TWI421137B - Method for applying envelop theory to build model of precision roller curve of skew-roll straightening machine - Google Patents

Method for applying envelop theory to build model of precision roller curve of skew-roll straightening machine Download PDF

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TWI421137B
TWI421137B TW100100451A TW100100451A TWI421137B TW I421137 B TWI421137 B TW I421137B TW 100100451 A TW100100451 A TW 100100451A TW 100100451 A TW100100451 A TW 100100451A TW I421137 B TWI421137 B TW I421137B
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equation
roller
bar
model
straightening machine
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TW201228745A (en
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Hsueh Cheng Yang
Yao Dong Kuo
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利用包絡理論建構斜輥式矯直機精輥段輥輪模型之 方法 Using envelope theory to construct the roller model of the fine roller section of the inclined roller straightening machine method

本發明是有關於一種利用包絡理論建構斜輥式矯直機精輥段輥輪模型之方法，特指一種針對斜輥式矯直機進行數學建構精輥段輥輪輪廓，利用數學建構輪廓後，進而計算出斜輥輪的精輥段的接觸線並得以消除接觸線的技術手段。 The invention relates to a method for constructing a roller model of a fine roller section of a skew roller type straightening machine by using an envelope theory, in particular to a mathematically constructing a fine roller section roller profile for a skew roller type straightening machine, and constructing a contour by using mathematics Then, the contact line of the fine roller section of the skew roller is calculated and the technical means of eliminating the contact line is obtained.

於工業上，於例如管、棒、線、帶等長形金屬型材在軋製、鍛造、擠壓、拉拔、運輸、冷卻及各種加工過程中常因為外力作用、溫度變化、殘留應力而發生變形或彎曲，製造過程中不管精確度多高，仍然會存在著一些缺陷，較大的問題是縱向彎曲和截面的圓度，而為了獲得更平直且真圓度高的金屬圓桿狀件，因此必須利用機器設備對應該金屬圓桿狀件向其縱面或橫向截面做輥壓動作，以使其由彎曲變平直，此過程稱為矯直，而影響斜輥式矯直機的因素有輥形輪廓尺寸、兩斜輥輥輪間距、兩輥輪的夾角、下壓量、材料摩擦力等，此外，還與毛管的材質、彎曲度和橢圓度等有關。 In the industry, long metal profiles such as tubes, rods, wires, belts, etc. are often deformed by external force, temperature change, residual stress during rolling, forging, extrusion, drawing, transportation, cooling, and various processing. Or bending, no matter how high the precision in the manufacturing process, there are still some defects. The larger problem is the longitudinal bending and the roundness of the section, and in order to obtain a more straight and rounded metal round rod, Therefore, it is necessary to use the machine equipment to perform the rolling action on the longitudinal or transverse section of the metal round rod to make it straight from the bending. This process is called straightening, and the factors affecting the inclined roller straightening machine There are roll profile size, two skewer roller pitches, the angle between the two rollers, the amount of pressing, material friction, etc. In addition, it is related to the material, curvature and ellipticity of the capillary.

而如何更佳地提高輥壓之功效，一直也是業界遭遇的瓶頸，目前國內的矯直機輥形加工上，仍舊多係依照操作者的經驗法則以及且做且調整之逆向工程來進行，如此一來在時間上耗費較多，且難以避免於 棒材表面會有輥壓之螺旋紋產生，這對於完工後之棒材的真圓度及光度來說為一種缺失，往往需要於完成後透過後製修飾做處理，十分費時費事，而業界未見有得以有效套用包絡理論而製作斜輥輥輪之外型的實例，若可以以包絡理論建構輥輪輪廓數學模型，當棒材進行矯直過程中，棒材在二斜輥輪的線接觸下會進行一邊前進一邊轉動的方式輥光，利用此運動原理使棒材做螺旋運動，以棒材曲面族及嚙合方程式完成被創成面精輥輪廓，這樣所求得的輥輪是完全模擬真實的矯直機其圓棒的運動方式，此數學模型的可期能讓棒材的真圓度提升，也可有效改善棒材表面光度，故基於上述不足點為考量，本發明之發明人思索並設計一種利用包絡理論建構斜輥式矯直機精輥段輥輪模型之方法，以期可針對現有技術之缺失加以改善，進而增進產業上之實施利用。 How to better improve the effect of rolling pressure has always been a bottleneck encountered by the industry. At present, the domestic straightening machine roll processing is still carried out according to the operator's rule of thumb and the reverse engineering of adjustment and adjustment. It’s time consuming and it’s hard to avoid There is a rolling spiral on the surface of the bar, which is a kind of lack of roundness and luminosity of the finished bar. It often needs to be processed after finishing, which is very time consuming and troublesome. There is no example of the shape of the inclined roller that can be effectively applied by the envelopment theory. If the mathematical model of the roller profile can be constructed by the envelope theory, the bar is in the line of the two inclined roller when the bar is straightened. Under the contact, the roller light will be rotated while moving forward. The motion principle is used to make the bar spiral, and the profile of the surface of the bar and the meshing equation are used to complete the contour of the surface roller. The roller thus obtained is completely simulated. The true straightening machine has the movement mode of the round bar. The mathematical model can increase the roundness of the bar and improve the surface luminosity of the bar. Therefore, based on the above shortcomings, the inventor of the present invention Considering and designing a method of constructing the roller model of the fine roller section of the inclined roller straightening machine by using the envelope theory, in order to improve the lack of the prior art, and to enhance the industrial implementation.

有鑑於上述習知之問題，本發明之主要目的就是在提供一種利用包絡理論建構斜輥式矯直機精輥段輥輪模型之方法，以期克服現有技術之難點。 In view of the above-mentioned problems, the main object of the present invention is to provide a method for constructing a fine roller section roller model of a skew roll straightening machine by using the envelope theory, in order to overcome the difficulties of the prior art.

為達到上述目的，本發明所採用之技術手段為設計一種利用包絡理論建構斜輥式矯直機精輥段輥輪模型之方法，其首先建立圓棒的幾何模型，假設座標系S 1(O 1,X 1,Y 1,Z 1)曲線是固定在圓棒上且圓棒半徑為r，得方程式一： In order to achieve the above object, the technical means adopted by the present invention is to design a method for constructing a roller model of a tapered roller straightening machine using an envelope theory, which first establishes a geometric model of a round bar, assuming a coordinate system S 1 ( O 1 , X 1 , Y 1 , Z 1 ) The curve is fixed on the round bar and the radius of the round bar is r. Equation 1 is obtained:

τ沿著Z 1軸向進行延伸成圓棒長度，其中上輥輪座標系S 2(X 2,Y 2,Z 2)為S h (X h ,Y h ,Z h )以Y h 為中心轉換α 1角而成，如第三圖所示，設座標系S h 與S f (X f ,Y f ,Z f )兩原點距離為E 1；當上輥輪座標系S 2繞Z h 軸旋轉角時，使圓棒座標系S 1(X 1,Y 1,Z 1)沿著Z f 軸上旋轉角，並沿著Z f 軸前進為；座標系S 1與S g (O g ,X g ,Y g ,Z g )兩原點距離為E 2，且其夾角為α 2，當下輥輪S 3繞Z g 軸作轉角時，將會帶動棒材座標系S 1繞Z f 軸旋轉角並平移距離，為求得棒材曲面族方程式，分別求得棒材從S 1到S 2與S 1到S 3座標轉換的曲面族方程式可表示為方程式二：R 2=M 2h ．M hf ．M f1．R 1及方程式三：R 3=M 3g ．M gf ．M f1．R 1 τ extends along the Z 1 axial direction into a round bar length, wherein the upper roller coordinate system S 2 ( X 2 , Y 2 , Z 2 ) is S h ( X h , Y h , Z h ) centered on Y h Converting α 1 angle, as shown in the third figure, set the distance between the coordinates of the coordinate system S h and S f ( X f , Y f , Z f ) as E 1 ; when the upper roller coordinate system S 2 is around Z H- axis rotation At the corner, the round bar coordinate system S 1 ( X 1 , Y 1 , Z 1 ) is rotated along the Z f axis Angle and advance along the Z f axis The coordinates of the coordinate system S 1 and S g ( O g , X g , Y g , Z g ) are E 2 , and the angle is α 2 , and the lower roller S 3 is rotated around the Z g axis. At the corner, it will drive the bar coordinate system S 1 to rotate around the Z f axis. Angle and pan Distance, in order to obtain the bar surface equation, the surface family equations of the bar from S 1 to S 2 and S 1 to S 3 coordinates can be expressed as Equation 2: R 2 = M 2 h . M hf . M f 1 . R 1 and Equation 3: R 3 = M 3 g . M gf . M f 1 . R 1

並將方程式一代入方程式二及方程式三可進一步獲得用於求得上、下輥輪的棒材曲面族方程式，表示為方程式四： 及方程式五： And the equation is substituted into Equation 2 and Equation 3 to further obtain the equation of the bar surface family for obtaining the upper and lower rollers, which is expressed as Equation 4: And equation five:

其中s為三角函數sin，c為三角函數cos，R 2及R 3分別表示棒材曲面族的位置向量，表示在S 2及S 3座標系，而這裡R 1是方程式一的棒材幾何方程式。 Where s is the trigonometric function sin, c is the trigonometric function cos, R 2 and R 3 respectively represent the position vector of the bar surface family, which is represented by the S 2 and S 3 coordinate systems, where R 1 is the bar geometry equation of Equation 1. .

由包絡原理得知棒材的法向量必須與棒材和輥輪的相對速度相互垂直，表示為方程式六： It is known from the envelope principle that the normal vector of the bar must be perpendicular to the relative velocity of the bar and the roller, expressed as Equation 6:

下標f表示在固定座標S f 下，而棒材的單位法向量n=[cos θ]i+[sin θ]j，令l=cos θ，m=sin θ，n=0，可將棒材的法向量表示在S f 座標系，表示為方程式七： The subscript f indicates that under the fixed coordinate S f , and the unit normal vector of the bar n = [cos θ ] i + [sin θ ] j , let l = cos θ , m = sin θ , n =0, the rod can be The normal vector of the material is expressed in the S f coordinate system and is expressed as Equation 7:

由相對速度的方法可求得棒材與輥輪的相對速度向量，並表示在固定座標，記為方程式八： 及方程式九： The relative velocity vector of the bar and the roller can be obtained by the relative velocity method and expressed at the fixed coordinate, which is written as Equation 8: And equation nine:

將方程式七和方程式八與方程式九分別代入方程式六，可得棒材與輥輪的嚙合條件，記為方程式十： 及方程式十一： Substituting Equation VII and Equation 8 and Equation IX into Equation 6 respectively, the meshing condition of the bar and the roller can be obtained, which is recorded as Equation 10: And Equation 11:

將l=cos θ，m=sin θ，n=0代入方程式十和方程式十一，並經過整理化簡，可得棒材與上輥輪的嚙合條件，記為方程式十二： Substituting l =cos θ , m =sin θ , n =0 into equations 10 and eleven, and after simplification, the meshing condition of the bar and the upper roller can be obtained, which is recorded as equation 12:

由上述相同的方法，可獲得棒材與下輥輪的嚙合條件方程式十三： According to the same method as described above, the meshing condition equation 13 of the bar and the lower roller can be obtained:

同時由方程式四及方程式十二可獲得上輥輪之幾何模型數學式，而由方程式五與方程式十三可獲得下輥輪之幾何模型數學式。將上面求得的上下輥輪數學模型， 輸入數學運算軟體，可繪出輥輪幾何模型，並使用Turbo C++將程式做點資料輸出，轉至Mastercam，再轉至SolidWorks做實體建模。 At the same time, the geometric model of the upper roller can be obtained from Equation 4 and Equation 12, and the geometric model of the lower roller can be obtained from Equation 5 and Equation 13. The mathematical model of the upper and lower rollers obtained above, Enter the mathematical software to draw the geometric model of the roller, and use Turbo C++ to output the program data, transfer to Mastercam, and then transfer to SolidWorks for solid modeling.

本發明利用包絡理論建構斜輥式矯直機精輥段輥輪模型之方法於設計上利用以棒材在矯直過程中螺旋前進的運動方式為條件，利用包絡理論建構其輥輪之輪廓，其可有效改善傳統矯直輥輪的弊端，而利用由棒材之螺旋前進方向為包絡方法的相對運動關係，完成後的精輥段輥輪輪廓，能有效改善傳統輥輪於加工後留下螺旋紋，對棒材表面的光度與真圓度有極大之改進，可提高斜輥式矯直機的矯直品質，而為了讓上述目的、技術特徵以及實際實施後之增益性更為明顯易懂，於下文中將係以較佳之實施範例輔佐對應相關之圖式來進行更詳細之說明。 The method for constructing the roller model of the fine roller section of the inclined roller straightening machine by using the envelope theory is designed to utilize the enveloping theory to construct the contour of the roller by using the movement mode of the spiral advancement of the bar during the straightening process. The utility model can effectively improve the disadvantages of the traditional straightening roller, and utilizes the relative motion relationship of the spiral traveling direction of the bar as the enveloping method, and the finished fine roller segment roller contour can effectively improve the traditional roller leaving after processing. The spiral pattern greatly improves the luminosity and roundness of the surface of the bar, and can improve the straightening quality of the inclined roller straightening machine, and the above purpose, technical features and gain after actual implementation are more obvious. In the following, a more detailed description will be given in conjunction with the corresponding drawings in the preferred embodiments.

為利 貴審查員瞭解本發明之發明特徵、內容與優點及其所能達成之功效，茲將本發明配合附圖，並以實施例之表達形式詳細說明如下，而其中所使用之圖式，其主旨僅為示意及輔助說明書之用，未必為本發明實施後之真實比例與精準配置，故不應就所附之圖式的比例與配置關係侷限本發明於實際實施上的專利範圍，合先敘明。 The present invention will be described in conjunction with the accompanying drawings in the accompanying drawings, and the drawings The subject matter is only for the purpose of illustration and supplementary description. It is not necessarily the true proportion and precise configuration after the implementation of the present invention. Therefore, the scope and configuration relationship of the attached drawings should not be limited to the scope of patent application of the present invention. Narration.

請配合參看第一圖所示，本發明係為一種利用包絡 理論建構斜輥式矯直機精輥段輥輪模型之方法，一般在矯直的後段，棒材須經過輥光的的過程，才能實現良好的表面光度效果，也就是棒材在連續旋轉前進的過程中，經過與兩輥輪上下線接觸推導出輥型曲線，對棒材才有輥光的效果，因此本發明係使用包絡理論和齊次座標轉換矩陣為工具，配合機構的座標系建立，建構創成面棒材在空間中運動時所產生的曲面族方程式，再配合包絡理論的方法，以獲得棒材與輥輪在空間中運動時與其相互共軛的嚙合條件，由嚙合條件及曲面族方程式的同時求解，可獲得被創成面之數學模型並畫出理論輥型曲面的幾何模型。 Please refer to the first figure, the invention is an envelope Theoretically, the method of constructing the roller model of the fine roller section of the inclined roller type straightening machine is generally in the latter stage of straightening, and the bar has to pass through the process of rolling light to achieve a good surface luminosity effect, that is, the bar is continuously rotating forward. In the process, the roll profile is derived by contacting the upper and lower wires of the two rollers, so that the bar has the effect of roller light. Therefore, the present invention uses the envelope theory and the homogeneous coordinate transformation matrix as tools to establish the coordinate system of the mechanism. To construct the surface family equation generated by the creation of the face bar in space, and then cooperate with the envelopment theory to obtain the meshing condition of the bar and the roller conjugate with each other when moving in space, by the meshing condition and the surface Simultaneously solving the family equations, the mathematical model of the created surface can be obtained and the geometric model of the theoretical roll surface can be drawn.

首先，根據微分幾何關係，棒材的幾何曲面輪廓以一條線繞一軸旋轉而得，請配合參看第一圖所示，設圓棒半徑為r，得方程式一為： First, according to the differential geometry relationship, the geometric surface contour of the bar is rotated by a line around an axis. Please refer to the first figure, and set the radius of the round bar to r, and the equation one is:

其中θ和τ為圓棒的兩個參數，再請進一步配合參看第二圖所示，進一步建立之座標系S 1(O 1,X 1,Y 1,Z 1)固定在棒材上，棒材可以r為半徑，繞θ角成為一平面圓，τ沿著Z 1軸向進行延伸成圓棒長度，而成為創成曲面。 Where θ and τ are the two parameters of the round bar, and further cooperation is shown in the second figure, and the further established coordinate system S 1 ( O 1 , X 1 , Y 1 , Z 1 ) is fixed on the bar, the rod The material may have a radius r, a plane circle around the angle θ , and τ extending along the Z 1 axial direction to form a round bar length, thereby forming a curved surface.

再請進一步配合參看第三圖所示，其中建立座標系S 2(X 2,Y 2,Z 2)為S h (X h ,Y h ,Z h )以Y h 為中心轉換α 1角而成，座標系S h 與S f (X f ,Y f ,Z f )兩原點距離為E 1。 Please further cooperate with the third figure, in which the coordinate system S 2 ( X 2 , Y 2 , Z 2 ) is established as S h ( X h , Y h , Z h ) and the α 1 angle is converted with Y h as the center. The distance between the coordinate system S h and S f ( X f , Y f , Z f ) is E 1 .

再者，請進一步配合參看第四圖所示，兩座標系S 1與 S g (X g ,Y g ,Z g )原點距離為E 2，且其夾角為α 2，當下輥輪S 3繞Z g 軸作轉角時，將會帶動座標系S 1繞Z f 軸旋轉角並移動距離。所以，將圖三及圖四兩座標系結合觀看，可知上下輥輪作旋轉運動時，圓棒將繞Z f 作螺旋運動前進，進行棒材輥光工作。分別求得棒材從S 1到S 2與S 1到S 3座標轉換的曲面族方程式可表示為方程式二：R 2=M 2h ．M hf ．M f1．R 1及方程式三：R 3=M 3g ．M gf ．M f1．R 1 Furthermore, please further refer to the fourth figure, the distance between the two coordinate systems S 1 and S g ( X g , Y g , Z g ) is E 2 , and the angle is α 2 , the current roller S 3 Turn around the Z g axis At the corner, it will drive the coordinate system S 1 to rotate around the Z f axis. Angle and move distance. Therefore, FIG and FIG forty-two three lines labeled binding view, upper and lower rollers during rotation understood rotational motion, around the rod a helical forward movement for Z f, for light work roll bar. The surface family equations for the transformation of the bar from S 1 to S 2 and S 1 to S 3 can be expressed as Equation 2: R 2 = M 2 h . M hf . M f 1 . R 1 and Equation 3: R 3 = M 3 g . M gf . M f 1 . R 1

將方程式一代入方程式二及方程式三可進一步獲得用於求得上、下輥輪的棒材曲面族方程式，而因座標轉換矩陣式子過長，故將三角函數sin簡化為s，三角函數cos簡化為c，表示為方程式四： 及方程式五： By substituting the equation into Equation 2 and Equation 3, the equations for the curved surface of the bar for obtaining the upper and lower rollers can be further obtained. Since the coordinate transformation matrix is too long, the trigonometric function sin is simplified to s, and the trigonometric function cos Simplified to c, expressed as equation four: And equation five:

R 2及R 3分別表示棒材曲面族的位置向量，表示在S 2及S 3座標系，而這裡R 1是方程式一的棒材幾何方程式。 R 2 and R 3 respectively represent position vectors of the bar surface family, which are represented by the S 2 and S 3 coordinate systems, where R 1 is the bar geometry equation of Equation 1.

由包絡原理得知棒材的法向量必須與棒材和輥輪的相對速度相互垂直，表示為方程式六： It is known from the envelope principle that the normal vector of the bar must be perpendicular to the relative velocity of the bar and the roller, expressed as Equation 6:

下標f表示在固定座標S f 下，根據微分幾何，棒材的單位法向量為n=[cos θ]i+[sin θ]j，令l=cos θ，m=sin θ，n=0，可將棒材的法向量表示在S f 座標系，表示為方程式七： The subscript f indicates that under the fixed coordinate S f , according to the differential geometry, the unit normal vector of the bar is n = [cos θ ] i + [sin θ ] j , let l = cos θ , m = sin θ , n =0 The normal vector of the bar can be expressed in the S f coordinate system, expressed as Equation 7:

由相對速度的方法可求得棒材與輥輪的相對速度向量，並表示在固定座標，記為方程式八： 及方程式九： The relative velocity vector of the bar and the roller can be obtained by the relative velocity method and expressed at the fixed coordinate, which is written as Equation 8: And equation nine:

將方程式七和方程式八與方程式九分別代入方程式六，可得棒材與輥輪的嚙合條件，記為方程式十： 及方程式十一： Substituting Equation VII and Equation 8 and Equation IX into Equation 6 respectively, the meshing condition of the bar and the roller can be obtained, which is recorded as Equation 10: And Equation 11:

將l=cos θ，m=sin θ，n=0代入方程式十和方程式十一，並經過整理化簡，可得棒材與上輥輪的嚙合條件，記為方程式十二： Substituting l =cos θ , m =sin θ , n =0 into equations 10 and eleven, and after simplification, the meshing condition of the bar and the upper roller can be obtained, which is recorded as equation 12:

由上述相同的方法，可獲得棒材與下輥輪的嚙合條件方程式十三： According to the same method as described above, the meshing condition equation 13 of the bar and the lower roller can be obtained:

同時由方程式四及方程式十二可獲得上輥輪之幾何模型數學式，而由方程式五與方程式十三可獲得下輥輪之幾何模型數學式。屆此完成數學模組之建構，而後便可利用數學軟體(例如：Mathematica)以進一步畫出圓棒與輥輪的圖形，可進一步配合參看第五圖所示：而根據所求的數學方程式確定無誤之後，更可進一步使用軟體Turbo C++將上下輥輪的數學模型，輸出成點資料至文書處理程式，而後利用電腦輔助軟體程式(例如：Mastercam)，將求得的點資料做連結，完成後的曲線再轉至立體繪圖軟體(例如：SolidWorks)完成幾何建模， 便可確實地建立斜輥式矯直機精輥段輥輪的幾何模型，可配合參看第六圖所示。 At the same time, the geometric model of the upper roller can be obtained from Equation 4 and Equation 12, and the geometric model of the lower roller can be obtained from Equation 5 and Equation 13. The construction of the mathematical module is completed, and then the mathematical software (for example, Mathematica) can be used to further draw the pattern of the round bar and the roller, which can be further matched with the fifth figure: and determined according to the mathematical equation sought. After the error, you can further use the software Turbo C++ to output the mathematical model of the upper and lower rollers to the point processing data, and then use the computer-assisted software program (for example, Mastercam) to link the obtained point data. The curve then goes to the stereoscopic drawing software (for example: SolidWorks) to complete the geometric modeling. The geometric model of the fine roller section roller of the inclined roller straightening machine can be surely established, as shown in the sixth figure.

而透過本發明利用包絡理論建構斜輥式矯直機精輥段輥輪模型之方法於設計上之巧思變化，其利用以棒材在輥光過程中棒材螺旋前進的運動方式為座標設定，利用包絡理論建構其輥輪之輪廓，其可有效改善傳統矯直輥輪的弊端，而利用由棒材與輥輪的運動方式之棒材螺旋前進運動及其座標設定後，可完成精輥段輥輪之輪廓，能有效改善傳統輥輪於加工後留下螺旋紋，對棒材表面的光度與真圓度有極大之改進，可提高斜輥式矯直機的矯直品質，為習知技術所不能及者，故可見其增益性所在。 Through the invention, the method of constructing the fine roller section roller model of the inclined roller straightening machine by using the envelope theory is ingeniously changed in design, and the coordinate setting of the bar spiral advancement during the roller light process is used as the coordinate setting. The envelope theory is used to construct the contour of the roller, which can effectively improve the disadvantages of the traditional straightening roller, and the fine roller can be completed by using the bar spiral forward motion and the coordinate setting by the movement mode of the bar and the roller. The contour of the segment roller can effectively improve the spiral pattern of the traditional roller after processing, greatly improve the luminosity and roundness of the surface of the bar, and improve the straightening quality of the inclined roller straightener. Knowing the technology can not be seen, so it can be seen that its gain.

以上所述之實施例僅係為說明本發明之技術思想及特點，其目的在使熟習此項技藝之人士能夠瞭解本發明之內容並據以實施，當不能以之限定本發明之專利範圍，即大凡依本發明所揭示之精神所作之均等變化或修飾，仍應涵蓋在本發明之專利範圍內。 The embodiments described above are merely illustrative of the technical spirit and the features of the present invention, and the objects of the present invention can be understood by those skilled in the art, and the scope of the present invention cannot be limited thereto. That is, the equivalent variations or modifications made by the spirit of the present invention should still be included in the scope of the present invention.

綜觀上述，可見本發明在突破先前之技術下，確實已達到所欲增進之功效，且也非熟悉該項技藝者所易於思及，其所具之進步性、實用性，顯已符合專利之申請要件，爰依法提出專利申請，懇請 貴局核准本件發明專利申請案，以勵發明，至感德便。 Looking at the above, it can be seen that the present invention has achieved the desired effect under the prior art, and is not familiar with the skill of the artist. The progress and practicability of the invention are in line with the patent. Apply for the requirements, 提出 file a patent application according to law, and ask your bureau to approve the application for the invention patent, in order to invent invention, to the sense of virtue.

第一圖為本發明之利用包絡理論建構斜輥式矯直機精輥段輥輪模型之方法之實施參考圖。 The first figure is an implementation reference diagram of a method for constructing a fine roller section roller model of a skew roll straightening machine by using the envelope theory.

第二圖為本發明之利用包絡理論建構斜輥式矯直機精輥段輥輪模型之方法之實施參考圖。 The second figure is an implementation reference diagram of a method for constructing a fine roller section roller model of a skew roll straightening machine by using the envelope theory.

第三圖為本發明之利用包絡理論建構斜輥式矯直機精輥段輥輪模型之方法之實施參考圖。 The third figure is a reference diagram for implementing the method for constructing the roller model of the fine roller section of the inclined roller straightening machine by using the envelope theory.

第四圖為本發明之利用包絡理論建構斜輥式矯直機精輥段輥輪模型之方法之實施參考圖。 The fourth figure is a reference diagram for implementing the method for constructing the roller model of the fine roller section of the inclined roller straightening machine by using the envelope theory.

第五圖為本發明之利用包絡理論建構斜輥式矯直機精輥段輥輪模型之方法之實施參考圖。 The fifth figure is a reference diagram for implementing the method for constructing the roller model of the fine roller section of the inclined roller straightening machine by using the envelope theory.

第六圖為本發明之利用包絡理論建構斜輥式矯直機精輥段輥輪模型之方法之實施參考圖。 The sixth figure is a reference diagram for implementing the method for constructing the roller model of the fine roller section of the inclined roller straightening machine by using the envelope theory.

Claims (6)

一種利用包絡理論建構斜輥式矯直機精輥段輥輪模型之方法，其首先建立圓棒的幾何模型，假設座標系S 1(O 1,X 1,Y 1,Z 1)是固定在圓棒上，且圓棒半徑為r，得方程式一： τ沿著Z 1軸向進行延伸成圓棒長度，而成為創成曲面；其中上輥輪座標系S 2(X 2,Y 2,Z 2)為S h (X h ,Y h ,Z h )以Y h 為中心轉換α 1角而成，可知座標系S h 與S f (X f ,Y f ,Z f )兩原點距離為E 1；當上輥輪座標系S 2繞Z h 軸旋轉角時，使圓棒座標系S 1(X 1,Y 1,Z 1)沿著Z f 軸上旋轉角，並沿著Z f 軸前進一距離；座標系S 1與S g (O g ,X g ,Y g ,Z g )兩原點距離為E 2，且其夾角為α 2，當下輥輪S 3繞Z g 軸作轉角時，將會帶動棒材座標系S 1繞Z f 軸旋轉角並平移距離；而後將兩座標系結合為求得棒材曲面族方程式，分別求得棒材從S 1到S 2與S 1到S 3座標轉換的曲面族方程式，可表示為方程式二：R 2=M 2h ．M hf ．M f1．R 1及方程式三：R 3=M 3g ．M gf ．M f1．R 1並將方程式一代入方程式二及方程式三可進一步獲得用於求得上、下輥輪的棒材曲面族方程式，表示為方程式四： 及方程式五： 其中s為三角函數sin，c為三角函數cos，R 2及R 3分別表示棒材曲面族的位置向量，表示在S 2及S 3座標系，這裡R 1是方程式一的棒材幾何方程式；由包絡原理得知棒材的法向量必須與棒材和輥輪的相對速度相互垂直，表示為方程式六： 下標f表示在固定座標S f 下，而棒材的單位法向量n=[cos θ]i+[sin θ]j，令l=cos θ，m=sin θ，n=0，可將棒材的法向量表示在S f 座標系，表示為方程式七： 由相對速度的方法可求得棒材與輥輪的相對速度向量，並表示在固定座標，記為方程式八： 及方程式九： 將方程式七和方程式八與方程式九分別代入方程式六，可得棒材與輥輪的嚙合條件，記為方程式十： 及方程式十一： 而後將l=cos θ，m=sin θ，n=0分別代入方程式十和方程式十一，並經過整理化簡，可得棒材與上輥輪的嚙合條件，記為方程式十二： 且可獲得棒材與下輥輪的嚙合條件方程式十三： 同時由方程式四及方程式十二得上輥輪之幾何模型數學式，而由方程式五與方程式十三得下輥輪之幾何模型數學式，以完成模型之數學模組建構。 A method for constructing a fine roller section roller model of a skew roll straightening machine by using envelope theory, firstly establishing a geometric model of a round bar, assuming that the coordinate system S 1 ( O 1 , X 1 , Y 1 , Z 1 ) is fixed at On the round bar, and the radius of the round bar is r, the equation one is obtained: τ extends along the Z 1 axial direction into a round bar length to form a curved surface; wherein the upper roller coordinate system S 2 ( X 2 , Y 2 , Z 2 ) is S h ( X h , Y h , Z h ) It is formed by converting α 1 angle around Y h , and it can be seen that the distance between the coordinates of the coordinate system S h and S f ( X f , Y f , Z f ) is E 1 ; when the upper roller coordinate system S 2 is around the Z h axis Rotate At the corner, the round bar coordinate system S 1 ( X 1 , Y 1 , Z 1 ) is rotated along the Z f axis Angle and advance a distance along the Z f axis The coordinates of the coordinate system S 1 and S g ( O g , X g , Y g , Z g ) are E 2 , and the angle is α 2 , and the lower roller S 3 is rotated around the Z g axis. At the corner, it will drive the bar coordinate system S 1 to rotate around the Z f axis. Angle and pan Distance; then combine the two coordinate systems to obtain the equation of the bar surface family, and obtain the surface family equations of the bar from S 1 to S 2 and S 1 to S 3 coordinates, which can be expressed as Equation 2: R 2 = M 2 h . M hf . M f 1 . R 1 and Equation 3: R 3 = M 3 g . M gf . M f 1 . R 1 and the first generation of the equation into Equation 2 and Equation 3 can further obtain the equation of the bar surface family for obtaining the upper and lower rollers, which is expressed as Equation 4: And equation five: Where s is the trigonometric function sin, c is the trigonometric function cos, R 2 and R 3 respectively represent the position vector of the bar surface family, denoted in the S 2 and S 3 coordinate systems, where R 1 is the bar geometry equation of Equation 1; It is known from the envelope principle that the normal vector of the bar must be perpendicular to the relative velocity of the bar and the roller, expressed as Equation 6: The subscript f indicates that under the fixed coordinate S f , and the unit normal vector of the bar n = [cos θ ] i + [sin θ ] j , let l = cos θ , m = sin θ , n =0, the rod can be The normal vector of the material is expressed in the S f coordinate system and is expressed as Equation 7: The relative velocity vector of the bar and the roller can be obtained by the relative velocity method and expressed at the fixed coordinate, which is written as Equation 8: And equation nine: Substituting Equation VII and Equation 8 and Equation IX into Equation 6 respectively, the meshing condition of the bar and the roller can be obtained, which is recorded as Equation 10: And Equation 11: Then l = cos θ , m = sin θ , n =0 are substituted into Equation 10 and Equation XI respectively, and after simplification, the meshing condition of the bar and the upper roller can be obtained, which is recorded as Equation 12: And the meshing condition of the bar and the lower roller can be obtained. At the same time, the geometric model of the roller is obtained from Equation 4 and Equation 12, and the geometric model of the roller is obtained from Equation 5 and Equation 13 to complete the mathematical module construction of the model. 如申請專利範圍第1項所述之利用包絡理論建構 斜輥式矯直機精輥段輥輪模型之方法，其中可利用一數學軟體以進一步畫出前述數學模組建構後之圓棒與輥輪的圖形。 Envelope theory construction as described in item 1 of the patent application scope The method of the fine roller section roller model of the inclined roller straightening machine, wherein a mathematical software body can be utilized to further draw the pattern of the round bar and the roller after the construction of the mathematical module. 如申請專利範圍第2項所述之利用包絡理論建構斜輥式矯直機精輥段輥輪模型之方法，其中該數學繪圖軟體為Mathematica。 The method for constructing a fine roller section roller model of a skew roll straightening machine according to the envelopment theory described in claim 2, wherein the mathematical drawing software is Mathematica. 如申請專利範圍第1項所述之利用包絡理論建構斜輥式矯直機精輥段輥輪模型之方法，其中可進一步使用軟體Turbo C++將輥輪數學式輸出的點資料輸出至文書處理程式，而後利用電腦輔助製造軟體將求得的點資料做連結，以連結完成一曲線。 The method for constructing the fine roller section roller model of the inclined roller straightening machine by using the envelope theory as described in the first aspect of the patent application, wherein the point data of the mathematical output of the roller can be further output to the word processing program by using the software Turbo C++. Then, the computer-assisted manufacturing software is used to link the obtained point data to complete the curve. 如申請專利範圍第1項，斜輥式矯直機精輥段輥輪模型的建立，是棒材做螺旋運動而得。 For example, in the first application of patent scope, the establishment of the roller model of the fine roller section of the inclined roller straightening machine is obtained by the spiral motion of the bar. 如申請專利範圍第4項所述之利用包絡理論建構斜輥式矯直機精輥段輥輪模型之方法，其中將該曲線儲存成一般繪圖軟體常用的工程用立體外觀圖形檔，再將該圖形檔輸入至工程用立體繪圖軟體完成幾何建模，便建立斜輥式矯直機精輥段輥輪的幾何模型。 The method for constructing a fine roll section roller model of a skew roll straightening machine by using the envelope theory as described in claim 4, wherein the curve is stored into a three-dimensional appearance graphic file commonly used for general drawing software, and then The graphic file is input into the engineering stereoscopic drawing software to complete the geometric modeling, and the geometric model of the fine roller section roller of the inclined roller straightening machine is established.
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