工業(yè)機(jī)械手設(shè)計(jì)（含三維proe仿真及CAD圖紙）,工業(yè),機(jī)械手,設(shè)計(jì),三維,proe,仿真,CAD,圖紙 開題報(bào)告 課題名稱 工業(yè)機(jī)械手設(shè)計(jì) 課題來源 社會生產(chǎn)實(shí)踐 課題類型 工程設(shè)計(jì)類 1．選題的背景及意義： 工業(yè)機(jī)械手是近幾十年發(fā)展起來的一種高科技自動化生產(chǎn)設(shè)備。工業(yè)機(jī)械手的是工業(yè)機(jī)器人的一個重要分支。它的特點(diǎn)是可通過編程來完成各種預(yù)期的作業(yè)任務(wù)，在構(gòu)造和性能上兼有人和機(jī)器各自的優(yōu)點(diǎn)，尤其體現(xiàn)了人的智能和適應(yīng)性。機(jī)械手作業(yè)的準(zhǔn)確性和各種環(huán)境中完成作業(yè)的能力，在國民經(jīng)濟(jì)各領(lǐng)域有著廣闊的發(fā)展前景。 2．研究內(nèi)容擬解決的主要問題： 1.對工業(yè)機(jī)械手的各主要組成部分的分析，設(shè)計(jì)方案的確定； 2.確定機(jī)械手的主要結(jié)構(gòu)，對各主要結(jié)構(gòu)進(jìn)行計(jì)算分析； 3.確定能夠?qū)崿F(xiàn)機(jī)械手的各種功能如：手抓去，腕回轉(zhuǎn)，臂伸縮； 4.液壓傳動系統(tǒng)的設(shè)計(jì)； 5.機(jī)械手各部件的可靠性； 3．研究方法技術(shù)路線： 采用同其它同等機(jī)械類設(shè)備的類比，方案比較等方法，根據(jù)工業(yè)機(jī)械手的實(shí)際應(yīng)用特征及現(xiàn)有的物質(zhì)、經(jīng)濟(jì)技術(shù)、人力等條件，以所學(xué)的理論知識為基礎(chǔ)，按照工業(yè)機(jī)械手工作的一般過程、設(shè)計(jì)標(biāo)準(zhǔn)，借鑒以往相似設(shè)備的成功經(jīng)驗(yàn)進(jìn)行初步設(shè)計(jì)，然后對初步設(shè)計(jì)方案進(jìn)行驗(yàn)算、修正，直至達(dá)到安全、經(jīng)濟(jì)、實(shí)用的目的。其中對于機(jī)械手設(shè)計(jì)中的關(guān)鍵問題、難點(diǎn)問題進(jìn)行重點(diǎn)分析解決，確保整個設(shè)計(jì)方案的可行性和最佳性。 4．研究的總體安排和進(jìn)度計(jì)劃： 1周：布置畢業(yè)設(shè)計(jì)題目，進(jìn)行畢業(yè)設(shè)計(jì)實(shí)習(xí)。 2周：收集相關(guān)資料。完成并提交開題報(bào)告。 3周：翻譯英文資料。 4-5周：初步構(gòu)設(shè)并確定設(shè)計(jì)方案。完成裝配圖草圖的繪制。 6周：計(jì)算確定各零件基本尺寸。 7-8周：繪制總裝配圖。 9-10周：編寫設(shè)計(jì)說明書。 11周：繪制零件圖。 12周：修訂初稿。 13周：完成答辯。 5．主要參考文獻(xiàn)： [1]穆亞飛.淺談機(jī)械手在機(jī)械工業(yè)中的應(yīng)用[J].工程管理與科學(xué)技術(shù)，2011，（1）：128. [2]韓夢丹，鄒曉宇.淺談機(jī)械手及其應(yīng)用與發(fā)展前景[J].企業(yè)技術(shù)開發(fā)，2012，31（2）：79-80. [3]張福學(xué).機(jī)器人技術(shù)及其應(yīng)用[M].北京：北京電子工業(yè)出版社.2000，18-19. [4]李建.多自由度機(jī)器人的設(shè)計(jì)與研究：[中國科學(xué)技術(shù)大學(xué)碩士學(xué)位論文].合肥：中國科學(xué)技術(shù)大學(xué)精密機(jī)械與精密儀器系，2009,8-9. [5]雷勇濤，李大明.機(jī)械手機(jī)械手運(yùn)動穩(wěn)定性分析[J].茂名學(xué)院學(xué)報(bào)，2006,2（1）：12-16. [6]劉會英，楊志強(qiáng)，張明勤等.機(jī)械原理[M].北京：中機(jī)出版社.2007，207-224. [7]郭柏林，胡正義.基于ADAMS的搬運(yùn)機(jī)械手軌跡規(guī)劃與仿真[J].湖北工業(yè)大學(xué)學(xué)報(bào)，2007.22（4）：37-39. [8]劉濤，楊鳳鵬.精通ANSYS[M].北京：清華大學(xué)出版社，2002:14-17. [9]吳小鋒.林業(yè)修剪機(jī)器人運(yùn)動學(xué)、動力學(xué)仿真:[南京林業(yè)大學(xué)碩士學(xué)位論文].南京：南京林業(yè)大學(xué)機(jī)械電子工程學(xué)院，2007，26-27. [10]崔吉等.一種六自由度機(jī)械手的運(yùn)動學(xué)分析[J]機(jī)械設(shè)計(jì)與研究，2009,36（11）：16-19. [11]Week M，Staimer D.Paraller kinematic machine tools-current state and future potentials.Annals of the CIRP,2002,51(2):671-1326. [12]蔣永彪.CAD技術(shù)的應(yīng)用與發(fā)展趨勢探析[J].中小企業(yè)管理與科技.2012,(19):282-283. [13]Denavit J,Hartenberg R S.A Kinematic Notation for Lower-Pair Mechanisms Based on Matrices[J].Journal of Applied Mechanics,2007,21:215-221. [14]劉國棟.我國的機(jī)器人研究和發(fā)展.江南學(xué)院學(xué)報(bào)[J].2001,16(4):28-35. [15]王茂兵，鄭小存.注塑機(jī)械手的研究及應(yīng)用[J].中國制筆，2007，（01）：71-73. [16]王炎歡，陳阿三，劉鑫茂.直角坐標(biāo)系機(jī)器人控制系統(tǒng)的研究[J].輕工機(jī)械，2010,28（4）.67-69. [17]KUKA公司.世界上最大的工業(yè)機(jī)器人[J]機(jī)械工程師，2008,7:11-12. 指導(dǎo)教師意見： 本課題擬采用的方法和技術(shù)路線可行，并能綜合運(yùn)用到所學(xué)的專業(yè)知識，有一定的難度，符合畢業(yè)設(shè)計(jì)要求，同意開題。 總體安排和進(jìn)度計(jì)劃合理，希望抓緊時(shí)間，按計(jì)劃、按規(guī)定高質(zhì)量完成本次畢業(yè)設(shè)計(jì)。 指導(dǎo)教師簽名： 年 月 日 教研室意見： 通過，同意開題 教研室主任簽名： 年 月 日 學(xué)院意見： 教學(xué)院長簽名： 年 月 日 4 A Cutter Orientation Modification Method for the Reduction of Non-linearity Errors in Five-Axis CNC Machining ABSTRACT In the machining of sculptured surfaces，five-axis CNC machine tools provide more flexibility to realize the cutter position as its axis orientation spatially changes .Conventional five-axis machining uses straight line segments to connect consecutive machining data points ,and uses linear interpolation to generate command signals for positions between end points，Due to five-axis simultaneous and coupled rotary and linear movements, the actual machining motion trajectory is a non-linear path. The non-linear curve segments deviate from the linearly interpolated straight line segments, resulting in a non-linearity machining error in each machining step. These non-linearity errors, in addition to linearity error, commonly create obstacles to the assurance of high machining precision. In this paper, a novel methodology for solving the non-linearity errors problem in five-axis CNC machining is presented. The propose method is based on the machine type-specific kinematics and the machining motion trajectory. Non-linearity errors are reduced by modifying the cutter orientations without inserting additional machining data points. An off-line processing of a set of tool path data for machining a sculptured surface illustrates that the proposed method increases machining precision. Keyword Non-linear error; Machine kinematics; Machining motion trajectory. INTRODUCTION In conventional five-axis machining, a tool path, represented by the cutter locations data (CLDATA), consists of the spatially varying cutter positions and its axis orientations. These CLDATA are generated based solely on the geometrical properties of the machined surfaces and the cutter. These CLDATA are further processed into NC-codes which is specific to a particular machine configuration. Linear interpolation is then used to generate the required commands for positions along line segment connecting the machining data points. The simultaneous linear and rotary movements are involved in five-axis machining since ever new cutter axis orientation requires the motion at least one other axis. There are also coupling effects of the cutter axis will affect the position of the cutter. These simultaneous and coupled movements cause the cutter contract point (CC point) to move in a non-linear manner. As a result, the machining error in each motion step is made up of not only the linear segmentation approximation error but also an additional machining error. As shown in figure 1 for machining is either a concave surface or a convex surface, a line segment is used to connect two consecutive machining data points (the spindle chunk is the machine control point MCP). Linear interpolation generate intermediate positions along the line segment. The desire surface is design curve(either concave or convex). The linear segment approximates to design curve resulting in the linearity error,δt. Apart from the linearity error . The non-linear CC point trajectory deviates from the straight line segment (the cutter gage length is constant and MCP is interpolated along the line segment)result in an additional machining error, referred to as the non-linearity error, δn. In the case that the desire surface is concave(see figure 1a), the total machining error is difference of the non-linearity error and the linearity error : δtotal=δt-δn. The non-linearity error, in this case, compensate for the total machining error(AIGP Post-processor,1996;Liu,1994). On the contrary, for the machining of convex surface as shown in figure 1b, the non-linearity error adds onto the linearity error and enlarges the machining error: δtotal=δt+δn(AIGP Post-processor,1996;Liu,1994). figure1. The multi-axis CNC machining error Consequently the non-linearity error have caused difficulties for ensuring ultra-precision machining requirements. In the machining of airfoil surface, for example, the machining of the contour surface of airfoil to the edges is problematic. The surface curvature on these area changes abruptly, and thus the cutter orientation varies inconsistently from one cutter to the next. These abrupt cutter orientation variations inconsistently from one cutter location to the next .These abrupt cutter orientation are a typical non-linearity error problem. In order to solve the five-axis CNC machining error problem, efforts have been made to treat non-linearity errors in generate NC codes. Some researchers and postprocessor producers used “l(fā)inearization processes” for this purpose. The basic function of “l(fā)inearization processes ” are inserting machining data points between NC codes where the total machining error is out of the specified tolerance range. Takeuchi et al. (1990) inserted points by subdividing the line segment with equally space d interval. Cho et al. (1993) inserted data points by limiting the maximum machining error within the line interval from the start point to the inserted point to be the tolerance. And, both of them set the cutter orientations varying linearly in successive positions. In the Automation Intelligence Generalization Postprocessor (AIGP)(1996), a “l(fā)inearization processes ” calculates the middle point (MP) between adjacent NC-codes and inserts the MP as an additional data in the NC code. The insertion can be performed further between the consecutive NC-coded until either all points are within the machining tolerance or until a maximum of 63 points are inserted between the consecutive data point. The current post-processors, such as the Vanguard Custom Post-processor Generator (1996) , the Ominimill Custom Postprocessor(1992),the AIX Numerical Control Post Generator(1996) , are all having the similar “l(fā)inearization processes ” as in the AIGP. In the current CAD/CAM software. Unigraphics(2001), the UG /post postprocessors inserts data points between adjacent NC-codes, thereby simulating a straight line with series of small curves. The number of the inserted points is determined based on the maximum allowable deviation and an iteration method is used to segment the move. In the extreme case, namely after looping 20 times, if the deviation between the segmented arcs and the line are still out of the specified tolerance limit, the process is aborted. “l(fā)inearization processes ” discussed above manipulate NC-codes by inserting extra machining data points. Although the produced NC-codes satisfy the machining requirement, they may contain dense sets of non-equally spaced data with constant or linearly varying cutter orientation. Consequently, the linearization process has raised the following problems. In the machining of complex contour surface, the cutter orientation varies from one cutter location to the next. The cutter position changes in this case can not be too small since the machine will produce either jerk motion or random rotary movements. As in an industrial procedure of machining airfoil surface of an impeller, a linearization process was used to reduce the non-linearity errors. Many data points were inserted between a pair of NC-codes. The insertion of many data points caused the cutter position change to be nearly equal to zero while the cutter orientation changed abruptly. As a consequence, the machine rotary movements were rapid with infinite feedrate. Random rotary movements resulted and the workpiece was damaged. The insertion of machining data points can also cause non-constant federate along the cutting curve. The insertion of additional data results in non-equally spaced segment, while acceleration and deceleration steps are required for each segment. Thus, the feederate varies in each segment and may never reach the desired value. The result of varying feederate causes a nonsmooth surface finish and the unreachable feedrate increases overall machining time. In addition, the insertion of constant cutter orientation variation also causes severe roughness around the end points along the surface. Linearly inaccurately since the change in cutter orientation is not necessarily linear. The non-linearity error problem arises from the fact that five-axis machining motion trajectories are non-linear curve segments. The simultaneous and coupled rotary and translation movements generate the non-linearity motion trajectory, and the linear interpolation technique is not capable to curve fit the nonlinear path. One solution to is to design new interpolation methods. Liang et al.(2002)presented a combine 3D linear and circular (3D L&C) interpolation technique. The new 3D L&C interpolation can on-line drive the rotation movement pivot along a pre-designed 3D curve path, so that the CC point motion trajectory is a via a straight line connecting machining data points, thus, the non-linearity error can be eliminated. Five-axis machining movements are kinematically related to the cutter location data. In other word, the non-linear motion trajectory depends on the cutter orientation changes and non-linearity errors are related to the tool path generation. Thus, another solution to the non-linearity error problem can be approached from tool path(CLDATA)generation with the requirements that the machining errors are minimized and there is no interference between the workpiece and the cutter. In tool path generation, various techniques for different surface representations have been used by the CAD/CAM package producers (CLDATA,1996;Unigraphics, 1990)and researchers. Huang and Oliver (1992) . Bedi et al.(1997) presented a principle curvature alignment technique for five-axis machining using a toroidal shaped tool. Liu (1995)presented the single point offset and the double point offset algorithms for five-axis flank milling tool path generation based on differential geometry and analytical geometry. Morishge et al.(1999)presented a tool path generation method for five-axis CNC machining, which applies the C-space(a 3D configuration space)to determine collision-free cutter positions and its orientation. These research work on tool path generation are all based exclusively on the geometric of the machined surfaces and the cutter, without considering the machining-specific machining kinematics. As a result, the generated tool paths(the machining NC-codes transformed from these CLDATA)commonly cause obstacles for meeting the ultra-precision machining requirements, particularly for the cutter orientation generation in five-axis machining. Thus, the problem with present off-line tool path generation approaches is that the real machining kinematics is not directly incorporated. To ensure machining precision, cutter orientation generation should be based not only on the geometry of the machined surfaces but also on the machine type-specific kinematics. In this paper, a novel methodology for solving the non-linearity error problem in five-axis machining is presented. The method optimizes the CLDATA based on machine-specific kinematics and machining motion trajectory, whereby the cutter orientations are modified to reduce the non-linearity errors provided that there is no interference between the cutter and the workpiece. A software program for implementing the proposed method is presented. As an application of proposed method, a case study is presented, which shows an increase in machining precision as compared with those processed by the existing AIGP’s method. PROPOSED TOOL PATH GENERATION METHOD The machining non-linearity errors depend upon the actual CC point trajectory, since a CC point trajectory is a function of the machine rotary variables, each actual CC point trajectory can be manipulated within the tolerance limit by changing the machine rotary variables, provided that there is no interference between the workpiece and the cutter. Further more, because of the machine rotary variables are kinematically related to the cutter orientation changes, the non-linearity error problem can be approached by manipulating cutter orientations. To proposed method reduces the non-linearity errors by determining the acceptable machine rotary variables employing the machine motion trajectory model, and by modifying the cutter orientation through the machine kinematic relations. It must be emphasized that the machine kinematic properties and motion trajectory are machine type-specific. Hence, the modification of CLDATA has to be carried out in teams of machine variables and subsequent use of the kinematic transformation to determine the modified CLDATA. The procedure of the proposed method starts with the transformation of the CLDATA to machining NC-codes by employing the machine-type specific inverse kinematic model. In teams of machine variables, the actual machining motion trajectory is determined by using the specific machine motion trajectory model. Then, the machining errors are determined. The linearity error is a function of surface local curvature on the cutting curve and the step-forward distance. From the cubic spline cutting curve function, the surface local curvature can be determined. The linearity error for each move then can be computed from the adjacent CC point data and the surface local curvature. By knowing the linearity error, the allowable non-linearity error can be determined as the difference of the linearity error from the specified machining tolerance. Using the machine trajectory model and the line segment equation, the maximum deviation can be determined. By taking sample points on both of the CC non-linear curve and the line segments, the maximum chord deviation is the maximum non-linearity error. In the steps where the maximum non-linearity error exceeds the allowable non-linearity error, the proposed method modifies the machine rotary variable changes. The modification is carried out by increasing/decreasing a machine rotary variable variation a small angle in the plane containing the two original cutter vectors, and by adding/subtracting the angle to the original machine rotary variables. The new rotary variables are then used to calculate the resultant non-linearity error, which in turn is compared again with the allowable non-linearity error. Thus, by using the difference between the allowable non-linearity error and modified non-linearity error as the criterion, the acceptable machine rotary variables can be determined iteratively. Finally, from the modified machine rotary variables, the corresponding cutter orientations can be determined by performing the forward kinematic transformation. In order to avoid interference between the workpiece and the cutter, the rotary angles were adjusted such that the angle changes are less than half of the orientation angle changes are less than one half of the original cutter orientation changes. Comparing to the existing “l(fā)inearization processes ”, the additional data points are inserted with cutter orientations either varying linearly or as the average variation(i.e., the one half)of the rotary angle change, and the interference problem is not considered. Alternatively, the modified machine rotary variables angle change from the proposed method are smaller than one half of angel change, which thus ensures the corresponding cutter orientation are within the range such that no interference occurs. For a set of CLDATA, the modification procedure can be performed by using the following algorithm. TOOL PATH MODIFICATION ALGORITHM Transform the initial CLDATA, into its corresponding machining NC-codes by using the specific machine inverse kinematic model; Determine the CC point coordinates by employing the machine motion trajectory model; Compute the desire tool path by using cubic spline function based on the CLDATA and calculate the local surface curvatures Kf of the tool path at the machining points; Computer the linearity error by using the formula given by Faux and Pratt(1979): δt =1/8 Kf (Δs)2 where, Kf-the surface local curvature determined from step(3); Δs-the segment length between consecutive CC points from step(2). Compute the allowable value of the non-linearity error: δa,n=tolerance-δt. Determined the points on the straight line segment and on the machine motion trajectory segment that correspond to the maximum chordal deviation. Compute the maximum non-linearity error , δmax, using the points from step(6); Modify the machine rotary angle change ifδmax>δa,n ,that is, increase or decreaseΔBm andΔCm such that the non-linearity error, δn1, will satisfy (δn1-δa,n)<0; Computer the machining NC-codes of Bm,i+1 and Cm,i+1 based on the machine rotary angle variation from step 8: Bm,i+1= Bm,iΔBm Cm,i+1=Cm,iΔCm Where, Bm,i, Cm,i are the i-th rotary variables , Bm,i+1 Cm,i+1 are the i+1-th rotary variables andΔBm ΔCm are modified rotary angle changes. The +and –sign depends on whether the angles in step i+1 increase or decrease, Determine the optimum cutter orientations by transforming the modified machining NC-codes using the specific machine forward kinematic model. The proposed method can be implemented with a software as shown in Figure 2. The pre-postprocessor accepts the initialδt CLDATA. Then ,by passing the modified CLDATA to a postprocessor, the obtained NC-codes will result in acceptable machining errors. The proposed method considers not only the geometry calculation of the complex surfaces by accepting the initial CLDATA, but also the five-axis machining kinematics by applying the machining motion trajectory and the process of dynamic properties in the postprocessor. Therefore, the proposed method provides a solution to the non-linearity problem without requiring the design of a new interpolators, and the method overcomes the drawbacks of the existing methods as described in “introduction”. CAM System Tool Path Generation Based on the geometry of The machined surfaces Pre-Prostprocessor Modify cutter orientation based on machine kinematics &motion trajectory Proprocessor Transform CLDATA to Machining NC-codes by Postprocessing Conclusion A novel tool path generation methodology for solving the five-axis CNC machining error problem is proposed. The new methods off-line modifies the cutter orientations based on the allowable change in machine rotary movements, which in turn reduces the non-linearity error to be within the machining tolerance. The proposed method employs machine type-specific kinematic models and the machining motion trajectory. Comparing with the data from the AIGP’s “l(fā)inearization processes ”,the proposed method ensures the machining precision without inserting additional cutter position points. The software for implementing the proposed method can be used to process CLDATAs that will be used on the OM-1 five-axis milling centre, and it can also be extended to other five-axis CNC machining tools. 用改變加工工具方向的方法來減少五軸聯(lián)動數(shù)控加工中的非線性誤差 摘要 五軸聯(lián)動數(shù)控加工通過改變軸在三維空間位置和方向，從而改變刀具的位置，為加工工件表面提供了一種靈活的方法。五軸聯(lián)動加工通常運(yùn)用直線來連接待加工的連貫數(shù)據(jù)點(diǎn)，通過直線插補(bǔ)來生成從起點(diǎn)到終點(diǎn)的指令代碼，由于加工過程中軸的旋轉(zhuǎn)運(yùn)動和直線進(jìn)給運(yùn)動是同時(shí)進(jìn)行的，所以實(shí)際的運(yùn)動軌跡是非線性的。曲線部分偏離線性插補(bǔ)部分使每個加工步驟中存在著非線性加工誤差。除了線性加工誤差，非線性加工誤差同樣也會影響到工件加工的高精度。在這篇文章中介紹了一套新的系統(tǒng)的方法來解決五軸聯(lián)動數(shù)控加工中存在的非線性誤差問題。這套方法是在特定加工運(yùn)動和加工軌跡下，在不另增加插補(bǔ)點(diǎn)，通過改變加工工具方向來實(shí)現(xiàn)。通過處理一系列的工具在加工表面輪廓偏離加工路徑的數(shù)據(jù)表明上述方法能提高加工精度。 關(guān)鍵詞 非線性誤差；機(jī)構(gòu)運(yùn)動；加工運(yùn)動軌跡； 導(dǎo)論 在傳統(tǒng)的五軸聯(lián)動加工中，刀具的路徑是由三維空間中切削工具的位置數(shù)據(jù)（CLDATA）來決定的，而這些位置數(shù)據(jù)是由軸的方向和工具的位置所組成的。位置數(shù)據(jù)的生成是依據(jù)加工表面和加工工具以及加工表面的幾何特性,而這些位置數(shù)據(jù)在特定加工輪廓下又進(jìn)一步的處理了成數(shù)控代碼，然后運(yùn)用直線插補(bǔ)原理將各個數(shù)據(jù)點(diǎn)用直線相連并生成所需的位置指令。在五軸聯(lián)動加工中，所有工具軸的方向的確定至少需要一根軸的運(yùn)動，那么直線運(yùn)動和旋轉(zhuǎn)運(yùn)動是同時(shí)進(jìn)行的。如此，改變工具軸的方向產(chǎn)生的旋轉(zhuǎn)動作和直線動作的合成運(yùn)動效應(yīng)同樣會影響到工具的位置，合成運(yùn)動使得切削工具連接點(diǎn)會沿著非直線運(yùn)動。所以，每個加工動作存在的加工誤差包括直線部分的近似誤差和額外的加工誤差，在圖1中，用直線連接二個連貫的加工數(shù)據(jù)點(diǎn)，不論加工是凹面還是凸面（大部分是軸的加工控制點(diǎn)），直線插補(bǔ)沿著直線生成中間位置點(diǎn)。假設(shè)設(shè)計(jì)所需的曲面（凹面或者凸面）。用直線近似地去逼近所設(shè)計(jì)的曲面而造成線性誤差，δt，除了線性誤差，非線性工具連接點(diǎn)的軌跡偏離直線部分（加工控制點(diǎn)是沿直線進(jìn)行插補(bǔ)的，所以工具計(jì)量長度是連續(xù)的，）造成額外的加工誤差，如非線性誤差δn。在圖1a中，所需的曲面是凹面，總的誤差等于線性誤差減去非線性誤差，即: δtotal=δt-δn。那么，非線性誤差縮小了總的誤差。相反的在圖1b中加工的凸面中，總的加工誤差是線性誤差與非線性誤差的和，就擴(kuò)大了總的誤差，即δtotal=δt+δn (AIGP Post-processor,1996;Liu,1994).。因此，非線性誤