往復式煤炭輸送機設計
往復式煤炭輸送機設計,往復式煤炭輸送機設計,往復,煤炭,輸送,設計
畢 業(yè) 設 計
論文題目 往復式煤炭輸送機設計
學 院 信息學院
專 業(yè) 機械制造及其自動化
年 級 2005級機制信052
姓 名 郝生全
指導老師 張文煥
職 稱 教授
2009年6月
山西農(nóng)業(yè)大學教務處制
山西農(nóng)業(yè)大學工程技術學院畢業(yè)論文
畢業(yè)設計說明書中文摘要
往復式煤炭輸送機設計
摘要：煤炭是我國能源安全的基石。煤炭工業(yè)是我國重要的基礎產(chǎn)業(yè)，我國的煤炭產(chǎn)量已是世界第一位，是煤炭生產(chǎn)大國，現(xiàn)在我國煤炭工業(yè)已具備了設計、施工、裝備及管理千萬噸露天煤礦和大中型礦井的能力。但是，我國煤炭開采技術裝備總體水平低，煤炭生產(chǎn)技術裝備是機械化、部分機械化和手工作業(yè)并存的多層次結構。技術和裝備水平低，嚴重影響煤炭的生產(chǎn)效率。
保障煤炭供應是國家加強煤炭工業(yè)宏觀調控的重點之一，煤炭深加工更是國家重工業(yè)發(fā)展的重中之重，輸送機設備作為煤礦生產(chǎn)系統(tǒng)的基礎設備,給煤設備的可靠性,特別是關鍵咽喉部位給煤設備的可靠性,直接影響整個生產(chǎn)系統(tǒng)的正常運行。生產(chǎn)實踐證明,現(xiàn)有的往復式給料機的生產(chǎn)能力小、安裝和拆卸不方便、受力不均勻等缺點。，隨著煤炭工業(yè)的發(fā)展,煤礦井型不斷地擴大,現(xiàn)有Ｋ型往復煤炭輸送機生產(chǎn)能力小,不能滿足大型礦井的要求，因此,改進和擴大現(xiàn)有Ｋ型往復煤炭輸送機是完全必要的。本設計的往復式煤炭輸送機是在原有的基礎上作了一些改進，具有結構簡單、維修量小、性能穩(wěn)定、噪音低、安裝方便等優(yōu)點。
本文主要介紹了：往復式煤炭輸送機的發(fā)展歷史，用途，組成及工作原理；往復式煤炭輸送機的特點；設計的一般步驟；使用中存在的問題及改進措施；安裝和維護等內容。在本次往復式煤炭輸送機的設計過程中，著重對減速器、傳動平臺進行了分析和設計。對重要的部件進行了受力分析、強度的校核，根據(jù)其常見失效形式、影響因素及基本設計要求，給出了重要部件的受力分析、強度和剛度的設計方法。
關鍵詞：往復式煤炭輸送機 減速器 受力分析 強度校核
畢業(yè)設計說明書外文摘要
Reciprocating coal conveyor
ABSTRACT
Coal is the cornerstone of China's energy security. The coal industry is an important basic industries，China's coal production is the first in the world, coal producing countries，however, coal mining technology and equipment of our overall low level of，coal production is mechanized equipment, part of both mechanized and manual operation of the multi-level structure. Low level of technology and equipment, seriously affect the efficiency of coal production.
To protect the supply of coal is the coal industry to strengthen macro-control of one of the key points，deep processing of coal is the most important national industrial development,coal mine production equipment is the one of the main equipment for coal equipment reliability, Special location is the key to the throat of coal equipment reliability, a direct impact on the entire production system to normal operation. Practice has proved that the existing reciprocating Feeder small production, With the development of coal industry and coal-wells continues to expand, the existing K-type reciprocating coal production capacity of the small plane, unable to meet the requirements of large-scale mine, therefore, improve and expand existing K-type reciprocating to the coal machine is totally necessary. The design of the reciprocating to the coal on the basis of the original made some improvements, it has a simple structure and a small amount of maintenance, stable performance, low noise, the installation is easy.
This paper introduced：Reciprocating coal conveyor history of the development, use, composition and physics; Reciprocating to the characteristics of coal; focusing on reducer, transmission platform, crank linkage, strength check, in accordance with its common failure mode, Factors and basic design requirements, is an important component of the stress analysis, strength and stiffness of the design method.
Keywords : Reciprocating coal conveyor Reducer Analysis Strength Check
目錄
1緒論 1
1.1 往復式煤炭輸送機的發(fā)展史 1
1.2 往復式煤炭輸送機的用途 1
1.3 煤炭輸送機的結構及其工作原理 2
1.4 往復式煤炭輸送機的優(yōu)越性 2
1.4.1 往復式煤炭輸送機的特點 2
1.4.2 往復式煤炭輸送機與其他煤炭輸送機的比較 2
1.5 設計往復式煤炭輸送機的必要性 3
2 往復式煤炭輸送機的結構設計 3
2.1 煤炭輸送機箱體尺寸的確定 4
2.2 煤炭輸送機整體結構布局 5
2.3煤炭輸送機的箱體設計 5
2.4 底托板的設計及校核 6
2.5 軸承選擇與校核 7
2.6 煤炭輸送機的受力分析 8
3往復式煤炭輸送機減速器的設計 8
3.1 電動機的選擇 8
3.1.1 選擇電動機類型 8
3.1.2 選擇電動機容量 8
3.1.3 確定電動機轉速 9
3.1.4 計算傳動裝置的運動和動力參數(shù) 10
3.2 齒輪的設計及校核計算 11
3.2.1 第一對齒輪的設計 11
3.2.2 第二對齒輪的設計 18
3.3 軸的設計及校核計算 24
3.3.1軸的設計及校核 24
3.3.2軸的設計及校核 27
3.3.3軸的設計及校核 31
3.4 軸承的選擇與校核計算 34
3.4.1軸上的軸承選擇與校核 34
3.4.2軸的軸承選擇與校核 34
3.4.3軸的軸承選擇與校核 35
3.5 鍵的選擇與校核計算 36
3.5.1軸上鍵的選擇與校核 36
3.5.2軸上鍵的選擇與校核 37
3.6 軸系部件的結構設計 37
3.7 減速器箱體的設計 38
4 往復式煤炭輸送機的改進措施及其發(fā)展趨勢 40
4.1 往復式煤炭輸送機的使用說明 40
4.2 往復式煤炭輸送機的安裝說明 42
4.3 往復式煤炭輸送機的維護措施 42
4.4往復式煤炭輸送機的發(fā)展趨勢 42
結 論 43
參考文獻 44
致 謝 45
科技譯文
英文原文
MICRO PLANETARY REDUCTION GEAR USING SURFACE-MICROMACHINING
Abstract
A micro planetary gear mechanism featuring a high gear reduction ratio with compactness in size ispresented in this paper. SUMMiT V is employed for the fabrication method so that the redundancy of assembling parts is eliminated. The design rules of which has also been checked. To make full use of the benefits of the surface- micro - machining, the planetary reduction gear is designed toward using the on-chip micro- engine. The expected gearreduction ratio is calculated and compared with the conventional chain gear mechanism. The microplanetary gear mechanism presented in this paper is expected to have 162:1 reduction ratio utilizing less space consumption. This is an order of magnitude higher than the previously reported design in a single reduction gear train.
Keywords:MEMS, planetary gear, reduction gear surface-micromachining, SUMMiT V process
Nomenclature
a sun gear
b planet gears
c internal gear (fixed)
d internal gear (rotary)
n the number of units of gear train
D diameter of the pitch circle
N number of teeth
P number of planets
angular velocity
Introduction
The gear mechanisms in microelectro mechanical systems(MEMS) are commonly expected to generate high torque in the confined micro-size systems. However, it is generally difficult for the micro-scale systems to have such a high torque without having multiple reduction systems.
The design of the reduction gear drive based on a planetary paradox gear mechanism can increase the torque within a compact area, since the microplanetary gear system has an advantage of high reduction ratio per unit volume [1]. However its mechanism is so complicated that relatively few attempts have been made to miniaturize the gear systems [2-3]. Suzumori et al. [2] used the mechanical paradox planetary gear mechanism to drive a robot for 1-in pipes forward or backward. They employed a single motor to drive the gear mechanisms with high reduction ratio. Precise gear fabrication was enabled by micro wire electrical discharge machining (micro-EDM). These parts, however, should be assembled before the drive motor is attached to the gearbox. Takeuchi et. al. [3] also used micro-EDM to fabricate the micro planetary gears. They suggested special cermets or High Carbon Steel for possible materials. While the design can achieve a reduction ratio of 200, the gears should also be assembled and motor driven.To enable the driving of the planetary gear by onchip means, Sandia Ultra- planar Multi-level MEMS Technology (SUMMiT-V) process [4] for planetary gear fabrication is adopted in this study. The SUMMiT-V process is the only foundry process available which utilizes four layers of releasable polysilicon, for a total of five layers (including a ground plane) [5]. Due to this fact, it is frequently used in complicated gear mechanisms being driven by on-chip electrostatic actuators [5].However, in many cases, the microengines may not produce enough torque to drive the desired mechanical load, since their electrostatic comb drives typically only generate a few tens of micronewtons of force. Fortunately, these engines can easily be driven at tens of thousands of revolutions per minutes. This makes it very feasible to trade speed for torque [7].Rodgers et al. [7] proposed two dual level gears with an overall gear reduction ratio of 12:1. Thus six of these modular transmission assemblies can have a 2,985,984:1 reduction ratio at the cost of the huge space.
With the desire for size compactness and at the same time, high reduction ratios, the planetary gear system is presented in this paper. It will be the first planetary gear mechanism using surface micromachining,to the authors knowledge. The principles of operations of the planetary gear mechanism, fabrication, and the expected performance of the planetary gear systems are described in this paper.
Principles of operation
An alternative way of using gears to transmit torque is to make one or more gears, i.e., planetary gears, rotate outside of one gear, i.e. sun gear. Most planetary reduction gears, at conventional size, are used as well-known compact mechanical power transmission systems [1]. The schematic of the planetary gear system employed is shown in Figure
Since SUMMiT V designs are laid out using AutoCAD 2000, the Figure 1 is generated automatically from the lay out masks (Appendix [1]). One unit of the planetary gear system is composed of six gears: one sun gear, a, three planetary gears, b, one fixed ring gear, c, one rotating ring gear, d, and one output gear. The number of teeth for each gear is different from one another except among the planetary gears. An input gear is the sun gear, a, driven by the arm connected to the micro-engine. The rotating ring gear, d, is served as an output gear. For example, if the arm drives the sun gear in the clockwise direction, the planetary gears, b, will rotate counter-clockwise at their own axis and at the same time, those will rotate about the sun gear in clockwise direction resulting in planetary motion. Due to the relative motion between the planetary gears, b, and the fixed ring gear, c, the rotating ring gear, d, will rotate counterclockwise direction. This is so called a 3K mechanical paradox planetary gear [1].
Fabrication procedure and test structures
The features of the SUMMiT V process offer four levels of structural polysilicon layers and an electrical poly level, and also employ traditional integrated circuit processing techniques [4]. The SUMMiT V technology is especially suitable for the gear mechanism. The planetary gear mechanism can be driven by the on-chip engine and thus is another reason of using the SUMMiT V process.
Since the Sandia process is such a well-known procedure [5-7], only brief explanation is presented. Figure 2 represents the cross-sectional view of Figure 1, and also was generated from the AutoCAD layout masks (Appendix [1]). The discontinuity in the cross-section is for the etch holes. The poly1 (gray) is used for the hubs and also patterned to make the fixed ring gear, i.e., c, the sun gear, i.e., a, the rotating ring gear, i.e., c, and the output gear is patterned in the poly2. Since the planetary gear needs to contact both the fixed ring and rotating ring gear, poly2 is added to poly3, where the gear teeth are actually formed. The poly4 layer is used for the arm that drives the sun gear. After the release etch, the planetary gears will fall down so that those will engage both the ring gears.
The figures for the test structures are presented in Appendix [2]. Since the aim of this paper is to suggest a gear reduction mechanism, the planetary gear system is decomposed to several gear units to verify its performance. The first test structure is about the arm, which rotates the sun gear, connected to the on-chip engine. The angular velocity of the arm depends on the engine output speed. The second test structure describes the point at which the sun gear and planetary gears are engaged to the fixed ring gear. Because of the fact that the ring gear is fixed, the planetary gear is just transmitting the torque from the sun gear to the fixed ring gear without planet motion, e.g., rotating its own axis not around the sun gear. When the rotating ring gear is mounted on top of the fixed ring gear, i.e., the third test structure, the planetary gears begin to rotate around the sun gear so that the planet motion are enabled. Therefore, once one output gear is attached to the rotating ring gear, i.e., the final test structure, the whole reduction unit is completed. Dismantling the
planetary gear into three test structures allows the pinpointing of possible errors in the gear system.
Solutions procedure and expected performance
The reduction ratio is defined as the ratio between the angular velocity of the driver gear and that of the driven gear. High reduction ratios indicate trading speed for torque. For example, a 10:1 gear reduction unit could increase torque an order of magnitude. Since the gears in the planetary system should be meshed to one another , the design of gear module should follow a restriction. For example, the number of teeth for the sun gear plus either that of the fixed ring gear or that of the rotating ring gear should be the multiple of the number of planets, P (equation 1). Equation 2, which represent the reduction ratio, should observe the equation 1 first. The N is the number of the teeth for corresponding gear.
Gears, a, b, c, d in the planetary gear system have a tooth module of 4 ìm, which is a comparable size of the current gear reduction units[5], and the tooth numbers are 12, 29, 69, and 72 respectively. Therefore the overall reduction ratio is 162:1 from equation (2). Rodgers et al. [7] reported a 12:1 reduction unit using surface micromachining, which is less than order of magnitude for the gear reduction ratio of the planetary gear system. Although the reduction from Rodgers et al. [7] needs to be occupied in approximately 0.093 mm2, the planetary gear system only utilizes an area of approximately 0.076 mm2. Thus, this planetary reduction design can achieve an order of magnitude higher reduction ratio with less space. Since thereduction module is composed of several reduction units, the advantage of using a planetary gear system is self evident in Figure 3.
Figure 3 shows the comparison of reduction ratios between the proposed planetary gear mechanism i.e. 162n, and the Sandia gear system [7], i.e. 12n, as a function of the number of units, i.e., n. The ordinate is drawn in log scale so that the orders of magnitude differences between two modules are evident. For example, in a module with five numbers of units, the reduction ratio difference between two is approximately six orders of magnitudes. Furthermore, the planetary gear system can save 8500 m2 in such a five unit reduction system.
Conclusion and discussions
The planetary gear reduction system using surface-micromachining, driven by an on-chip engine, first appears in this paper within the authors’ knowledge. The single reduction unit can achieve an order of magnitude higher reduction ratio than that of the previous design. However, due to the surface friction, and the backlash, which is inevitable for the gear manufacturing process, the overall reduction ratio may be less than 162:1 in the real situation. Even though some loss might be expected in the real application, the overall reduction ratio should be order of magnitude higher and the space consumption is less than the previous design [7].
The authors learned a lot about the surfacemicromachining process during the project grant,and realized that a lot of the design needed to be revisited and corrected. This became prevalent when drawing the cross-sectional views of the design. Since the authors utilized the SUMMit V Advanced design Tools Software package and verified the design rules, the planetary gear layout is ready for fabrication. The authors hope that this planetary reduction unit will continue to be updated by successive researchers.
Acknowledgement
The authors would acknowledge that discussions with Prof. Kris Pister, Prof. Arun Majumdar, Ms. Karen Cheung, and Mr. Elliot Hui contributed to this work tremendously.
References
1. Hori, K., and Sato, A., “Micro-planetary reduction gear” Proc. IEEE 2nd Int. Symp. Micro Machine and Human Sciences, pp. 53- 60 (1991).
2. Suzumori, K., Miyagawa, T., Kimura, M., and Hasegawa, Y., “Micro Inspection Robot for 1-in Pipes”, IEEE/ASME Trans. On Mechatronics, Vol. 4., No. 3, pp. 286-292 (1999).
3. Takeuchi, H., Nakamura, K., Shimizu, N., and Shibaike, N., “Optimization of Mechanical Interface for a Practical Micro-Reducer”, Proc. IEEE 13th Int. Symp. Micro Electro Mechanical Systems, pp. 170-175 (2000).
4. Sandia National Laboratories, “Design Rules Design Rules”, Microelectronics
Development Laboratory, Version 0.8, (2000)
5. Krygowask, T. W., Sniegowask, J. J., Rodgers, M. S., Montague, S., and Allen, J. J., “Infrastructure, Technology and Applications of Micro-Electro-Mechanical Systems (MEMS)”, Sensor Expo 1999 (1999).
6. Sniegowski, J. J., Miller, S. L., LaVigne, G. F., Rodgers, M. S., and McWhorter, P. J., “Monolithic Geared-Mechanisms Driven by aPolysilicon Surface-Micromachined On-Chip Electrostatic Microengine”, Solid-State Sensor and Actuator Workshop, pp. 178-182, (1996).
7. Rogers, M. S., Sniegowski, S. S., Miller, S., and LaVigne, G. F., “Designing and Operating Electrostatically Driven Microengines”, Proceedings of the 44th International Instrumentation Symposium, Reno, NV, May 3-7, pp. 56-65 (1998).
Figure 3. The comparison of reduction ratios as a function of the number of units
中文翻譯
采用表面微加工技術制造微型行星齒輪減速器
摘要
這篇文章論述了一種結構緊湊、傳動比高的微型行星齒輪減速機構。這種機構的加工方法采用桑迪亞國家實驗室研發(fā)的過度平面的多極微機電系統(tǒng)技術去除整體結構的冗余部分，而且這種設計原理已經(jīng)得到承認。為了充分利用表面微加工技術，我們在設計加工這種行星減速齒輪時，需要使用安裝在芯片上的微電機。我們將計算這種齒輪預期的減速比，并把它與傳統(tǒng)的鏈傳動和齒輪傳動相比較。在這篇論文中演示的微行星輪占用較少的空間，消耗較少的材料，減速比卻有望達到162：1。這比以前的論文中設計的減速器的傳動比要高的多，簡直是一個神話。
關鍵字：微機電 行星齒輪 減速器 表面微加工 過度平面的多極微機電系統(tǒng)的加工（簡稱為SUMMiT V）
術語：
a.太陽輪
b.行星輪
c.內齒圈（固定）
d.內齒圈（旋轉）
n.齒輪系組成單元的數(shù)目
D.節(jié)圓的直徑
N.齒數(shù)
P.行星輪的數(shù)目
.角速度
介紹
在微機電系統(tǒng)中的齒輪結構通常希望用來在微小的體積內產(chǎn)生較大的扭矩。但是沒有較大重量的減速器，往往是很難達到這樣的目的。研究發(fā)現(xiàn)擁有微行星齒輪的減速機構能夠在狹小的空間內增加扭矩，這好像有點自相矛盾。這是因為微行星齒輪系統(tǒng)能在每單位體積內產(chǎn)生更大的傳動比。然而它的結構是如此的復雜，以至于我們很少嘗試將齒輪系統(tǒng)微型化。Suzumori以及他的小組成員曾經(jīng)用類似的行星齒輪結構來驅動一個機器人，并使它在
直徑為一寸的鋼管里前后移動。他們利用一個馬達來驅動高傳動比的齒輪機構，通過微電線的放電加工技術能夠實現(xiàn)這種齒輪機構的精確加工。但是這些部件應該在裝配驅動馬達之前安裝在齒輪箱上。Takeuchi 等人也用這種技術制造了微行星齒輪。他們建議用特殊的含陶合金和高碳鋼作為最佳選擇材料。當這種齒輪系統(tǒng)的傳動比達到200的時候，才可以安裝馬達并使之驅動。為了實現(xiàn)用芯片的方法來實現(xiàn)行星齒輪的驅動，在研究中我們采用SUMMiT V方法來加工微行星齒輪。SUMMiT V過程是唯一可以實現(xiàn)對于總數(shù)為五層(其中一層為地平面)的硅中釋放四層的鑄造過程由于這個原因，它經(jīng)常被用來通過安裝在芯片上的電子執(zhí)行器來驅動復雜的齒輪機構。然而, 在許多情形,微電機不可能提供充足的轉力矩來驅動機械負荷,因為它們的靜電梳的典型驅動只產(chǎn)生幾十微牛頓的力。幸運的是,這些引擎能容易地達到每分鐘幾萬轉的速度。這就使將轉矩轉化為速度變成是可行的。羅杰等人設計了二個傳動比為12：1的雙重的水平齒輪。如此六個這樣的模組的傳輸集合在以占據(jù)極大的空間為代價的前提下可以達到2,985,984:1的傳動比。為了達到結構緊湊，同時達到高傳動比的目的少比, 行星齒輪系統(tǒng)將被作為研究對象。根據(jù)作者的認識，它將會是第一個使用表面微加工原理設計的行星齒輪結構。我們還將闡述行星齒輪的操作規(guī)則，加工過程和希望達到的行星齒輪系統(tǒng)的性能。
操作原則
使用齒輪傳輸轉矩的其它可行的方法是將一個或者多個的齒輪,也就是, 行星齒輪,在另一個齒輪的外面旋轉,也就是太陽輪。按照傳統(tǒng)的尺寸設計的行星齒輪減速器是使整體結構緊湊的常用的傳輸系統(tǒng)。圖1是上述的行星齒輪的示意圖。自從用AutoCAD設計SUMMiT V以來,圖（1）可以通過軟件自動產(chǎn)生(附[1])。一個完整的行星齒輪系統(tǒng)是由六個齒輪組成的: 一個太陽齒輪 a，三個行星齒輪 b，一個固定的內齒圈 c,一個旋轉的內齒圈 d,和一個輸出齒輪 e。除了行星齒輪之外,每個齒輪的齒數(shù)都不相同。 太陽齒輪 a是輸入齒輪，由與微引擎連接的機械手驅動。內齒圈 d,被視為輸出齒輪。舉例來說,如果機械手驅動太陽輪按照順時針方向方向旋轉, 那么行星輪 b, 將繞著它們自己的軸按照逆時針方向宣戰(zhàn)，同時也將繞著太陽輪按照順時針方向的方向旋轉，這樣就形成了行星運動。 由于多個行星齒輪b和固定內齒圈c之間的運動相似，所以旋轉的內齒圈d將按照逆時針方向旋轉。這也被叫做3K行星齒輪。
加工過程和結構測試
SUMMiT V程序的特征體現(xiàn)了硅層結構、電解聚乙烯, 以及傳統(tǒng)的集成電路處理等技術水平的四個層次。SUMMiT V技術尤其適應于齒輪機構。行星齒輪機構由芯片上的微引擎驅動，而且這也是采用SUMMiT V技術的另一個理由。
因為桑迪亞程序是一款眾所周知的程序 ,所以我們只簡要的作些解釋。圖2是圖 1的截面視圖,也是由AutoCAD按照附錄[1]設計產(chǎn)生的，其中截面中的不連續(xù)的部分是為了鉆孔而設置的。聚乙烯1(灰色)用來制造輪轂以及固定的內齒圈c,太陽齒輪a,旋轉的內齒圈 c,而輸出齒輪是由聚乙烯2制造的。圖 1.是由SUMMiT V設計軟件產(chǎn)生的行星齒輪機構的視圖
附錄 [2]是描述測試結構的圖形。因為這篇文章的主旨是介紹一種齒輪減速機構,所以我們將整個行星齒輪系統(tǒng)分解成各個組成部分，以檢測它的性能。第一個測試結構是驅動太陽齒輪的機械手,如前述，這個機械手是由芯片上的引擎驅動的，所以機械手的角速度是由引擎的輸出速度決定的。 第二個測試結構描述的是太陽輪和行星輪與固定的內齒圈嚙合的點。因為事實上內齒圈是固定的, 所以行星輪將太陽輪輸入的轉矩傳到固定的內齒圈，因此這個過程并沒有經(jīng)過行星運動。也就是說，行星輪只繞它自己的軸轉動，而沒有繞太陽輪轉動。第三個測試結構是旋轉的內齒圈，它安裝在固定的內齒圈的頂端上，行星輪開始繞太陽輪旋轉，這樣就可以實現(xiàn)行星傳動。因此,一但輸出齒輪被安裝到旋轉的內齒圈，也就是最后一個測試結構，整個減速系統(tǒng)完成。將行星齒輪成拆解成三個測試結構的過程中允許齒輪系統(tǒng)存在極微小的誤差。
解決程序和預期的表現(xiàn)
傳動比被定義為驅動輪和被驅動輪之間的角速度之比。高傳動比意味著將速度轉化為轉矩。舉例來說, 一個傳動比為10:1的齒輪可以按照一定的數(shù)量級增加轉矩。因為行星輪系的齒輪要保證相互之間嚙合，除了行星齒輪，所以齒輪模數(shù)的設計應該遵從一定得限制。舉例來說，太陽輪的齒數(shù)加上固定的或者旋轉的內齒圈的齒數(shù)應該等于行星輪齒數(shù)的整數(shù)倍星， P(可以為1)。P代表著傳動比，如果P=2,應該首先觀察P=1的情況 。 N 是對應齒輪的齒數(shù)。
Ns + Nc (Nd ) = (1)
(2)
行星輪系的齒輪a、b、c、d的齒型模數(shù)為4 um, 這是可以與現(xiàn)在的齒輪減速器相比較的模數(shù)，而齒數(shù)分別是12,29,69,和72。因此根據(jù)等式（2）可知，輪系的傳動比為162:1。根據(jù)羅杰等人的報告，他們設計出傳動比為12:1的減速器，但是要比行星輪系減速器的傳動比小一個數(shù)量級。雖然羅杰等人設計的減速器尺寸大約達到 0.093 mm 到2 mm之間, 但是本文的行星齒輪減速器設計大約可以達到0.076mm到 2mm的范圍. 因此, 行星齒輪減速器設計的傳動比能夠達成更高的數(shù)量級，同時占用更少的空間。因為減速器是由數(shù)個部分組成，所以圖3充分顯示了使用行星齒輪系統(tǒng)的優(yōu)點。
圖3利用數(shù)字的功能來顯示本文提議的行星齒輪機制，也就是, 與桑迪亞齒輪系統(tǒng)，也就是,之間的比較?？v坐標以較大的比例單位作圖來顯示兩者之間的區(qū)別是很顯然的。 舉例來說, 在一個由5個部分構成的組件中，兩組之間的區(qū)別大約達到。此外,在這個由五個部分組成的減速器因為采用了行星輪系，面積減少了8500。
結論和討論
我們首先討論了利用表面微加工技術制造的行星齒輪減速系統(tǒng)，它是由芯片上的引擎驅動的。這種減速器系統(tǒng)在傳動比方面比早先設計減速器提高了一個數(shù)量級。然而,由于表面的摩擦和反作用力在齒輪制造加工過程中是不可避免的。所以在實際情形中，減速器的傳動比可能比 162:1 要小。即使在實際情形中一些可能的損失被考慮,減速器的傳動比還是應該比以前的設計提高一個數(shù)量級，而占據(jù)的空間會小很多。作者在設計過程中學習了許多關與微表面加工有關的知識，而且發(fā)現(xiàn)許多設計需要再研究和改正。當畫這些設計得截面視圖時，這些知識已經(jīng)變得很熟悉了。因為我們利用了基于SUMMiT V的先進的設計工具軟件包并確定了設計規(guī)則,行星齒輪的設計為制造加工做好了準備。我們希望這種行星齒輪減速器能夠被研究人員繼續(xù)更新、完善。
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