TWI460365B - Rigid Ring Gear and Flexible Planetary Wheel of Harmonic Reducer and Its Method - Google Patents
Rigid Ring Gear and Flexible Planetary Wheel of Harmonic Reducer and Its Method Download PDFInfo
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本發明係有關一種諧波減速機之剛性環齒輪與撓性行星輪及其製法，特別是指一種齒形為連續平滑曲線之諧波減速機之剛性環齒輪與撓性行星輪及其製法，具有低相對滑動比、低磨耗、低溫昇、低接觸應力、高減速比、效率高、能耗低之優點及功效。The invention relates to a rigid ring gear and a flexible planetary wheel of a harmonic reducer and a method for manufacturing the same, in particular to a rigid ring gear and a flexible planetary wheel with a toothed continuous harmonic curve reducer and a method for manufacturing the same, It has the advantages and functions of low relative sliding ratio, low wear, low temperature rise, low contact stress, high reduction ratio, high efficiency and low energy consumption.
傳統之諧波齒輪(或稱諧波減速機，英文為harmonic drive)的技術，早已為人所熟知，主要機構由內至外有諧波產生器、撓性行星輪與剛性環齒輪。其諧波產生器猶如行星輪系之太陽輪，旋轉中心是固定的，具非圓形節曲線並推擠撓性行星輪產生變形。The technology of the traditional harmonic gear (or harmonic reducer, English harmonic drive) has long been known. The main mechanism has harmonic generators, flexible planetary gears and rigid ring gears from the inside to the outside. Its harmonic generator is like the sun gear of a planetary gear train. The center of rotation is fixed, with a non-circular pitch curve and pushing the flexible planet wheel to deform.
傳統諧波減速機其撓性行星輪與剛性環齒輪之齒形多為習知漸開線齒型，如第一圖所示為內嚙合漸開線齒形，其包括一剛性環齒輪齒形線91與撓性行星輪齒形線92。In the conventional harmonic reducer, the tooth shape of the flexible planetary gear and the rigid ring gear is mostly a conventional involute tooth type, as shown in the first figure is an internal mesh involute tooth profile, which includes a rigid ring gear tooth profile. Line 91 and flexible planet gear line 92.
其次，如第二圖所示，為美國專利US4974470之另一種傳統諧波減速機的齒型為S型，其齒形係由曲線a、b、c三段接合而成。Next, as shown in the second figure, another conventional harmonic reducer of the U.S. Patent No. 4,974,470 has an S-shaped tooth profile, and the tooth profile is formed by joining three segments of curves a, b, and c.
另外，如第三圖所示，其為再一種傳統之傳統諧波減速機，即美國專利US 7694607B2，此案係提出由圓弧線a1、直線a2、圓弧線a3及圓弧線b1、直線b2、圓弧線b3來接合齒形。In addition, as shown in the third figure, it is a conventional conventional harmonic reducer, that is, US Pat. No. 7,694,607 B2, which proposes a circular arc line a1, a straight line a2, a circular arc line a3, and a circular arc line b1. The straight line b2 and the circular arc line b3 are joined to each other.
然而，上述這兩案之齒形皆為多線段接合，推導嚙合理論耗時費工，且因片段連續易產生數學上不可微分點(即singular point)。However, the tooth shapes of the above two cases are all multi-segment joints, and the theory of inductive meshing is time-consuming and labor-intensive, and the mathematically non-differentiable points (ie, singular points) are easily generated due to the continuous segments.
諧波齒輪之關鍵技術在於齒形的設計，由齒形方程式經包絡理論於圓節曲線93(參閱第一圖)上建構齒形，建構之漸開線齒形與齒冠圓94、齒根圓95作線段接合。但是，從漸開線齒 形生成數學模型中可發現：The key technology of the harmonic gear lies in the design of the tooth profile. The tooth profile is constructed on the circular curve 93 (refer to the first figure) by the envelope equation. The involute tooth profile and the crown circle 94 and the root are constructed. Circle 95 is used for line segment bonding. However, from involute teeth The mathematical model of shape generation can be found:
(1)無法經由一條方程式建構整個齒輪齒形，為間斷連續之齒形，間斷連續之齒形在連接處易產生不連續點(cusp)，於齒形嚙合過切不易設計，此接合處之不連續點，亦數學上不可微分點，運轉中易造成跳動。(1) It is impossible to construct the entire gear tooth shape through an equation, which is a discontinuous continuous tooth shape. The discontinuous continuous tooth shape is easy to generate a discontinuity point (cusp) at the joint, and it is difficult to design the tooth shape meshing overcut. The discontinuity point is also mathematically indivisible, and it is easy to cause jumping during operation.
(2)因不連續凸對凸之嚙合齒形，具較大相對滑動比，無平滑之曲率半徑變化與較大之相對曲率半徑，產生齒面之接觸應力較大、高磨耗與高溫昇。(2) Due to the discontinuous convex to convex meshing tooth shape, with a large relative sliding ratio, no smooth curvature radius change and a large relative curvature radius, the contact stress of the tooth surface is large, high wear and high temperature rise.
因此，有必要研發新技術，以解決上述缺弊。Therefore, it is necessary to develop new technologies to solve the above shortcomings.
本發明之目的，在於提供一諧波減速機之剛性環齒輪與撓性行星輪及其製法，其兼具低相對滑動比、低磨耗、低溫昇、低接觸應力、高減速比、效率高、能耗低等優點。特別是，本發明所欲解決之問題包括：傳統裝置無法經由一條方程式建構整個齒輪齒形、運轉中易造成跳動、齒面之接觸應力較大、高磨耗與高溫昇之問題。The object of the present invention is to provide a rigid ring gear and a flexible planetary gear of a harmonic reducer and a method for manufacturing the same, which have a low relative sliding ratio, low wear, low temperature rise, low contact stress, high reduction ratio, high efficiency, Low energy consumption and other advantages. In particular, the problems to be solved by the present invention include that the conventional device cannot construct the entire gear tooth shape via an equation, the bounce is likely to occur during operation, the contact stress of the tooth surface is large, and the high wear and high temperature rise are caused.
解決上述問題之技術手段係提供： 一種諧波減速機之剛性環齒輪之製法，其包括：[a]準備步驟；及[b]剛性環齒輪製造步驟。The technical means to solve the above problems are: A method for manufacturing a rigid ring gear of a harmonic reducer, comprising: [a] a preparation step; and [b] a rigid ring gear manufacturing step.
一種諧波減速機之撓性行星輪之製法，其包括： [a]準備步驟；[b]剛性環齒輪製造步驟；[c]撓性行星輪製造步驟。A method for manufacturing a flexible planetary gear of a harmonic reducer, comprising: [a] preparation step; [b] rigid ring gear manufacturing step; [c] flexible planetary wheel manufacturing step.
一種諧波減速機之剛性環齒輪與撓性行星輪，其包括一剛性環齒輪及一撓性行星輪，其中，該剛性環齒輪及該撓性行星輪其中之一之齒形之方程式係為：L 1 =[x 1y 1 0] T A rigid ring gear and a flexible planetary gear of a harmonic reducer include a rigid ring gear and a flexible planetary gear, wherein the rigid ring gear and the tooth profile of one of the flexible planetary wheels are : L 1 =[ x 1 y 1 0] T
而另一之齒形之方程式係為：L 2 =[x 2y 2 0] T The other equation of the tooth profile is: L 2 =[ x 2 y 2 0] T
其中：
其中：h
為齒高係數，其值之範圍最小值係為0，其最大值經由
下列方程式定義：
該齒高係數係介於0及上列公式最大值之間；Φ為輸入參數；i為任意數；m為模數；z1、z2為該剛性環齒輪及該撓性行星輪其中之一及另一之齒數。The tooth height coefficient is between 0 and the maximum value of the above formula; Φ is an input parameter; i is an arbitrary number; m is a modulus; z1, z2 are one of the rigid ring gear and the flexible planetary gear The other number of teeth.
本發明係為一種諧波減速機之剛性環齒輪與撓性行星輪及其製法，其包括製法與成品兩大部份。The invention relates to a rigid ring gear and a flexible planetary wheel of a harmonic reducer and a manufacturing method thereof, which comprise two parts of a manufacturing method and a finished product.
請參閱第五至第八圖，關於製法方面，一般之製法為：先製出滾齒刀(習知結構，圖中未示)，由此滾齒刀依傳統之創成法製出剛性環齒輪21，再由剛性環齒輪21依傳統之嚙合方程式來製出撓性行星輪22。當然，也可將後二者之順序對調，而為先製出滾齒刀，由此滾齒刀依傳統之創成法製出撓性行星輪22，再由撓性行星輪22依傳統之嚙合方程式製出剛性環齒輪21。之後，與一諧波產生器23組合，即可成為一諧波減速機20。Please refer to the fifth to eighth figures. In terms of the manufacturing method, the general method is as follows: a hobbing cutter (a conventional structure, not shown) is first prepared, whereby the hobbing cutter produces a rigid ring gear 21 according to a conventional creation method. The flexible planet gear 22 is then fabricated from the rigid ring gear 21 in accordance with a conventional meshing equation. Of course, the order of the latter two can also be reversed, and the hobbing cutter is first produced, whereby the hobbing cutter produces the flexible planetary gear 22 according to the conventional creation method, and then the flexible planetary gear 22 is in accordance with the conventional meshing equation. A rigid ring gear 21 is produced. Thereafter, in combination with a harmonic generator 23, it becomes a harmonic reducer 20.
請參閱第四A圖，關於本發明之諧波減速機之剛性環齒輪之製法，其包括：[a]準備步驟11：準備一滾齒刀及一剛性環形待加工元件，該滾齒刀係形成一創成滾齒刀之曲線圖(如第九圖所示)，該創成滾齒刀之曲線方程式係由下列之(C1)至(C5)其中之一數學式定義出：f(Φ)=h ．g(i．Φ)………(C1)Referring to FIG. 4A, a method for manufacturing a rigid ring gear of a harmonic reducer according to the present invention includes: [a] preparation step 11: preparing a hobbing cutter and a rigid annular processing component, the hobbing cutter system Forming a graph of a toothed knives (as shown in the ninth figure), the curve equation of the hobbing cutter is defined by one of the following mathematical formulas (C1) to (C5): f(Φ)= h . g(i.Φ).........(C1)
f(Φ)=h ．g(g(i．Φ))………(C2)f(Φ)= h . g(g(i.Φ))............(C2)
f(Φ)=h ．g(g(g(i．Φ)))………(C3)f(Φ)= h . g(g(g(i.Φ)))............(C3)
f(Φ)=h ．g(g(g(g(i．Φ))))………(C4)f(Φ)= h . g(g(g(g(i.Φ)))))......(C4)
f(Φ)=h ．g(g(g(g(g(i．Φ)))))………(C5)f(Φ)= h . g(g(g(g(i.Φ))))))......(C5)
其中g(Φ)=sin(Φ)；h
為齒高係數，其值之範圍最小值係為0，其最大值經由下列方程式定義：
該齒高係數係介於0及上列公式最大值之間；Φ為輸入參數；i為任意數、於齒形上之可變周節，影響齒形大小；m為模數；z1為剛性環齒輪之齒數；茲舉例一組數據範例，例如：模數m=0.3，輸入參數Φ=(2π)x齒數；i=m/2=1.5；而齒高係數h約為0.3。關於此例而言，在外圈之剛性環齒輪之齒數為82齒，而在內圈之撓性行星輪之齒數為80齒。The tooth height coefficient is between 0 and the maximum value of the above formula; Φ is the input parameter; i is an arbitrary number, variable circumference on the tooth shape, affecting the tooth shape; m is the modulus; z1 is the rigidity The number of teeth of the ring gear; for example, a set of data examples, for example: modulus m = 0.3, input parameter Φ = (2π) x number of teeth; i = m / 2 = 1.5; and the tooth height coefficient h is about 0.3. In this example, the number of teeth of the rigid ring gear in the outer ring is 82 teeth, and the number of teeth of the flexible planet gear in the inner ring is 80 teeth.
[b]剛性環齒輪製造步驟12：由前述滾齒刀利用傳統之創成法(generating method)對該剛性環形待加工元件切削加工，而形成一諧波減速機20之剛性環齒輪21。[b] Rigid Ring Gear Manufacturing Step 12: The rigid ring gear to be machined is cut by the aforementioned hobbing cutter using a conventional generating method to form a rigid ring gear 21 of a harmonic reducer 20.
當完成前述步驟後，即製成該諧波減速機20之剛性環齒輪21。When the foregoing steps are completed, the rigid ring gear 21 of the harmonic reducer 20 is fabricated.
之後，還可進行下列步驟(如第四B圖所示)：[c]撓性行星輪製造步驟13：由該諧波減速機20之剛性環齒輪21之齒形，利用傳統之嚙合方程式，對一撓性圓形待加工元件進行切削加工，進而形成該諧波減速機20之撓性行星輪22。Thereafter, the following steps (as shown in FIG. 4B) can also be performed: [c] flexible planetary gear manufacturing step 13: the tooth shape of the rigid ring gear 21 of the harmonic reducer 20, using a conventional meshing equation, A flexible circular to-be-processed component is machined to form the flexible planet gear 22 of the harmonic reducer 20.
當完成此步驟後，即製成該諧波減速機20之撓性行星輪 22。When this step is completed, the flexible planetary gear of the harmonic reducer 20 is made. twenty two.
若將製成之剛性環齒輪21、撓性行星輪22與一習知的諧波產生器23組裝，則成為諧波減速機20。參閱第五、第六、第七及第八圖分別表示諧波減速機20之立體圖、前視圖、側視圖及分解立體圖。When the manufactured rigid ring gear 21 and the flexible planetary gear 22 are assembled with a conventional harmonic generator 23, the harmonic reducer 20 is obtained. Referring to the fifth, sixth, seventh and eighth figures, respectively, a perspective view, a front view, a side view and an exploded perspective view of the harmonic reducer 20 are shown.
更詳細的說，前述之諧波減速機20之剛性環齒輪齒形之方程式(L1)係為：L 1 =[x 1y 1 0] T In more detail, the equation (L1) of the rigid ring gear tooth profile of the aforementioned harmonic reducer 20 is: L 1 = [ x 1 y 1 0] T
其中：
其次，前述之諧波減速機之撓性行星輪之齒形之方程式係為：L 2 =[x 2y 2 0] T Secondly, the equation of the tooth profile of the flexible planetary gear of the aforementioned harmonic reducer is: L 2 =[ x 2 y 2 0] T
其中：z2為撓性行星輪之齒數；
由於本案之創成滾齒刀之曲線方程式係由前述之(C1)至(C5)其中之一數學式定義出。當h=1且i=1時，由方程式(C1)至(C5)所定義出之齒形如第十圖之曲線S1,S2,S3,S4,S5所示。Since the curve equation of the created gear cutter of the present invention is defined by one of the aforementioned mathematical formulas (C1) to (C5). When h=1 and i=1, the tooth shapes defined by the equations (C1) to (C5) are as shown by the curves S1, S2, S3, S4, and S5 of the tenth figure.
若選定以方程式(C5)，而控制i=1不變，而改變齒高係數h=0.5、1及1.5時，所產生之齒形如第十一圖之曲線S6,S7,S8所示。If Equation (C5) is selected and control i = 1 is unchanged, and the tooth height coefficients h = 0.5, 1 and 1.5 are changed, the resulting tooth profile is as shown by the curves S6, S7, S8 of the eleventh figure.
若選定以方程式(C5)，而控制齒高係數h=1不變，而改變i=0.5、1及1.5時，所產生之齒形如第十二圖之曲線S9,S10,S11所示。If equation (C5) is selected and the tooth height coefficient h = 1 is unchanged, and i = 0.5, 1 and 1.5 are changed, the resulting tooth profile is as shown by the curve S9, S10, S11 of the twelfth figure.
由於本發明經由具連續函數曲線之滾齒刀來創成一整圈完全封閉連續之曲線齒輪，如剛性環齒輪齒形，進而求得撓性行星輪齒形，藉此獲得整圈連續皆可微分之共軛齒輪系。Since the present invention creates a full-closed continuous curved gear, such as a rigid ring gear tooth shape, via a hobbing cutter having a continuous function curve, thereby obtaining a flexible planetary gear tooth shape, thereby obtaining a continuous rotation of the entire circle. Conjugate gear train.
有關「滑動係數(sliding coefficient)」之分析，請參閱第十三圖，其中本發明是選定方程式(C5)之情形(以曲線S12表示)，與習知的漸開線齒形(以曲線S13)進行比較，由第十三圖可知，本發明之滑動係數一直維持在0附近(約正負0.1 之內)近乎純滾動。而習知的漸開線齒形之滑動係數並非維持在正負0.1之內，代表齒與齒間之相對滑動較大。使得本發明具有低相對滑動比、低磨耗、低溫昇、低接觸應力之優點。For the analysis of the "sliding coefficient", please refer to the thirteenth figure, wherein the present invention is the case where the equation (C5) is selected (indicated by the curve S12), and the conventional involute tooth profile (with the curve S13). Comparing, from the thirteenth figure, the sliding coefficient of the present invention is maintained at around zero (about plus or minus 0.1). Within) almost pure scrolling. However, the slip coefficient of the conventional involute tooth profile is not maintained within plus or minus 0.1, indicating that the relative sliding between the tooth and the tooth is large. The invention has the advantages of low relative sliding ratio, low abrasion, low temperature rise and low contact stress.
請參閱第十四圖，其中，將本發明之方程式(C1)、(C3)及(C5)進行比較，結果(分別以曲線S14、S15與S16表示)僅有微量差異，三者均維持在0附近，且(C5)略優於(C3)，(C3)又優於(C1)，但是均極好。由於(C2)及(C4)與方程式(C1)、(C3)及(C5)屬性相同，由此可推論(C2)及(C4)也具有前段所述之優點。Please refer to Fig. 14, in which the equations (C1), (C3) and (C5) of the present invention are compared, and the results (represented by curves S14, S15 and S16, respectively) are only slightly different, and all three are maintained at Near 0, and (C5) is slightly better than (C3), (C3) is better than (C1), but both are excellent. Since (C2) and (C4) have the same properties as the equations (C1), (C3), and (C5), it can be inferred that (C2) and (C4) also have the advantages described in the previous paragraph.
再者，關於「相對曲率半徑(Relative Radius of Curvature)」之分析，請參閱第十五圖，其中，將本發明之方程式(C1)、(C3)及(C5)進行比較，結果(分別以曲線S17、S18與S19表示)三者均維持在0.01m至0.06m之間，並無劇大之變動。換言之，相對接觸時之接觸應力低，同樣產生低磨耗、低溫昇之優點。另外，由於(C2)及(C4)與方程式(C1)、(C3)及(C5)屬性相同，由此可推論(C2)及(C4)也具有前段所述之優點。Furthermore, for the analysis of "Relative Radius of Curvature", please refer to the fifteenth figure, in which the equations (C1), (C3) and (C5) of the present invention are compared, and the results are respectively Curves S17, S18 and S19 indicate that all three are maintained between 0.01m and 0.06m, and there is no dramatic change. In other words, the contact stress at the time of contact is low, which also has the advantages of low wear and low temperature rise. In addition, since (C2) and (C4) have the same properties as the equations (C1), (C3), and (C5), it can be inferred that (C2) and (C4) also have the advantages described in the previous paragraph.
另外，諧波減速機原本就具有高減速比、效率高、能耗低之優點。In addition, the harmonic reducer originally has the advantages of high reduction ratio, high efficiency and low energy consumption.
又，請參閱第十六圖及第十七圖，本發明之剛性環齒輪21之內表面也可改為內凹弧面或內凸弧面，當然，相對應之撓性行星輪22之外表面則也要改為內凸弧面或內凹弧面。亦即要將這兩式(L 1 =[x 1y 1 0] T 及L 2 =[x 2y 2 0] T )中之z方向之值進行修改(而非0)。此時，兩者之較不易產生側向滑動或脫落(z軸方向)之功效。又，此兩型態亦屬於本發明之保護範圍。Moreover, referring to the sixteenth and seventeenth embodiments, the inner surface of the rigid ring gear 21 of the present invention may also be changed to a concave curved surface or an inner convex curved surface, of course, corresponding to the flexible planetary gear 22. The surface should also be changed to a convex or concave curved surface. That is, the value of the z direction in the two equations ( L 1 =[ x 1 y 1 0] T and L 2 =[ x 2 y 2 0] T ) is modified (not 0). At this time, the two are less likely to produce side sliding or falling off (z-axis direction). Moreover, these two types are also within the scope of protection of the present invention.
當然，前述之製法若不採用滾齒刀，亦可採用線切割之方式來達成，因此本發明係為一種諧波減速機之剛性環齒輪與撓性行星輪，其包括一剛性環齒輪21及一撓性行星輪22，其中，該剛性環齒輪21及該撓性行星輪22其中之一之齒形之方程式 係為：L 1 =[x 1y 1 0] T Of course, the above method can be achieved by using a hobbing cutter, and can also be achieved by wire cutting. Therefore, the present invention is a rigid ring gear and a flexible planetary gear of a harmonic reducer, which includes a rigid ring gear 21 and A flexible planet gear 22, wherein the equation of the tooth profile of one of the rigid ring gear 21 and the flexible planet gear 22 is: L 1 =[ x 1 y 1 0] T
而另一之齒形之方程式係為：L 2 =[x 2y 2 0] T The other equation of the tooth profile is: L 2 =[ x 2 y 2 0] T
由於上述二方程式之x1,y1,x2,y2均已在前面定義過，在此不贅述。Since x1, y1, x2, and y2 of the above two equations have been previously defined, they will not be described here.
故，本發明具有低相對滑動比、低磨耗、低溫昇、低接觸應力、高減速比、效率高、能耗低之優點及功效。Therefore, the invention has the advantages and effects of low relative sliding ratio, low wear, low temperature rise, low contact stress, high reduction ratio, high efficiency and low energy consumption.
11‧‧‧準備步驟11‧‧‧Preparation steps
12‧‧‧剛性環齒輪製造步驟12‧‧‧Rigid ring gear manufacturing steps
13‧‧‧撓性行星輪製造步驟13‧‧‧Flexible planetary wheel manufacturing steps
20‧‧‧諧波減速機20‧‧‧Harmonic reducer
21‧‧‧剛性環齒輪21‧‧‧Rigid ring gear
22‧‧‧撓性行星輪22‧‧‧Flexible planetary gear
23‧‧‧諧波產生器23‧‧‧Harmonic generator
91‧‧‧剛性環齒輪齒形線91‧‧‧Rigid ring gear tooth line
92‧‧‧撓性行星輪齒形線92‧‧‧Flexible planetary gear line
93‧‧‧圓節曲線93‧‧‧ round curve
94‧‧‧齒冠圓94‧‧‧Tooth crown
95‧‧‧齒根圓95‧‧‧ tooth root circle
a1、a3、b1、b3‧‧‧圓弧線A1, a3, b1, b3‧‧‧ arc lines
a2、b2‧‧‧直線A2, b2‧‧‧ straight line
a、b、c、S1、S2、S3、S4、S5、S6、S7、S8、S9、S10、S11 S12、S13、S14、S15、S16、S17、S18、S19‧‧‧曲線a, b, c, S1, S2, S3, S4, S5, S6, S7, S8, S9, S10, S11, S12, S13, S14, S15, S16, S17, S18, S19‧‧
第一圖係傳統之具有漸開線齒形的諧波減速機之示意圖The first picture is a schematic diagram of a conventional harmonic reducer with an involute profile.
第二圖係習知第一種不連續齒形諧波減速機之示意圖The second figure is a schematic diagram of the first type of discontinuous tooth harmonic reducer.
第三圖係習知第二種不連續齒形諧波減速機之示意圖The third figure is a schematic diagram of a second type of discontinuous tooth harmonic reducer.
第四A圖係本發明之諧波減速機之剛性環齒輪之製法The fourth A picture is a method for manufacturing the rigid ring gear of the harmonic reducer of the present invention
第四B圖係本發明之諧波減速機之撓性行星輪之製法The fourth B diagram is a method for manufacturing the flexible planetary gear of the harmonic reducer of the present invention
第五圖係本發明之諧波減速機之立體圖The fifth figure is a perspective view of the harmonic reducer of the present invention
第六圖係本發明之諧波減速機之前視圖Figure 6 is a front view of the harmonic reducer of the present invention
第七圖係本發明之諧波減速機之側視圖The seventh figure is a side view of the harmonic reducer of the present invention
第八圖係本發明之諧波減速機之分解立體圖The eighth figure is an exploded perspective view of the harmonic reducer of the present invention
第九圖係本發明之滾齒刀之曲線之示意圖The ninth diagram is a schematic view of the curve of the hob cutter of the present invention
第十圖本發明之創成滾齒刀之曲線方程式(C1)至(C5)之齒形之示意圖Figure 10 is a schematic view showing the tooth profile of the curve equations (C1) to (C5) of the indented cutter of the present invention.
第十一圖係本發明在選用不同齒高係數h之所產生齒形之示意圖The eleventh figure is a schematic diagram of the tooth profile produced by the invention with different tooth height coefficients h
第十二圖係本發明在選用不同任意數i之所產生齒形之示意圖The twelfth figure is a schematic diagram of the tooth form produced by the invention using different arbitrary numbers i
第十三圖係本發明之方程式(C5)與習知漸開線齒形之滑動係數之示意圖The thirteenth diagram is a schematic diagram of the sliding coefficient of the equation (C5) of the present invention and the conventional involute profile
第十四圖係本發明之方程式(C1)、(C3)及(C5)之滑動係數之示意圖Figure 14 is a schematic view showing the sliding coefficients of the equations (C1), (C3) and (C5) of the present invention.
第十五圖係本發明之方程式(C1)、(C3)及(C5)之相對曲率半徑之示意圖The fifteenth diagram is a schematic diagram of the relative curvature radii of the equations (C1), (C3) and (C5) of the present invention.
第十六圖係本發明之剛性環齒輪與撓性行星輪之變化例一之立體圖Figure 16 is a perspective view showing a variation of the rigid ring gear and the flexible planetary gear of the present invention.
第十七圖係本發明之剛性環齒輪與撓性行星輪之變化例二之立體圖Figure 17 is a perspective view showing a variation of the rigid ring gear and the flexible planetary gear of the present invention.
20‧‧‧諧波減速機20‧‧‧Harmonic reducer
21‧‧‧剛性環齒輪21‧‧‧Rigid ring gear
22‧‧‧撓性行星輪22‧‧‧Flexible planetary gear
23‧‧‧諧波產生器23‧‧‧Harmonic generator
Claims (5)
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| TW101120609A TWI460365B (en) | 2012-06-08 | 2012-06-08 | Rigid Ring Gear and Flexible Planetary Wheel of Harmonic Reducer and Its Method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| TW101120609A TWI460365B (en) | 2012-06-08 | 2012-06-08 | Rigid Ring Gear and Flexible Planetary Wheel of Harmonic Reducer and Its Method |
Publications (2)
| Publication Number | Publication Date |
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| TW201350711A TW201350711A (en) | 2013-12-16 |
| TWI460365B true TWI460365B (en) | 2014-11-11 |
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| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| TW101120609A TWI460365B (en) | 2012-06-08 | 2012-06-08 | Rigid Ring Gear and Flexible Planetary Wheel of Harmonic Reducer and Its Method |
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| TW (1) | TWI460365B (en) |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| TWI513925B (en) * | 2014-06-16 | 2015-12-21 | Hiwin Tech Corp | Can improve the bite rate of the harmonic reducer |
| JP2019015365A (en) * | 2017-07-07 | 2019-01-31 | 日本電産シンポ株式会社 | Speed reducer |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4922781A (en) * | 1985-08-24 | 1990-05-08 | Shen Peiji | Cycloidal equidistant curved gear transmission mechanism and its device |
| US4974470A (en) * | 1987-09-21 | 1990-12-04 | Harmonic Drive Systems Inc. | Tooth profile of one of circular splines of flat-shaped strain wave gearing |
| CN1142864A (en) * | 1994-12-19 | 1997-02-12 | 谐波传动***有限公司 | Flexible meshing type gear having a negative deflection over-running tooth profile |
| CN1864018A (en) * | 2003-10-30 | 2006-11-15 | 谐波传动***有限公司 | Wave gear device having widely engaging tooth profile |
| US7694607B2 (en) * | 2006-02-09 | 2010-04-13 | Harmonic Drive Systems Inc. | Wave gear drive with continuous meshing, high ratcheting torque tooth profile |
-
2012
- 2012-06-08 TW TW101120609A patent/TWI460365B/en not_active IP Right Cessation
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4922781A (en) * | 1985-08-24 | 1990-05-08 | Shen Peiji | Cycloidal equidistant curved gear transmission mechanism and its device |
| US4974470A (en) * | 1987-09-21 | 1990-12-04 | Harmonic Drive Systems Inc. | Tooth profile of one of circular splines of flat-shaped strain wave gearing |
| CN1142864A (en) * | 1994-12-19 | 1997-02-12 | 谐波传动***有限公司 | Flexible meshing type gear having a negative deflection over-running tooth profile |
| CN1864018A (en) * | 2003-10-30 | 2006-11-15 | 谐波传动***有限公司 | Wave gear device having widely engaging tooth profile |
| US7694607B2 (en) * | 2006-02-09 | 2010-04-13 | Harmonic Drive Systems Inc. | Wave gear drive with continuous meshing, high ratcheting torque tooth profile |
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| Publication number | Publication date |
|---|---|
| TW201350711A (en) | 2013-12-16 |
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