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邵陽(yáng)學(xué)院機(jī)械工程專業(yè)英語(yǔ)論文 Gearbox Noise —— Correlation with Transmission Error and Influence of Bearing Preload 變速箱噪聲——相關(guān)的傳輸錯(cuò)誤和軸承預(yù)壓的影響 摘要 ABSTRACT The five appended papers all deal with gearbox noise and vibration. The first paper presents a review of previously published literature on gearbox noise and vibration. The second paper describes a test rig that was specially designed and built for noise testing of gears. Finite element analysis was used to predict the dynamic properties of the test rig, and experimental modal analysis of the gearbox housing was used to verify the theoretical predictions of natural frequencies.In the third paper, the influence of gear finishing method and gear deviations on gearbox noise is investigated in what is primarily an experimental study. Eleven test gear pairs were manufactured using three different finishing methods. Transmission error, which is considered to be an important excitation mechanism for gear noise, was measured as well as predicted. The test rig was used to measure gearbox noise and vibration for the different test gear pairs. The measured noise and vibration levels were compared with the predicted and measured transmission error. Most of the experimental results can be interpreted in terms of measured and predicted transmission error. However, it does not seem possible to identify one single parameter,such as measured peak-to-peak transmission error, that can be directly related to measured noise and vibration. The measurements also show that disassembly and reassembly of the gearbox with the same gear pair can change the levels of measured noise and vibration considerably.This finding indicates that other factors besides the gears affect gear noise.In the fourth paper, the influence of bearing endplay or preload on gearbox noise and vibration is investigated. Vibration measurements were carried out at torque levels of 140 Nm and 400Nm, with 0.15 mm and 0 mm bearing endplay, and with 0.15 mm bearing preload. The results show that the bearing endplay and preload influence the gearbox vibrations. With preloaded bearings, the vibrations increase at speeds over 2000 rpm and decrease at speeds below 2000 rpm, compared with bearings with endplay. Finite element simulations show the same tendencies as the measurements.The fifth paper describes how gearbox noise is reduced by optimizing the gear geometry for decreased transmission error. Robustness with respect to gear deviations and varying torque is considered in order to find a gear geometry giving low noise in an appropriate torque range despite deviations from the nominal geometry due to manufacturing tolerances. Static and dynamic transmission error, noise, and housing vibrations were measured. The correlation between dynamic transmission error, housing vibrations and noise was investigated in speed sweeps from 500 to 2500 rpm at constant torque. No correlation was found between dynamic transmission error and noise. Static loaded transmission error seems to be correlated with the ability of the gear pair to excite vibration in the gearbox dynamic system. 論文描述了該試驗(yàn)臺(tái)是專門設(shè)計(jì)和建造噪音齒輪測(cè)試。有限元分析，用于預(yù)測(cè)試驗(yàn)臺(tái)的動(dòng)態(tài)特性和實(shí)驗(yàn)的變速箱殼體模態(tài)分析用于驗(yàn)證自然試驗(yàn)臺(tái)。這第三個(gè)文件，齒輪精加工方法和變速箱齒輪的偏差影響的理論預(yù)測(cè)噪聲主要是研究在什么的實(shí)驗(yàn)研究。十對(duì)被測(cè)試設(shè)備制造使用三種不同的整理方法。傳輸錯(cuò)誤，這被認(rèn)為是一個(gè)重要的激勵(lì)機(jī)制齒輪噪音，測(cè)量以及預(yù)測(cè)。該試驗(yàn)臺(tái)是用于測(cè)量變速箱噪音及不同的測(cè)試裝置對(duì)振動(dòng)。測(cè)得的噪音和振動(dòng)水平進(jìn)行比較，預(yù)測(cè)和實(shí)測(cè)的傳輸錯(cuò)誤。實(shí)驗(yàn)結(jié)果大多可以解釋和預(yù)測(cè)傳輸測(cè)量誤差項(xiàng)。但是，它似乎并不能夠確定一個(gè)單一的參數(shù)，如測(cè)得的峰 - 峰值傳輸錯(cuò)誤，可直接與測(cè)得的噪聲和振動(dòng)。測(cè)量結(jié)果還顯示，拆卸和使用相同的變速箱齒輪副重組可以改變測(cè)得噪聲和振動(dòng).這個(gè)水平發(fā)現(xiàn)表明，除了其他因素的影響齒輪齒輪噪音。第四，軸承影響或變速箱噪音和振動(dòng)預(yù)緊力進(jìn)行了調(diào)查。振動(dòng)測(cè)量均在140牛米和400nm的扭矩水平，用0.15毫米和0毫米軸承間隙，并用0.15 mm軸承預(yù)緊力。結(jié)果表明，軸承間隙和預(yù)緊力影響變速箱的振動(dòng)。預(yù)裝軸承，振動(dòng)增加超過(guò)2000轉(zhuǎn)和2000轉(zhuǎn)的速度低于下降速度，相比與軸端間隙軸承。有限元模擬表現(xiàn)出同樣的傾向作為測(cè)量值。第五本文介紹如何通過(guò)優(yōu)化變速箱噪聲為減少傳輸錯(cuò)誤齒輪幾何減少。關(guān)于齒輪偏差和不同扭矩的魯棒性考慮，以便找到一個(gè)齒輪幾何給予盡管從名義幾何由于制造公差偏差范圍內(nèi)以適當(dāng)?shù)呐ぞ?，噪音低。靜態(tài)和動(dòng)態(tài)的傳輸錯(cuò)誤，噪聲，振動(dòng)測(cè)量和該。之間的動(dòng)態(tài)傳輸錯(cuò)誤，房屋振動(dòng)和噪聲的相關(guān)性研究了掃描速度從500到2500在恒轉(zhuǎn)矩轉(zhuǎn)速。沒(méi)有相關(guān)關(guān)系的動(dòng)態(tài)傳遞誤差和噪聲。靜態(tài)加載的傳輸錯(cuò)誤似乎與齒輪副的能力，激發(fā)動(dòng)力系統(tǒng)中的齒輪箱振動(dòng)相關(guān)。 Keywords: gear, gearbox, noise, vibration, transmission error, bearing preload. 關(guān)鍵詞：齒輪，變速箱，噪聲，振動(dòng)，傳輸錯(cuò)誤，軸承預(yù)緊力。 1 INTRODUCTION 1 引言 1.1 Background Noise is increasingly considered an environmental issue. This belief is reflected in demands for lower noise levels in many areas of society, including the working environment. Employees spend a lot of time in this environment and noise can lead not only to hearing impairment but also to decreased ability to concentrate, resulting in decreased productivity and an increased risk of accidents. Quality, too, has become increasingly important. The quality of a product can be defined as its ability to fulfill customers’ demands. These demands often change over time, and the best competitors in the market will set the standard.Noise concerns are also expressed in relation to construction machinery such as wheel loaders and articulated haulers. The gearbox is sometimes the dominant source of noise in these machines.Even if the gear noise is not the loudest source, its pure high frequency tone is easily distinguished from other noise sources and is often perceived as unpleasant. The noise creates an impression of poor quality. In order not to be heard, gear noise must be at least 15 dB lower than other noise sources, such as engine noise. 1.1背景 噪音是越來(lái)越認(rèn)為是環(huán)境問(wèn)題。這種信念體現(xiàn)在許多領(lǐng)域中的社會(huì)，包括工作環(huán)境，降低噪音水平的要求。在這種環(huán)境下員工花了很多時(shí)間和噪聲不僅會(huì)導(dǎo)致聽(tīng)力損傷，而且要集中能力下降，生產(chǎn)力下降和事故造成的風(fēng)險(xiǎn)增加。質(zhì)量也變得越來(lái)越重要。一個(gè)產(chǎn)品的質(zhì)量可以被定義為有能力滿足客戶的需求。這些要求往往隨時(shí)間而改變，而在市場(chǎng)上最好的競(jìng)爭(zhēng)對(duì)手將設(shè)置標(biāo)準(zhǔn)。噪音問(wèn)題也涉及到工程機(jī)械的輪式裝載機(jī)和鉸接式這樣表示。變速箱是有時(shí)在這些機(jī)械中。甚至噪音的主要來(lái)源，如果齒輪噪音并不是最響亮的來(lái)源，它的純高頻音很容易區(qū)別于其他噪聲源，通常為不愉快的感覺(jué)。噪音創(chuàng)建了一個(gè)質(zhì)量差的印象。為了不被聽(tīng)到，齒輪噪聲必須至少15分貝外，其他噪聲源，例如發(fā)動(dòng)機(jī)噪音低 1.2 Gear noise This dissertation deals with the kind of gearbox noise that is generated by gears under load.This noise is often referred to as “gear whine” and consists mainly of pure tones at high frequencies corresponding to the gear mesh frequency and multiples thereof, which are known as harmonics. A tone with the same frequency as the gear mesh frequency is designated the gear mesh harmonic, a tone with a frequency twice the gear mesh frequency is designated the second harmonic, and so on. The term “gear mesh harmonics” refers to all multiples of the gear mesh frequency.Transmission error (TE) is considered an important excitation mechanism for gear whine. Welbourn [1] defines transmission error as “the difference between the actual position of the output gear and the position it would occupy if the gear drive were perfectly conjugate.” Transmission error may be expressed as angular displacement or as linear displacement at the pitch point. Transmission error is caused by deflections, geometric errors, and geometric modifications.In addition to gear whine, other possible noise-generating mechanisms in gearboxes include gear rattle from gears running against each other without load, and noise generated by bearings.In the case of automatic gearboxes, noise can also be generated by internal oil pumps and by clutches. None of these mechanisms are dealt with in this work, and from now on “gear noise” or “gearbox noise” refers to “gear whine”. MackAldener [2] describes the noise generation process from a gearbox as consisting of three parts: excitation, transmission, and radiation. The origin of the noise is the gear mesh, in which vibrations are created (excitation), mainly due to transmission error. The vibrations are transmitted via the gears, shafts, and bearings to the housing (transmission). The housing vibrates, creating pressure variations in the surrounding air that are perceived as noise (radiation).Gear noise can be affected by changing any one of these three mechanisms. This dissertation deals mainly with excitation, but transmission is also discussed in the section of the literature survey concerning dynamic models, and in the modal analysis of the test gearbox in Paper B. Transmission of vibrations is also investigated in Paper D, which deals with the influence of bearing endplay or preload on gearbox noise. Differences in bearing preload influence a bearing’s dynamic properties like stiffness and damping. These properties also affect the vibration of the gearbox housing. 1.2齒輪噪音 隨著變速箱噪聲是一種由下負(fù)載。這種噪音齒輪生成此論文交易是通常被稱為“齒輪哀鳴”，并包括在高頻率所對(duì)應(yīng)的齒輪嚙合頻率和倍數(shù)，這是已知的純色調(diào)為主為諧波。一個(gè)與齒輪嚙合頻率相同的頻率音調(diào)被指定為諧波齒輪嚙合，一個(gè)頻率音調(diào)的兩倍齒輪嚙合頻率被指定為二次諧波，依此類推。術(shù)語(yǔ)“諧波齒輪嚙合”指的是齒輪嚙合頻率。變速箱錯(cuò)誤（TE）的倍數(shù)被認(rèn)為是重要的激勵(lì)機(jī)制齒輪哀鳴。Welbourn [1]定義為“之間的輸出齒輪的實(shí)際位置和地位，將占據(jù)如果齒輪傳動(dòng)是完美結(jié)合的差異?！眰鬏斿e(cuò)誤傳輸錯(cuò)誤可能表現(xiàn)為角位移或在球場(chǎng)上點(diǎn)線位移。傳輸錯(cuò)誤是由變形，幾何誤差和幾何變動(dòng)。除了齒輪嗲引起的，其他可能產(chǎn)生噪聲的機(jī)制，包括在變速箱齒輪嘎嘎從對(duì)對(duì)方的情況下運(yùn)行負(fù)荷齒輪，噪音軸承的情況下產(chǎn)生的自動(dòng)變速箱，噪音也可以由內(nèi)部生成的油泵和離合器。這些機(jī)制沒(méi)有得到處理，在此工作，并從“齒??輪噪音”或“齒輪箱噪音”現(xiàn)在是指“齒輪哀鳴”。奧爾登 描述了從以三部分組成的變速箱噪音的產(chǎn)生過(guò)程：激發(fā)，傳播和輻射。噪聲的來(lái)源是齒輪嚙合，其中振動(dòng)產(chǎn)生（激勵(lì)），主要是由于傳輸錯(cuò)誤。的振動(dòng)傳輸通過(guò)齒輪，軸和軸承的該（傳輸）。該震動(dòng)，創(chuàng)造了周圍的空氣都作為噪聲（輻射）感知壓力的變化。齒輪噪音可以通過(guò)改變?nèi)魏芜@三種機(jī)制之一的影響。本論文主要涉及激勵(lì)，但傳輸也是在文獻(xiàn)關(guān)于動(dòng)態(tài)模型統(tǒng)計(jì)調(diào)查組討論，并在文件中B.振動(dòng)模態(tài)分析傳輸測(cè)試變速箱也是，這與交易調(diào)查影響軸承的軸端間隙或變速箱噪音預(yù)緊力。軸承預(yù)緊力影響的差異像軸承剛度和阻尼的動(dòng)態(tài)特性。這些屬性也影響了變速箱外殼的振動(dòng)。 1.3 Objective The objective of this dissertation is to contribute to knowledge about gearbox noise. The following specific areas will be the focus of this study: 1. The influence of gear finishing method and gear modifications and errors on noise and vibration from a gearbox. 2. The correlation between gear deviations, predicted transmission error, measured transmission error, and gearbox noise. 3. The influence of bearing preload on gearbox noise. 4. Optimization of gear geometry for low transmission error, taking into consideration robustness with respect to torque and manufacturing tolerances. 1.3目標(biāo) 本論文的目的是幫助有關(guān)變速箱噪聲的知識(shí)。以下具體領(lǐng)域?qū)⑹潜狙芯康闹攸c(diǎn)： 1.齒輪的加工方法和齒輪噪音和修改，并從變速箱振動(dòng)誤差的影響。 2.齒輪之間的偏差的相關(guān)性，預(yù)測(cè)傳輸錯(cuò)誤，傳輸測(cè)量誤差和變速箱噪音。 3.對(duì)變速箱的噪聲影響軸承預(yù)緊力。 4.齒輪低傳輸錯(cuò)誤幾何優(yōu)化，同時(shí)考慮到穩(wěn)健性方面的扭矩和制造公差。 2 AN INDUSTRIAL APPLICATION ? TRANSMISSION NOISE REDUCTION 2 工業(yè)應(yīng)用 - 傳輸降噪 2.1 Introduction This section briefly describes the activities involved in reducing gear noise from a wheel loader transmission. The aim is to show how the optimization of the gear geometry described in Paper E is used in an industrial application. The author was project manager for the “noise work team” and performed the gear optimization. One of the requirements when developing a new automatic power transmission for a wheel loader was improving the transmission gear noise. The existing power transmission was known to be noisy. When driving at high speed in fourth gear, a high frequency gear-whine could be heard. Thus there were now demands for improved sound quality. The transmission is a typical wheel loader power transmission, consisting of a torque converter, a gearbox with four forward speeds and four reverse speeds, and a dropbox partly integrated with the gearbox.The dropbox is a chain of four gears transferring the powerto the output shaft. The gears are engaged by wet multi-disc clutches actuated by the transmission hydraulic and control system. 2.1簡(jiǎn)介 本節(jié)簡(jiǎn)要介紹了減少?gòu)妮喪窖b載機(jī)傳動(dòng)齒輪噪音所涉及的活動(dòng)。其目的是展示如何在文件中所述的齒輪結(jié)構(gòu)優(yōu)化在工業(yè)應(yīng)用。作者是項(xiàng)目經(jīng)理“噪音工作隊(duì)”，并進(jìn)行了齒輪的優(yōu)化。在發(fā)展的要求為輪式裝載機(jī)新的自動(dòng)輸電之一就是提高傳動(dòng)齒輪的噪音?，F(xiàn)有的電力傳輸被稱為是嘈雜。當(dāng)在四檔高速駕駛，高頻齒輪嗲可聞。因此，現(xiàn)在有改善音質(zhì)的要求。傳輸是一種典型的輪式裝載機(jī)動(dòng)力傳輸，扭矩轉(zhuǎn)換器，帶有四個(gè)前進(jìn)速度和四速變速箱扭轉(zhuǎn)，部分與變速箱。升降梭箱升降梭箱是一個(gè)集成了四個(gè)轉(zhuǎn)移功率到輸出軸齒輪鏈組成。所從事的齒輪由濕式多盤由液壓傳動(dòng)和控制系統(tǒng)驅(qū)動(dòng)離合器。此液壓系統(tǒng)油是由內(nèi)部提供的石油由輸入軸驅(qū)動(dòng)泵。 2.2 Gear noise target for the new transmission Experience has shown that the high frequency gear noise should be at least 15 dB below other noise sources such as the engine in order not to be perceived as disturbing or unpleasant.Measurements showed that if the gear noise could be decreased by 10 dB, this criterion should be satisfied with some margin. Frequency analysis of the noise measured in the drivers cab showed that the dominant noise from the transmission originated from the dropbox gears. The goal for transmission noise was thus formulated as follows: “The gear noise (sound pressure level) from the dropbox gears in the transmission should be decreased by 10 dB compared to the existing transmission in order not to be perceived as unpleasant. It was assumed that it would be necessary to make changes to both the gears and the transmission housing in order to decrease the gear noise sound pressure level by 10 dB. 2.2齒輪傳動(dòng)噪聲的新目標(biāo) 經(jīng)驗(yàn)表明，高頻齒輪噪音至少應(yīng)為15分貝以下，如發(fā)動(dòng)機(jī)等噪聲源分貝，以免被視為干擾或不愉快的。測(cè)量值表明，如果齒輪噪音可降低10分貝，這個(gè)標(biāo)準(zhǔn)應(yīng)該滿足于一定的余量。頻率在駕駛室測(cè)量的噪聲分析表明，從傳輸主要的噪音從投寄箱齒輪起源。對(duì)傳輸噪聲的目標(biāo)是這樣表述為如下：“齒輪噪音在傳輸?shù)纳邓笙潺X輪（聲壓級(jí)）應(yīng)10分貝下降相比，以現(xiàn)有的傳輸不被視為不愉快的感覺(jué)。”位置在投寄箱齒輪。有人認(rèn)為有必要使這兩個(gè)齒輪和變速器殼體的變化，以減少齒輪噪音10分貝的聲壓水平。 2.3 Noise and vibration measurements In order to establish a reference for the new transmission, noise and vibration were measured for the existing transmission. The transmission is driven by the same type of diesel engine used in a wheel loader. The engine and transmission are attached to the stand using the same rubber mounts that are used in a wheel loader in order to make the installation as similar as possible to the installation in a wheel loader. The output shaft is braked using an electrical brake. 2.3噪聲和振動(dòng)測(cè)量 為了建立一個(gè)新的傳輸參考，噪音和振動(dòng)測(cè)量的現(xiàn)有傳輸。傳輸是由相同的柴油發(fā)動(dòng)機(jī)在輪式裝載機(jī)的類型。發(fā)動(dòng)機(jī)和變速器連接到使用相同的立場(chǎng)是在一個(gè)橡膠輪式裝載機(jī)使用，以使安裝盡可能類似的安裝在輪式裝載機(jī)坐騎。輸出軸制動(dòng)采用電氣制動(dòng)。 2.4 Optimization of gears Noise-optimized dropbox gears were designed by choosing macro- and microgeometries giving lower transmission error than the original (reference) gears. The gear geometry was chosen to yield a low transmission error for the relevant torque range, while also taking into consideration variations in the microgeometry due to manufacturing tolerances. The optimization of one gear pair is described in more detail in Paper E.Transmission error is considered an important excitation mechanism for gear whine. Welbourn [1] defines it as “the difference between the actual position of the output gear and the position it would occupy if the gear drive were perfectly conjugate.” In this project the aim was to reduce the maximum predicted transmission error amplitude at gear mesh frequency (first harmonic of gear mesh frequency) to less than 50% of the value for the reference gear pair. The first harmonic of transmission error is the amplitude of the part of the total transmission error that varies with a frequency equal to the gear mesh frequency. A torque range of 100 to 500 Nm was chosen because this is the torque interval in which the gear pair generates noise in its design application. According to Welbourn [1], a 50% reduction in transmission error can be expected to reduce gearbox noise by 6 dB (sound pressure level, SPL). Transmission error was calculated using the LDP software (Load Distribution Program) developed at the Gear Laboratory at Ohio State University [3].The “optimization” was not strictly mathematical. The design was optimized by calculating the transmission error for different geometries, and then choosing a geometry that seemed to be a good compromise, considering not only the transmission error, but also factors such asstrength, losses, weight, cost, axial forces on bearings, and manufacturing. When choosing microgeometric modifications and tolerances, it is important to take manufacturing options and cost into consideration. The goal was to use the same finishing method for the optimized gears as for the reference gears, namely grinding using a KAPP VAS 531 and CBN-coated grinding wheels.For a specific torque and gear macrogeometry, it is possible to define a gear microgeometry that minimizes transmission error. For example, at no load, if there are no pitch errors and no other geometrical deviations, the shape of the gear teeth should be true involute, without modifications like tip relief or involute crowning. For a specific torque, the geometry of the gear should be designed in such a way that it compensates for the differences in deflection related to stiffness variations in the gear mesh. However, even if it is possible to define the optimal gear microgeometry, it may not be possible to manufacture it, given the limitations of gear machining. Consideration must also be given to how to specify the gear geometry in drawings and how to measure the gear in an inspection machine. In many applications there is also a torque range over which the transmission error should be minimized. Given that manufacturing tolerances are inevitable, and that a demand for smaller tolerances leads to higher manufacturing costs, it is important that gears be robust. In other words, the important characteristics, in this case transmission error, must not vary much when the torque is varied or when the microgeometry of the gear teeth varies due to manufacturing tolerances.LDP [3] was used to calculate the transmission error for the reference and optimized gear pair at different torque levels. The robustness function in LDP was used to analyze the sensitivity to deviations due to manufacturing tolerances. The “min, max, level” method involves assigning three levels to each parameter. 2.4優(yōu)化的齒輪 噪音優(yōu)化的升降梭箱齒輪的設(shè)計(jì)選擇宏觀和微觀給予低于原（參考）齒輪傳動(dòng)誤差。齒輪的幾何形狀是選擇產(chǎn)量為相關(guān)的扭矩范圍低傳輸錯(cuò)誤，同時(shí)也將在微觀幾何形態(tài)由于制造公差考慮到變化。一對(duì)齒輪的優(yōu)化是描述紙張E.傳輸錯(cuò)誤被認(rèn)為是重要的激勵(lì)機(jī)制齒輪哀鳴在更多的細(xì)節(jié)。 Welbourn [1]定義在這個(gè)項(xiàng)目它的目的是減少傳輸?shù)淖畲箢A(yù)測(cè)在齒輪嚙合誤差幅度為“之間的輸出齒輪的實(shí)際位置和地位，將占據(jù)如果齒輪傳動(dòng)是完美結(jié)合的差異。”頻率（首先是齒輪嚙合頻率諧波）小于50的參考價(jià)值齒輪副％。對(duì)傳輸錯(cuò)誤第一諧波是總傳輸錯(cuò)誤的一部分，其頻率等于齒輪嚙合頻率變化幅度。扭矩范圍 100至500牛頓米的選擇，因?yàn)檫@是扭矩區(qū)間，其中齒輪副在其設(shè)計(jì)中的應(yīng)用產(chǎn)生的噪音。據(jù)Welbourn [1]，在傳輸錯(cuò)誤減少50％，可以預(yù)計(jì)將減少6分貝（聲壓級(jí)，SPL）變速箱噪音。傳輸錯(cuò)誤計(jì)算自民黨軟件（負(fù)載分配方案）在實(shí)驗(yàn)室開發(fā)的齒輪在俄亥俄州立大學(xué)[3]?！皟?yōu)化”是沒(méi)有嚴(yán)格的數(shù)學(xué)。該設(shè)計(jì)進(jìn)行了優(yōu)化，通過(guò)計(jì)算不同幾何形狀的傳??輸錯(cuò)誤，然后選擇一個(gè)幾何這似乎是一個(gè)很好的妥協(xié)，不僅考慮傳輸錯(cuò)誤等因素，還得考慮損失，重量，成本，對(duì)軸承的軸向力和制造的影響。當(dāng)選擇微觀幾何形態(tài)修改和公差，重要的是要考慮選擇和制造成本。我們的目標(biāo)是要利用作為參考齒輪優(yōu)化的齒輪精加工方法相同，即使用一個(gè)卡普磨VAS 531和CBN涂層磨輪。輸入特定的扭矩和齒輪轉(zhuǎn)速，它可以定義一個(gè)齒輪微觀幾何形態(tài)的最大限度地減少傳輸錯(cuò)誤。例如，在無(wú)負(fù)載，如果沒(méi)有錯(cuò)誤，沒(méi)有其他球場(chǎng)幾何偏差，齒的齒輪漸開線形狀應(yīng)是真實(shí)的，沒(méi)有像尖或漸開線救濟(jì)加冕修改。對(duì)于一個(gè)特定的扭矩，在齒輪幾何設(shè)計(jì)應(yīng)以這樣一種方式，它在撓度與在齒輪嚙合剛度變化差異進(jìn)行補(bǔ)償。然而，即使有可能確定最佳齒輪微觀幾何形態(tài)，它可能無(wú)法制造它，鑒于齒輪加工的局限性。還必須考慮如何在指定的圖紙和如何衡量在驗(yàn)機(jī)的齒輪幾何。在許多應(yīng)用中也有一個(gè)以上的扭矩范圍傳輸錯(cuò)誤應(yīng)盡量減少。由于制造公差是不可避免的，而且為更小的公差要求導(dǎo)致制造成本較高，這是很重要的齒輪是強(qiáng)大的。換句話說(shuō)，重要的特征，在這種情況下傳輸錯(cuò)誤，必須變化不大時(shí)，扭矩是多種多樣的，或當(dāng)齒輪微觀幾何形態(tài)變化由于制造誤差。LDP [3]是用來(lái)計(jì)算的傳輸錯(cuò)誤參考和不同層次優(yōu)化扭矩齒輪副。在自民黨的魯棒性功能是用來(lái)分析到，由于制造公差偏差的靈敏度。而“最小，最大，水平”的方法包括三個(gè)層次分配給每個(gè)參數(shù)。 2.5 Optimization of transmission housing Finite element analysis was used to optimize the transmission housing. The optimization was not performed in a strictly mathematical way, but was done by calculating the vibration of the housing for different geometries and then choosing a geometry that seemed to be a good compromise.Vibration was not the sole consideration, also weight, cost, available space, and casting were considered. A simplified shell element model was used for the optimization to decrease computational time. This model was checked against a more detailed solid element model of the housing to ensure that the simplification had not changed the dynamic properties too much. Experimental modal analysis was also used to find the natural frequencies of the real transmission housing and to ensure that the model did not deviate too much from the real housing.Gears shafts and bearings were modeled as point masses and beams. The model was excited at the bearing positions by applying forces in the frequency range from 1000 to 3000 Hz. The force amplitude was chosen as 10% of the static load from the gears. This choice could be justified because only relative differences are of interest, not absolute values. The finite element analysis was performed by Torbjrn Johansen at Volvo Technology. The author’s contribution was the evaluation of the results of different housing geometries.A number of measuring points were chosen in areas with high vibration velocities. At each measuring point the vibration response due to the excitation was evaluated as a power spectral density (PSD) graph. The goal of the housing redesign was to decrease the vibrations at all measuring points in the frequency range 1000 to 3000 Hz. 2.5優(yōu)化傳輸該 有限元分析，用于優(yōu)化傳輸該。優(yōu)化是在不進(jìn)行嚴(yán)格的數(shù)學(xué)方法，但通過(guò)計(jì)算不同幾何形狀的房屋震動(dòng)，然后選擇一個(gè)幾何形態(tài)，這似乎是一個(gè)很好的妥協(xié)。振動(dòng)不是唯一要考慮的，重量，成本，可用做空間，鑄造進(jìn)行了審議。一個(gè)簡(jiǎn)化的殼單元模型進(jìn)行優(yōu)化，以減少計(jì)算時(shí)間。這種模式是核對(duì)更詳細(xì)的房屋實(shí)體單元模型，以確保簡(jiǎn)化并沒(méi)有改變太多的動(dòng)態(tài)特性。實(shí)驗(yàn)?zāi)B(tài)分析也被用來(lái)尋找真正的變速器殼體的固有頻率，并確保該模型并沒(méi)有偏離實(shí)際外殼。齒輪分別為軸和齒輪，梁建模軸承太多。該模型是興奮，通過(guò)在軸承位置的頻率范圍內(nèi)的力量，從1000到3000赫茲。這支部隊(duì)的幅度被選為10從齒輪靜載荷％。這種選擇可能是合理的，因?yàn)橹挥邢鄬?duì)差異的利益，而不是絕對(duì)值。有限元分析是由羅多約翰森沃爾沃技術(shù)。作者的貢獻(xiàn)是選擇了不同的測(cè)量點(diǎn)。數(shù)量評(píng)價(jià)結(jié)果分別在高振動(dòng)速度的地區(qū)選擇。在每個(gè)測(cè)點(diǎn)的振動(dòng)響應(yīng)，由于激勵(lì)被認(rèn)定為功率譜密度（PSD）的圖形。房屋重新設(shè)計(jì)的目標(biāo)是減少在頻率范圍1000至3000赫茲的所有測(cè)點(diǎn)的振動(dòng)。 2.6 Results of the noise measurements The noise and vibration measurements described in section 2.3 were performed after optimizing the gears and transmission housing.The total sound power level decreased by 4 dB. 2.6噪聲測(cè)量的結(jié)果 噪聲和振動(dòng)測(cè)量在2.3節(jié)中描述了進(jìn)行優(yōu)化后的齒輪和變速器殼體。 2.7 Discuss