3D nature of the global motion of the hip joint, in the present work a simple 2D approach is presented, which takes into account the most significant hip action, i.e. the flexion-extension motion. With regard to Fig. 2 the translational and rotational equation of motion of the head, for both free flight mode and contact mode, can be written by employing the Newton–Euler's equations [18] and [19], yieldingequation(1)∑MOk=Iθ¨ k,∑MO={Mk ?(Rj)n×FPjtδ0Mkδ≤0equation(2)∑FX=mx¨,∑ FX={fx+(FPjt+FPjn)?iδ0fxδ≤0equation(3)4∑FY=my¨,∑ FY={fy+(FPjn+FPjt)?j?mgδ0fy δ≤0where FPjn and FPjt denote the normal and tangential contact forces developed during the contact between the ball and cup, as it is represented in the diagram of Fig. 3. In Eqs. (1), (2) and (3), x, y and θ are the generalised coordinates used to define the system's configuration. In turn, variable m and I are the mass and moment of inertia of ball, respectively. The external generalised forces are denoted by fx, fy and M and they act at the centre of the ball as it is shown in Fig. 3. The gravitational acceleration is represented by parameter g, Rj is the ball radius and δ represents relative penetration depth between the ball and cup surfaces.Fig. 1. A schematic of the artificial hip implant with the cross section A-A (Left figure), and the head and cup separated from the neck and stem through the cross section A-A (Right figure).Figure options? Download full-size imageDownload high-quality image (142 K)Download as PowerPoint slideFig. 2. A schematic of the head and cup interaction observed in the Sagittal plane.Figure options6? Download full-size imageDownload high-quality image (87 K)Download as PowerPoint slideFig. 3. Free body diagram of ball and corresponding external, internal and body forces and moment.Figure options? Download full-size imageDownload high-quality image (87 K)Download as PowerPoint slideTheDownload as PowerPoint slideThe penetration depth can be expressed as [20]equation(4)δ=r?(Rb?Rj)δ=r?(Rb? Rj)in which Rb denotes the cup radius and (Rb?Rj) represents the joint radial clearance, which is a parameter specified by user.In the present study, the cup is assumed to be stationary, while the head describes the global motion. With regard to Fig. 2, it can be observed that Oj and Ob denote the head and cup centres, respectively. While Pj and Pb represent the contact points on the head and cup, respectively. The magnitude and orientation of the clearance vector are denoted by r and α, respectively. In general, r and α can be expressed as 7functions of the generalised coordinates used to describe the configuration of multibody mechanical system. The normal and tangential unit vectors at the contact point can be written asequation(5)n=cosαi+sinαjequation(6)t=?sinαi+cos αjIn order to compute the normal contact and tangential forces, it is first necessary to evaluate the relative tangential and normal velocities at the contact points, which can be obtained as follows: [17]equation(7)vpj/pb=?n+(rα+Rjωj)t=vnn+vttwhere vnvn and vtvt are module of the normal and tangential velocities, respectively. Thus, Eqs. (2) and (3) can be re-written as follows:equation(8)[m00m][x¨y¨]=[∑FX∑FY]8Using now the concept of the state space representation, the second order equations of motion (8), can be expressed as a first order equation set asequation(9)?=H(z)where z=[z1z2z3z4]=[xy??] and H(z)H(z) is expressed as follows:equation(10)?=[?1?2?3?4]=[z3z4∑FX(z) ∑FY(z)]It must be mentioned that the r, α and their time derivatives can be obtained with respect to state space parameters as follows:equation(11)α=atan(z2z1)equation(12)r=z12+z22equation(13)α= ?z2z3+z1z4z12+z22z12equation(14)?=z1z3+z2z4z12+z22It is known that the evaluation of the contact forces developed during an impact event plays a crucial role in the dynamic analysis of mechanical systems [21], [22] and [23]. The contact forces must be computed by using a suitable constitutive law that takes into account material properties of the contacting bodies, the geometric characteristics of impacting surfaces and impact velocity. Additionally, the numerical approach for the calculation of the contact forces should be stable in order to allow for the integration of the mechanical systems equations of motion [24]. Different constitutive laws are suggested in the literature, being one of the more prominent proposed by Hertz [25]. However, this law is purely elastic in nature and cannot explain the energy loss during the impact process. Thus, Lankarani and Nikravesh [26] overcame this difficulty by separating the contact force into elastic and dissipative components asequation(15)Fpjn=(Kδn+D δ)n10Regarding Lankarani and Nikravesh model, normal contact force on the head is expressed asequation(16)Fpjn=?Kδ3/2(1+3(1?ce2)4δδ(?))nwhere δ and δ(?) are the relative penetration velocity and the initial impact velocity, respectively, and ce is the coefficient of restitution. The generalised stiffness parameter K depends on the geometry and physical properties of the contacting surfaces, which for two internal spherical contacting bodies with radii Ri and Rj can be expressed as [25]equation(17)K=43(σi+σj)(RiRjRi? Rj)2in which the material properties σiσi and σjσj are given byequation(18)σz=1? υz2Ez11At this stage, it must be said the use of Eq. (15) is limited by Love's criterion, that is, it is only valid for impact velocities lower than the propagation velocity of elastic waves across the solids [27].It is known that the way in which the friction phenomena are modelled, plays a key role in the systems behaviour [28]. In the present study, the tangential friction force are evaluated by using a modified Coulomb friction law, which can be expressed as [29] and [30]equation(19)Fpjt=?μ(vt)||Fpjn||vt|vt|tThe friction force is described in the sense of Coulomb's approach, and is proportional to the magnitude of the normal force developed at the contact points, where the ratio is the coefficient of friction, μ, which is dependent on the relative tangential velocity. The model considered in reference [17] is employed here for the purpose of evaluating the coefficient of friction, which can be written asequation(20)μ(vt)={(?cfv02(|vt|?v0)2+cf)sgn(vt),|vt|Fig. 4. Stribeck characteristic for dry friction.Figure options? Download full-size imageDownload high-quality image (102 K)Download as PowerPoint slideNormal and tangential forces described above are present if the system isin contact situation, which means detecting impact or contact is one important step. Moreover, to compute the contact force, the initial impact velocity has to be calculated as an initial condition for following regimes, which could be in contact or in free flight, the following condition should be checked during the solution process by progressing time. Therefore, a contact event is detected when the following condition is verifiedequation(21)δ(ti)0Indeed, the precise instant in which the phase changes from free flight to contact is of paramount important instant because initial conditions for the next dynamic scenario are provided from exactly this instant [31].3. Computing quasi-static and dynamic maximum contact pressuresFor the CoC hip implants used nowadays, with 5, 3 and 2 mm thick ceramic insert, it has been demonstrated that the radius of the contact area between the femoral head and the acetabular cup is relatively small compared with that of the femoral head and the ceramic insert thickness. Therefore, the Hertzian contact theory can be utilised to estimate the contact parameters such as the maximum contact pressure and the contact area [1]. Hertzian contact theory can also be considered to evaluate contact pressures in CoC hip arthroplasty even though the ball is in contact with the cup as edge loading in CoC hip arthroplasty [5]. When the system is in edge-loading, the contact area is no longer circle but ellipse [4] and [5]. In the present study, contact pressure and contact area are determined using two different approaches, namely quasi-statics and dynamics.Assuming that the cup and head held in contact by a force F, as it is shown in Fig. 5, such that their point of contact expands into a circular area of radius a, [32]equation(22)a=KaF3whereequation(23)Ka=(34(1?υ12/E1)+(1? υ22/E2)(1/Rj ?1/Rb))1/314in which υ1 υ1, E1E1 and υ2υ2, E2E2 are Poisson's ratios and elastic modulii for the ball and cup, respectively. The maximum contact pressure occurs at the centre point of the contact area and can be calculated asequation(24)Pmax=3F2πa2Fig. 5. Head and cup held in contact by a force F.Figure options? Download full-size imageDownload high-quality image (73 K)Download as PowerPoint slideThe15The local coordinate system (XYZ) is located at the centre point of the contact area as it is illustrated in Fig. 1. Since the coordinate system is defined as a local system, the tangential stresses can expressed as [32]equation(25)σXZ=?μ(vt)vt|vt|limY→0σY=Pmax μ(vt)vt|vt|For an element close to the contact point, when Y approaches zero, the principal stresses are written asequation(26)σ1=?Pmax,σ2= ?Pmax(υ+0.5+μ(vt)) σ3=?Pmax(υ+0.5?μ(υt))If (υ+μ(vt))0.5( υ+ μ(vt))0.5 so that σmax= ?Pmax(υ+0.5+ μ (vt))σmax=? Pmax(υ+0.5+μ(vt)) if (υ+ μ(vt))≤0.5(υ+μ(vt))≤0.5 so that σmax= ?Pmaxσmax=?Pmax.Normal contact force, Eq. (16), is calculated as a function of time, solving resultant equations of multibody dynamic system. This normal contact force is substituted into Eqs. (22) and (24) to determine contact pressure distribution and contact area in ceramic-on-ceramic hip implants dynamically. To acquire quasi-static results, external normal contact loads (F) based on ISO14242-1 testing standard are introduced into Eqs. (22) and (24). These two approaches allows for the comparison between dynamic and quasi-static situations. Therefore, it is convenient to define a parameter, dif., that conveys the difference between quasi-static and dynamic results of maximum contact pressures. Projection of the governing motion equations, Eq. (8), on the normal direction vector n provides the ball motion equation in normal direction asequation(27)16mδ¨=fxcos α +(fy?mg)sinα?FPjn=fext,n?fcont,nwhere δ¨ denotes the indentation acceleration. Substituting contact area from Eq. (22), normal contact force computed from Eq. (15) and normal contact force from ISO 14242-1 testing standard into Eq. (24), then, the difference between the cube of maximum contact pressures computed from quasi-static analysis and dynamic analysis can be evaluated as follows:equation(28)dif.=σmax,qs3?σmax,d3=278π3ka6m δ¨The angular acceleration of femoral head can be calculated as the derivative of the ball angular velocity during a normal walking cycle. An external moment, M, which acts on the ball centre is required to cause hip implant to rotate with the known angular acceleration during a corresponding activity cycle. Therefore, the angular momentum, Eq. (1), has to be solved to obtain the external moment as follows:equation(29)Mk={Iθ¨k+(Rj)n×FPjtδ0Iθ¨kδ≤0174. Description of numerical model utilisedIt is known that the resultant equations of multibody dynamic models for hip implants, Eq. (9), are nonlinear and must be solved by using numerical method. Thus, in the present work, an adaptive Runge–Kutta–Fehlberg method is considered to discretise the interval of time of analysis. An error threshold is defined. The error magnitude is calculated by comparing results obtained from explicit method with different orders. If the error magnitude is greater than the error threshold, the time step, h, must be halved and computation is done again in order to acquire accurate and stable outcomes. In the present study, the angular velocity around the flexion/extension direction z, ωj, together with the force in the vertical direction, fy, are considered. Vertical load and angular velocity are illustrated according to ISO14242-1 in Fig. 6 and Fig. 7, respectively. The geometrical and material properties of the head and cup are listed in Table 1. Moreover, integration step sizes for free flight and contact modes are assumed to be 0.00001 s and 0.0000001 s, respectively, being the corresponding integration tolerances 0.000001 and 0.00000001.Fig. 6. The vertical load during a normal walking cycle based on ISO14242-1 testing standard [33] and [34].18Figure options? Download full-size imageDownload high-quality image (83 K)Download as PowerPoint slideFig. 7. (a) Rotation angle of ball; (b) The corresponding angular velocity based on ISO14242-1 testing standard.Figure options? Download full-size imageDownload high-quality image (124 K)Download as PowerPoint slideTable 1. Material and geometrical characteristics of the artificial hip joints.Clearance size [mm] 0.05Ceramic density [kg/m3] 4370Young modulus (cup-head) [GPa] 3.58e11Poisson's ratio [?] 0.2319Restitution coefficient [?] 0.9Friction coefficients (Cf/Cd) [?] 0.15/0.15. Results and discussionThe comparison of maximum contact pressure and contact area outcomes between the multibody dynamic model and the quasi-static approaches are listed in Table 2. The data reported is for different radial clearances and cup radii, and it shows a good agreement between both methodologies. The data is relative to a cycle of 0.11 s, which corresponds to maximum external force, 3 kN, initial normal distance between head and cup is 0.0001 mm.Table 2. Comparison of the predicted maximum contact pressure and contact area between the present multibody dynamic study and quasi-static approach.Cup radius (mm)Radial clearance (μm)Maximum contact pressure (MPa)Contact area (mm2)Multibody dynamic approachQuasi-static approachMultibody dynamic approachQuasi-static approach14 50 110.31 110.77 40.29 40.6316 50 92.29 92.68 48.14 48.5620 30 48.77 48.97 91.12 91.8920 50 68.50 68.80 64.87 65.4120 100 108.58 109.03 40.94 41.2725 50 50.87 51.07 87.37 88.10Full-size tableTable optionsView in workspaceDownload as CSV205.1. Effect of ball initial condition on hip implant maximum contact pressure and momentThe influence of the initial conditions on contact pressure developed in hip implants is depicted in Fig. 8. Initial ball position can be associated either with the separation of the head and cup at the start phase or with the likely start phase, in which fluid-film lubrication