《立軸傳動(dòng)風(fēng)力發(fā)電機(jī)總體設(shè)計(jì)畢業(yè)設(shè)計(jì)說(shuō)明書》由會(huì)員分享，可在線閱讀，更多相關(guān)《立軸傳動(dòng)風(fēng)力發(fā)電機(jī)總體設(shè)計(jì)畢業(yè)設(shè)計(jì)說(shuō)明書（54頁(yè)珍藏版）》請(qǐng)?jiān)谘b配圖網(wǎng)上搜索。

1、 畢業(yè)設(shè)計(jì)（論文）說(shuō)明書 題目：立軸傳動(dòng)風(fēng)力發(fā)電機(jī)總體設(shè)計(jì) 系 名 機(jī)械工程系 專 業(yè) 機(jī)械設(shè)計(jì)制造及其自動(dòng)化 學(xué) 號(hào) 姓 名 指導(dǎo)教師 2013年 6月 9 日 摘 要 風(fēng)力發(fā)電是應(yīng)用前景十分廣闊的一種潔凈可再生能源，而目前大型風(fēng)力發(fā)電機(jī)的關(guān)鍵部件都放置于

2、機(jī)艙內(nèi)。目前風(fēng)力發(fā)電機(jī)都需要定期進(jìn)行維護(hù)，而大型風(fēng)力發(fā)電機(jī)高度都達(dá)到30米以上，所以在定期維護(hù)是就需要耗費(fèi)大量的人力和財(cái)力。本人運(yùn)用所學(xué)的基礎(chǔ)知識(shí)和專業(yè)知識(shí)，從設(shè)備可靠性、強(qiáng)度出發(fā)進(jìn)行了設(shè)備的機(jī)構(gòu)和結(jié)構(gòu)的全新設(shè)計(jì)，為了提高風(fēng)力發(fā)電機(jī)的經(jīng)濟(jì)性，根據(jù)課題組提供的參數(shù)，采用CAD優(yōu)化設(shè)計(jì)，排定最佳傳動(dòng)方案，選擇穩(wěn)定可靠的構(gòu)件和具有良好力學(xué)特性以及在環(huán)境極端溫差下仍然保持穩(wěn)定的結(jié)構(gòu)。 根據(jù)原始數(shù)據(jù)：傳動(dòng)軸輸出端的額定轉(zhuǎn)速為100r/min左右，額定承載功率為600kW，切入風(fēng)速為5級(jí)清風(fēng)，風(fēng)速為10m/s，原始輸入端轉(zhuǎn)速為50r/min，風(fēng)輪葉片數(shù)為3，葉片直徑為50m，輪轂高度為30m。為了使維護(hù)

3、成本降低將主要傳動(dòng)設(shè)備轉(zhuǎn)移至地面，通過(guò)立軸傳動(dòng)將動(dòng)能從風(fēng)機(jī)輸入轉(zhuǎn)移至地面設(shè)備輸入端，從而完成設(shè)計(jì)目的，并完成相關(guān)動(dòng)力學(xué)和運(yùn)動(dòng)學(xué)計(jì)算。 關(guān)鍵字：風(fēng)力發(fā)電機(jī)；齒輪傳動(dòng)；立軸傳動(dòng) ABSTRACT Wind power is a very broad application prospects of a clean renewable energy, and the key components of large wind turbines are placed in the cabin. Wind turbine require regular

4、 maintenance, large wind turbines have reached more than 30 meters height, so regular maintenance requires a lot of human and financial resources. I apply the basic knowledge and expertise, starting from equipment reliability, strength of the institutions and structures of the new design, in order t

5、o improve the economics of wind turbines, based on the parameters provided by the Task Force, the optimal design using CAD, scheduled the optimum transmission program, choose a stable and reliable components and has good mechanical properties and ambient extreme temperature remains stable structure.

6、 Based on the original data: the rated speed of the drive shaft output of about 100r/min rated load power of 600kW,Cut-in speed of 5 breeze, wind speed of 10m / s, speed 50r/min primary inputs，Wind turbine blades is 3, a rotor diameter of 50m, 30m hub height. The main transmission equipment to the

7、ground, through the vertical shaft drive fan input kinetic energy transferred to ground equipment input terminal so as to complete the design purposes and to complete the relevant dynamics and kinematics calculation in order to reduce maintenance costs. Keywords Wind turbines ;Vertical shaft drive

8、 目 錄 第一章 軸（一）的強(qiáng)度校核1 1.1 初步估算軸徑1 1.2 軸上受力分析1 1.3 求支反力1 1.4 作彎矩和轉(zhuǎn)矩圖2 1.5 軸的強(qiáng)度校核3 第二章 花鍵的校核4 2.1 初始數(shù)據(jù)4 2.2 接觸應(yīng)力計(jì)算4 2.3 齒根抗彎強(qiáng)度計(jì)算4 2.4 齒根抗剪強(qiáng)度計(jì)算4 2.5 齒面耐磨損能力計(jì)算5 第三章 斜齒圓柱齒輪設(shè)計(jì)計(jì)算6 3.1 選材料確定試驗(yàn)齒輪的疲勞極限應(yīng)力6 3.2 按接觸強(qiáng)度初步確定中心距并初選主要參數(shù)6 3.3

9、校核齒面接觸疲勞強(qiáng)度6 3.4 校核齒根彎曲疲勞強(qiáng)度8 3.5 主要幾何參數(shù)9 第四章 直齒錐齒輪設(shè)計(jì)計(jì)算10 4.1 初步設(shè)計(jì)10 4.2 幾何計(jì)算10 4.3 齒面接觸疲勞強(qiáng)度校核11 4.4 齒根抗彎疲勞強(qiáng)度校核12 第五章 軸（二）的強(qiáng)度校核14 5.1 初步估算軸徑14 5.2 軸上受力分析14 5.3 求支反力14 5.4 作彎矩和轉(zhuǎn)矩圖15 5.5 最大合成彎矩15 5.6 作轉(zhuǎn)矩圖15 5.7 軸的強(qiáng)度校核16 第六章 軸（三）的強(qiáng)度校核18

10、6.1 初步估算軸徑18 6.2 軸上受力分析18 6.3 求支反力18 6.4 作彎矩和轉(zhuǎn)矩圖19 6.5 最大合成彎矩19 6.6 作轉(zhuǎn)矩圖19 6.7 軸的強(qiáng)度校核19 參考文獻(xiàn)21 外文翻譯22 中文譯文34 致謝43 6 第一章 軸（一）的強(qiáng)度校核 1.1 初步估算軸徑 選擇軸的材料為40Cr。 調(diào)質(zhì)處理，由表19.1.1查得材料力學(xué)性能數(shù)據(jù)位： 根據(jù)表19.3-1公式初步計(jì)算軸徑，由于材料為40Cr 1.2 軸上受力分析 1.

11、2.1 齒輪的圓周力 1.3 求支反力 1.3.1 在水平面內(nèi)的支反力 1.3.2 在垂直面內(nèi)的支反力 1.4 作彎矩和轉(zhuǎn)矩圖 1.4.1 齒輪作用在水平平面的彎矩圖 1.4.2 齒輪作用在垂直平面的彎矩圖 1.4.3 作轉(zhuǎn)矩圖 T=57294N.m 圖1-1 1.5 軸的強(qiáng)度校核 1.5.1 確定危險(xiǎn)截面 根據(jù)圖1.1由于C處合成彎矩最大 所以選擇C面為危險(xiǎn)截面。 1.5.2 安全系數(shù)校核計(jì)算

12、 式中W為抗彎斷面系數(shù)，由表19.3-1查得 根據(jù)式（19.3-2） 切應(yīng)力幅為 根據(jù)式（19.3-3） 第2章 花鍵的校核 2.1 初始數(shù)據(jù) 花鍵規(guī)格14x176f7x200a11x25d10 P=600KW n=100r/min 表面硬度58~64HRC 2.2 接觸應(yīng)力計(jì)算 2.3 齒根抗彎強(qiáng)度計(jì)算 2.3.1 齒根彎曲應(yīng)力 2.3.2 齒根許用彎曲應(yīng)力 2.4 齒根抗剪強(qiáng)度計(jì)算 2.4.1 齒根最大剪切應(yīng)力

13、 2.4.2 許用切應(yīng)力 2.5 齒面耐磨損能力計(jì)算 2.5.1 花鍵副在循環(huán)數(shù)下工作時(shí)耐磨損能力計(jì)算 2.5.2 花鍵副在長(zhǎng)期工作無(wú)磨損是耐磨損能力計(jì)算 2.5.3 外花鍵的抗扭與抗彎強(qiáng)度計(jì)算 第3章 斜齒圓柱齒輪設(shè)計(jì)計(jì)算 3.1 選材料 確定試驗(yàn)齒輪的疲勞極限應(yīng)力 40Cr 調(diào)質(zhì)處理 硬度217~255HBS 由表16.2-59,60,65查得 3.2 按接觸強(qiáng)度初步確定中心距并初選主要參數(shù) 3.3 校核齒面接

14、觸疲勞強(qiáng)度 根據(jù)齒輪的圓周速度參考表16.2-73選擇齒輪的精度等級(jí)為8級(jí)精度 首先計(jì)算當(dāng)量齒數(shù) 3.4 校核齒根彎曲疲勞強(qiáng)度 3.5 主要幾何參數(shù) 第4章 直齒錐齒輪設(shè)計(jì)計(jì)算

15、4.1 初步設(shè)計(jì) 4.2 幾何計(jì)算 4.3 齒面接觸疲勞強(qiáng)度校核 4.4 齒根抗彎疲勞強(qiáng)度校核 第5章 軸（二）的強(qiáng)度校核 5.1 初步估算軸徑 選擇軸的材料為45號(hào)鋼 調(diào)制處理，由表19.1.1查得材料力學(xué)性能數(shù)據(jù)為 根據(jù)表19.3-1公式初步估算軸徑，由于材料為45號(hào)鋼由表19.3-2選取[]=40

16、 5.2 軸上受力分析（如圖5-1） 5.3 求支反力 5.3.1 在水平面內(nèi)的支反力 5.3.2 在垂直平面內(nèi)的支反力 5.4 作彎矩圖和轉(zhuǎn)矩圖 5.4.1 水平面彎矩 5.4.2 垂直平面彎矩 5. 5 最大合成彎矩 5.5.1 A處最大合成彎矩 5.5.2 B處最大合成彎矩 5.6 作扭矩圖 T=57294N/m 圖5-1 5.7 軸的強(qiáng)度校核 5.7.1 確定危險(xiǎn)

17、截面 根據(jù)圖5-1得A處受彎矩最大，并且軸徑最小，所以選擇截面A處為危險(xiǎn)截面。 5.7.2 安全系數(shù)校核計(jì)算 式中W為抗彎斷面系數(shù)，由表19.3-15查得 由于是對(duì)稱循環(huán)應(yīng)力，故平均應(yīng)力=0 根據(jù)式（19.3-2） 根據(jù)式（19.3-3）得 第6章 軸(三)的強(qiáng)度校核 6.

18、1 初步估算軸徑 選擇軸的材料為40Cr。 調(diào)質(zhì)處理，由表19.1.1查得材料力學(xué)性能數(shù)據(jù)位： 根據(jù)表19.3-1公式初步計(jì)算軸徑，由于材料為40Cr 6.2 軸上受力分析（如圖6-1） 6.2.1 齒輪的圓周力 6.3 求支反力 6.3.1 在水平面內(nèi)的支反力 6.3.2 在垂直面內(nèi)的支反力 6.4 作彎矩和轉(zhuǎn)矩圖 6.4.1 齒輪作用在水平面的彎矩圖 6.4.2 齒輪作用在垂直平面的彎矩圖 6.5

19、作最大合成彎矩圖 6.6 作轉(zhuǎn)矩圖 T=57294N/m 圖6-1 6.7 軸的強(qiáng)度校核 6.7.1 確定危險(xiǎn)截面 由于C截面處合成彎矩最大，所以選擇截面C處為危險(xiǎn)截面。 6.7.2 安全系數(shù)校核計(jì)算 由于是對(duì)稱循環(huán)彎曲應(yīng)力，故平均應(yīng)力 根據(jù)式（19.3-2） 根據(jù)式（19.3-3） 參考文獻(xiàn) [1] 包耳.風(fēng)力發(fā)電技術(shù)發(fā)展現(xiàn)狀[J].可再生能源雜志，2004，(2):12～15. [2] GWE

20、C.Global wind 2005 report，2006. [3] Sawin,Janet,Langhlin.Wind power in the United States[D]. Doctors thesis, The Fletcher School of Law and Diplomacy.2001:500～513. [4] Kramer,Marcel.Long-term costs of electricity generation in Germany[M].Wind Engineering, Multi-Science Publishing Co.

21、 Ltd, 2004, 4(28): 465～478. [5] 劉忠明，王長(zhǎng)路，段守敏.風(fēng)力發(fā)電齒輪箱設(shè)計(jì)制造技術(shù)的發(fā)展和展望[J]. 機(jī)械傳動(dòng).2006,6(30): 1～6. [6] 濮良貴，紀(jì)名剛．機(jī)械設(shè)計(jì)．第８版．北京：高等教育出版社，2005 [7] ANSI/AGMA 6006-A03. AGMA. 2003. [8] ISO 81400-4:2005. Wind Turbines - Part 4:Design and Specification of Gearbox. 2004. [9] 龔淮義，羅圣國(guó)，李平林，張立乃，黃少顏.機(jī)械設(shè)計(jì)

22、課程設(shè)計(jì)指導(dǎo)書（第二 版）.北京：高等教育出版社，1990.4（2006重印） [10] 湯克平.風(fēng)電增速箱結(jié)構(gòu)設(shè)計(jì)敘談[J].機(jī)械傳動(dòng)，2004, 28(5):1-3. [11] 機(jī)械設(shè)計(jì)手冊(cè)（新編軟件版）2008.化學(xué)工業(yè)出版社 [12] 劉鴻文主編.材料力學(xué)（I、II）.北京：高等教育出版社，2004.1 [13] 何貢．互換性與測(cè)量技術(shù)．中國(guó)計(jì)量出版社，2000 [14] 高金蓮．工程圖學(xué)．第２版．北京：機(jī)械工業(yè)出版社，2005 [15] 王先逵．機(jī)械加工工藝手冊(cè)．第２版．北京：機(jī)械工業(yè)出版社，2007 [16] 湯克平.風(fēng)電增速箱結(jié)構(gòu)設(shè)計(jì)敘談. 機(jī)械傳動(dòng)，20

23、04，28（5）：33～34 [17] 武楊名.風(fēng)力發(fā)電齒輪箱國(guó)產(chǎn)化的材料、工藝和結(jié)構(gòu)研究：[學(xué)位論文]，杭 州：浙江大學(xué)，2001 [18] 朱才朝，黃琪，唐倩.風(fēng)力發(fā)電升速齒輪箱傳動(dòng)系統(tǒng)接觸齒數(shù)及載荷分配. 農(nóng)業(yè)機(jī)械學(xué)報(bào)，2006(7)：87～89 [19] 佘勃強(qiáng).風(fēng)力發(fā)電增速裝置的研究：[學(xué)位論文]，西安：西安理工大學(xué)，2008 [20] 張展.風(fēng)力發(fā)電傳動(dòng)裝置的設(shè)計(jì)與制造.通用機(jī)械，2007（4）：31～34 [21] 饒振剛.行星齒輪傳動(dòng)設(shè)計(jì)[M].北京:化學(xué)工業(yè)出版社，2003. [22] 張展.風(fēng)力發(fā)電機(jī)組的傳動(dòng)裝置[J].傳動(dòng)技術(shù).2003

24、, 6: 35-36. [23] 會(huì)田俊夫主編，張展譯.齒輪的精度與性能[M].北京:中國(guó)農(nóng)業(yè)機(jī)械出版社， 1985. 外文資料 DESIGN AND DEVELOPMENT OF A 1/3 SCALE VERTICAL AXIS WIND TURBINE FOR ELECTRICAL POWERG Abstract: This research describes the electrical power generation in Malaysia by the measurement of wind velocity acting on the wi

25、nd turbine technology. The primary purpose of the measurement over the 1/3 scaled prototype vertical axis wind turbine for the wind velocity is to predict the performance of full scaled H-type vertical axis wind turbine. The electrical power produced by the wind turbine is influenced by its two majo

26、r part, wind power and belt power transmission system. The blade and the drag area system are used to determine the powers of the wind that can be converted into electric power as well as the belt power transmission system. In this study both wind power and belt power transmission system has been co

27、nsidered. A set of blade and drag devices have been designed for the 1/3 scaled wind turbine at the Thermal Laboratory of Faculty of Engineering, Universiti Industri Selangor (UNISEL). Test has been carried out on the wind turbine with the different wind velocities of 5.89 m/s, 6.08 m/s and 7.02 m/s

28、. From the experiment, the wind power has been calculated as 132.19 W, 145.40 W and 223.80W.The maximum wind power is considered in the present study. Keywords: Belt power transmission system; Reynolds number; wind power; wind turbine INTRODUCTION Wind energy is the kinetic energy associated w

29、ith the movement of atmospheric air. It has been used for hundreds of years for sailing, grinding grain, and for irrigation. Wind energy systems convert this kinetic energy to more useful forms of power. Wind energy systems for irrigation and milling have been in use since ancient times and si

30、nce the beginning of the 20th century, it is being used to generate electric power. Windmills for water pumping have been installed in many countries particularly in the rural areas. Wind turbine is a machine that converts the winds kinetic energy into rotary mechanical energy, which is then used

31、to do work. In more advanced models, the rotational energy is converted into electricity, the most versatile form of energy, by using a generator (Fitzwater et al., 1996). For thousands of years people have used windmills to pump water or grind grain. Even into the twentieth century tall, slende

32、r, multi-vaned wind turbines made entirely of metal were used in American homes and ranches to pump water into the houses plumbing system or into the cattles watering trough. After World War I, work was begun to develop wind turbines that could produce electricity. Marcellus Jacobs invented a

33、prototype in 1927 that could provide power for a radio and a few lamps but little else. When demand for electricity increased later, Jacobss small inadequate wind turbines fell out of use. The first large-scale wind turbine built in the United States was conceived by Palmer Cosslett Putnam in 19

34、34; he completed it in 1941. The machine was huge. The tower was 36.6 yards (33.5 meters) high, and its two stainless steel blades had diameters of 58 yards (53 meters). Putnams wind turbine could produce 1,250 kilowatts of electricity, or enough to meet the needs of a small town (Monett et al.

35、, 1994). It was, however, abandoned in 1945 because of mechanical failure. With the 1970s oil embargo, the United States began once more to consider the feasibility of producing cheap electricity from wind turbines. In 1975 the prototype Mod-O was in operation. This was a 100 kilowatt turbine

36、with two 21-yard (19-meter) blades. More prototypes followed (Mod-OA, Mod-1, Mod-2, etc.), each larger and more powerful than the one before. Currently, the United States Department of Energy is aiming to go beyond 3,200 kilowatts per machine. Many different models of wind turbines exist, the mos

37、t striking being the vertical-axis Darrieus, which is shaped like an egg beater (Fitzwater et al., 1996). The model most supported by commercial manufacturers, however, is a horizontal-axis turbine, with a capacity of around 100 kilowatts and three blades not more than 33 yards (30 meters) in len

38、gth. Wind turbines with three blades spin more smoothly and are easier to balance than those with two blades. Also,while larger wind turbines produce more energy, the smaller models are less likely to undergo major mechanical failure, and thus are more economical to maintain. Wind farms have spru

39、ng up all over the United States, most notably in California. Wind farms are huge arrays of wind turbines set in areas of favorable wind production. A great number of interconnected wind turbines are necessary in order to produce enough electricity to meet the needs of a sizable population. Curren

40、tly, 17,000 wind turbines on wind farms owned by several wind energy companies produce 3.7 billion kilowatt-hours of electricity annually, enough to meet the energy needs of 500,000 homes. A wind turbine consists of three basic parts: the tower, the nacelle, and the rotor blades. The tower is eith

41、er a steel lattice tower similar to electrical towers or a steel tubular tower with an inside ladder to the nacelle. The first step in constructing a wind turbine is erecting the tower. Although the towers steel parts are manufactured off site in a factory, they are usually assembled on site. The

42、 parts are bolted together before erection, and the tower is kept horizontal until placement. A crane lifts the tower into position, all bolts are tightened, and stability is tested upon completion. Next, the fiberglass nacelle is installed. Its inner workings main drive shaft, gearbox, and blad

43、e pitch and yaw controls are assembled mounted onto a base frame at a factory (Hammons, 2004). The nacelle is then bolted around the equipment. At the site, the nacelle is lifted onto the completed tower and bolted into place. In addition, the aerodynamics of a wind turbine at the rotor surface i

44、s very much important in aerodynamic fields. The rotor axis is brought to a vertical orientation with a wind vane mounted on a control shaft to orientate the blades with changing wind direction. Using pitch regulation the rotor blades turn around their axis so that the aerodynamic characteristics

45、 of the blade and rotor are controlled. The rotor is yaw out of the wind which turns the rotor plane to follow the changing wind direction. The hub is connected to the rotor with rigid bolt connection and the rotational speed of the rotor is fixed relative to the frequency of the grid. The futur

46、e can only get better for wind turbines. The potential for wind energy is largely untapped. The total amount of electricity that could potentially be generated from wind in the United States has been estimated at 10,777 billion kWh annually (Keith, 2005). These new wind farms demonstrate how wind

47、energy can help to meet the nation’s growing need for affordable, reliable power. With continued government encouragement to accelerate its development, this increasingly competitive source of renewable energy will provide at least six percent of the nation’s electricity by 2020. Research is now b

48、eing done to increase the knowledge of wind resources. This involves the testing of more and more areas for the possibility of placing wind farms where the wind is available and strong. Plans are in effect to increase the life span of the machine from five years to 20 to 30 years, improve the effi

49、ciency of the blades, provide better controls, develop drive trains that last longer, and allow for better surge protection and grounding. The United States Department of Energy has recently set up a schedule to implement the latest research in order to build wind turbines with a higher efficie

50、ncy rating than is now possible (the efficiency of an ideal wind turbine is 59.3 percent (Milligan & Artig, 1999). That is, 59.3 percent of the wind’s energy can be captured. Turbines in actual use are about 30 percent efficient). The United States Department of Energy has also contracted three

51、 corporations to investigate ways to reduce mechanical failure. This project began in the spring of 1992 and will extend to the end of the century. Wind turbines will become more prevalent in upcoming years. The turn of the century should see wind turbines that are properly placed, efficient, d

52、urable, and numerous. From the investigation of this wind turbine background, an H-type, vertical axis wind turbine has been designed and built in thermal Laboratory Universiti Industri Selangor that has the capability to self-start. In addition, this turbine has been designed to allow a varie

53、ty of modifications such as blade profile and pitching to be tested. The first part of the design process, which included research, brainstorming, engineering analysis, turbine design selection, and prototype testing have been incorporated. Using data obtained through proper investigation resul

54、ts, the final full-scale turbine has been designed and built. Wind turbines can be separated into two types based by the axis in which the turbine rotates namely horizontal axis wind turbine (HAWT) and the vertical axis wind turbine (VAWT). HAWT has difficulty operating in near ground, turbule

55、nt winds because their yaw and blade bearing need smoother, more laminar wind flows, difficult to install needing very tall and expensive cranes and skilled operators, downwind variants suffer from fatigue and structural failure caused by the turbulence and height can be a safety hazard for lo

56、w-altitude aircraft. Other than that, the aerodynamics of a horizontal-axis wind turbine is complex. The air flow at the blades is not the same as the airflow far away from the turbine. The very nature of the way in which energy is extracted from the air also causes air to be deflected by the t

57、urbine. In addition, the aerodynamics of a wind turbine at the rotor surface includes effects that are rarely seen in other aerodynamic fields. A wide variety of VAWT configurations have been proposed. The Darrieus vertical type wind turbine is the most common and us used extensively for power

58、 generation. However, the Darrieus turbine suffered from structural problems as well as a poor energy market. To improve the performance of a wind turbine, this study has been concentrated on design and built an 1/3 scale H-type, vertical axis wind turbine that has the capability to self-star

59、t due to the wind flow and efficient performance of the VAWT that could lead to a change in the standard thinking of how wind energy is harnessed, and may spur future VAWT design and research. The study on the enhanced performance of the wind turbine is also given by incorporating drag devices

60、. WIND TURBINE DESIGN Theoretical analysis The belt drive system consists of several parts of the belt drive calculation and the V–Type belt is considered in this study. Thus the main calculation that has been done at this system are angle of wrap for small and large pulley, belt length, p

61、ulley speed, the tension ratio and the power transmitted by the belt. The structure of the V-belt is shown in Fig. 1, which illustrates the main parts in V-belt such as the large pulley diameter indicated by the number 3 and the small pulley by the number 2 and the angle of wrap of large pulley indicated by θ3 and small pulley by θ2. C indicates the centered radius between large and small pulleys. Angle of wrap for