餃子機(jī)及輸送成型部件設(shè)計(jì)【包餃子機(jī)】,包餃子機(jī),餃子機(jī)及輸送成型部件設(shè)計(jì)【包餃子機(jī)】,餃子機(jī),輸送,成型,部件,設(shè)計(jì) 編號 無錫太湖學(xué)院 畢業(yè)設(shè)計(jì)（論文） 相關(guān)資料 題目： 餃子機(jī)及輸送成型部件設(shè)計(jì) 信機(jī) 系 機(jī)械工程及自動化專業(yè) 學(xué) 號： 　　　　　　 學(xué)生姓名： 指導(dǎo)教師： 　 （職稱：副教授 ） （職稱： ） 2013年5月25日 目 錄 一、畢業(yè)設(shè)計(jì)（論文）開題報(bào)告 二、畢業(yè)設(shè)計(jì)（論文）外文資料翻譯及原文 三、學(xué)生“畢業(yè)論文（論文）計(jì)劃、進(jìn)度、檢查及落實(shí)表” 四、實(shí)習(xí)鑒定表 無錫太湖學(xué)院 畢業(yè)設(shè)計(jì)（論文） 開題報(bào)告 題目： 餃子機(jī)及輸送成型部件設(shè)計(jì) 信機(jī) 系 機(jī)械工程及自動化 專業(yè) 學(xué) 號： 學(xué)生姓名： 指導(dǎo)教師： 戴寧 （職稱：副教授 ） （職稱： ） 2012年11月25日 課題來源 自擬題目 科學(xué)依據(jù)（包括課題的科學(xué)意義；國內(nèi)外研究概況、水平和發(fā)展趨勢；應(yīng)用前景等） （1）課題科學(xué)意義 餃子食品機(jī)械的應(yīng)用前景和發(fā)展現(xiàn)狀 餃子食品在我國歷史悠久，伴隨著幾千年的文明的發(fā)展已經(jīng)成為我國食品文化中的代表，如餃子、包子、餛飩是主食的一部分；湯圓、月餅、粽子是傳統(tǒng)節(jié)日中必不可缺的食物。如今，經(jīng)濟(jì)的迅速增長、人民生活水平的提高和生活節(jié)奏的加快，對食品行業(yè)提出了新的要求。而本人認(rèn)為這些要求可以歸納為兩大類： 其一是食品的質(zhì)量：如食用口感、衛(wèi)生狀況、營養(yǎng)含量等。 其二便是食品供應(yīng)的速度。 而解決這兩個(gè)矛盾要求的辦法便是實(shí)現(xiàn)食品生產(chǎn)的機(jī)械化和自動化， 通過機(jī)械動作可以極大程度的提高食品的生產(chǎn)率； 采用環(huán)保的機(jī)械材料和嚴(yán)格的密封技術(shù)可以很好的保證食品衛(wèi)生；而合理的工藝編排更能改善食品的口感。 （2）餃子機(jī)的研究狀況及其發(fā)展前景 目前國內(nèi)外廠家在包餡夾餡食品機(jī)械化上的研究已經(jīng)取得了一定的成果成功研發(fā)了餃子機(jī)、包子機(jī)、餛飩機(jī)、湯圓機(jī)、月餅機(jī)以及自動化程度更高的全自動萬能包餡機(jī)。 因東西方飲食文化的差異， 目前國外包餡成型類機(jī)械主要為日本所生產(chǎn)，如日產(chǎn)的自動萬能包餡機(jī)，其最大生產(chǎn)能力可達(dá)每小時(shí) 8000 個(gè)，且加工范圍極廣，能生產(chǎn)各式饅頭、包子、餃子、夾餡餅干、壽司、等等近百種產(chǎn)品，采用可拆卸料斗能實(shí)現(xiàn)快速更換餡料，內(nèi)置的無級變速調(diào)控裝置可以實(shí)現(xiàn)皮和餡的任意配比。廣泛用于各種帶餡食品的加工。 而國內(nèi)相關(guān)機(jī)械雖然在自動化和多功能方面較之日本產(chǎn)品還有一定的差距， 但是通過改革開放以后二十余年的發(fā)展亦取得了很大的進(jìn)步。 以上海滬信飲料食品機(jī)械有限公司生產(chǎn)的水餃機(jī)為例：配備 1.1Kw 的電動機(jī)，生產(chǎn)效率達(dá)每小時(shí) 7000 個(gè)。已相當(dāng)接近日產(chǎn)餃子機(jī)的生產(chǎn)水平。 每逢過年過節(jié)現(xiàn)做現(xiàn)賣餃子往往出現(xiàn)供不應(yīng)求的現(xiàn)象。當(dāng)然也有很多人選擇在家里自己做餃子，卻需要提前半天甚至一天進(jìn)行準(zhǔn)備，而包餃子的時(shí)候更是要叫上好幾個(gè)親朋過來幫忙方可。 因此如果能研究開發(fā)一種能夠以機(jī)械動作代替人工勞動的機(jī)器， 那么除了可以節(jié)約大量的時(shí)間、降低餃子的生產(chǎn)成本、提高利潤之外，更可以免除人們冬日里冒寒排隊(duì)購物之苦，一舉多得。餃子生產(chǎn)機(jī)的初步目標(biāo)確定為能夠?qū)崿F(xiàn)　子包餡工藝的機(jī)械化。 未來可在此基礎(chǔ)上加以改進(jìn)和擴(kuò)展，以實(shí)現(xiàn)橫縱兩方向發(fā)展，即餃子生產(chǎn)全過程的無人干預(yù)自動化與多功能化 研究內(nèi)容 ① 熟悉餃子機(jī)的工作原理與結(jié)構(gòu)； ② 熟悉餃子機(jī)輸送成型部件的布置與結(jié)構(gòu)； ③ 熟練掌握絞龍、葉片泵的設(shè)計(jì)計(jì)算方法； ④ 掌握ＣＡＤ的使用方法。 擬采取的研究方法、技術(shù)路線、實(shí)驗(yàn)方案及可行性分析 （1）實(shí)驗(yàn)方案 對餃子機(jī)的整體的設(shè)計(jì)，確定面料和餡料的輸送方式與設(shè)備結(jié)構(gòu)，確定餃子成型方式，使其能夠半自動的進(jìn)行加工。 （2）研究方法 ① 用ＣＡＤ進(jìn)行二維畫圖，對餃子機(jī)結(jié)構(gòu)有個(gè)全面的了解。 ② 對餃子機(jī)的輸送成型部分進(jìn)行計(jì)算與結(jié)構(gòu)設(shè)計(jì)，使其滿足物料的輸送要求，并加工出合適形狀的餃子。 研究計(jì)劃及預(yù)期成果 研究計(jì)劃： 2012年10月12日-2012年12月31日：按照任務(wù)書要求查閱論文相關(guān)參考資料，完成畢業(yè)設(shè)計(jì)開題報(bào)告書。 2013年1月1日-2013年1月27日：學(xué)習(xí)并翻譯一篇與畢業(yè)設(shè)計(jì)相關(guān)的英文材料。 2013年1月28日-2013年3月3日：畢業(yè)實(shí)習(xí)。 2013年3月4日-2013年3月31日：餃子機(jī)輸送和成型部件設(shè)計(jì)。 2013年4月1日-2013年4月14日：餃子機(jī)總體結(jié)構(gòu)設(shè)計(jì)。 2013年4月15日-2013年4月28日：部件圖和零件圖設(shè)計(jì)。 2013年4月29日-2013年5月21日：畢業(yè)論文撰寫和修改工作。 預(yù)期成果： 達(dá)到預(yù)期的畢業(yè)設(shè)計(jì)要求，設(shè)計(jì)出的餃子機(jī)可以進(jìn)行半自動加工，可以快速美觀的加工出餃子，并且輸送穩(wěn)定有效、成型簡單、滿足工作要求。 特色或創(chuàng)新之處 ①餃子機(jī)可以無需手工進(jìn)行制作。 ② 餃子制作過程安全，方便，快速，可以批量生產(chǎn)。 已具備的條件和尚需解決的問題 ① 設(shè)計(jì)方案思路已經(jīng)明確，已經(jīng)具備機(jī)械設(shè)計(jì)能力和餃子機(jī)方面的知識。 ② 進(jìn)行結(jié)構(gòu)設(shè)計(jì)的能力尚需加強(qiáng)。 指導(dǎo)教師意見 指導(dǎo)教師簽名： 年 月 日 教研室（學(xué)科組、研究所）意見 教研室主任簽名： 年 月 日 系意見 主管領(lǐng)導(dǎo)簽名： 年 月 日 英文原文 Case Study Theoretical and practical aspects of the wear of vane pumps Part A. Adaptation of a model for predictive wear calculation Abstract The aim of this investigation is the development of a mathematical tool for predicting the wear behaviour of vane pumps uscd in the standard method for indicating the wcar charactcristics of hydraulic fluids according to ASTM D 2882/DIN 51 389. The derivation of the corresponding mathematical algorithm is based on the description of the combined abrasive and adhesive wear phenomena occurring on the ring and vanes of the pump by the shear energy hypothesis, in connection with stochastic modelling of the contacting rough surfaces as two-dimensional isotropic random fields. Starting from a comprehensive analysis of the decisive ring-vane tribo contact, which supplies essential input data for the wear calculation, the computational method is adapted to the concrete geometrical, motional and loading conditions of thetribo system vane pump and extended by inclusion of partial elastohydrodynamic lubrication in the mathematical modej. For comparison of the calculated wear behaviour with expenmental results, a test series on a rig described in Part B was carried out. A mineral oil-based lubricant without any additives was used to exclude the influence of additives which cannot be described in the mathematical model. A good qualitative correspondence between calculation and experiment regarding the temporal wear progress and the amount of calculated wear mass was achieved. Keywords: Mathematical modelling; Simulation of wear mechanisms; Wear testing devices; Hydraulic vane pumps; Elastohydrodynamic lubrication; Surface roughness 1. Introduction In this study, the preliminary results of a newmethodological approach to the development of tribo- meters for complicated tribo sysLems are presented. The basic concept involves the derivation of a mathematical algofithm for wear calculation in an interactive process with experiments, which can be used model of the tribo system to be simulated. In this way, an additional design tool to achieve the correlation of the wear rates of the model and original system is created. The investigations are performed for the Vickers vane pump V104 C usedin the standard method forindicating the wear characteristics of hydraulic fluids according to ASTM D 2882/DIN 51 389. In a first step, a mathematical theory based on the description of abrasive and adhesive wear phenomena by the shear energy hypothesis, and including stochastic modelling of the contacting rough surfaces, is adapted to the tribological reality of the vane pump, extended by aspects of partial elastohydrodynamic lubrication and verified by corresponding experiments. Part A of this study is devoted to the mathematical modelling of the wear behaviour of the vane pump and to the verification of the resulting algorithm; experimental wear investigations represent the focal point of Part B, and these are compared with the results of the computational method derived in Part A. 2. Analysis of the tribo contact The Vickers vane pump V 104 C is constructed as a pump for constant volume flow per revolution. The system pressure is led to the bottom side of the 12 vanes in the rotor slots to seal the cells formed by each pair of vanes, the ring, the rotor and the bushings in the tribologically interesting line contact of the vane and inner curvature of the ring (Fig. 1). Simultaneously, all other vane sides are stressed with different and periodically alternating pressures of the fiuid. A comprehensive structure and stress analysis based on quasistatic modelling of all inertial forces acting on the pump, and considering the inner curvature of the ring, the swivel motion of the vanes in relation to the tangent of curvature and the loading assumptions, is described in Refs. [1-3]. Thereby, a characteristic graph for the contact force Fe as a function of the turn angle can be obtained, which depends on the geometry of the vanes used in each run and the system pressure. From this, the inner curvature of the ring can be divided into four zones of different loading conditions in vane-ring tribo contact (Fig. 2), which is in good agreement with the wear measurements on the rings: in the area of maximum contact force (zone n), the highest linear wear could be found [2,3] (see also Part B). 3. Mathematical modelling 3.1. Basic relations for wear calculation The vane and ring show combined abrasive and adhesive wear phenomena (Fig. 3). The basic concepts of the theory for the predictive calculation of such wear phenomena are described in Refs. [4-6]. Starting from the assumption that wear is caused by shear effects in the surface regions of contacting bodies in relative motion, the fundamental equation (1) for the linear wear intensity Ih in the stationary wear state can be derived, which contains the specific shear energy density es/ro, interpretable as a material constant, and the real areaArs of the asperity contacts undergoing shear. To determine this real contact area, the de- scription of the contacting rough surfaces as two-dimensional isotropic gaussian fields according to Ref. [7] is included in the modelling. Thus the implicit functional relation with the weight function (2) is found, which can be used to calculate the surface ratio in Eq. (1) for unlubricated contacts from the hertzian pressure Pa acting in the investigated tribo contact by a complicated iterative process described in Refs. [6,8]. The concrete structure of the functions F and c depends on the relative motion of the contacting bodies (sliding, rolling). The parameter a- （m0m4）/m22represents the properties of the rough surface by its spectral moments, which can be deter- mined statistically from surface profilometry, and the plasticity index妒= (mOm4)y4(E'/H) is a measure of the ratio of elastic and plastic microcontacts. 3.2. Extension to lubricated contacts The algorithm resulting from the basic relations for wear calculation was applied successfully to unlubricated tribo systems [8]. The first concepts for involving lubrication in the mathematical model are developed in Ref. [8]. They are based on the application of the classical theory of elastohydrodynamic lubrication (EHL) to the microcontacts of the asperities, neglecting the fact that there is also a "macrolubrication film" which separates the contacting bodies and is interrupted in the case of partial lubrication by the asperity microcontacts. Therefore their use for calculating practical wear problems leads to unsatisfactory results [9]. They are extended here by including the following assump- tions in the mathematical model. (1) Lubrication causes the separation of contacting bodies by a macrofilm with a mean thickness u. which can be expressed in terms of the surface roughness by [10] (3) Where u0 is the mean film thinkness according to classical EHL theory between two ideally smooth bodies, which can be determined for line contact of the vane and ring by[11] (2) In the case of partial lubrication, the macrofilm is interrupted during asperity contacts. A plastic microcontact is interpreted as a pure solid state contact, whereas for an elastic contact the roughness is superimposed by a microlubrication film. Because of the modelling of the asperities as spherical indenters, the microfilm thickness can be determined using the EHL theory for sphere-plane contacts, which is represented in the random model by the sliding number [8] (5) (3) The hertzian pressure acting in the macrocontact works in two parts: as a hydrodynamic pressure pEH borne by the macrolubrication film and as a pressure pFK borne by the roughness in solid body contact. (4) For pure solid state contacts, it is assumed that the limit for the mean real pressure prFK which an asperity can resist without plastic deformation can be estimated by one-fifth to one-sixth of its hardness (6) Investigations on the contact stiffness in Ref. [11] have led to the conclusion that the elastic properties of the lubrication film cause a relief of the asperities, which means that the real pressure working on the asperity is damped. Therefore, in the mathematical model for lubricated tribo systems, an additional term fffin, which corrects the upper limit of the real pressure as a function of the film thickness, is introduced p,EH =prFK[1 -fcorr(U)] (7) This formula can be used to determine a modified plasticity index {PEH for lubricated contacts according to Ref. [8]. Altogether, the basic model for wear calculation can be extended for lubricated tribo systems by replacing relation (2) by (8) (3)3.3. Adaptation to the tribo’system vane pump To apply the mathematical model for wear calculation to a concrete tribo system, all material data (specific material and fluid properties, roughness parameters) used by the algorithm must be determined (see Part B). Moreover, the model must be adapted to the mechanical conditions of the wear process investigated. On the one hand, this is related to the relative motion of the bodies in tribo contact, which influences the concrete structure of function f in formulae (2) and (8). In the case of vane-ring contact, sliding with superimposed rolling due to the swivel motion of the vanes was modelled (9) A detailed derivation of the corresponding formulae for fsliding and f.olling can be found in Refs. [8,9]. On the other hand, the hertzian presstire Pa acting on tribo contact during the wear process has an esseritial importance in the wear calculation. For the tribo system vane pump, the mean contact force Fe in each loading zone can be regarded as constant, whereas the hertzian pressure decreases with time. The reason for this is the wear debris on the vane, which causes a change 'n the vane tip shape with time,leading to an increased contact radius and, accordingly, a larger contact area To describe this phenomenon by the mathematical wear model, the volume removal Wvl of one vane in terms of the respective contact radius Ri(t) at time t and the sliding distance SR(Rl(t》 is given by (10) where the constants a and b can be determined by regression from the geometrical data of the tested vanes. The corresponding sliding distance necessary to reach a certain radius Ri due to vane wear can be expressed using the basic equation (1): (11) Thus, applying Eq. (11) together with Eq. (10) to the relation (12) it is possible to derive the following differential equation for the respective volume removal Wvll of the ring, which can be solved by a numerical procedure (13) The required wear intensities of the vane and ring can be calculated by Eq. (8) as a function of the contact radius from the hertzian pressures working in each loading zone, which are available from the contact force by the well-known hertzian formulae. 3.4 Possibilities of verification If all input data are available for a concrete vane pump run (the concrete geometrical, material and mechanical conditions in the cartridge used and the specific fluid properties, see Part B), the mathematical model for the calculation of the wear of vane pumps derived above can describe quantitatively the following relations. (1) The sliding distance SR(RI) and, if the number of revolutions of the pump and the size of the inner ring surface are known, the respective run time t of the pump which is necessary to reach a certain shape of the vane tips due to wear. (2) The volume removal W,.:uri(t) and the wear masses WmW(t) of the vane and ring as a function of the run time t. (3) The mean local linear wear Wl(t) in every loading zone on the ring at time t. Thus an immediate comparison between the calculated and experimentally established wear behaviour, with regard to the wear progress in time, the local wear progress on the ring and the wear masses at a certain time t, becomes possible. 4。Results In this study, the verification of the theoretical results obtained by comparison with experiments is based on a test series on a rig according to DIN 51 389 described in detail in Part B. The same mineral oil-based lubricant, without any additives, was used in each run to exclude the influence of additives on the wear behaviour, which could not be described in the mathematical model. As input data for the calculation, the mean values of all the quantities needed by the algorithm were determined from four 250 h test runs which were carried out under equivalent test conditions. The following results were obtained. (1) The calculated temporal wear curve for the vanes, resulting from approximation (9), is in good qualitative agreement w:ith the measurements in Ref. [2] (degressive character and length of the inlet phase (see Part B》. Moreover, the calculated wear masses after a run time of 250 h correspond quantitatively with the experimental results (Fig. 5). (2) For the ring, a degressrve wear trend was found by calculation, which is assumed to be a realistic result in association with the corresponding degressive trend of vane wear experimentally established in Ref. [2]. The calculated total wear masses, which represent the sum of the wear masses achieved in each loading zone at time t, conform with the wear masses measured in 250 h runs as well as short-time runs of 10 h (Fig. 6). (3) The wear masses calculated for each separate loading zone on the ring are in quantitative agreement with the corresponding order of the contact force Fe (Fig. 6). (4) The dependence of the wear behaviour on temperature during tribo contact, represented in the mathematical model by the dependence of thelubricant properties on temperature, is suitably reflected by the calculation (Fig. 7). Further results, especially with regard to a comparison of the calculated and measured local linear wear on the ring, are dcscribcd in Part B. 5. Conclusions The mathematical algorithm for the calculation of wear on vane pumps presented in this study enables the experimentally established wear behaviour of the tribo system investigated to be retraced qualitatively and quantitatively. Thus the extensions introduced to cover partial elastohydrodynamic lubrication have proved a success and represent an essential improvement of the results achieved so far [9]. In this way, the preconditions for the development of a mathematical tool for wear prediction and for simulation of the wear behaviour of a tribometer for the tribo system vane pump have been created. For further qualification of the mathematical model to achieve a real forecast of the wear behaviour, theoretical investigations combined with experiments must be enforced, espeaally with regard to the following topics: (1) inclusion of the inlet phase of the wear process in the model (so far, the mathematical modelis related only to the stationary wear state; an algorithm must be created which is based exclusively on the input data obtainable before starting the wear process and which can successively adapt the data used by the calculation to real wear progress); (2) extension of the model to practically important lubricants with additives (this can be achieved in a first step by using a heuristic relation to describe the influence of additives on the wear behaviour, derived from corresponding test ScrieS with scVeral lubricants). 中文譯文 在理論和實(shí)踐方面葉片泵磨損的研究（A部分）:為適應(yīng)預(yù)測磨損計(jì)算模型 R. Gellrich a, A. Kunz b, G. Beckmann ‘, E. Broszeit b a大學(xué)科技，經(jīng)濟(jì)和社會科學(xué)Zittaul/Gorlitz，數(shù)學(xué)和自然科學(xué)學(xué)院，Th.- Kiirner-阿利16處， 02763齊陶，德國 b材料科學(xué)研究所，達(dá)姆施塔特技術(shù)大學(xué)，Grafenstr。二，64283達(dá)姆施塔特，GermanyPetersilienshz二維，03044科特布斯，德國 1994年3月29日收到，1994年11月1日接受 摘要 本次調(diào)查的目標(biāo)是預(yù)測用于判斷液壓流體的磨損特性的葉片泵的磨損行為的一種數(shù)學(xué)工具的發(fā)展，根據(jù)ASTM D 2882/DIN 51標(biāo)準(zhǔn)方法389。 相應(yīng)的數(shù)學(xué)算法的推導(dǎo)是基于合并后的描述和磨料粘著磨損現(xiàn)象發(fā)生在環(huán)和假說的剪切能在葉片泵連接，與隨機(jī)建模為二維各向同性隨機(jī)粗糙表面接觸領(lǐng)域。 從環(huán)葉片摩擦接觸的決定性全面分析開始，為磨損計(jì)算，適應(yīng)具體的幾何，運(yùn)動和摩擦系統(tǒng)葉片泵的負(fù)荷條件，被部分彈流潤滑延長列入數(shù)學(xué)模型的計(jì)算方法提供了必要的輸入數(shù)據(jù)。 對于磨損性能的計(jì)算與試驗(yàn)結(jié)果的比較，對鉆機(jī)的一系列測試在B部分的敘述中會提出。不含任何添加劑的礦物油基潤滑劑，采用排除添加劑的影響，不能在數(shù)學(xué)模型描述出來。在計(jì)算和實(shí)驗(yàn)之間的一個(gè)良好的定性關(guān)系隨著時(shí)間磨損過程和計(jì)算磨損質(zhì)量的量達(dá)到了。 關(guān)鍵詞：數(shù)學(xué)模型 ;磨損機(jī)理模擬;磨損試驗(yàn)裝置，液壓葉片泵;彈流潤滑;表面粗糙度 1. 簡介 在這項(xiàng)研究中，對于復(fù)雜的摩擦系統(tǒng)摩擦計(jì)的發(fā)展的一種新的方法的初步結(jié)果被提出來了。這個(gè)基本概念涉及到一個(gè)在實(shí)驗(yàn)的相互影響的過程中的的磨損計(jì)算的數(shù)學(xué)算法的起源，它可用于預(yù)測的摩擦磨損性能系統(tǒng)的力學(xué)模型可以模擬互動的過程推導(dǎo)。這樣，一個(gè)額外的設(shè)計(jì)工具，實(shí)現(xiàn)了模型和原系統(tǒng)的磨損率的相關(guān)性創(chuàng)建。調(diào)查是執(zhí)行了用于判斷按照美國ASTM 2882/DIN 51 389 D型液壓流體的磨損特性威格士葉片泵V 104的標(biāo)準(zhǔn)方法。在第一個(gè)步驟，一個(gè)以磨料和粘結(jié)磨損現(xiàn)象的描述剪能量假說為基礎(chǔ)，包括隨機(jī)粗糙表面接觸模型的數(shù)學(xué)理論，是適應(yīng)了現(xiàn)實(shí)的葉片泵摩擦磨損，延長了部分問題彈流潤滑和相應(yīng)的實(shí)驗(yàn)驗(yàn)證。 這項(xiàng)研究的一個(gè)部分是專門用來對葉片泵的磨損行為的數(shù)學(xué)模型，并由此產(chǎn)生的算法驗(yàn)證; 實(shí)驗(yàn)?zāi)p調(diào)查代表了B部分的焦點(diǎn)，這些都是與計(jì)算方法和在A部分所得結(jié)果進(jìn)行比較 2．分析部落接觸 威格士葉片泵V 104C是一個(gè)每轉(zhuǎn)流量不變的泵。系統(tǒng)壓力導(dǎo)致了在轉(zhuǎn) 子槽12個(gè)葉片的底部來封住由每一個(gè)葉片 環(huán) 槽盒和葉片的線接觸和環(huán)的內(nèi)部彎曲組成的單元。同時(shí)，所有其他的不同的和定期交變的流體壓力葉片面也都被強(qiáng)調(diào)了。一個(gè)在泵慣性力作用的所有準(zhǔn)靜態(tài)建模，考慮到環(huán)內(nèi)曲率，和切線曲率和裝載假設(shè)相關(guān)的葉片旋轉(zhuǎn)運(yùn)動在文獻(xiàn)中有描述，從接觸力F的特征圖上，作為轉(zhuǎn)角度的功能可以得到，這由每次運(yùn)行和系統(tǒng)壓力所使用的葉片幾何形狀而 定。由此可見，環(huán)內(nèi)彎曲可分為葉片環(huán)摩擦接觸（圖2） 這與上環(huán)的磨損測量吻合分為四種不同的負(fù)荷條件區(qū)：在最大接觸面積部分（第二區(qū)），最高的線性磨損可以發(fā)現(xiàn)[2,3]（見B部分） 3．?dāng)?shù)學(xué)建模 3.1．磨損計(jì)算基本關(guān)系 葉片和環(huán)形顯示聯(lián)合磨料和粘結(jié)磨損現(xiàn)象（圖3）。預(yù)測磨損計(jì)算現(xiàn)象的理論的基本概念在文獻(xiàn)中有描述。 【4-6】。從磨損是由在具有相對運(yùn)動的接觸表面的高剪切效應(yīng)引起的這個(gè)假設(shè)開始，基本方程如下：（1） 在靜態(tài)磨損狀況中的線性方程組的磨損強(qiáng)度I可以得到，，其中包含具體的剪能量密度，可作為材料常數(shù)解釋，和真正的A區(qū)粗糙的接觸發(fā)生型剪切，為了確定 這個(gè)實(shí)際的接觸面積，作為二維的基礎(chǔ)粗糙表面的描述根據(jù)文獻(xiàn)中的高斯領(lǐng)域。[7]是包含在建模。因此，隱函數(shù)關(guān)系 被發(fā)現(xiàn)，它可以用來計(jì)算式中的表面比。（1）從赫茲壓力作用的研究摩擦接觸，由一個(gè)復(fù)雜的迭代過程每年在文獻(xiàn)中描述無潤滑接觸。 [6,8]。對混凝土結(jié)構(gòu)的函數(shù)F和c取決于身體的接觸（滑動，滾動）的相對運(yùn)動。參數(shù)：u=通過它光譜表示了表面粗糙度的特