To get the minimum value of s ,let:
 
So the largest height Δh in the residual area can be obtained:
 
 
Fig.4 Residual area after grinding

The resolutions are Δh1, Δh2 , …, Δhn and there must be the maximum height Δhmax among them. According to varied value of grinding wheel’s radius ,a serial of Δh can be obtained. Among these items, corresponding to the maximum value Δhmax ,the radius Rg is the optimum value of the roller’s radius under the condition of given feed value f. The equation of motion track can be inferred according to Fig.4.
 
  means Unit of tangent vector.   means the radius vector of any point in the roller.
    
        Fig .5 The structure of the simulation system

B. The Simulation System
The main function modules in the roller simulation system are as follows: the parameter-inputting module, simulation module and the analyzing module etc.. The block diagram is shown as Fig5.
V. RESULTS
The roller of flat-bottom spline which has machining module m=2.5, number of teeth z=16 and the pressure angle in graduated circleθ=30o is designed in this method. Rolling test is done using designed roller and then 3-D measure to spline gained by machining is taken. As shown in Fig.6, the machined spline outline accords with the theoretical spline outline very well.
 
Fig.6 Compare theoretical spline outline with machined spline outline

VI. CONCLUSIONS
The rolling principle is discussed and analyzed. According to the continuity of scale pision ,a new method for the roller design is put forward ---helicoids forming method with equal pitch .The design model of roller is builtand the amend project is offered to modify the model because of the elastic and plastic deformation. The low precision of forming method can be solved. The solving arithmetic is researched. The roller CAD system is developed and have put into practice. The roller simulating model is made. The simulation system of roller offers reliable data for roller’s grinding. In particular, the motion track can be used for programmer in numerical control machine. And furthermore, the grinding precision of roller can be assured.
 加工渐开线花键辊的设计和仿真
    冷轧渐开线花键有许多优点。这种方法可以提高生产效率，节省材料，延长刀具寿命，提高尺寸精度。由于花键的齿之间的金属纤文连续，耐磨的花键的齿侧的牙齿更好，强度更高。渐开线花键冷轧是制造业的发展趋势。与滚筒的设计是冷轧加工的关键点。本文分析了渐开线花键冷滚轧原理并建立了轧辊的设计模型。由于塑性变形，修改的方法是根据实验数据介绍。在对主要算法研究的基础上，轧辊CAD系统是为渐开线花键与滚轮模拟系统的建立。轧辊CAD系统与仿真系统已投入实践和轧辊的设计模型和修正的方法被证明在实践中是正确的。满足实际应用的迫切需要在样条的制造。指数条款-渐开线花键；轧辊；设计模型；CAD模拟。
Ⅰ.引言
作为一种重要的链接的方法，对渐开线花键轴被广泛用于汽车、拖拉机。渐开线花键可以由铣齿，滚齿，插齿、拉在传统制造业。与传统的方法相比，冷轧具有许多优势：节省材料，延长刀具寿命，提高生产效率和提高尺寸精度。由于花键的齿之间的金属纤文连续，耐磨的花键的齿侧面是更好的。因此，冷轧为发展趋势在渐开线花键。在冷轧过程中，对具有一定形状向某一方向持续前进的轴坯辊塑性变形了。所以正确的花键齿是建立在空白的地方的。滚筒安装在两个偏心轴分别连接到高速旋转轴。两个轴旋转是不同步骤不同方向的。辊坯每一次向空的地方前进。当他们接触空处的时候，两辊就啮合了。在轧制过程中，部分旋转侧在轴向方向设置和改变如图1所示。在辊轮向空处前进的时候，空白地方的轴沿自身轴线旋转和改变。这样的过程可以被看作是连续侧滚法。在轧制过程中，轧辊围绕高速轴的旋转轴和空白处不断改变沿自身轴线。所以通过辊挤压表面螺旋面。如上所述，轧制是虚空的生成方法不扩展刀片切割方法。中国在辊的设计研究，主要方法是映射向内辊和使用在辊设计的映射的数据，这对于加工是很困难的。另一种方法是使轧辊的形状配合的花键的轮廓，并基于假设辊轴向截面适合端面断面。但事实上，目前的运动是传播刀片切割方法被忽略。因此滚子偏离的渐开线花键精度的影响进一步的模型设计。 加工渐开线花键辊英文文献和中文翻译(4):http://www.youerw.com/fanyi/lunwen_4689.html