TWI772924B - Tooth profile design method of involute gear set for two-stage planetary reducers with high speed reduction ratio - Google Patents
Tooth profile design method of involute gear set for two-stage planetary reducers with high speed reduction ratio Download PDFInfo
- Publication number
- TWI772924B TWI772924B TW109136113A TW109136113A TWI772924B TW I772924 B TWI772924 B TW I772924B TW 109136113 A TW109136113 A TW 109136113A TW 109136113 A TW109136113 A TW 109136113A TW I772924 B TWI772924 B TW I772924B
- Authority
- TW
- Taiwan
- Prior art keywords
- design
- tooth profile
- planetary gear
- reduction ratio
- involute
- Prior art date
Links
- 239000003638 chemical reducing agent Substances 0.000 title claims abstract description 65
- 230000009467 reduction Effects 0.000 title claims abstract description 30
- 238000000034 method Methods 0.000 title claims abstract description 27
- 238000005457 optimization Methods 0.000 claims abstract description 11
- 210000000332 tooth crown Anatomy 0.000 claims abstract description 10
- 230000008859 change Effects 0.000 claims abstract description 8
- 238000006073 displacement reaction Methods 0.000 claims abstract description 5
- 230000007246 mechanism Effects 0.000 description 14
- 238000010586 diagram Methods 0.000 description 8
- 238000005516 engineering process Methods 0.000 description 2
- 230000007423 decrease Effects 0.000 description 1
- 238000012938 design process Methods 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 230000002452 interceptive effect Effects 0.000 description 1
- 238000003754 machining Methods 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 230000008569 process Effects 0.000 description 1
- 230000003245 working effect Effects 0.000 description 1
Images
Landscapes
- Gears, Cams (AREA)
- Retarders (AREA)
Abstract
一種具高減速比之二階行星齒輪減速機的漸開線齒輪組的齒廓設計方法，主要步驟包含：在一定高減速比和某些性能要求下，首先透過齒數配對找出二階行星齒輪減速機其兩組基本行星齒輪組的合適的齒數組合，再分別對基本行星齒輪組進行齒廓設計。本發明透過內外齒輪的齒廓移位，齒冠高度的變動，以及內外齒其中一齒使用非標準模數與非標準壓力角的三個技術方法，即能找出最適合的齒形輪廓，並借助最佳化的方法設計出無干涉的的嚙合齒輪齒廓，以達到最佳化的其它工作性能，藉以滿足一定機械效率的要求者。 A tooth profile design method for an involute gear set of a second-order planetary gear reducer with a high reduction ratio. The main steps include: under a certain high reduction ratio and certain performance requirements, first find a second-order planetary gear reducer through tooth number matching. The appropriate combination of the number of teeth of the two groups of basic planetary gear sets, and then carry out tooth profile design for the basic planetary gear sets respectively. The present invention can find the most suitable tooth profile through three technical methods of tooth profile displacement of internal and external gears, change of tooth crown height, and use of non-standard modulus and non-standard pressure angle for one of the internal and external teeth. And with the help of the optimization method, the non-interference meshing gear tooth profile is designed to achieve the optimized other working performance, so as to meet the requirements of certain mechanical efficiency.
Description
本發明係關於一種具高減速比之二階行星齒輪減速機的漸開線齒輪組的齒廓設計方法，更詳而言之，乃在一定高減速比和一些性能要求下如要求機械效率要超過某一數值，首先透過配齒的方法找出二階基本行星齒輪減速機的兩組漸開線齒輪組的合適的齒數組合，然後再同時透過齒廓移位、齒冠高度的變動以及內外齒其中一齒使用非標準模數與非標準壓力角的三個技術手段，並借助最佳化的方法設計出無干涉的的嚙合齒廓並最佳化其它一些工作性能，如較大的接觸比和較小的工作壓力角。 The present invention relates to a tooth profile design method for an involute gear set of a second-order planetary gear reducer with a high reduction ratio. For a certain value, first find the appropriate combination of the number of teeth of the two involute gear sets of the second-order basic planetary gear reducer through the method of tooth matching, and then simultaneously through the tooth profile shift, the change of the crown height and the inner and outer teeth. One tooth uses three technical means of non-standard modulus and non-standard pressure angle, and uses the optimized method to design a non-interfering meshing tooth profile and optimize some other working properties, such as a larger contact ratio and Smaller working pressure angle.
習知慣用之一階基本行星齒輪減速機，請參閱圖1和圖2，圖1係一階基本行星齒輪減速機的機構示意圖：圖2係一階基本行星齒輪減速機另一角度的示意圖。一階基本行星齒輪減速機是將普通行星齒輪減速機的中心太陽齒移走，內齒輪(或環齒輪)22當作機架，偏心轉軸(或行星架)26當作輸入件，外齒行星輪(或行星輪)21當作輸出件。圖2中省略了偏心轉軸26。這種基本
行星齒輪減速機中若內外齒輪組的齒數差非常小時，特別是一齒差時可以獲得非常高的減速比。例如，內外齒的齒數各為101與100齒，則可以得到減速比-100。此外，請參閱圖1，一階漸開線少齒差基本行星齒輪減速機是以外齒行星輪21為輸出件，為使輸出軸與輸入軸同心，必須有一個等角速機構25，而實務上是使用多個銷孔搭配圓柱銷來達成，但圓柱銷有容易磨損的缺點。
For the conventional first-order basic planetary gear reducer, please refer to Figures 1 and 2. Figure 1 is a schematic diagram of the mechanism of the first-order basic planetary gear reducer: Figure 2 is a schematic diagram of another angle of the first-order basic planetary gear reducer. The first-order basic planetary gear reducer removes the central sun gear of the ordinary planetary gear reducer, the inner gear (or ring gear) 22 is used as the frame, the eccentric shaft (or planetary frame) 26 is used as the input, and the outer gear planetary gear The wheel (or planetary wheel) 21 serves as the output. The
另外，漸開線少齒差的基本行星齒輪減速機的設計非常困難，這是因為內外輪齒的頂端非常容易干涉。因此目前最常見的少齒差基本行星齒輪減速機為擺線針輪減速機與諧波減速機。然而擺線針輪減速機需要相當精確的中心距與相當精確的齒形，否則輸出速度相當容易產生波動。諧波減速機由於兩齒差的緣故，具漸開線外齒的柔輪的齒數必須是減速比的兩倍。例如減速比要達到-100，則柔輪的齒數為200齒，環齒輪的齒數為202齒。對相同減速比與相同節圓大小的漸開線少齒差基本行星齒輪減速機與諧波減速機，後者的模數只有前者的一半，因此後者節圓上的齒厚只有前者的一半，因此剛性與強度都較差，此外製造成本也很高。 In addition, the design of a basic planetary gear reducer with a small involute tooth difference is very difficult because the tips of the inner and outer gear teeth are very easy to interfere. Therefore, the most common basic planetary gear reducers with small tooth difference are cycloid reducers and harmonic reducers. However, the cycloid reducer requires a fairly precise center distance and a fairly precise tooth profile, otherwise the output speed is quite prone to fluctuations. Due to the difference between the two teeth of the harmonic reducer, the number of teeth of the flex wheel with involute external teeth must be twice the reduction ratio. For example, if the reduction ratio is to reach -100, the number of teeth of the flex wheel is 200 teeth, and the number of teeth of the ring gear is 202 teeth. For the basic planetary gear reducer and harmonic reducer with the same reduction ratio and the same pitch circle with less tooth difference, the modulus of the latter is only half of the former, so the thickness of the teeth on the pitch circle of the latter is only half of the former, so Rigidity and strength are poor, and manufacturing costs are high.
在相同高減速比下，通常二階減速機的尺寸會較一階減速機小很多。目前二階減速機除了可以兩階都使用少齒差擺線針輪機構，另一種常見的是RV減速機，其第一階乃使用漸開線行星齒輪減速機構，第二階則使用少齒差擺線針輪減速機構。由於第一階是由太陽齒帶動行星齒輪，其第一階減速比不大。因 此在相同高減速比之下，RV減速機之尺寸會遠大於兩階都使用少齒差漸開線基本行星齒輪機構的減速機。 Under the same high reduction ratio, the size of the second-order reducer is usually much smaller than that of the first-order reducer. At present, the second-order reducer can use the cycloidal pinwheel mechanism with small tooth difference in both stages. Another common type is the RV reducer. The first stage uses an involute planetary gear reduction mechanism, and the second stage uses a small tooth difference. Cycloidal pin wheel reduction mechanism. Since the first stage is driven by the sun gear, the reduction ratio of the first stage is not large. because Under the same high reduction ratio, the size of the RV reducer will be much larger than that of the two-stage reducer using the involute basic planetary gear mechanism with small tooth difference.
本發明主要係針對前述少齒差基本行星齒輪減速機的各種缺點，所為的全新發明。 The present invention is mainly a brand-new invention aimed at various shortcomings of the aforementioned basic planetary gear reducer with small tooth difference.
本發明的主要目的在於提供一種具高減速比之二階行星齒輪減速機的漸開線齒輪組的齒廓設計方法，針對二階漸開線少齒差基本行星齒輪減速機的內外齒輪組在一定高減速比和一定性能的限制條件下，如要求機械效率性能要超過某一數值，提供一種齒廓的最佳化設計方法，除了可以排除干涉的情形，並能最佳化其它工作性能，例如降低工作壓力角與增加接觸比，以及得出相關的設計變數，當設計變數得到後，便能得到齒輪組的齒廓。 The main purpose of the present invention is to provide a tooth profile design method of the involute gear set of the second-order planetary gear reducer with high reduction ratio, aiming at the inner and outer gear sets of the second-order involute small tooth difference basic planetary gear reducer at a certain height Under the constraints of the reduction ratio and certain performance, if the mechanical efficiency performance is required to exceed a certain value, an optimal design method for the tooth profile is provided, in addition to eliminating the interference situation, and can optimize other working performance, such as reducing The working pressure angle and the increased contact ratio, and the related design variables are obtained. When the design variables are obtained, the tooth profile of the gear set can be obtained.
本發明的另一目的在於提供一種具高減速比之二階行星齒輪減速機的漸開線齒輪組的齒廓設計方法，其不僅可以適用於二階漸開線少齒差基本行星齒輪減速機的兩個齒輪組的齒廓設計，也能夠適用於一階漸開線少齒差基本行星齒輪減速機的一個齒輪組的齒廓設計。 Another object of the present invention is to provide a tooth profile design method for an involute gear set of a second-order planetary gear reducer with a high reduction ratio, which is not only applicable to the two-stage involute basic planetary gear reducer with small tooth difference The tooth profile design of one gear set can also be applied to the tooth profile design of one gear set of the first-order involute small tooth difference basic planetary gear reducer.
本發明的又一目的在於提供一種具高減速比之二階行星齒輪減速機的漸開線齒輪組的齒廓設計方法，其技術手段係同時透過齒廓的移位，齒冠高度的變動，以及內外齒其中一齒使用非標準模數與非標準壓力角的三個技術手段，並採用最佳化的方法，提供一個最佳化設計的流程 圖，以使得漸開線少齒差基本行星齒輪減速機的困難的齒廓設計能夠電腦程式化，最終可以得到具最佳性能的設計變數，即可畫出齒輪的齒廓，以便後續之電腦輔助加工。 Another object of the present invention is to provide a tooth profile design method for an involute gear set of a second-order planetary gear reducer with a high reduction ratio. One of the internal and external teeth uses three technical means of non-standard module and non-standard pressure angle, and adopts the optimization method to provide an optimized design process In order to make the difficult tooth profile design of the involute small tooth difference basic planetary gear reducer can be programmed by computer, and finally the design variables with the best performance can be obtained, and the tooth profile of the gear can be drawn for the subsequent computer. Auxiliary processing.
為了達成本發明，本發明一種具高減速比之二階行星齒輪減速機的漸開線齒輪組的齒廓設計方法，其步驟包括：步驟S10，決定二階漸開線行星齒輪減速機的減速比及某些性能要求；步驟S20，配齒後決定適當的兩組內外齒輪組的齒數；步驟S30，確認一個齒輪組的設計參數；步驟S40，透過三個齒廓設計技術的手段可以對應到一個齒輪組的五個設計變數；步驟S50，進入最佳化演算法迭代求解設計變數，並給定預設設計目標函數值的門檻或迭代的最多次數；步驟S60，給定五個設計變數的初始值；步驟S70，計算其他的設計參數的值；步驟S80，檢查所有的無干涉條件與性能條件是否滿足。若不滿足且還在初始值階段，則重新回到步驟S60；若果不滿足且已進入迭代階段，則回到步驟S100；步驟S90，計算設計目標函數值並判斷目標函數值的門檻或迭代的總次數是否已滿足，其中設計目標函數為其他性能的權重和。如果目標值不符合給定的門檻值且尚未達到預設的迭代次數，則進入步驟S100；若目標函數值小於給定的門檻值或者迭代次數已達到預設的最大次數則進入步驟S110；步驟S100，依照使用的最佳化演算法的規則決定下一次迭代時設計變數的新的預測值後回到步驟S70；步驟S110，依據最後得到的設計變數的值以及相關的設計參數畫出兩個齒輪的輪廓。 In order to achieve the present invention, the present invention provides a tooth profile design method for an involute gear set of a second-order planetary gear reducer with a high reduction ratio. Certain performance requirements; Step S20, determine the appropriate number of teeth of the two sets of internal and external gear sets after the teeth are matched; Step S30, confirm the design parameters of a gear set; Step S40, through the means of three tooth profile design techniques can correspond to a gear five design variables of the group; step S50, enter the optimization algorithm to iteratively solve the design variables, and give the threshold of the preset design objective function value or the maximum number of iterations; step S60, give the initial values of the five design variables ; Step S70, calculate the values of other design parameters; Step S80, check whether all non-interference conditions and performance conditions are satisfied. If it is not satisfied and it is still in the initial value stage, go back to step S60; if it is not satisfied and it has entered the iteration stage, go back to step S100; in step S90, calculate the design objective function value and determine the threshold or iteration of the objective function value Whether the total number of times has been satisfied, where the design objective function is the weight sum of other properties. If the target value does not meet the given threshold value and has not reached the preset number of iterations, go to step S100; if the objective function value is less than the given threshold value or the number of iterations has reached the preset maximum number, then go to step S110; step S100, determine the new predicted value of the design variable in the next iteration according to the rules of the optimization algorithm used, and then return to step S70; step S110, draw two design variables according to the finally obtained value of the design variable and related design parameters Outline of gears.
11:第一外齒行星輪 11: The first outer gear planetary gear
12:第一內齒輪 12: The first internal gear
13:第二外齒行星輪 13: The second outer gear planetary gear
14:第二內齒輪 14: Second internal gear
16:偏心轉軸 16: Eccentric shaft
21:外齒行星輪 21: External gear planetary gear
22:內齒輪 22: Internal gear
25:等角速機構 25: Equal angular velocity mechanism
26:偏心轉軸 26: Eccentric shaft
27:軸承 27: Bearings
S10:步驟S10 S10: Step S10
S20:步驟S20 S20: Step S20
S30:步驟S30 S30: Step S30
S40:步驟S40 S40: Step S40
S50:步驟S50 S50: Step S50
S60:步驟S60 S60: Step S60
S70:步驟S70 S70: Step S70
S80:步驟S80 S80: Step S80
S90:步驟S90 S90: Step S90
S100:步驟S100 S100: Step S100
S110:步驟S110 S110: Step S110
圖1係一階基本行星齒輪減速機的機構示意圖。 Figure 1 is a schematic diagram of the mechanism of a first-order basic planetary gear reducer.
圖2係一階基本行星齒輪減速機另一角度的示意圖。 Figure 2 is a schematic diagram of another angle of the first-order basic planetary gear reducer.
圖3係本發明二階基本行星齒輪減速機的機構示意圖。 3 is a schematic view of the mechanism of the second-order basic planetary gear reducer of the present invention.
圖4係本發明二階漸開線基本行星齒輪減速機的機構分解示意圖。 FIG. 4 is a schematic diagram of the exploded mechanism of the second-order involute basic planetary gear reducer of the present invention.
圖5係本發明最佳化設計的流程圖。 Figure 5 is a flow chart of the optimized design of the present invention.
圖6係本發明移位齒輪的示意圖。 FIG. 6 is a schematic diagram of the shift gear of the present invention.
圖7係本發明齒冠高度變動的示意圖。 Fig. 7 is a schematic diagram of the height variation of the tooth crown of the present invention.
請同時參閱圖3及圖4，圖3係本發明二階基本行星齒輪減速機的機構示意圖，圖4係本發明二階漸開線行星齒輪減速機的機構分解示意圖。由於偏心軸與齒輪之間的軸承，如圖2中的軸承27並不會影響齒廓的設計，因此圖4省略了軸承零件的顯示。二階漸開線少齒差基本行星齒輪減速機可以免去等角速機構25，也可以大幅降低減速機大小。第二內齒輪14是固接於機架，偏心轉軸16是輸入旋轉件，偏心轉軸16帶動第二外齒行星輪13繞第二內齒輪14做行星運動或偏心旋轉運動，第一外齒行星輪11與第二外齒行星輪13固接在一起旋轉，最後由第一外齒行星輪11帶動第一內齒輪12做輸出旋轉運動。二階漸開線少齒差行星齒輪減速機相當於有兩組一階漸開線行星齒輪機構的齒廓必須設計，以及四個內外齒輪的齒數事先需要先配對(這裡稱為配齒)。根據二階漸開線行星齒輪減速機的減速比公式，兩組內外齒輪有相當多的齒數組合可以達成該減速比，但對那一個齒數組合具有最好的性能，業界並無從知曉。由上所述，一階與二階漸開線少齒差行星齒輪減速機相較諧波減速機、一階與二階少齒差擺線針輪減速機與
RV減速機有其一定的優勢，然而受限於使用標準漸開線齒輪的輪廓會遭遇內外齒輪嚙合時的干涉問題而無法推廣到相關產業界，因此產業界甚至大部分學界並不孰悉此種減速機。同前所述，一階與二階少齒差漸開線行星齒輪減速機的齒廓設計是一個難題，雖然採用移位齒輪或許可以克服干涉問題，但其設計出的減速機性能不佳，例如工作壓力角太大、或齒輪接觸比太低等。此外，若機械效率要求相當高時，僅僅使用移位齒輪往往無法克服干涉問題、或接觸比小於1、或工作壓力角過大等缺點。
Please refer to FIG. 3 and FIG. 4 at the same time, FIG. 3 is a schematic view of the mechanism of the second-order basic planetary gear reducer of the present invention, and FIG. 4 is a schematic exploded view of the mechanism of the second-order involute planetary gear reducer of the present invention. Since the bearing between the eccentric shaft and the gear, such as the bearing 27 in FIG. 2 , does not affect the design of the tooth profile, the illustration of the bearing parts is omitted in FIG. 4 . The second-order involute basic planetary gear reducer with small tooth difference can eliminate the constant
請參閱圖5，圖5係本發明為解決前述問題的一個最佳化設計流程圖。在本實施例中，一個最佳化設計的流程圖適用於二階或一階漸開線少齒差行星齒輪減速機的困難的齒廓設計，最終可以得到具最佳性能的設計變數，即可畫出齒輪的齒廓，以便後續之電腦輔助加工。此最佳化設計的流程圖的步驟包括： Please refer to FIG. 5. FIG. 5 is a flow chart of an optimized design of the present invention to solve the aforementioned problems. In this embodiment, an optimized design flow chart is suitable for the difficult tooth profile design of the second-order or first-order involute planetary gear reducer with small tooth difference, and finally the design variables with the best performance can be obtained, that is, Draw the tooth profile of the gear for subsequent computer-aided machining. The steps of this optimized design flow chart include:
步驟S10，決定二階漸開線行星齒輪減速機的減速比
步驟S20，配齒後決定適當的兩組內外齒輪組的齒數，即z 1、z 2與z 3、z 4。 Step S20, after the teeth are matched, determine the appropriate number of teeth of the two groups of inner and outer gear sets, namely z 1 , z 2 and z 3 , z 4 .
步驟S30，確認一個齒輪組的設計參數，包含齒數z 1、z 2(或z 3、z 4)、其中一個齒輪的模數與標準節圓壓力角採用標準值以及相關的性能A、B...之要求。在本實施例中第一內齒輪12(或第二內齒輪14)的模數m 2(或m 4)與標準節圓壓力角α 2(或α 4)採用標準值，此外在本實施例中要求性能為機 械效率要超過某一數值。符號m i (i=1,2,3或4)表示齒輪i的模數，α i (i=1,2,3或4)表示齒輪i的標準節圓的壓力角。 Step S30, confirming the design parameters of a gear set, including the number of teeth z 1 , z 2 (or z 3 , z 4 ), the modulus of one of the gears and the standard pitch circle pressure angle using standard values, and related performances A and B. .. requirements. In this embodiment, the module m 2 (or m 4 ) of the first internal gear 12 (or the second internal gear 14 ) and the standard pitch circle pressure angle α 2 (or α 4 ) adopt standard values. The required performance is that the mechanical efficiency exceeds a certain value. The symbol m i ( i = 1, 2, 3 or 4) represents the modulus of the gear i , and α i ( i = 1, 2, 3 or 4) represents the pressure angle of the standard pitch circle of the gear i .
步驟S40，確認一個齒輪組的五個設計變數，此五個設計變數來自本發明所採取的技術手段，配合圖示說明如後。 Step S40 , confirming five design variables of a gear set, the five design variables are derived from the technical means adopted by the present invention, and are described below with the illustrations.
本發明技術手段之一是使用移位齒輪，如圖6所示。移位齒輪與原標準齒輪仍是相同基圓所展開之漸開線，差別在於截取的部位不同，因此齒廓移位後齒厚、齒間寬度、齒冠、齒根已不相同。兩齒輪的齒廓移位會多出一個設計變數，即所謂移位係數x 1或x 2(x 3或x 4)。x i (i=1,2,3或4)表示齒輪i的移位係數。本實施例中以x 1(x 3)作為設計變數，另一個移位係數x 2(x 4)可以由零背隙的嚙合方程式得到。為了避免齒頂或其他干涉情形發生或保有適當的徑向間隙，本發明的技術手段之二是讓兩齒輪的齒冠可以個別變動y 1 m 1與y 2 m 2(y 3 m 3與y 4 m 4)，y i (i=1,2,3或4)表示齒輪i的齒冠變動係數。兩齒輪的齒冠高度可以變動會多出兩個設計變數，即齒冠變動係數y 1與y 2(y 3與y 4)。當齒冠變動係數大於零代表齒冠增加，當齒冠變動係數小於零代表齒冠減少，如圖7的示意圖。產業界的齒輪組都使用相同的標準模數與標準節圓壓力角，因此當兩齒輪的模數、標準節圓壓力角與齒數確定後，兩齒輪的齒廓就已確定。本發明的技術手段之三是兩齒輪其中一個齒輪使用標準模數與標準節圓壓力角，但另一個齒輪則不使用標準模數與標準節圓壓力角，這可以讓設計更為靈活，但兩齒輪仍須滿足正確的嚙合條件，即m 1 cos α 1=m 2 cos α 2(m 3 cos α 3=m 4 cos α 4)，其中在本實施例中齒輪1(或3)使用非標準模數，則會多出一個設計變數m 1(或m 3)，而非標準節圓壓力角α 1(或α 3)的值可以由上述的嚙合條件計算得到。漸開線齒 輪組的一個嚙合特性是中心距d c 與工作節圓壓力角α w 的餘弦的乘積等於兩齒輪的基圓半徑之差。漸開線齒輪組中心距的變動不會造成輸出速度的變動，可以選擇中心距或工作節圓壓力角當作設計變數。在本實施例中選擇中心距d c 作為設計變數，則工作節圓壓力角α w 的值可由上述嚙合特性條件計算得到。 One of the technical means of the present invention is to use shifting gears, as shown in FIG. 6 . The shift gear and the original standard gear are still involutes developed by the same base circle. The difference is that the intercepted parts are different. Therefore, the tooth thickness, inter-tooth width, tooth crown and tooth root are different after the tooth profile is displaced. The tooth profile shift of the two gears will have an additional design variable, the so-called shift factor x 1 or x 2 ( x 3 or x 4 ). x i ( i = 1, 2, 3 or 4) represents the shift coefficient of gear i . In this embodiment, x 1 ( x 3 ) is used as a design variable, and another shift coefficient x 2 ( x 4 ) can be obtained from the meshing equation with zero backlash. In order to avoid the occurrence of tooth top or other interference situations or to maintain proper radial clearance, the second technical means of the present invention is to allow the tooth crowns of the two gears to change individually y 1 m 1 and y 2 m 2 ( y 3 m 3 and y ) 4 m 4 ), y i ( i = 1, 2, 3 or 4) represents the tooth crown variation coefficient of gear i . The height of the crowns of the two gears can be changed, and there are two additional design variables, namely the crown variation coefficients y 1 and y 2 ( y 3 and y 4 ). When the crown variation coefficient is greater than zero, the crown increases, and when the crown variation coefficient is less than zero, the crown decreases, as shown in the schematic diagram in Figure 7. Gear sets in the industry all use the same standard module and standard pitch circle pressure angle, so when the module, standard pitch circle pressure angle and number of teeth of the two gears are determined, the tooth profile of the two gears has been determined. The third technical means of the present invention is that one gear of the two gears uses the standard module and the standard pitch circle pressure angle, but the other gear does not use the standard module and the standard pitch circle pressure angle, which can make the design more flexible, but The two gears still have to meet the correct meshing conditions, that is, m 1 cos α 1 = m 2 cos α 2 ( m 3 cos α 3 = m 4 cos α 4 ), in which gear 1 (or 3) uses non- If the standard modulus is used, there will be an additional design variable m 1 (or m 3 ), and the value of the non-standard pitch circle pressure angle α 1 (or α 3 ) can be calculated from the above meshing conditions. One of the meshing characteristics of the involute gear set is that the product of the center distance d c and the cosine of the working pitch circle pressure angle α w is equal to the difference between the base circle radii of the two gears. The change of the center distance of the involute gear set will not cause the change of the output speed, and the center distance or the pressure angle of the working pitch circle can be selected as the design variable. In this embodiment, the center distance d c is selected as the design variable, then the value of the working pitch circle pressure angle α w can be calculated from the above meshing characteristic conditions.
因此本發明藉由三個技術手段會有五個設計變數需決定，五個設計變數為x 1(x 3)、y 1、y 2(y 3、y 4)、m 1(m 3)及d c 。 Therefore , in the present invention , there are five design variables to be determined by three technical means . dc .
步驟S50，進入最佳化演算法迭代求解設計變數，並給定預設設計目標函數值的門檻或迭代的最多次數。本發明的技術手段與設計方法適用任何一種最佳化演算法。 Step S50, enter the optimization algorithm to iteratively solve the design variables, and set the threshold of the preset design objective function value or the maximum number of iterations. The technical means and design method of the present invention are applicable to any optimization algorithm.
步驟S60，給定五個設計變數的初始值。 In step S60, the initial values of the five design variables are given.
步驟S70，計算其他的設計參數的值，如兩齒輪的基圓半徑、齒冠圓半徑、移位係數x 2(x 4)、工作節圓壓力角α w 等等非獨立的設計參數皆可由已知的設計參數以及已給定的設計變數之值計算得到。 In step S70, the values of other design parameters are calculated, such as the base circle radius of the two gears, the tooth crown circle radius, the displacement coefficient x 2 ( x 4 ), the working pitch circle pressure angle αw and other non-independent design parameters. Calculated from the known design parameters and the values of the given design variables.
步驟S80，檢查所有的無干涉條件與給定的性能條件(本實施例係以機械效率作為舉例說明，但非為限制本發明)是否滿足。若不滿足且還在初始值階段，則重新回到步驟S60；若不滿足且已進入迭代階段，則回到步驟S100。 Step S80 , checking whether all the non-interference conditions and the given performance conditions (this embodiment takes the mechanical efficiency as an example, but is not intended to limit the present invention) are satisfied. If it is not satisfied and it is still in the initial value stage, go back to step S60; if it is not satisfied and it has entered the iteration stage, go back to step S100.
步驟S90，計算設計目標函數值並判斷目標函數值的門檻或迭代的總次數是否已滿足，其中設計目標函數為其他性能的權重和。在本實施例中其他性能為接觸比與工作節圓的壓力角，對應設計目標函數為此兩種性能的權重和。如果目標值不符合給定的門檻值且尚未達到預設的迭代次數，則進入步驟S100；若目標值小於給定的門檻值或者迭代次數已達到預設的最 大次數則進入步驟S110。 Step S90: Calculate the design objective function value and determine whether the threshold of the objective function value or the total number of iterations have been satisfied, wherein the design objective function is the weight sum of other performances. In this embodiment, the other properties are the contact ratio and the pressure angle of the working pitch circle, and the corresponding design objective function is the weight sum of these two properties. If the target value does not meet the given threshold value and has not reached the preset number of iterations, go to step S100; if the target value is less than the given threshold value or the number of iterations has reached the preset maximum number of iterations If the number of times is large, go to step S110.
步驟S100，依照使用的最佳化演算法的規則決定下一次迭代時設計變數的新的預測值後回到步驟S70。 In step S100, a new predicted value of the design variable in the next iteration is determined according to the rules of the optimization algorithm used, and then the process returns to step S70.
步驟S110，依據最後得到的設計變數的值以及相關的設計參數畫出兩個齒輪的輪廓。 本發明的設計步驟，除了適用於二階基本行星齒輪減速機的漸開線齒輪組的齒廓設計，對於一階也同樣適用，亦即本發明的設計步驟同樣適用於一階與二階基本行星齒輪減速機的漸開線齒輪組的齒廓設計。此外，本發明的設計步驟係同時透過三個技術手段，包含：透過內外齒輪齒廓的移位，內外齒輪齒冠高度的變動，以及內外齒輪其中一齒輪使用非標準模數與非標準壓力角的三個技術手段，來達成本發明的目的。另外，本發明的設計步驟係採用最佳化的方法，提供一個最佳化設計的流程圖，因此使得漸開線少齒差行星齒輪減速機的困難的齒廓設計能夠達成電腦程式化的設計。 In step S110, the outlines of the two gears are drawn according to the finally obtained values of the design variables and related design parameters. The design steps of the present invention, in addition to being applicable to the tooth profile design of the involute gear set of the second-order basic planetary gear reducer, are also applicable to the first-order, that is, the design steps of the present invention are also applicable to the first-order and second-order basic planetary gears The tooth profile design of the involute gear set of the reducer. In addition, the design steps of the present invention are carried out through three technical means at the same time, including: through the displacement of the tooth profile of the internal and external gears, the change in the height of the tooth crowns of the internal and external gears, and the use of a non-standard module and a non-standard pressure angle for one of the internal and external gears three technical means to achieve the purpose of the present invention. In addition, the design steps of the present invention adopt the optimization method to provide a flow chart of the optimization design, so that the difficult tooth profile design of the involute planetary gear reducer with small tooth difference can achieve a computer-programmed design .
如上所述，本發明的特點在於：藉由同時可變動齒冠高度、可變動齒厚與可變動截取適合的漸開線段落三個技術手段，並採取最佳化的技術能自動調整找出最適合的齒形輪廓，以滿足一定機械效率的要求並得到最佳的工作性能如降低工作壓力角與增加接觸比。 As mentioned above, the feature of the present invention is: by adopting the three technical means of variable crown height, variable tooth thickness and variable interception of suitable involute segments at the same time, and adopting the optimized technology, it can automatically adjust and find out The most suitable tooth profile to meet the requirements of a certain mechanical efficiency and obtain the best working performance such as reducing the working pressure angle and increasing the contact ratio.
綜上所述，本發明具高減速比之二階行星齒輪減速機的漸開線齒輪組的齒廓設計方法，藉由透過內外齒輪齒廓的移位，讓內外齒輪齒冠高度的變動，以及內外齒輪其中一齒輪使用非標準模數與非標準壓力角等設計方法，即能找出最適合的齒形輪廓，以滿足一定機械效率的要求，並能降低工作壓力角，增加接觸比，合 於產業上之利用性。而本發明藉由同時可變動齒冠高度、可變動齒厚、與可變動截取適合的漸開線段落等方式，其與使用標準漸開線齒輪的輪廓容易產生內外齒輪嚙合時的干涉等習知技術相較，明顯具備功效之增進，具有進步性。另本發明申請前並未見於刊物，其新穎性亦毋庸置疑。本創作合於專利法之規定，爰依法提出發明專利之申請，祈請惠予審查並賜予專利，實感德便綜合上述事實。 To sum up, the tooth profile design method of the involute gear set of the second-stage planetary gear reducer with high reduction ratio of the present invention allows the height of the tooth crown of the inner and outer gears to change by shifting the tooth profile of the inner and outer gears, and One of the internal and external gears uses non-standard modulus and non-standard pressure angle design methods, that is, the most suitable tooth profile can be found to meet the requirements of a certain mechanical efficiency, and the working pressure angle can be reduced, and the contact ratio can be increased. Utilization in industry. In the present invention, by simultaneously changing the height of the tooth crown, the thickness of the tooth, and the involute segment suitable for the variable interception, it is easy to produce interference when the internal and external gears are meshed with the contour of the standard involute gear. Compared with the known technology, it has obvious improvement in efficacy and progress. In addition, the present invention has not been seen in publications before the application, and its novelty is beyond doubt. This creation complies with the provisions of the Patent Law, and it is required to file an application for a patent for invention in accordance with the law, and I pray that it will be reviewed and granted a patent.
S10:步驟S10 S10: Step S10
S20:步驟S20 S20: Step S20
S30:步驟S30 S30: Step S30
S40:步驟S40 S40: Step S40
S50:步驟S50 S50: Step S50
S60:步驟S60 S60: Step S60
S70:步驟S70 S70: Step S70
S80:步驟S80 S80: Step S80
S90:步驟S90 S90: Step S90
S100:步驟S100 S100: Step S100
S110:步驟S110 S110: Step S110
Claims (6)
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| TW109136113A TWI772924B (en) | 2020-10-19 | 2020-10-19 | Tooth profile design method of involute gear set for two-stage planetary reducers with high speed reduction ratio |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| TW109136113A TWI772924B (en) | 2020-10-19 | 2020-10-19 | Tooth profile design method of involute gear set for two-stage planetary reducers with high speed reduction ratio |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| TW202217626A TW202217626A (en) | 2022-05-01 |
| TWI772924B true TWI772924B (en) | 2022-08-01 |
Family
ID=82558794
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| TW109136113A TWI772924B (en) | 2020-10-19 | 2020-10-19 | Tooth profile design method of involute gear set for two-stage planetary reducers with high speed reduction ratio |
Country Status (1)
| Country | Link |
|---|---|
| TW (1) | TWI772924B (en) |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| TWI284719B (en) * | 2003-04-28 | 2007-08-01 | Shiau-Chuen Wang | Anti-skidding differential with variable transmission ratio |
| WO2016150149A1 (en) * | 2015-03-26 | 2016-09-29 | 李照廷 | Improved wobble plate decelerator |
| CN106015516A (en) * | 2016-05-24 | 2016-10-12 | 北京航空航天大学 | Inside engaged gear tooth form design method based on B-spline engaging line |
-
2020
- 2020-10-19 TW TW109136113A patent/TWI772924B/en not_active IP Right Cessation
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| TWI284719B (en) * | 2003-04-28 | 2007-08-01 | Shiau-Chuen Wang | Anti-skidding differential with variable transmission ratio |
| WO2016150149A1 (en) * | 2015-03-26 | 2016-09-29 | 李照廷 | Improved wobble plate decelerator |
| CN106015516A (en) * | 2016-05-24 | 2016-10-12 | 北京航空航天大学 | Inside engaged gear tooth form design method based on B-spline engaging line |
Non-Patent Citations (1)
| Title |
|---|
| 柯峻宇,"漸開線少齒差行星傳動機構齒型之最佳化研究,"國立交通大學論文, 2016/10/07. https://hdl.handle.net/11296/6g65y4 * |
Also Published As
| Publication number | Publication date |
|---|---|
| TW202217626A (en) | 2022-05-01 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| US11002353B2 (en) | Cycloidal pin wheel harmonic transmission device | |
| US10527149B2 (en) | Conjugate gears with continuous tooth flank contact | |
| US9903459B2 (en) | Strain wave gearing having continuous-contact tooth profile formed using arcuate tooth profile | |
| CN107387721B (en) | Wide-tooth double-arc harmonic gear | |
| WO2019104777A1 (en) | Arc-shaped surface contact-based worm and worm gear transmission type power device | |
| WO2020015590A1 (en) | Planetary reduction electrical machine capable of achieving full closed-loop control and articulated robot | |
| CN108730480B (en) | Cycloidal gear of RV reducer and tooth profile reverse active modification method thereof | |
| CN109084006B (en) | Trigonometric function shape modifying method for cycloid gear and cycloid pin gear speed reducer | |
| CN110704968A (en) | RV reducer multi-target optimization method based on cycloidal gear tooth profile modification | |
| TWI772924B (en) | Tooth profile design method of involute gear set for two-stage planetary reducers with high speed reduction ratio | |
| US8562481B2 (en) | Gearing with cylindrical tooth forms | |
| CN113446377A (en) | Conjugate cycloid tooth profile harmonic speed reducer | |
| US10975946B1 (en) | Differential reducer with high ratio | |
| CN105844078B (en) | Active design method of low-pulsation gear pump | |
| WO2023097802A1 (en) | Design method for inner tooth profile of complex-wave oscillating-tooth speed reducer, and two-stage speed reducer | |
| TWM591134U (en) | Gear variable-speed mechanism | |
| CN114673764A (en) | Non-orthogonal oval ring surface worm gear pair | |
| CN112182795B (en) | Different tooth form comparison modeling method for harmonic speed reducer | |
| Lin et al. | Optimum design of involute tooth profiles for KHV planetary drives with small teeth number differences | |
| Liang et al. | Calculation method of sliding ratios for conjugate-curve gear pair and its application | |
| JP2017172696A (en) | Involute spur gear with tooth form corrected in curve | |
| CN111173895A (en) | Two-stage closed type undercut cycloid oscillating tooth transmission unit | |
| JPH08247045A (en) | Internal gear type fluid device | |
| CN117407989B (en) | Internal gear shaping design method based on meshing line with variable circle center | |
| JP7477655B2 (en) | Gear Pair |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| MM4A | Annulment or lapse of patent due to non-payment of fees |