TWI819918B - A method for forming and processing spiral workpieces - Google Patents

A method for forming and processing spiral workpieces Download PDF

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TWI819918B
TWI819918B TW111147037A TW111147037A TWI819918B TW I819918 B TWI819918 B TW I819918B TW 111147037 A TW111147037 A TW 111147037A TW 111147037 A TW111147037 A TW 111147037A TW I819918 B TWI819918 B TW I819918B
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spiral
workpiece
grinding wheel
grinding
linear speed
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TW202423579A (en
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黃金龍
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國立虎尾科技大學
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Abstract

一種螺旋工件的成形加工方法，係利用一砂輪以一砂輪線速輪磨一待成形螺旋工件以形成一螺旋工件之一齒面，取得該待成形螺旋工件接觸該砂輪時的一節圓直徑的一底徑及一大徑，所分別對應之該待成形螺旋工件的一第一螺旋線速及一第二螺旋線速；接著，以一介於該第一螺旋線速及該第二螺旋線速之間的螺旋線速的輪磨進給率，驅動該砂輪對該待成形螺旋工件進行輪磨加工。A method of forming a spiral workpiece, which uses a grinding wheel to grind a spiral workpiece to be formed with a grinding wheel linear speed wheel to form a tooth surface of the spiral workpiece, and obtains a pitch diameter of the spiral workpiece to be formed when it contacts the grinding wheel. The bottom diameter and the major diameter respectively correspond to a first spiral linear speed and a second spiral linear speed of the spiral workpiece to be formed; then, a value between the first spiral linear speed and the second spiral linear speed is used. The grinding feed rate of the spiral linear speed in between drives the grinding wheel to grind the spiral workpiece to be formed.

Description

一種螺旋工件的成形加工方法A method for forming and processing spiral workpieces

本發明關於一種工件的成形加工方法，尤指一種螺旋工件的成形加工方法。 The present invention relates to a forming and processing method of a workpiece, in particular to a forming and processing method of a spiral workpiece.

螺旋工件(例如蝸桿)為以蝸桿成形輪磨機加工而成，輪磨加工蝸桿的效率取決於輪磨的螺旋線速(Helical Speed)。當螺旋線速低時，加工效率不佳；但當螺旋線速過高，則會產生加工表面燒焦的問題，因此可以理解的是，砂輪對待加工蝸桿有一適當的螺旋線速區間，可以在不發生燒焦問題的前提下，有效地加工蝸桿。 Spiral workpieces (such as worms) are processed by worm-forming wheel grinders. The efficiency of wheel grinding to process worms depends on the helical speed (Helical Speed) of the wheel grinding. When the spiral linear speed is low, the processing efficiency is poor; but when the spiral linear speed is too high, the problem of burning of the processed surface will occur. Therefore, it is understandable that the grinding wheel has an appropriate spiral linear speed range for the worm to be processed, which can be Efficiently process the worm without causing scorching problems.

然而，對於市售或已知的蝸桿成形輪磨機來說，僅可供使用者輸入及設定輪磨的進給率(Feed Rate)，而砂輪則按照該輪磨進給率對待加工蝸桿加工。換言之，使用者並無法輸入及設定螺旋線速，也不會知道當下對應的螺旋線速，僅能以經驗或試誤法來操作輪磨機。不僅缺乏一致性，且可能在嘗試的過程中造成工件毀損。 However, for commercially available or known worm shaping wheel grinders, the user can only input and set the feed rate of the wheel grinding, and the grinding wheel processes the worm to be processed according to the grinding feed rate. . In other words, the user cannot input and set the spiral linear speed, nor does he know the current corresponding spiral linear speed. He can only operate the wheel grinder based on experience or trial and error. Not only is there a lack of consistency, but the workpiece may be damaged in the attempt.

本發明的主要目的在於解決習知因為無法得知實際輪磨時的螺旋線速，而無法有效加工螺旋工件的問題。 The main purpose of the present invention is to solve the conventional problem of being unable to effectively process spiral workpieces because the spiral linear speed during actual wheel grinding cannot be known.

為達上述目的，本發明提供螺旋工件的成形加工方法，係利用一砂輪輪磨一待成形螺旋工件以形成一螺旋工件之一齒面，該砂輪接觸該待成形螺旋工件，該方法包括以下步驟： In order to achieve the above object, the present invention provides a forming processing method of a spiral workpiece, which uses a grinding wheel to grind a spiral workpiece to be formed to form a tooth surface of the spiral workpiece, and the grinding wheel contacts the spiral workpiece to be formed. The method includes the following steps :

步驟S1-1：由下式1取得對應該待成形螺旋工件接觸該砂輪時的一節圓直徑的一底徑D p,d1及一大徑D p,d2之該待成形螺旋工件的一第一螺旋線速H s,d1及一第二螺旋線速H s,d2。 Step S1-1: Obtain a base diameter D p, d 1 and a major diameter D p, d 2 of the spiral workpiece to be formed corresponding to the pitch circle diameter when the spiral workpiece to be formed contacts the grinding wheel from the following formula 1. The linear speed of the first spiral is H s,d 1 and the linear speed of the second spiral is H s,d 2 .

Figure 111147037-A0305-02-0003-1
Figure 111147037-A0305-02-0003-1

其中，s為該待成形螺旋工件相對該砂輪的一平移速度，且

Figure 111147037-A0305-02-0003-2
，p為該待成形螺旋工件的一螺旋參數，
Figure 111147037-A0305-02-0003-3
，λ為該待成形螺旋工件的一螺旋導程，F r 為一輪磨進給率。 Among them, s is the translation speed of the spiral workpiece to be formed relative to the grinding wheel, and
Figure 111147037-A0305-02-0003-2
, p is a spiral parameter of the spiral workpiece to be formed,
Figure 111147037-A0305-02-0003-3
, λ is the spiral lead of the spiral workpiece to be formed, F r is the feed rate of one-wheel grinding.

其中，

Figure 111147037-A0305-02-0003-4
，ω為該待成形螺旋工件相對該砂輪的一角 速率，
Figure 111147037-A0305-02-0003-5
。 in,
Figure 111147037-A0305-02-0003-4
, ω is the angular velocity of the spiral workpiece to be formed relative to the grinding wheel,
Figure 111147037-A0305-02-0003-5
.

步驟S1-2：得到該第一螺旋線速H s,d1及該第二螺旋線速H s,d2後，以介於該第一螺旋線速H s,d1及該第二螺旋線速H s,d2之間的一加工螺旋線速所對應的一加工輪磨進給率，驅動該砂輪對該待成形螺旋工件進行輪磨加工。 Step S1-2: After obtaining the first spiral linear speed H s,d 1 and the second spiral linear speed H s,d 2 , calculate the linear speed between the first spiral linear speed H s ,d 1 and the second spiral linear speed H s,d 1 A processing wheel grinding feed rate corresponding to a processing spiral line speed between the linear speed H s,d 2 drives the grinding wheel to grind the spiral workpiece to be formed.

為達上述目的，本發明還提供一種螺旋工件的成形加工方法，包括以下步驟： In order to achieve the above object, the present invention also provides a forming and processing method of a spiral workpiece, which includes the following steps:

步驟S2-1：取得一第一砂輪對一第一待成形螺旋工件的一第一輪磨進給率。 Step S2-1: Obtain a first grinding feed rate of a first grinding wheel on a first spiral workpiece to be formed.

步驟S2-2：根據該第一輪磨進給率，由下式1取得該第一砂輪接觸並加工該第一待成形螺旋工件時的一螺旋線速H s ：

Figure 111147037-A0305-02-0003-6
其中，s為該第一待成形螺旋工件相對該第一砂輪的一平移速度，且
Figure 111147037-A0305-02-0004-7
，p為該第一待成形螺旋工件的一螺旋參數，
Figure 111147037-A0305-02-0004-9
，λ為該第一待成形螺旋工件的一螺旋導程，F r 為該第一輪磨進給率，v=
Figure 111147037-A0305-02-0004-10
，ω為該第一待成形螺旋工件相對該第一砂輪的一角速率，ω
Figure 111147037-A0305-02-0004-11
，D p 為該待成形螺旋工件接觸該砂輪時的一節圓直徑。 Step S2-2: According to the first wheel grinding feed rate, obtain a spiral linear speed H s when the first grinding wheel contacts and processes the first spiral workpiece to be formed by the following formula 1:
Figure 111147037-A0305-02-0003-6
 Where, s is a translation speed of the first spiral workpiece to be formed relative to the first grinding wheel, and
Figure 111147037-A0305-02-0004-7
, p is a spiral parameter of the first spiral workpiece to be formed,
Figure 111147037-A0305-02-0004-9
, λ is the spiral lead of the first spiral workpiece to be formed, F r is the feed rate of the first wheel grinding, v =
Figure 111147037-A0305-02-0004-10
, ω is the angular velocity of the first spiral workpiece to be formed relative to the first grinding wheel, ω
Figure 111147037-A0305-02-0004-11
, D p is the diameter of the pitch circle when the spiral workpiece to be formed contacts the grinding wheel.

步驟S2-3：提供一與該第一砂輪相同材質的第二砂輪以及一與該第一待成形螺旋工件相同材質但不同規格的第二待成形螺旋工件。 Step S2-3: Provide a second grinding wheel of the same material as the first grinding wheel and a second spiral workpiece to be formed of the same material but different specifications as the first spiral workpiece to be formed.

步驟S2-4：以該螺旋線速H s 作為一螺旋線速參考值，根據該第二待成形螺旋工件的參數利用(式1)，從該螺旋線速參考值取得該第二砂輪對該第二待成形螺旋工件的一第二輪磨進給率。 Step S2-4: Use the spiral linear speed H s as a spiral linear speed reference value, and use (Formula 1) according to the parameters of the second spiral workpiece to be formed to obtain the second grinding wheel's response to the spiral linear speed reference value from the spiral linear speed reference value. A second grinding feed rate for the second spiral workpiece to be formed.

步驟S2-5：以該第二輪磨進給率驅動該第二砂輪對該第二待成形螺旋工件進行輪磨加工。 Step S2-5: Drive the second grinding wheel at the second grinding feed rate to grind the second spiral workpiece to be formed.

綜上所述，透過本發明方法，可以得知該螺旋線速，以提供作為加工時的參考。 In summary, through the method of the present invention, the spiral linear speed can be known to provide a reference during processing.

1:待成形螺旋工件 1: Spiral workpiece to be formed

4:砂輪 4: Grinding wheel

D p,d1:底徑 D p,d 1 : bottom diameter

D p,d2:大徑 D p,d 2 : major diameter

F r :進給率 F r : feed rate

s:平移速度 s : translation speed

ω:角速率 ω: angular rate

γ:導程角 γ:lead angle

E:中心距 E: center distance

S1-1、S1-2、S2-1、S2-2、S2-3、S2-4、S2-5:步驟 S1-1, S1-2, S2-1, S2-2, S2-3, S2-4, S2-5: steps

(Xw,g,Yg,Zg):砂輪座標系統 (X w,g ,Y g ,Z g ): Grinding wheel coordinate system

(Xw,g,Yw,Zw):工件座標系統 (X w,g ,Y w ,Z w ): workpiece coordinate system

『圖1』，為本發明一實施例中，蝸桿成形輪磨機的示意圖。 [Fig. 1] is a schematic diagram of a worm forming wheel grinder in one embodiment of the present invention.

『圖2』，為本發明一實施例的步驟流程圖。 [Fig. 2] is a step flow chart of an embodiment of the present invention.

『圖3』，為本發明一實施例中，砂輪與待成形螺旋工件的關係示意圖。 [Fig. 3] is a schematic diagram of the relationship between the grinding wheel and the spiral workpiece to be formed in an embodiment of the present invention.

『圖4』，為本發明一實施例中，待成形螺旋工件的示意圖。 [Fig. 4] is a schematic diagram of a spiral workpiece to be formed in an embodiment of the present invention.

『圖5』，為本發明一實施例中，砂輪的進給速率與合成速率的示意圖。 [Fig. 5] is a schematic diagram of the feed rate and synthesis rate of the grinding wheel in an embodiment of the present invention.

『圖6』，為本發明另一實施例的步驟流程圖。 [Fig. 6] is a step flow chart of another embodiment of the present invention.

本發明公開一種螺旋工件的成形加工方法，參閱『圖1』，為本發明一實施例中蝸桿成形輪磨機的示意圖，係利用一砂輪4輪磨一待成形螺旋工件1，以在該待成形螺旋工件1上形成預期的一螺旋工件之一齒面。在輪磨時，該砂輪4接觸該待成形螺旋工件1，且該砂輪4是以一螺旋線速對該待成形螺旋工件1進行加工。在以下實施例中，該待成形螺旋工件1是以一蝸桿作為舉例說明，但本發明並不限於此，在其他實施例中，該待成形螺旋工件1亦可為其他工件。 The present invention discloses a forming processing method of a spiral workpiece. Refer to "Figure 1", which is a schematic diagram of a worm forming wheel grinder in one embodiment of the present invention. A grinding wheel 4 is used to grind a spiral workpiece 1 to be formed, so that the spiral workpiece 1 is to be formed. A tooth surface of a desired spiral workpiece is formed on the forming spiral workpiece 1 . During wheel grinding, the grinding wheel 4 contacts the spiral workpiece 1 to be formed, and the grinding wheel 4 processes the spiral workpiece 1 to be formed at a spiral linear speed. In the following embodiments, the spiral workpiece 1 to be formed is a worm as an example, but the invention is not limited thereto. In other embodiments, the spiral workpiece 1 to be formed can also be other workpieces.

根據本發明一實施例，該蝸桿成形輪磨機僅能供使用者輸入及設定輪磨的進給率(Feed Rate，F r )，而該砂輪4則按照該進給率對該待成形螺旋工件1加工。根據本發明一實施例的方法，係可以在已知該進給率F r 的情況下，求出對應的螺旋線速(Helical Speed，H s )。換言之，使用者可以根據該進給率F r 及該螺旋線速H s 之間的關係，利用期望的該螺旋線速H s 對該待成形螺旋工件1加工。 According to an embodiment of the present invention, the worm forming wheel grinder only allows the user to input and set the feed rate ( Fr ) of the wheel grinding, and the grinding wheel 4 grinds the spiral to be formed according to the feed rate. Workpiece 1 is processed. According to the method of an embodiment of the present invention, the corresponding helical speed ( H s ) can be obtained when the feed rate Fr is known. In other words, the user can process the spiral workpiece 1 to be formed using the desired spiral linear speed H s according to the relationship between the feed rate Fr and the spiral linear speed H s .

參閱『圖2』，以下為本發明一實施例的方法，包括步驟S1-1至步驟S1-2： Referring to "Figure 2", the following is a method according to an embodiment of the present invention, including step S1-1 to step S1-2:

步驟S1-1：基於該待成形螺旋工件1的輪廓，當加工時，該砂輪4會接觸該待成形螺旋工件1的一底徑D p,d1(螺旋最小直徑)以及一大徑D p,d2(螺旋最大直徑)，如『圖4』所示。本步驟是利用下式1取得該待成形螺旋工件1接觸該砂輪4時的一節圓直徑的一底徑 D p,d1及一大徑D p,d2所對應之該待成形螺旋工件1的一第一螺旋線速H s,d1及一第二螺旋線速H s,d2：

Figure 111147037-A0305-02-0006-12
Step S1-1: Based on the contour of the spiral workpiece 1 to be formed, when processing, the grinding wheel 4 will contact a bottom diameter D p, d 1 (minimum diameter of the spiral) and a major diameter D p of the spiral workpiece 1 to be formed. ,d 2 (maximum diameter of spiral), as shown in "Figure 4". This step is to use the following formula 1 to obtain a base diameter D p, d 1 and a major diameter D p, d 2 of the pitch circle diameter of the spiral workpiece 1 to be formed when it contacts the grinding wheel 4 . A first spiral linear speed H s,d 1 and a second spiral linear speed H s,d 2 :
Figure 111147037-A0305-02-0006-12

s為該待成形螺旋工件1相對該砂輪4的一平移速度，且s=

Figure 111147037-A0305-02-0006-13
，p為該待成形螺旋工件1的一螺旋參數，
Figure 111147037-A0305-02-0006-14
，λ為該待成形螺旋工件1的一螺旋導程，F r 為一輪磨進給率。 s is the translation speed of the spiral workpiece 1 to be formed relative to the grinding wheel 4, and s =
Figure 111147037-A0305-02-0006-13
, p is a spiral parameter of the spiral workpiece 1 to be formed,
Figure 111147037-A0305-02-0006-14
, λ is the spiral lead of the spiral workpiece 1 to be formed, and F r is the feed rate of one-wheel grinding.

v為該節圓直徑處的切線速度，

Figure 111147037-A0305-02-0006-15
，ω為該待成形螺旋 工件1相對該砂輪4的一角速率，
Figure 111147037-A0305-02-0006-16
。 v is the tangent velocity at the diameter of the pitch circle,
Figure 111147037-A0305-02-0006-15
, ω is the angular velocity of the spiral workpiece 1 to be formed relative to the grinding wheel 4,
Figure 111147037-A0305-02-0006-16
.

在以上的參數中，該平移速度s以及該輪磨進給率F r 可視為該砂輪4輪磨該待成形螺旋工件1的預期加工條件，為一預先設定且已知的值。 Among the above parameters, the translation speed s and the grinding feed rate F r can be regarded as the expected processing conditions of the grinding wheel 4 grinding the spiral workpiece 1 to be formed, and are a preset and known value.

該螺旋導程λ為同螺旋線上相鄰對應點的軸向距離，參閱『圖3』，顯示了砂輪座標系統(Xw,g,Yg,Zg)及工件座標系統(Xw,g,Yw,Zw)，『圖3』中的E為一中心距，一導程角γ可由下式2取得：

Figure 111147037-A0305-02-0006-17
The spiral lead λ is the axial distance between adjacent corresponding points on the same spiral line. Refer to "Figure 3", which shows the grinding wheel coordinate system (X w, g , Y g , Z g ) and the workpiece coordinate system (X w, g ,Y w ,Z w ), E in "Figure 3" is a center distance, and a lead angle γ can be obtained from the following formula 2:
Figure 111147037-A0305-02-0006-17

m x 為該待成形螺旋工件1的一軸向模數，Z為該待成形螺旋工件1的一蝸桿齒數，D p 為該待成形螺旋工件1的一節圓直徑。該軸向模數m x 以及該蝸桿齒數Z為與該待成形螺旋工件1相關的參數，為已知的值。 m x is an axial module of the spiral workpiece 1 to be formed, Z is the number of worm teeth of the spiral workpiece 1 to be formed, and D p is the pitch circle diameter of the spiral workpiece 1 to be formed. The axial module m x and the number of worm teeth Z are parameters related to the spiral workpiece 1 to be formed, and are known values.

得到該導程角γ後，將該導程角γ代入下式3，可取得該螺旋導程λ：λ=πD p tan γ (式3) After obtaining the lead angle γ, substitute the lead angle γ into the following equation 3 to obtain the spiral lead λ: λ=π D p tan γ (equation 3)

在本實施例中，式2及式3的該節圓直徑D p 是採用該砂輪4接觸該待成形螺旋工件1的假想圓柱體的最小直徑以及最大直徑的一任意值，例如平均值。 In this embodiment, the pitch circle diameter D p in Equations 2 and 3 is an arbitrary value, such as an average value, of the minimum diameter and the maximum diameter of the imaginary cylinder in which the grinding wheel 4 contacts the spiral workpiece 1 to be formed.

有關該角速率ω的公式推導，詳述如後。參閱『圖5』，為本發明一實施例中，砂輪的進給速率與合成速率的示意圖，該角速率ω與該平移速度s之關係可由螺旋同動時之螺旋參數p得知，如下式4表示：根據『圖5』以及式4可得到下式5：

Figure 111147037-A0305-02-0007-40
The derivation of the formula for the angular rate ω is detailed below. Refer to "Figure 5", which is a schematic diagram of the feed rate and the combined rate of the grinding wheel in an embodiment of the present invention. The relationship between the angular rate ω and the translation speed s can be known from the spiral parameter p when the spiral moves together, as shown in the following formula 4 means: According to "Figure 5" and Formula 4, the following Formula 5 can be obtained:
Figure 111147037-A0305-02-0007-40

整理後即得：

Figure 111147037-A0305-02-0007-19
。 After sorting, you will get:
Figure 111147037-A0305-02-0007-19
.

步驟S1-2：得到該第一螺旋線速H s,d1及該第二螺旋線速H s,d2後，以介於該第一螺旋線速H s,d1及該第二螺旋線速H s,d2之間的一加工螺旋線速所對應的一加工輪磨進給率，驅動該砂輪4對該待成形螺旋工件1進行輪磨加工。本步驟中，係先定義出該加工螺旋線速，例如可取該第一螺旋線速H s,d1及該第二螺旋線速H s,d2之間的平均值，亦可為該第一螺旋線速H s,d1及該第二螺旋線速H s,d2之間的任意值。 Step S1-2: After obtaining the first spiral linear speed H s,d 1 and the second spiral linear speed H s,d 2 , calculate the linear speed between the first spiral linear speed H s ,d 1 and the second spiral linear speed H s,d 1 A processing wheel grinding feed rate corresponding to a processing spiral line speed between the linear speed H s,d 2 drives the grinding wheel 4 to grind the spiral workpiece 1 to be formed. In this step, the processing spiral linear speed is first defined. For example, it can be the average value between the first spiral linear speed H s,d 1 and the second spiral linear speed H s,d 2 , or it can be the Any value between the first spiral linear speed H s,d 1 and the second spiral linear speed H s,d 2 .

由於在加工時，該待成形螺旋工件1和該砂輪4所接觸的一假想圓柱體的最小直徑以及最大直徑即分別為該底徑D p,d1以及該大徑D p,d2。換言之，若以超過該大徑D p,d2所對應的螺旋線速或是低於該底徑D p,d1所對應的的螺旋線速來進行加工，可能會有過度加工或線速偏低的問題。 During processing, the minimum diameter and the maximum diameter of an imaginary cylinder in contact with the spiral workpiece 1 to be formed and the grinding wheel 4 are the bottom diameter D p,d 1 and the major diameter D p,d 2 respectively. In other words, if processing is performed at a spiral linear speed exceeding the major diameter D p,d 2 or lower than the spiral linear speed corresponding to the bottom diameter D p,d 1 , there may be over-processing or linear speed. Low problem.

另一方面，特定材料的砂輪對於特定材料的螺旋工件係具有相同的最佳螺旋線速。換言之，對於不同規格(例如不同的尺寸、 輪廓或齒數)的螺旋工件來說，只要所使用的砂輪的材料以及螺旋工件的材料相同，適合的螺旋線速就相同。但對於一般的成形輪磨機或成形加工方法來說，並無法得知加工當下的螺旋線速，又對於不同規格的螺旋工件，軸向模數m x 、蝸桿齒數Z以及/或節圓直徑D p 也會不同，因此，即便知道了螺旋線速，也無法準確地得知應該在成形輪磨機輸入或設定的螺旋線速。 On the other hand, a grinding wheel of a specific material has the same optimal spiral linear speed for a spiral workpiece of a specific material. In other words, for spiral workpieces with different specifications (such as different sizes, profiles or number of teeth), as long as the material of the grinding wheel used and the material of the spiral workpiece are the same, the suitable spiral linear speed is the same. However, for general forming wheel grinders or forming processing methods, it is impossible to know the current spiral line speed during processing, and for spiral workpieces of different specifications, the axial module m x , the number of worm teeth Z and/or the pitch circle diameter D p will also be different. Therefore, even if the spiral linear speed is known, the spiral linear speed that should be input or set in the forming wheel grinder cannot be accurately known.

根據本發明另一實施例，提供一種螺旋工件的成形加工方法，本方法適用於輪磨多個相同材質且不同規格的待成形螺旋工件，參閱『圖6』，包括以下步驟S2-1至步驟S2-5： According to another embodiment of the present invention, a method for forming spiral workpieces is provided. This method is suitable for grinding multiple spiral workpieces of the same material and different specifications to be formed. Refer to "Figure 6" and includes the following steps S2-1 to steps S2-5:

步驟S2-1：先取得一第一砂輪對一第一待成形螺旋工件的一第一輪磨進給率。在一實施例中，例如可預先以試誤法取得一參考用的輪磨進給率，在該參考用的輪磨進給率下，該第一砂輪相對該第一待成形螺旋工件有一較佳或最佳的加工效率。 Step S2-1: First obtain a first grinding feed rate of a first grinding wheel on a first spiral workpiece to be formed. In one embodiment, for example, a reference wheel grinding feed rate can be obtained in advance through a trial and error method. At the reference wheel grinding feed rate, the first grinding wheel has a relatively large gap relative to the first spiral workpiece to be formed. Best or best processing efficiency.

步驟S2-2：根據該第一輪磨進給率，由式1取得該第一砂輪接觸並加工該第一待成形螺旋工件時的一螺旋線速H s ：

Figure 111147037-A0305-02-0008-20
s為該第一待成形螺旋工件相對該第一砂輪的一平移速度s，s=
Figure 111147037-A0305-02-0008-21
，p為該第一待成形螺旋工件的一螺旋參數，
Figure 111147037-A0305-02-0008-22
，λ為該第 一待成形螺旋工件的一螺旋導程，F r 為該第一輪磨進給率，
Figure 111147037-A0305-02-0008-23
，ω為該第一待成形螺旋工件相對該第一砂輪的一角速率，ω=
Figure 111147037-A0305-02-0008-24
，D p 為該待成形螺旋工件接觸該砂輪時的一節圓直徑。 Step S2-2: According to the first wheel grinding feed rate, obtain a spiral linear speed H s when the first grinding wheel contacts and processes the first spiral workpiece to be formed by Equation 1:
Figure 111147037-A0305-02-0008-20
 s is a translation speed s of the first spiral workpiece to be formed relative to the first grinding wheel, s =
Figure 111147037-A0305-02-0008-21
, p is a spiral parameter of the first spiral workpiece to be formed,
Figure 111147037-A0305-02-0008-22
, λ is the spiral lead of the first spiral workpiece to be formed, F r is the feed rate of the first wheel grinding,
Figure 111147037-A0305-02-0008-23
, ω is the angular velocity of the first spiral workpiece to be formed relative to the first grinding wheel, ω =
Figure 111147037-A0305-02-0008-24
, D p is the diameter of the pitch circle when the spiral workpiece to be formed contacts the grinding wheel.

步驟S2-3：接下來，提供一第二砂輪以及一第二待成形螺旋工件，該第二砂輪與該第一砂輪為相同材質，而該第二待成形螺旋 工件與該第一待成形螺旋工件為相同材質但不同規格，例如不同的尺寸、輪廓及/或齒數；亦可理解為該第二待成形螺旋工件與該第一待成形螺旋工件具有不同的參數，包括螺旋參數p，螺旋導程λ、軸向模數m x 、蝸桿齒數Z及/或節圓直徑D p 等。 Step S2-3: Next, provide a second grinding wheel and a second spiral workpiece to be formed. The second grinding wheel and the first grinding wheel are made of the same material, and the second spiral workpiece to be formed and the first spiral workpiece to be formed are The workpieces are made of the same material but have different specifications, such as different sizes, profiles and/or number of teeth; it can also be understood that the second spiral workpiece to be formed and the first spiral workpiece to be formed have different parameters, including the spiral parameter p , the spiral guide The process λ, the axial module m x , the number of worm teeth Z and/or the pitch circle diameter D p , etc.

步驟S2-4：在加工前，先以該螺旋線速H s 作為一螺旋線速參考值，根據該第二待成形螺旋工件的參數，如螺旋參數p，螺旋導程λ、軸向模數m x 、蝸桿齒數Z及節圓直徑D p ，利用式1取得該第二砂輪對該第二待成形螺旋工件的第二輪磨進給率。 Step S2-4: Before processing, first use the spiral linear speed H s as a spiral linear speed reference value, based on the parameters of the second spiral workpiece to be formed, such as spiral parameter p , spiral lead λ, axial module m x , the number of worm teeth Z and the pitch circle diameter D p , use Equation 1 to obtain the second grinding feed rate of the second grinding wheel on the second spiral workpiece to be formed.

步驟S2-5：取得該第二輪磨進給率後，以該第二輪磨進給率驅動該第二砂輪對該第二待成形螺旋工件進行輪磨加工。 Step S2-5: After obtaining the second grinding feed rate, drive the second grinding wheel at the second grinding feed rate to grind the second spiral workpiece to be formed.

在以上的方法中，由於該第一砂輪與該第二砂輪為相同材質，而該第一待成形螺旋工件與該第二待成形螺旋工件為相同材質但不同規格，因此，該第一待成形螺旋工件與該第二待成形螺旋工件適合的螺旋線速為相同，但因為該第一待成形螺旋工件與該第二待成形螺旋工件的規格不同，因此實際應採用(或對應)的輪磨進給率為不同。透過本發明的方法，即可以根據該第一砂輪對該第一待成形螺旋工件的加工條件，找出適用於該第二砂輪對該第二待成形螺旋工件的加工條件。 In the above method, since the first grinding wheel and the second grinding wheel are made of the same material, and the first spiral workpiece to be formed and the second spiral workpiece to be formed are of the same material but different specifications, therefore, the first spiral workpiece to be formed is The suitable spiral line speeds of the spiral workpiece and the second spiral workpiece to be formed are the same. However, because the specifications of the first spiral workpiece to be formed and the second spiral workpiece to be formed are different, (or corresponding) wheel grinding should actually be used. Feed rates are different. Through the method of the present invention, based on the processing conditions of the first grinding wheel on the first spiral workpiece to be formed, the processing conditions suitable for the second grinding wheel on the second spiral workpiece to be formed can be found.

舉例來說，先使用砂輪A加工待成形螺旋工件A，利用試誤法得到輪磨進給率參考值F r,A ，當要使用砂輪A加工相同材料但不同規格的待成形螺旋工件B，待成形螺旋工件A、B適合的螺旋線速為相同，但對應的輪磨進給率為不同。因此，可以利用以上方法先根據待成形螺旋工件A的參數從輪磨進給率參考值F r,A 得到對應的螺旋 線速參考值H s,A ，在利用以上方法根據待成形螺旋工件B的參數從輪磨進給率參考值F r,A 得到對應的螺旋線速參考值H s,B ，並使用螺旋線速參考值H s,B 驅動砂輪A對待成形螺旋工件B進行輪磨加工。 For example, first use grinding wheel A to process the spiral workpiece A to be formed, and use the trial and error method to obtain the wheel grinding feed rate reference value F r,A . When grinding wheel A is used to process the spiral workpiece B to be formed of the same material but different specifications, The suitable spiral linear speeds for the spiral workpieces A and B to be formed are the same, but the corresponding wheel grinding feed rates are different. Therefore, the above method can be used to first obtain the corresponding spiral linear speed reference value H s,A from the wheel grinding feed rate reference value F r,A based on the parameters of the spiral workpiece A to be formed, and then use the above method to obtain the corresponding spiral linear speed reference value H s,A according to the spiral workpiece B to be formed. The corresponding spiral linear speed reference value H s,B is obtained from the wheel grinding feed rate reference value F r ,A , and the spiral linear speed reference value H s,B is used to drive the grinding wheel A for wheel grinding of the spiral workpiece B to be formed. .

S1-1、S1-2:步驟 S1-1, S1-2: steps

Claims (8)

一種螺旋工件的成形加工方法，係利用一砂輪輪磨一待成形螺旋工件以形成一螺旋工件之一齒面，該砂輪接觸該待成形螺旋工件，該方法包括以下步驟：步驟S1-1：由下式1取得對應該待成形螺旋工件接觸該砂輪時的一節圓直徑的一底徑D p,d1及一大徑D p,d2之該待成形螺旋工件的一第一螺旋線速H s,d1及一第二螺旋線速H s,d2：
Figure 111147037-A0305-02-0011-25
 其中，s為該待成形螺旋工件相對該砂輪的一平移速度，且s=
Figure 111147037-A0305-02-0011-26
，p為該待成形螺旋工件的一螺旋參數，
Figure 111147037-A0305-02-0011-27
，λ為該待成形螺旋工件的一螺旋導程，F r 為一輪磨進給率； 其中，
Figure 111147037-A0305-02-0011-28
，ω為該待成形螺旋工件相對該砂輪的一角速率，ω
Figure 111147037-A0305-02-0011-29
；以及步驟S1-2：得到該第一螺旋線速H s,d1及該第二螺旋線速H s,d2後，以介於該第一螺旋線速H s,d1及該第二螺旋線速H s,d2之間的一加工螺旋線速所對應的一加工輪磨進給率，驅動該砂輪對該待成形螺旋工件進行輪磨加工。 A method for forming a spiral workpiece, which uses a grinding wheel to grind a spiral workpiece to be formed to form a tooth surface of the spiral workpiece, and the grinding wheel contacts the spiral workpiece to be formed. The method includes the following steps: Step S1-1: The following formula 1 obtains a base diameter D p, d 1 and a major diameter D p, d 2 corresponding to the pitch circle diameter of the spiral workpiece to be formed when it contacts the grinding wheel. A first spiral linear speed H of the spiral workpiece to be formed is obtained. s,d 1 and a second spiral linear speed H s,d 2 :
Figure 111147037-A0305-02-0011-25
 Among them, s is the translation speed of the spiral workpiece to be formed relative to the grinding wheel, and s =
Figure 111147037-A0305-02-0011-26
, p is a spiral parameter of the spiral workpiece to be formed,
Figure 111147037-A0305-02-0011-27
, λ is the spiral lead of the spiral workpiece to be formed, F r is the feed rate of one-wheel grinding; where,
Figure 111147037-A0305-02-0011-28
, ω is the angular velocity of the spiral workpiece to be formed relative to the grinding wheel, ω
Figure 111147037-A0305-02-0011-29
; and step S1-2: After obtaining the first spiral linear speed H s,d 1 and the second spiral linear speed H s,d 2 , set a value between the first spiral linear speed H s,d 1 and the second spiral linear speed H s,d 1 A processing wheel grinding feed rate corresponding to a processing spiral line speed between the two spiral line speeds H s,d 2 drives the grinding wheel to grind the spiral workpiece to be formed. 如請求項1所述的方法，其中該待成形螺旋工件為一蝸桿。 The method of claim 1, wherein the spiral workpiece to be formed is a worm. 如請求項1所述的方法，其中該螺旋導程λ為由下式2及下式3取得，
Figure 111147037-A0305-02-0011-30
 λ=πD p tan γ (式3) 其中，m x 為該待成形螺旋工件的一軸向模數，Z為該待成形螺旋工件的一蝸桿齒數。 The method as described in claim 1, wherein the spiral lead λ is obtained by the following equation 2 and the following equation 3,
Figure 111147037-A0305-02-0011-30
 λ=π D p tan γ (Equation 3) Among them, m x is the axial module of the spiral workpiece to be formed, and Z is the number of worm teeth of the spiral workpiece to be formed. 一種螺旋工件的成形加工方法，包括以下步驟：步驟S2-1：取得一第一砂輪對一第一待成形螺旋工件的一第一輪磨進給率；步驟S2-2：根據該第一輪磨進給率，由下式1取得該第一砂輪接觸並加工該第一待成形螺旋工件時的一螺旋線速H s ：
Figure 111147037-A0305-02-0012-31
 其中，s為該第一待成形螺旋工件相對該第一砂輪的一平移速度，且
Figure 111147037-A0305-02-0012-32
，p為該第一待成形螺旋工件的一螺旋參數，
Figure 111147037-A0305-02-0012-33
，λ為該第 一待成形螺旋工件的一螺旋導程，F r 為該第一輪磨進給率，
Figure 111147037-A0305-02-0012-34
，ω 為該第一待成形螺旋工件相對該第一砂輪的一角速率，
Figure 111147037-A0305-02-0012-35
，D p 為該待成形螺旋工件接觸該砂輪時的一節圓直徑；步驟S2-3：提供一與該第一砂輪相同材質的第二砂輪以及一與該第一待成形螺旋工件相同材質但不同規格的第二待成形螺旋工件；步驟S2-4：以該螺旋線速H s 作為一螺旋線速參考值，根據該第二待成形螺旋工件的參數利用(式1)，從該螺旋線速參考值取得該第二砂輪對該第二待成形螺旋工件的一第二輪磨進給率；以及步驟S2-5：以該第二輪磨進給率驅動該第二砂輪對該第二待成形螺旋工件進行輪磨加工。 A method for forming a spiral workpiece, including the following steps: Step S2-1: Obtain a first grinding feed rate of a first grinding wheel on a first spiral workpiece to be formed; Step S2-2: According to the first grinding The grinding feed rate is obtained from the following formula 1: a spiral linear speed H s when the first grinding wheel contacts and processes the first spiral workpiece to be formed:
Figure 111147037-A0305-02-0012-31
 Where, s is a translation speed of the first spiral workpiece to be formed relative to the first grinding wheel, and
Figure 111147037-A0305-02-0012-32
, p is a spiral parameter of the first spiral workpiece to be formed,
Figure 111147037-A0305-02-0012-33
, λ is the spiral lead of the first spiral workpiece to be formed, F r is the feed rate of the first wheel grinding,
Figure 111147037-A0305-02-0012-34
, ω is the angular velocity of the first spiral workpiece to be formed relative to the first grinding wheel,
Figure 111147037-A0305-02-0012-35
, D p is the pitch diameter of the spiral workpiece to be formed when it contacts the grinding wheel; Step S2-3: Provide a second grinding wheel of the same material as the first grinding wheel and a second grinding wheel of the same material as the first spiral workpiece to be formed but different Specification of the second spiral workpiece to be formed; Step S2-4: Use the spiral linear speed H s as a spiral linear speed reference value, and use (Formula 1) according to the parameters of the second spiral workpiece to be formed, from the spiral linear speed The reference value is used to obtain a second grinding feed rate of the second grinding wheel to the second spiral workpiece to be formed; and step S2-5: drive the second grinding wheel to the second to-be-formed spiral workpiece at the second grinding feed rate. The formed spiral workpiece is wheel ground. 如請求項4所述的方法，其中該第一待成形螺旋工件及該第二待成形螺旋工件分別為一蝸桿。 The method of claim 4, wherein the first spiral workpiece to be formed and the second spiral workpiece to be formed are respectively a worm. 如請求項4所述的方法，其中該第一砂輪與該第二砂輪為相同規格。 The method of claim 4, wherein the first grinding wheel and the second grinding wheel are of the same specifications. 如請求項4所述的方法，其中該第一砂輪與該第二砂輪為同一砂輪。 The method of claim 4, wherein the first grinding wheel and the second grinding wheel are the same grinding wheel. 如請求項4所述的方法，其中該螺旋導程λ為由下式2及下式3取得，
Figure 111147037-A0305-02-0013-36
 λ=πD p tan γ (式3)其中，m x 為該第一待成形螺旋工件的一軸向模數，Z為該第一待成形螺旋工件的一蝸桿齒數。 The method as described in claim 4, wherein the spiral lead λ is obtained by the following equation 2 and the following equation 3,
Figure 111147037-A0305-02-0013-36
 λ=π D p tan γ (Formula 3) Where, m x is an axial module of the first spiral workpiece to be formed, and Z is the number of worm teeth of the first spiral workpiece to be formed.
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US20030207650A1 (en) * 2001-01-03 2003-11-06 Jie Tan Method for forming a grinding worm for forming a conical face gear that meshes with a conical involute pinion
EP2383073A1 (en) * 2008-12-22 2011-11-02 Mitsubishi Heavy Industries, Ltd. Internal gear grinding machine and method for dressing a barrel shape spiral grinding tool
TW202031396A (en) * 2019-02-15 2020-09-01 國立虎尾科技大學 Worm gear processing method to greatly increase the accuracy during cutting and reduce the trial and error process time during tooth profile dressing
CN114918494A (en) * 2022-05-10 2022-08-19 重庆大学 Gear generating grinding instantaneous equivalent model and design method thereof

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US20030207650A1 (en) * 2001-01-03 2003-11-06 Jie Tan Method for forming a grinding worm for forming a conical face gear that meshes with a conical involute pinion
EP2383073A1 (en) * 2008-12-22 2011-11-02 Mitsubishi Heavy Industries, Ltd. Internal gear grinding machine and method for dressing a barrel shape spiral grinding tool
TW202031396A (en) * 2019-02-15 2020-09-01 國立虎尾科技大學 Worm gear processing method to greatly increase the accuracy during cutting and reduce the trial and error process time during tooth profile dressing
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