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齒輪和齒輪傳動(dòng)
在所有的機(jī)械傳動(dòng)形式中，齒輪傳動(dòng)是一種最結(jié)實(shí)耐用的傳動(dòng)方式。它們可以傳遞很大的功率，效率可以達(dá)到98%，并且服務(wù)年限長(zhǎng)。由于具有以上優(yōu)點(diǎn)，齒輪傳動(dòng)比皮帶裝置等其它傳動(dòng)方式更常見(jiàn)于自動(dòng)式傳動(dòng)機(jī)構(gòu)和重載機(jī)構(gòu)中。在另一方面，齒輪比其它傳動(dòng)方案貴得多，特別是精加工齒輪和合金鋼材料的。齒輪的制造成本會(huì)隨便著精度和公差的要求急劇增加。因此，在合適的范圍內(nèi)選一個(gè)合理的公差帶就顯得尤其重要。用于大功率傳遞和高速傳遞的齒輪傳動(dòng)系統(tǒng)不是特別的貴，但是用合金鋼材料和精加工的齒輪成本比較高。
低噪聲齒輪機(jī)構(gòu)也很昂貴。精密儀器和電腦里用的齒輪機(jī)構(gòu)住住是相當(dāng)昂貴的，因?yàn)樗鼈儗?duì)速度和傳動(dòng)比的要求很高。低速的開(kāi)式傳動(dòng)的被定義為非臨界狀態(tài)，并且以此作為齒輪的最小標(biāo)準(zhǔn)。齒輪的形狀、尺寸、性質(zhì)和工業(yè)用途都遵循美國(guó)齒輪制造協(xié)會(huì)所制定的標(biāo)準(zhǔn)。
美國(guó)齒輪制造協(xié)會(huì)發(fā)布的標(biāo)準(zhǔn)說(shuō)明齒輪系的傳動(dòng)比分配比例和齒的輪廓。齒的幾何形狀主要是由節(jié)距、齒高和壓力角來(lái)確定的。
節(jié)距：標(biāo)準(zhǔn)節(jié)距通常都是整數(shù)。大節(jié)距齒輪的節(jié)距直徑比它的節(jié)距的二十倍還大，一般在0.5～19.99之間。小節(jié)距齒輪的節(jié)距直徑一在20～200之間。
齒高：以節(jié)距為標(biāo)準(zhǔn)，齒輪的工作齒面高度是全齒高的一半。如果齒輪有相同的齒高那么齒高是節(jié)距的倒數(shù)。變位齒輪它的工作時(shí)的嚙合深度通常比它的全齒高少20%，以防止產(chǎn)生根切身。不變位齒輪比變位齒輪的傳動(dòng)比更大。齒數(shù)較少的齒輪可能會(huì)產(chǎn)生根切，所以大切削深度的齒輪比起它們來(lái)在嚙合時(shí)候齒輪互不影響。減少齒輪的有效齒廓會(huì)使齒輪的強(qiáng)度削弱。讓變位齒輪和不變位齒輪相嚙和能傳遞比標(biāo)準(zhǔn)齒輪更大的功率。兩個(gè)個(gè)嚙合的齒輪當(dāng)變位齒輪齒高減小時(shí)，不變位齒輪向變位后的齒輪深入一些，保證嚙合高度不變。這就是眾所周知的間歇性齒輪。
壓力角：壓力角通常取和。早期的壓力角還包括14-1/2，現(xiàn)在仍然在使用。壓力角的大小會(huì)影響相嚙合齒輪的強(qiáng)度。大的壓力角可以減少齒輪在嚙合時(shí)的齒數(shù)，而且利用不變位齒輪還能夠傳遞更大的功率。
齒側(cè)間隙：在兩個(gè)嚙合的齒之間非接觸最小的那個(gè)間隙。齒輪傳動(dòng)系統(tǒng)都嚴(yán)格按照美國(guó)齒輪制造協(xié)會(huì)所制定的等級(jí)制造，每個(gè)指標(biāo)都表示齒輪的一項(xiàng)重要性能。特性指數(shù)表示齒輪元素的公差，等級(jí)數(shù)目越高，它越接近于公差。等級(jí)3～5應(yīng)用于大節(jié)距齒輪，8～16應(yīng)用于小節(jié)距齒輪。
齒輪通過(guò)熱處理提高強(qiáng)度，比如表面硬化、淬火、氮化、回火。一般而言，硬齒面的齒輪系統(tǒng)比軟齒面的齒輪系統(tǒng)使用壽命更長(zhǎng)更堅(jiān)固。因而，淬火可以減小齒輪的尺寸和重量。有些處理方式，例如表面淬火可以提高齒輪的使用壽命但是沒(méi)有必要提高它的強(qiáng)度。
齒輪傳動(dòng)系統(tǒng)的校核項(xiàng)目：
在一對(duì)相嚙合的齒輪中，大的那個(gè)是從動(dòng)輪，小的是主動(dòng)輪。
齒數(shù)比：大齒輪的齒數(shù)除以小齒輪的齒數(shù)。同樣也是小齒輪的線(xiàn)速度除以大齒輪的線(xiàn)速度。在齒輪減速機(jī)構(gòu)中，是輸入速度與輸出速度的比值。
齒輪傳動(dòng)的效率：齒輪輸出功率與輸入功率的比值。（包括考慮傳動(dòng)時(shí)的功率損失，軸承、聯(lián)軸器、和潤(rùn)滑的功率損失）
在一些給定的齒輪中，節(jié)圓線(xiàn)速度是限定的。齒輪傳動(dòng)速率可以通過(guò)提高齒輪制造精度、增加回轉(zhuǎn)件的平衡性來(lái)提高。負(fù)荷速度和傳遞功率大小受齒輪尺寸和齒輪類(lèi)型的限制。斜齒輪和斜齒輪系所能傳遞的功率最大，可以近似達(dá)到30000馬力、弧齒錐齒輪一般限制在5000馬力、蝸輪蝸桿傳動(dòng)限制在大約750馬力。
工藝要求：
齒輪配合：在工藝上要求比較高精度的齒輪系統(tǒng)中，對(duì)于防止錯(cuò)齒、齒廓與齒廓接觸和從動(dòng)齒輪的嚙合，不會(huì)超過(guò)規(guī)定的范圍是很有必要的。
齒間隙：有些齒輪對(duì)齒廓的精度要求相當(dāng)高，因此，齒輪的規(guī)格等級(jí)必須符合所規(guī)定的精度等級(jí)。
無(wú)聲傳動(dòng)裝置：將齒輪傳動(dòng)系統(tǒng)制造得盡可能的靜音。為了達(dá)到此目的可以有以下多種方法供選擇，選擇小螺距齒輪來(lái)滿(mǎn)足負(fù)荷狀態(tài)的要求；在某些特定情況下，可以改變齒輪的嚙合次數(shù)來(lái)使傳動(dòng)聲音減小，或者使聲音更加低沉以達(dá)到靜音的目的；用壓力角較小和對(duì)齒輪根尖都進(jìn)行過(guò)修正的齒輪；允許足夠大的齒間隙；采用高的特性指數(shù)；保證表面粗糙度在20或者更小；合理分配齒輪系的傳動(dòng)比；采用一個(gè)非整數(shù)的傳動(dòng)比，那么一樣的齒輪就不會(huì)重復(fù)的嚙合如果它們都是硬化鋼材料。如果齒輪由軟鋼制成且傳動(dòng)比為整數(shù)，則齒輪必須冷作處理以滿(mǎn)足工作的要求，從而實(shí)現(xiàn)無(wú)聲傳動(dòng)。保證速度臨界點(diǎn)大于全速運(yùn)行的20%或者通過(guò)增加齒輪嚙合次數(shù)來(lái)成倍增加的轉(zhuǎn)速。
齒輪系傳動(dòng)裝置是指在一個(gè)傳動(dòng)裝置中有不只一對(duì)齒輪在嚙合工作?？梢允窍嗷テ叫谢虿黄叫械妮S，相交或不相交的軸。在實(shí)際應(yīng)用中，他們可以達(dá)到很高的速度比相對(duì)于只有一對(duì)齒輪嚙合的傳動(dòng)裝置。串聯(lián)齒輪系，所有嚙合齒輪的傳動(dòng)比都是將輸入軸的轉(zhuǎn)速降到輸出軸的轉(zhuǎn)速?？偟膫鲃?dòng)比是所有傳動(dòng)比的乘積，行星輪系不適用這種計(jì)算方法。這種傳動(dòng)裝置的傳動(dòng)比很好計(jì)算，就是將每一對(duì)嚙合齒輪的傳動(dòng)比相乘。增速器在設(shè)計(jì)和制造方面有特殊的工藝要求。他們通常包括很高的速度還可能有一些齒輪動(dòng)力學(xué)里一些很極端的問(wèn)題，同樣，摩擦力和拉力也包含在里面，在這種情況下還可能進(jìn)一步導(dǎo)致操作的問(wèn)題。
行星輪系傳動(dòng)：通常在一個(gè)傳動(dòng)裝置中，齒輪軸線(xiàn)是固定不變的的僅僅是軸上的齒輪在轉(zhuǎn)動(dòng)。但是在一個(gè)行星輪系中，不同的齒輪軸圍著太陽(yáng)輪地軸線(xiàn)轉(zhuǎn)動(dòng)給特定的輸出裝置提供動(dòng)力。行星輪傳動(dòng)再配合離合器和剎車(chē)裝置，就可以組成一個(gè)無(wú)級(jí)變速的自動(dòng)駕駛系統(tǒng)。行星輪傳動(dòng)可以用直齒或者斜齒，內(nèi)齒輪或者外齒輪，或者錐齒輪。在傳遞過(guò)程中，可以通過(guò)增加行星輪的個(gè)數(shù)來(lái)達(dá)到傳遞更大功率的要求。
在許多情況下, 提高齒輪系中相嚙合齒輪的運(yùn)動(dòng)精確度可以降低機(jī)構(gòu)運(yùn)行的噪音。修改齒輪漸開(kāi)線(xiàn)齒形可以提高齒輪的精確度，用高精度的制造公差來(lái)保證高質(zhì)量的齒輪嚙合質(zhì)量；提高齒面的粗糙度。但是，如果在一個(gè)傳動(dòng)系統(tǒng)的某個(gè)地方發(fā)生振動(dòng)那么一個(gè)“完美”的齒輪機(jī)構(gòu)將會(huì)減少振動(dòng)和噪聲。修正齒輪的齒廓可以避免在傳動(dòng)過(guò)程中由于偏差、軸的偏移、機(jī)殼的不標(biāo)準(zhǔn)而產(chǎn)生干涉。如果齒輪干涉不能通過(guò)修正齒廓來(lái)消除那么齒輪上的載荷應(yīng)該減少。當(dāng)齒輪載荷很大時(shí)，機(jī)構(gòu)噪聲會(huì)更大因?yàn)閮?nèi)部傳遞的齒輪發(fā)生了干涉。消除干涉可以通過(guò)改變齒高、齒側(cè)間隙或者兩者都做。齒輪變位對(duì)于重載機(jī)構(gòu)和高速傳動(dòng)機(jī)構(gòu)尤其重要。聲音壓力水平曲線(xiàn)圖可以很形象地說(shuō)明齒輪變位可以影響齒輪機(jī)構(gòu)的噪聲。如果減少的量比最適宜量小的話(huà)，那么機(jī)構(gòu)會(huì)產(chǎn)生更大的噪聲，因?yàn)辇X輪干涉。減少過(guò)多的齒高度噪聲也會(huì)增強(qiáng)因?yàn)榻佑|比例減小了。
高制造公差等級(jí)的齒輪也可以實(shí)現(xiàn)無(wú)聲傳動(dòng)，那樣的公差等級(jí)作為齒廓的形位誤差可以達(dá)到美國(guó)齒輪制造協(xié)會(huì)的質(zhì)量水平。這個(gè)圖表描述了速度和齒輪質(zhì)量對(duì)聲音壓力水平的影響，還有如何減小噪聲的方法。當(dāng)齒輪的精度等級(jí)由美國(guó)齒輪制造協(xié)會(huì)規(guī)定的11級(jí)增加到15級(jí)時(shí)，噪聲明顯的減小了。但是對(duì)于商業(yè)用的傳動(dòng)機(jī)構(gòu)來(lái)說(shuō)，花費(fèi)這么大的代價(jià)在降低噪聲上是不劃算的，因?yàn)檫€有別的更廉價(jià)的方式來(lái)降低噪聲。
以前有個(gè)說(shuō)法，為了防止齒輪干涉兩個(gè)相嚙合的齒輪必須經(jīng)過(guò)修正。齒頂高和齒側(cè)間隙都是很常用的齒廓修正以保證齒輪不發(fā)生干涉。齒輪傳動(dòng)系統(tǒng)也需要有適當(dāng)?shù)凝X側(cè)間隙和齒根修正。在設(shè)計(jì)齒輪機(jī)構(gòu)中，齒側(cè)間隙是評(píng)定噪聲的一個(gè)重要參數(shù)。必須有足夠的齒側(cè)間隙和合理的載荷、溫度狀況來(lái)防止齒輪的干涉，否則會(huì)產(chǎn)生很大的噪聲。干涉是由于齒側(cè)間隙不足造成，工作的齒面和不工作齒面同時(shí)接觸上了。另一方面，過(guò)大的齒側(cè)間隙也會(huì)產(chǎn)生噪聲，因?yàn)樵邶X輪無(wú)載荷嚙合周期內(nèi)或回動(dòng)載荷會(huì)對(duì)齒輪產(chǎn)生沖擊。要獲得合理的齒側(cè)間隙，減少齒的個(gè)數(shù)比增加軸的中心距效果更好。減少齒數(shù)不會(huì)減少齒輪接觸比例，反之增大中心距也不會(huì)。但是減少齒數(shù)會(huì)減小齒輪的撓曲疲勞，這個(gè)減小量對(duì)一個(gè)齒輪系統(tǒng)來(lái)說(shuō)是很小的。
Gears and gear drive
Gears are the most durable and rugged of all mechanical drives. They can transmit high power at efficiencies up to 98% and with long service lives. For this reason, gears rather than belts or chains are found in automotive transmissions and most heavy-duty machine drives. On the other hand, gears are more expensive than other drives, especially if they are machined and not made from power metal or plastic.
Gear cost increases sharply with demands for high precision and accuracy. So it is important to establish tolerance requirements appropriate for the application. Gears that transmit heavy loads or than operate at high speeds are not particularly expensive, but gears that must do both are costly.
Silent gears also are expensive. Instrument and computer gears tend to be costly because speed or displacement ratios must be exact. At the other extreme, gears operating at low speed in exposed locations are normally termed no critical and are made to minimum quality standards.
For tooth forms, size, and quality, industrial practice is to follow standards set up by the American Gear Manufactures Association (AGMA).
Tooth form
Standards published by AGMA establish gear proportions and tooth profiles. Tooth geometry is determined primarily by pitch, depth, and pressure angle.
Pitch：Standards pitches are usually whole numbers when measured as diametral pitch P. Coarse-pitch gearing has teeth larger than 20 diametral pitch –usually 0.5 to 19.99. Fine-pitch gearing usually has teeth of diametral pitch 20 to 200.
Depth: Standardized in terms of pitch. Standard full-depth have working depth of 2/p. If the teeth have equal addenda(as in standard interchangeable gears) the addendum is 1/p. Stub teeth have a working depth usually 20% less than full-depth teeth. Full-depth teeth have a larger contract ratio than stub teeth. Gears with small numbers of teeth may have undercut so than they do not interfere with one another during engagement. Undercutting reduce active profile and weakens the tooth.
Mating gears with long and short addendum have larger load-carrying capacity than standard gears. The addendum of the smaller gear (pinion) is increased while that of larger gear is decreased, leaving the whole depth the same. This form is know as recess-action gearing.
Pressure Angle: Standard angles are and . Earlier standards include a 14-pressure angle that is still used. Pressure angle affects the force that tends to separate mating gears. High pressure angle decreases the contact ratio (ratio of the number of teeth in contact) but provides a tooth of higher capacity and allows gears to have fewer teeth without undercutting.
Backlash: Shortest distances between the non-contacting surfaces of adjacent teeth .
Gears are commonly specified according to AGMA Class Number, which is a code denoting important quality characteristics. Quality number denote tooth-element tolerances. The higher the number, the closer the tolerance. Number 8 to 16 apply to fine-pitch gearing.
Gears are heat-treated by case-hardening, through-hardening, nitriding, or precipitation hardening. In general, harder gears are stronger and last longer than soft ones. Thus, hardening is a device that cuts the weight and size of gears. Some processes, such as flame-hardening, improve service life but do not necessarily improve strength.
Design checklist
The larger in a pair is called the gear, the smaller is called the pinion.
Gear Ratio: The number of teeth in the gear divide by the number of teeth in the pinion. Also, ratio of the speed of the pinion to the speed of the gear. In reduction gears, the ratio of input to output speeds.
Gear Efficiency: Ratio of output power to input power. (includes consideration of power losses in the gears, in bearings, and from windage and churning of lubricant.)
Speed: In a given gear normally limited to some specific pitchline velocity. Speed capabilities can be increased by improving accuracy of the gear teeth and by improving balance of the rotating parts.
Power: Load and speed capacity is determined by gear dimensions and by type of gear. Helical and helical-type gears have the greatest capacity (to approximately 30,000 hp). Spiral bevel gear are normally limited to 5,000 hp, and worm gears are usually limited to about 750 hp.
Special requirements
Matched-Set Gearing: In applications requiring extremely high accuracy, it may be necessary to match pinion and gear profiles and leads so that mismatch does not exceed the tolerance on profile or lead for the intended application.
Tooth Spacing: Some gears require high accuracy in the circular of teeth. Thus, specification of pitch may be required in addition to an accuracy class specification.
Backlash: The AMGA standards recommend backlash ranges to provide proper running clearances for mating gears. An overly tight mesh may produce overload. However, zero backlash is required in some applications.
Quiet Gears: To make gears as quit as possible, specify the finest pitch allowable for load conditions. (In some instances, however, pitch is coarsened to change mesh frequency to produce a more pleasant, lower-pitch sound.) Use a low pressure angle. Use a modified profile to include root and tip relief. Allow enough backlash. Use high quality numbers. Specify a surface finish of 20 in. or better. Balance the gear set. Use a nonintegral ratio so that the same teeth do not repeatedly engage if both gear and pinion are hardened steel. (If the gear is made of a soft material, an integral ratio allows the gear to cold-work and conform to the pinion, thereby promoting quiet operation.) Make sure critical are at least 20% apart from operating speeding or speed multiples and from frequency of tooth mesh.
Multiple mesh gear
Multiple mesh refers to move than one pair of gear operating in a train. Can be on parallel or nonparallel axes and on intersection or nonintersecting shafts. They permit higer speed ratios than are feasible with a single pair of gears .
Series trains:Overall ratio is input shaft speed divided by output speed ,also the product of individual ratios at each mesh ,except in planetary gears .Ratio is most easily found by dividing the product of numbers of teeth of driven gears by the product of numbers of teeth of driving gears.
Speed increasers (with step-up rather than step-down ratios) may require special care in manufacturing and design. They often involve high speeds and may creste problems in gear dynamics. Also, frictional and drag forces are magnified which, in extreme cases , may lead to operational problems.
Epicyclic Gearing:Normally, a gear axis remains fixed and only the gears rotates. But in an epicyclic gear train, various gears axes rotate about one anther to provide specialized output motions. With suitable clutchse and brakes, an epicyclic train serves as the planetary gear commonly found in automatic transmissions.
Epicyclic trains may use spur or helical gears, external or internal, or bevel gears. In transmissions, the epicyclic (or planetary) gears usually have multiple planets to increase load capacity.
In most cases, improved kinematic accuracy in a gearset decreases gear mesh excitation and results in lower drive noise. Gearset accuracy can be increased by modifying the tooth involute profile, by substituting higher quality gearing with tighter manufacturing tolerances, and by improving tooth surface finish. However, if gear mesh excitation generaters resonance somewhere in the drive system, nothing short of a “perfect” gearset will substantially reduce vibration and noise.
Tooth profiles are modified to avoid interferences which can result from deflections in the gears, shafts, and housing as teeth engage and disendgage. If these tooth interferences are not compensated for by profile modifications, gears load capacity can be seriously reduced. In addition, the drive will be noisier because tooth interferences generate high dynamic loads. Interferences typically are eliminated by reliving the tooth tip, the tooth flank, or both. Such profile modifications are especially important for high-load , high-speed drives. The graph of sound pressure levelvs tip relief illustrates how tooth profile modifications can affect overall drive noise. If the tip relief is less than this optimum value, drive noise increases because of greater tooth interference; a greater amount of tip relief also increase noise because the contact ratio is decreased.
Tighter manufacturing tolerances also produce quietier gears. Tolerances for such parameters as profile error, pitch AGMA quality level. For instance, the graph depicting SPL vs both speed and gear quality shows how noise decreases example, noise is reduced significantly by an increase in accuracy from an AGMA Qn 11 quality to an AGNA Qn 15 quality. However, for most commercial drive applications, it is doubtful that the resulting substantial cost increase for such an accuracy improvement can be justified simply on the basis of reduced drive noise.
Previously, it was mentioned that gears must have adequate clearance when loaded to prevent tooth interference during the course of meshing. Tip and flank relief are common profile modifications that control such interference. Gears also require adequate backlash and root clearance. Noise considerations make backlash an important parameter to evaluate during drive design. Sufficient backlash must be provided under all load and temperature conditions to avoid a tight mesh, which creates excessively high noise level. A tight mesh due to insufficient backlash occurs when the drive and coast side of a tooth are in contact simultaneously. On the other hand, gears with excessive backlash also are noisy because of impacting teeth during periods of no load or reversing load. Adequate backlash should be provided by tooth thinning rather than by increase in center distance. Tooth thinning dose not decrease the contact ratio, whereas an increase in center distance does. However, tooth thinning does reduce the bending fatigue, a reduction which is small for most gearing systems.
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