雙缸柴油機(jī)氣缸體鉆削組合機(jī)床總體及夾具設(shè)計(jì)【三圖一卡16張圖紙-3A0優(yōu)秀】

資源目錄里展示的全都有，所見(jiàn)即所得。下載后全都有,請(qǐng)放心下載。原稿可自行編輯修改=【QQ：401339828 或11970985 有疑問(wèn)可加】 ORIGINAL ARTICLEOptimal machine tool spindle drive gearbox designD. R. Salgado&F. J. AlonsoReceived: 4 August 2006 /Accepted: 23 March 2007 /Published online: 4 May 2007#Springer-Verlag London Limited 2007Abstract Many machine tools are equipped with a motor-gearbox to extend the constant power range of the machinetool spindle drive motor at low speeds. Currently, in thelatest spindle drive motor technology, the gearboxes areintegrated in-line between the water-cooled motor and thespindle inside the machine tools ram. The functionality ofa spindle gearbox depends directly upon its constructionalsolution, and on the kinetic energy corresponding to thissolution. In this work, spindle gearboxes are optimizedtaking this design factor into account. In the authorsopinion, the results could be of great interest for spindledrive gearbox manufacturers.Keywords Spindlegearbox design.Optimaldesign.Minimumkineticenergy.OptimizationNomenclatureHHertz contact stressFBending stressHPAllowable Hertz contact stressFPAllowable bending stressHONominal Hertz contact stressFONominal bending stressHlimMaximum allowed Hertz contact stressFlimMaximum allowed bending stressPressure angleFtTangential gear forcebFace widthHelix angledPitch diametermModuleKAApplication factorKHatrans. load sharing factor for pitting resistanceKHblong. load sharing factor for pitting resistanceKFatrans. load sharing factor for bending strengthKFblong. load sharing factor for bending strengthYFaForm factor for bending strengthYNTLife factor for bending strengthYRrelTRelative rugosity factorYSaStress concentration factorYSTStress concentration factorYXSize factor for bending strengthYdrelTNotch relative sensitivity factorYContact ratio factor for bending strengthYbHelix angle factor for bending strengthZEMaterial factorZHGeometry factor for pitting resistanceZLViscosity factorZNLife factor for pitting resistanceZRRugosity factor for pitting resistanceZVVelocity factorZWHardness ratio factorZXSize factor for pitting resistanceZbHelix angle factor for pitting resistanceZContact ratio factor for pitting resistanceKVDynamic factorNpNumber of planet gearsKEKinetic energy of planetary systemiAngular speed of gear iInt J Adv Manuf Technol (2008) 37:851860DOI 10.1007/s00170-007-1028-6D. R. Salgado (*)Department of Electronics and Electromechanical Engineering,University of Extremadura,Sta. Teresa de Jornet 38,06800 Mrida, Spaine-mail: drsunex.esF. J. AlonsoDepartment of Electronics and Electromechanical Engineering,University of Extremadura,Avda. Elvas s/n,06071 Badajoz, Spainv4Speed of the planet gearmiMass of gear iIiMoment of inertia of gear iZiNumber of teeth on gearZnlTooth ratio of the gear pair formed by links n and lEfficiency of planetary gear train (spindle speeder)oOrdinary or stationary efficiency of the gear pair1 IntroductionThe spindle is one of the main mechanical components inmachining centers, since its design directly affects thefinished quality of workpieces and machining productivity.Consequently, spindle design has been studied in depth inseveral works 14. Machine tools cannot provide hightorques over their entire speed range unless the motor isoversized. Nevertheless, the requirements of such anoversized motor to provide consistent torque across themachine tools speed range increase not only the cost of themotor but also the operating costs due to higher powerconsumption. Additionally, the motors weight wouldexceed the weight of a motor-gearbox combination. Forthese reasons, spindle drive gearboxes are used.The use of machine tool spindle drive gearboxes allowsone to extend the constant power range of the machine toolspindle drive motors. This range extension of power andtorque is illustrated in Fig. 1, in which the dashed linerepresents the range extension when the reducer gearbox isintroduced between the motor and the tool axis. Figure 1arepresents the power extension and Fig. 1b the torqueextension versus the output speed (data from an industrialmachine tool). In sum, the use of the reducer gearboxincreases the flexibility of manufacturing, enabling machinetools to operate at:high torque for hogging out steel or cast iron (reducerspeed ratio R:1, R1)high speed for finishing cuts (direct speed ratio 1:1)Traditionally, these gearboxes are used in conventionalapplications where the motor and gearbox are mountedoutside the headstock, and the spindle is driven by belts,chains, or gears. Nowadays, the gearboxes are integrated in-line between the water-cooled motor and the spindle insidethe machine tools ram. This integration enables the unit tofit into the bore of the machine tool ram and share in thecoolant system. This compact, light-weight configurationmaximizes efficiency while minimizing vibrations andnoise. It is the design of this configuration that is studiedin the present work.Note that in the in-line gearbox integrated design, theoptimal design depends mainly on the design of thetransmission for the required speed ratio and power. Hence,and for the same reasons mentioned above for the spindledesign, spindle drive gearboxes also need to be studied indepth for their design to be optimized. In this context, themost important design factor for spindle drive gearboxes isthat the kinetic energy of the transmission is minimal, foran optimal functionality during machining and ensuring along working life.Planetary gear trains (PGTs) are used for the gearboxdesign since they offer a very compact (reduced weight andsize) and efficient solution (high speed ratios and highefficiency) in comparison to ordinary gear trains.The objective of this paper is to give a set of optimaldesigns of spindle gearboxes for different powers and speed101001000100000200400600800100012001400Output speed (rpm)Torque (Nm)1010010001000001020304050Output speed (rpm)Power (kW)Range extension Range extensionabFig. 1 Range extension of pow-er and torque using a spindlegearbox852Int J Adv Manuf Technol (2008) 37:851860ratios. In particular, the two spindle gearbox configurationsused by manufacturers are studied for all the marketedrange of powers and speed ratios, and the optimal designsof these configurations are given and compared for all thatrange.2 Considerations on the design of spindle drivegearboxesIn this section we explain some important considerationsthat must be taken into account for spindle gearbox design.The members of PGTs are of three types, depending ontheir movements and links with other members. In thepresent work, they will be called suns, arms, and planets.Two different PGT configurations are used by spindlegearbox manufacturers. They are shown in Fig. 2a and b. Inthese figures, members 1 and 2 are the suns, 3 is the arm,and 4 and 4 are the planets.2.1 Economic and operating considerationsThe spindle gearbox configuration of Fig. 2b has theadvantage of being more interesting economically, since itdoes not include a ring gear. The reason is that spindlegearbox gears must be hardened, tempered, and ground toavoid high heating, and a ground ring gear is moreexpensive than a non-ground ring gear. Also, if the ringgear is not ground, heat buildup will occur more quickly,and this heating limits and reduces the input speed andtorque.2.2 Efficiency considerationsAnother interesting consideration in spindle gearbox designis that it is possible to prove that the efficiency of thereducers based on these two PGT configurations is greaterif they are designed with the input being the sun member.This is why all spindle gearboxes are designed as reducerPGTs with the sun (member 1) as input and the arm(member 3) as output, as shown in Fig. 2a and b.2.3 Planet member considerationsIn spindle gearbox design, it is quite important to choose anoptimal number of planets for the required power and speedratio. In this context, the number of planet members in aPGT (Np) is the number of these members that are arrangedaround the PGTs principal axis. For example, the com-mercial spindle gearbox shown in Fig. 2c has two planetmembers, i.e., Np=2. This number must be as small aspossible to reduce the weight and the kinetic energy of thetransmission, while ensuring a good distribution of the loadto each of the planet gears. This number can be two, three,four, or even more, depending on the application. Which-ever the case, the planets must always be arrangedconcentrically around the PGTs principal axis to balancethe mass distribution.3 The formulation of constraints in spindle gearboxdesignThis section describes the constraints in spindle gearboxdesign. They are grouped into three sets, according to thetype of constraint. These are:Constraints involving gear size and geometryPlanetary gear train meshing requirementsContact and bending stresses3.1 Constraints involving gear size and geometryThe first constraint is a practical limitation in the range ofacceptable face widths b. This constraint is as follows:9m ? b ? m1where m is the module.Input memberOutput memberInput memberOutput memberabcFig. 2 a, b, Constructional so-lutions of the PGTs used toextend the constant powerrange. c An example of spindlegearbox based on the PGT ofFig. 2bInt J Adv Manuf Technol (2008) 37:851860853All the kinematic and dynamic parameters of thetransmission depend on the values of the tooth ratios Znl,where Znlis the tooth ratio of the gear pair formed by thelinking members n and l. In particular, Znlis defined as:ZnlZnZl2For the definition of the tooth ratios to satisfy the Willisequations, Znlmust be positive if the gear is external andnegative if it is internal 5. For the train of Fig. 2a, onewould have to take Z140 and Z240.In theory, tooth ratios can take any value, but in practicethey are limited mainly for technical reasons because of thedifficulty of assembling gears beyond a certain range oftooth ratios. In this work, the tooth ratios considered for thedesign of spindle gearboxes are quite close to therecommendation of Mller 6 and the AGMA norm 7.They are:0:2 Znl 53?7 Znl ?2:24where the constraint of Eq. (3) is for external gears, and thatof Eq. (4) is for internal gears. In this way one also ensuresthat there exists no interference between the gears.Another constraint that will be imposed is on the ratio ofthe diameters of the gears constituting the planets (members4 and 4):13D4D04 35Other relationships must be satisfied as a consequenceof the geometry of these PGTs. For example, in the PGT ofFig. 2a the tooth ratios Z14and Z24are related to the radii ofthe gears constituting the planets. In particular, thefollowing geometric relationship must be satisfied:R1 R4 R2? R046Expressing the above equation in terms of the module ofthe gears, it is straightforward to find that the ratio of thediameters of gears 4 and 4 conditions the value of Z14andZ24. This ratio is:R04R4Z14 1Z240jj ? 17Likewise, for the case of the PGT of Fig. 2b one obtainsthe expression:R04R4Z14 1Z240 18Lastly, one assumes a minimum pinion tooth number:Zmin? 1893.2 Planetary gear train meshing requirementsThe meshing requirement for equally spaced planets withthe configurations of Fig. 2a and b is given by the AGMAnorm 7, and is:Z2P2? Z1P1Np aninteger10where Z1and Z2are the number of teeth on members 1 and2, respectively, and P1and P2are the numerator anddenominator of the irreducible fraction equivalent to thefraction Z04?Z4, where Z04and Z4are the number of teeth onthe planet gears (see Fig. 2):Z04Z4P1P23.3 Contact and bending stressesThe torques on each gear of the proposed spindle gearboxdesigns were calculated taking power losses into account.This aspect allows one to really optimize the spindlegearbox design, unlike optimization studies in which theselosses are not considered 8, 9. The procedure fordetermining the torques and the overall efficiency of thespindle gearbox is described in 10.For each of the gears, the following constraints relativeto the Hertz contact and bending stresses must be satisfied:sH sHP11sF sFP12For the calculation of the gears, the ISO norm wasfollowed. The values of the stresses of Eq. (11) andEq. (12) are defined by this norm as:sHffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiKA? KV? KHb? KHap? ZH? ZE? Ze? ZbffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiFtb ? d?u 1ur13sF KA? KV? KFb? KFa?Ftb ? m? YFa? YSa? Ye? Yb14The values of HPand FPare given by:sHP sH lim? ZN? ZL? ZR? ZV? ZW? ZX15sFP sF lim? YST? YNT? YdrelT? YRrelT? YX16854Int J Adv Manuf Technol (2008) 37:851860It is important to emphasize that power losses weretaken into account in obtaining the tangential force Ftfrom the calculation of the torques. To include powerlosses in the overall efficiency calculation, we used theconcept of ordinary efficiency 5, 10, which is what theefficiency of the gear pair would be if the arm linked tothe planet were fixed. By means of this efficiency, oneintroduces into the overall efficiency calculation of thespindle gearbox the friction losses that take place in eachgear pair. For example, if 14=0.98, then 2% of the powerpassing through the gear pair formed by members 1 and 4is lost by friction between these gears.In the design process, we took a value of 0=0.98 for theordinary efficiencies. In studies that do not take this aspectinto account, the value of the tangential forces is onlyapproximate, and may be quite different in the case of PGTsbecause of the possibility of power recirculation 5.Given the start-up characteristics of machine tools ingeneral, we took an application factor of KA=1. Thepressure angle is =20. The material chosen for the gearsis steel with Hlim=1,630 N/mm2, Flim=500 N/mm2and7,000 kg/m3of density.Lastly, the distribution of the loads to which each of theplanet gears is subjected was determined using thedistribution factors recommended in the AGMA 6123 A-88 norm 7 as a function of the number of planets (Np).4 Optimal spindle drive gearbox designVarious works have presented methods for the optimizationof a conventional transmission 1120, but only a few forthe design of PGTs 8, 9. Furthermore, none of the latterstudies calculate exactly the torques to which each of thegears is subjected, since they do not consider the powerlosses in the different gear pairs of the PGT. This questionis taken into account in the present work to ensure anoptimal spindle drive gearbox design. For an optimalspindle gearbox design, the kinetic energy must beminimal. In mathematical terms, for the gearboxes designsbased on Fig. 2a and b, the following objective functionmust be minimized:KE 12I1w2112Npm4 m40v2412NpI4 I40w2417where Iiis the moment of inertia, wiis the rotational speed,miis the mass, viis the translation speed (center of the gear)of member i, and Npis the number of planet gears.In Eq. (17) the energy of the arm has been neglectedbecause this member can be designed in different andvariable forms, and because it is considerably less than thatof the planetary system. The design variables are thenumber of planet gears (Np), the module of the gears (mi),the number of teeth on each gear (Zi), the face width (bi)and the helix angle (i). When these design parameters aredetermined by minimizing the above objective function, thePGT is perfectly defined.5 Results and discussionThe optimization problem of spindle drive gearboxesdescribed in this paper was applied to a set of 24 differentdesigns (i.e., different speed ratios and powers) covering allthe marketed range. Table 1 lists these designs and analphanumeric identification code. In this code, the letteridentifies the speed ratio, and the number the nominaloutput torque and the maximum input speed. For example,code D3 represents the spindle gearbox with a speed ratioof 4.5:1, 2,300 Nm of nominal torque, and a maximuminput speed of 6,500 rpm.Tables 2 and 3 summarize the results for the optimalspindle gearbox designs based on the different construc-tional solutions of Fig. 2a and b, respectively. In thesetables, the first column gives the specific spindle gearboxTable 1 Data of the proposed designsReduction ratio1234Code3:1230 Nm8,000 rpm620 Nm6,000 rpm2,200 Nm5,000 rpm4,400 Nm5,000 rpmA3.5:1B4:1670 Nm12,000 rpm1,300 Nm8,000 rpm2,300 Nm6,500 rpm3,500 Nm6,500 rpmC4.5:1D4.61:1E5:1FInt J Adv Manuf Technol (2008) 37:851860855design according to the code given in Table 1. The second,third,andfourthcolumns givethe helixangle,themoduleandthe face width of the gears corresponding to the gear pairformedbymembers 1and4,respectively.Thefollowingthreecolumnsgivethe same information for members 2 and 4. Theeighth and ninth columns give the tooth number of eachmember for the optimal spindle gearbox design. Finally,columns ten to thirteen give the kinetic energy, the moment ofTable 2 Optimal spindle gearbox designs based on the constructional solution of Fig. 2a14m14(mm)b14(mm)24m24(mm)b24(mm)Z1/Z4Z2/Z4KE(J)J(kg mm2)Vol.(103mm3)?(mm)A119.51.521.0026.11.2513.9520/2288/4047455452128.3A219218.0021.81.2511.2520/22121/55681,165609162.8A3302.522.5027219.2020/2299/452486,3181,617222.2A426.52.535.0023224.4520/2299/452997,4522,159215.0B1291.521.00291.513.5018/1860/2423204287102.9B25228.0029.31.513.9318/1870/2829449478120.5B3212.535.0029.4222.5018/1870/28872,0301,165160.7B49.6342.0016.52.527.7518/1870/281774,1171,824182.5C115.41.521.00291.2516.0020/2584/3535460418120.0C20225.60211.517.3520/2596/40611,427803154.3C3302.522.514225.0420/25108/452137,4181,851222.7C426.42.535.0012.72.530.4920/2584/352518,5962,384215.3D1191.521.0022.41.515.5318/2777/3348880466124.9D20225.9229.91.513.5018/2791/39822,692885157.5D3142.535.0026.2226.9518/2791/3921410,1381,998202.8D42342.0027.32.525.3218/2784/3629013,1162954236.4E1191.521.00281.513.8018/2742/2826465403118.9E20225.9225.81.516.818/2790/36441,390755150.0E3142.535.00252.523.1718/2770/281175,2491,705193.2E42342.0027.32.526.1018/2780/3224911,2052,710225.1F191.521.00171.514.1222/40110/50852,148822172.6F227.81.521.0019.71.514.9022/40121/55773,4501,048192.8F302.531.9021.7223.2522/40132/6038825,1533,498284.2F4202.535.0024.62.524.7522/40110/5053834,7544,291302.4856Int J Adv Manuf Technol (2008) 37:851860inertia, the volume, and the diameter of the optimal spindlegearbox design, respectively.For example, for the A1 design (speed ratio 3:1, nominaltorque 230 Nm, and maximum input speed 8,000 rpm), theoptimal spindle gearbox design based on the configurationof Fig. 2a has Z1=20, Z4=22, Z2=88, and Z4=40. Thehelix angle of members 1 and 4 is 19.5, the module is1.5 mm, and the face width 21.00 mm. For the other gearTable 3 Optimal spindle gearbox designs based on the constructional solution of Fig. 2b14m14(mm)b14(mm)24m24(mm)b24(mm)Z1/Z4Z2/Z4KE(J)J(kg mm2)Vol.(103mm3)?(mm)A127.51.521.0027.51.517.0418/3636/18234965692152.2A20225.920221.6018/3636/185662,3381,209180.0A3122.535.00122.529.4418/3636/187968,4272,667230.0A4302.535.33302.529.0918/3636/181,30513,8143,414259.8B1141.513.50301.513.6018/4536/202481,474754166.8B20224.4827.3218.0018/4536/204624,8981,556216.0B3122.535.0029.622.557.5018/4536/201,21118,4303,440276.0B429.52.535.0021.8327.0018/4536/201,96129,9374,685310.2C1151.515.21201.2517.5020/4050/20287757619155.3C24218.84291.519.2020/4050/204373,8551,204200.8C362.523.1222224.5920/4050/208737,8332,367251.3C4222.527.5030226.3220/4050/201,36412,1963,072269.6D124.51.513.50301.2511.5420/5025/555131,870769197.8D20219.24301.515.1520/5025/557005,7251,555240.0D315228.00301.528.1720/5025/557799,6972,722248.4D418.72.526.9030223.0920/5025/551,97224,4913,937316.7E1301.513.5024.81.513.5018/4520/463871,506741187.0E230218.0024.9218.0018/4520/467256,3521,758249.4E330224.9424.9226.0118/4520/466658,8372,489249.4E4302.523.9024.92.524.8018/4520/461,55520,6663,717311.7F1301.513.50161.2516.2620/4020/603031,014701173.2F229218.10291.519.4518/3618/543582,6821,249205.8F3282.522.5020227.9618/3618/546957,9372,572254.8F426327.0042.534.7318/3618/541,61318,4554,375300.4Int J Adv Manuf Technol (2008) 37:851860857pair, i.e., for members 2 and 4, the results are helix angle26.1, module 1.25 mm, and face widt