外文翻译----设计加工螺杆式压缩机的内摆线

附录

1 The Original English

THE KEY TECHNOLOGY OF DESIGN HOB FOR

HOBBING SCREW COMPRESSOR ROTORS

WITH CUCLOID-ARC PROFILE

ABSTRCT

The profile of cycloid-arc screw compressor rotors is not a smooth profile; it has a tip on it. When design the hob cutter used for machining this kind of rotors, the profile of hob edge will appear separation. In this paper, the author made researches on the design theory of hob cutter for hobbing the cycloid-arc rotor with tip profile, and got the best way for design this kind of hob cutter with a separate edge. It is good practice to design the hob cutter and hob the cycloid-arc rotor according to practical design, manufacture and test.

(1) INTRODUCTION

The efficiency and reliability of screw compressor mainly depend on manufacturing technology of screw rotors. At present, the machining method of our country for machining screw rotors is milling the shortcoming of milling is low productivity and machining accuracy. Hobbing characteristic is high productivity and machining accuracy, so the machining method for hobbing instead of milling screw compressor rotors is now becoming more and more popular.

Hobbing instead of milling for machining screw compressor rotors has much more advantage, but the key problem for carrying out hobbing the screw compressor rotors is that the profile of screw compressor rotors must be suited to hobbing. Our national standard profile for screw compressor rotors have no-symmetric cycloid-arc profile and symmetric are profile [1], since no-symmetric cycloid-arc profile screw compressor has much more advantage than symmetric are profile screw compressor, our national factory all adopt the former at present. The property of no-symmetric

cycloid-arc profile is that the conjoint curve of profile isn’t slick curve, it has a tip on the profile, it is still a great difficult for hobbing instead of milling this kind of screw rotors in our cou ntry as the design problem of hob cutter. In this paper, we’ll make researches on the design theory of hob cutter for hobbing the no-symmetric cycloid-arc rotor with tip profile.

(2 ) EXISTING PROBLEM

Fig.1 shows the end section of no-symmetric cycloid-arc rotors, its end profile is composed of radial line ab, arc bc, prolonged cycloid cd and radial line de. The point of intersection of prolonged cycloid cd and radial line de exist a tip d, that is, the d point of intersection hasn’t common tangent. As we calculate the corresponding axial profile of hob cutter according to cutting tool design handbook or other cutting tool design data, we’ll find that the axial profile of hob cutter becomes two separate curves, like the one shown in Fig.2.

Fig.1 The end profile of screw rotor Fig.2 The axial profile of hob

In order to machining the required rotor profile and insure the tip not being cut out, people can usually take following two ways to solve this problem. One way is to prolong curve cd and radial line de as Fig.3 shows, this way can avoid appearing separate curve of hob edge, but hob profile will become Fig.4 shows, this kind of hob edge can neither be machined nor be used. Another way is to make a concave curve to link the separate hob edge as Fig.5 shows.

Fig.3 The end profile of screw rotor Fig.4 The axial profile of hob Fig.5 The concave curve This way can avoid the tip being cut out, but it will produce two new tips on hob edge. This kind of hob is not only difficult to be machined but also easy to be worn on the tips. Form above discussing we can see that above two ways is not the best way to solve this problem. The best way to solve this kind of problem is to figure out the intermediate curve between separate edge curves accurately.

(3) THE BEST WAY FOR CALCULATING INTERMEDIATE CURVE ACCURATELY

Here we make use of the intermediate rack to calculate the intermediate curve between separate edge curves. That is, in the first place, we figure out the intermediate profile of rack according to the mesh of intermediate rack and rotor, in the second place, we figure out the intermediate profile of hob edge curve according to the mesh of intermediate rack and hob worm.

According to gear mesh theorem, we can figure out the profile of intermediate rack mesh with rotor easily. As the tip exists on the profile of rotor, calculated profile of rotor will be two separate curves as Fig.2 shows. The two coordinates points d1 and d2 can easily figure out as following d1(x1, y1) and d2(x2, y2), obviously, the formation of separate curve of rack profile is that the tip d on rotor profile move around the rack to form when rack meshes with rotor. According to Fig.6 we can see, the mesh of rack and rotor is equal to pitch circle of rotor rolling on the pitch line of rack, the point d on rotor formed moving track is the intermediate curve of rack.

Fig.6 The formation of separate curve on rack

The separate curve on rack can easily be given by the following equation:

11sin()cos()

t t x r y r θρθφρθφ=-+??=-++? (1) Where r is the pitch circle radius of rotor, ρ is the length of radial line od, Ф is the angle included between the radial line oe and the coordinate axis Y .

θ is a variable, its bound is θ1≤θ≤θ2, θ1 and θ2 value can be calculated by the equation (1) according to the coordinate value of d1(x1, y1) and d2(x2, y2).

As we know the separate curve equation on rack, we can figure out the separate curve equation of rack at the end of hob worm by the Fig.7 as following:

1211cos /cos t t t t x x y y ββ=??=? (2) Where β1 is the spiral angle of rotor, β2 is the spiral angle of hob worm.

According to gear mesh theorem [2], we can figure out the separate curve equation of hob worm mesh with the separate curve equation on rack by the Fig.7 as following:

Fig.7 The common rack mesh with the rotor and the hob worm

31111113111111

11()cos ()sin ()cos ()sin ()//t t t t t t t

t t x r x y r y y r x r y tgu x r u tg dy dx ???????-=-+-??=-+-??=+??=? (3) According to formula (1), (2) and (3), we can accurately figure out the separate curve between the two separate profiles on hob edge.

We can insure to hob the right profile of cycloid-arc rotor according to above formula to design the hob. It is good practice to design the hob cutter and hob the cycloid-arc rotor according to practical design, manufacture and test.

4 REFERENCES

[1] Li Wenling. Rotary Compressor for Refrigeration.Beijing: Mechanical Industry Press, 1992. 110~122. (in Chinese)

[2] Li Rusheng. Design Principle of Cutting Tools. Nanjin: Science & Technology Press, 1985. 475~485. (in Chinese)

2 中文翻译

设计加工螺杆式压缩机的内摆线—弧轮廓

所用滚刀的关键技术

摘要

螺杆式压缩机的内摆线—弧部分的轮廓并不是光滑的，它存在一个尖端。当设计用来加工这种机器旋转部分的滚齿刀刀具时，这种滚刀的刃口将出现分离的现象。在本文里，作者研究了用于加工带有末端轮廓的摆线—弧的旋转部分滚齿刀刀具的设计原理，并且找到了设计这种具有分界线边沿的滚齿刀刀具的最佳设计方法。通过实际的设计、生产和测试证实这种这种理论对滚齿刀刀具和滚齿刀摆线—弧机械的旋转部分的设计有很大的作用。

(1) 概述

螺杆压缩机的效率和可靠性，主要取决于螺杆机械旋转部分的加工技术。目前，我国制造螺旋转子的机加工方法是铣削，但缺陷是生产效率和加工精度都比较低。滚齿加工的特点是生产效率和加工精度高。因此，目前相对于铣削加工的

方法，滚齿加工变的越来越普遍。

采用滚齿加工代替铣削来制造螺杆压缩机机械旋转部分有很多优点。但是，实现滚齿加工螺杆压缩机机械旋转部分的主要问题是，螺杆压缩机机械旋转部分的轮廓必须适合于滚齿加工。我们的国家标准中螺杆压缩机的机械旋转部分外形有不对称的摆线—弧轮廓和对称的弧轮廓[1]。由于不对称的摆线—弧轮廓螺旋压缩机比对称的弧轮廓有很多优越之处，目前，我们国家的工厂都采用前者。不对称的摆线—弧轮廓是联合的曲线轮廓，而不是光滑的曲线，在轮廓上有一个尖端，在我们国家，由于滚齿刀刀具的设计问题，那仍然是滚齿加工代替铣削这种螺杆机械旋转部分的过程中的一个相当大的难题。在本文里，我们将对用于滚齿加工不对称具有尖端外形的摆线—弧轮廓的滚刀的设计原理进行深入研究。(2) 存在的问题

图1显示了不对称摆线—弧机械旋转部分的末端部分，它的末端轮廓由直线ab、弧bc、摆线延长线cd和直线de构成。摆线延长线cd和直线de的交点处存在一个尖端d，也就是说，也就是说在交点d出存在一个共同的切点。当我们通过切削刀具设计手册或者其它切削刀具设计资料计算与滚齿刀具相应的轴向轮廓时，我们将发现滚刀的轴向轮廓变成两条分开的曲线，如图2所示：

图1 螺杆的旋转部分末端轮廓图图2 滚齿刀的轴向轮廓

为了加工生产产品所需的机械旋转部分轮廓，并且确保尖端不被切除，人们通常采用以下两种方法来解决这个问题。一种方法是延长曲线cd和直线de，如图3所示，这种方法可以防止滚刀边沿刃口出现独立的曲线，但是滚刀轮廓将变成图4所示，这种滚刀即不能生产也不能可能使用。另一种方法是做一条凹形的曲线去连接分开的滚刀刀刃，如图5所示。

图3螺杆旋转部分末端图4 滚刀的轴向轮廓图5 凹形曲线

(3) 准确的计算出中间曲线的最好方法

这里我们利用中间的齿轨来推算分开的边沿曲线中间曲线。也就是说，我们首先根据相啮合的中间齿轨和机械的旋转部分来弄清楚齿轨的中间轮廓，其次，我们根据相啮合的中间齿轨和滚刀的螺旋部分来弄清楚齿轨中间的轮廓。

根据齿轮啮合定理，我们可以很容易的理解机械旋转部分中间的齿轨啮合。由于机械的旋转部分轮廓存在尖端，机械旋转部分的计算轮廓将是图2所示的两段分开的曲线。两个坐标点d1和d2可以很容易的由d1（x1，y1）和d2（x2，y2）表示出，显然，当齿轨和机械的旋转部分捏合时，机械的旋转部分轮廓围绕齿轨移动的尖端d形成齿轨轮廓分开的曲线结构。根据图6，我们可以看出，齿轮和机械旋转部分的啮合与机械的旋转部分在齿轨调节线上的滚动调节圆是相同的，在机械的旋转部分点d形成的运动轨迹是齿轨中间的曲线。

图6 齿轨上分开的曲线结构

齿轨上分开的曲线可以由下面的等式很容易的得出：

???++-=+-=)cos(

)sin(11φθργφθρθχr r t t (1) 等式中r 是转子节距圆的半径，ρ是直线od 的长度，φ是直线oe 和纵坐标Y 的夹角。

θ是可变的，它的变化范围是θ1≤θ≤θ2，θ1和θ2的值可以依据d 1（x 1，y 1）和d 2（x 2，y 2）的坐标值算由等式（1）出。

当我们知道关于机械的旋转部分分开的曲线等式后，我们可以通过图7，弄清楚在滚齿刀螺旋部分末端机械的旋转部分分开的等式，如下：

???==1

121t cos /cos t t t γγββχχ(2) 等式里β1是机械旋转部分的螺旋角，β2是滚齿刀螺旋部分的螺旋角。 依据齿轮啮合原理[2]，我们可以通过图7，弄清楚滚齿刀螺旋部分与齿轨上分开的曲线等式相啮合组合曲线方程如下：

图7

???????=+=-+-=-+-=-1111

111113111113//)(sin )(cos )(sin )(cos )(χχγ???χ?γγ?γ?χ?χd dy tg u r tgu r r r r t t

t t t t t t t (3) 根据方程式（1）、（2）和（3），我们可以准确的画出滚刀刃口上两个分离轮廓之间的独立曲线。

根据以上设计滚齿刀的理论，我们可以确保摆线—弧机器的旋转部分滚齿加工出正确的轮廓。实际的设计、生产和测试证实这种理论对滚齿刀刀具和滚齿刀摆线—弧机械的旋转部分的设计有很大的作用。