1、04FTM2Noise Optimized Modifications:Renaissance of the Generating Grinders?by: Dr.-Ing. Hansjrg Geiser, Hofler Maschinenbau GmbHTECHNICAL PAPERAmerican Gear ManufacturersAssociationNoise Optimized Modifications: Renaissance of theGenerating Grinders?Dr.-Ing. Hansjrg Geiser, Hofler Maschinenbau GmbHT
2、he statements and opinions contained herein are those of the author and should not be construed as anofficial action or opinion of the American Gear Manufacturers Association.AbstractModerngearcalculationprogramsgiveusthepossibilitytodeterminetheloadcarryingcapacityandthenoisebehavior of a gear tran
3、smission considering the shaft and bearing system, the tooth modifications and theproduction deviations. While load and stress optimized tooth modifications are quite insensible to the normalproduction deviations; noise and vibration optimized tooth modifications need a much higher productionaccurac
4、y because of the low values of the transmission errors caused by the changes of the mesh stiffness.The numerical simulation leads often to more complex modifications which can not be realized with normalstandard modifications like crowning and root or tip relief. Topological modifications are requir
5、ed and have tobe realized in the grinding process. Differences between the common profile grinding method and thegenerating grinding method based on the different contact situations between grinding wheel and gear gapwill be shown.More and more companies discover the high improvement potential of to
6、pological modifications with whichgearscanbemodifiedwhereitisrequired - thegeneratingengagementreliefofahelicalgearcorrespondstothe normal tip and root relief of a spur gear. The teeth are modified in the area of highest pressure (at thebeginning and the end of the mesh). A contact area with a lower
7、 Herzian pressure can transmit more load.The topologicalmodifications show big advantages for the noise and vibration behavior also due to the muchhigher variability in direction of contact pattern. Gears with even overlap ratio should for instance be modifiedas less as possible, otherwise the basic
8、 advantages of the constant contact line is not given anymore.Unfortunately, a load optimized tooth flank modification is not always a noise optimized modification also - acompromise between optimized load distribution and low noise has to be found.The basic of the modern gear calculation programs i
9、s the exact determination of the mesh stiffness. All thesecondary influences like shaft bending and deflection in the bearings should also to be considered. For theload distribution calculation a static view is often sufficient. The basic of the dynamic analysis is the load overthe time in form of a
10、 FFT analysis. The running speed and the behavior of the oscillating system have also tobeconsidered.Inapracticalexamplethecalculationpossibilitieswillbeshown.Itwillbedemonstratedhowanoptimized tooth modification can be found. In the calculation possible production deviations have to beconsidered -
11、the feedback from the production to the design department is essential.To satisfy the new requirements the gear grinders manufactures had and have to improve their machinesevery year. Today, a serial production of gears in quality Q=1 according DIN 3962 (AGMA 15) is possible, ifrequested. This impro
12、vement was basically been possible with the substitution of the mechanicaltransmissionsinthegrinderwiththemodernCNCcontrols.By introducingthe torquemotor asthe maintabledrive of a grinder the last gear transmission disappeared in the gear grinder field.The accuracy of a gear grinder depends basicall
13、y from the accuracy of the table drive. The modern torquemotor shows together with the direct mounted encoder high advantages in comparison to the mechanicalworm/worm gear drive. Problems like worm gear wear, backlash and deviations are not known in a torquemotor anymore. Without excitation, it real
14、izes an incredible constant movement of the table axis. Machinefrequencies - the main reason for the almost disappearing of the generating grinders in the nineties - are nottransmittedtothegearanymore.Thisandthepossibilitytorealizetopologicalmodificationscouldnowleadtoa Renaissance of the generating
15、 grinders. They can be built in such a way that also form grinding is possibleon the same machine.Copyright 2004American Gear Manufacturers Association500 Montgomery Street, Suite 350Alexandria, Virginia, 22314October, 2004ISBN: 1-55589-825-41Noise Optimized Modifications: The Renassance of the Gene
16、rating Grinders ? Dr.-Ing. Hansjrg Geiser Customers demands and the legislation on gear noise emission increased in the last years. Theoretical basics regarding noise excitation are discussed in this paper and some general recommendations are given. Modern gear calculations result very often in topo
17、logical tooth modifications: for production accuracy and variability reasons the generating grinding could be more often used in the industrial gear field in future. Modern gear calculation programs give us the possibility to determine the load carrying capacity and the noise behavior of a gear tran
18、smission by considering tooth modifications, production deviations and deflections of the shaft and bearing system. The time variability of the tooth force Fz(t) and the time variability of the transmission error xd(t) are generally the result of the following three factors: - the periodically chang
19、ing of the mesh stiffness Figure 1: mesh stiffness of spur and helical gears - variations resulting from manufacturing tolerances and modifications - the elastic deflection of the teeth under load leading to mesh interferences at the beginning and at the end of the line of action, which is also know
20、n as the engagement shock (increase of length of action) As shown in figure 1 for both spur and helical gears the variation of the mesh stiffness cs(t) is basically influenced by the changing number of teeth in contact combined with the corresponding single tooth stiffness c(t) at the beginning and
21、at the end of line of action. At spur gears a tooth carries load over the whole face width at the beginning of the line of action. Because in first assumption the single tooth stiffness c(t) is proportional to the length of the line of contact the coming in contact of a new tooth leads to a signific
22、ant step in the value of the mesh stiffness cs(t). For helical gears, the length of the line of contact and therefore also the transmitted force increases slowly. The result is a much smoother progression of the mesh stiffness cs (t) in comparison to spur gears. To evaluate the excitation of a gear
23、the function of - the mesh stiffness cs(t) under load - the transmission error xd(t) under load (n-0) - the tooth force Fz(t) (n- ) can be developed in a Fourier-series. It is important to point out, that the spectral information is equivalent for Fz(t) , xd(t) and cs(t). Figure 2: Fourier coefficie
24、nts of the tooth force The example in Figure 2 illustrates the development in a Fourier-series with a sin and a trapezoidal function of the tooth force. The force is used because it causes noise and also takes themedium mesh stiffness c into account. The lower the excitation amplitude, the lower is
25、the answer from the system. Tonal problems can be clearly recognized by looking at the excitation amplitudes. For each coefficient Fiof the over critical (n- ) tooth force Fz(t) a corresponding amplitude level LAican be calculated (Fn nominal Load): dBFFLniAi=22lg10 To optimize gear noise it is nece
26、ssary to know and to understand the basic mechanisms of both excitation and 2reaction of the system. An analysis of the excitation only is not sufficient. For a better understanding of numerical results a linear view of the most simple model of a gear stage (one mass system) is very helpful. ndddddx
27、tctFtxctxktxm =+)()()()()()()( txtxxdn=+ )()( tctccsd=+)()( tFtFFzdn=+ This simplification explains why the amplitudes of the tooth force and the amplitudes of the transmission error depend on the amplitudes of excitation of the mesh stiffness under load cs(t) and the running speed of the gear stage
28、 relative to the natural frequency like the numerical results shown in Figure 3. Figure 3: tooth force and transmission error depending on the running speed The resonance ratio N (acc. ISO 6336) is a basic information to optimize gear modifications regarding noise. Noise optimized modifications are
29、a function of the load and of the running speed. Each order of excitation is enlarged depending on the coefficient of magnification VI : ()()222241iiiiNDNNV+=The coefficient of magnification of each order is a function of: the resonance ratio N, the contact ratio the damping coefficient D Figure 4:
30、Coefficient of magnification Vi depending on the resonance ratio N (=1.5, D=0.05) The order with the highest answer depends on the operating speed. It has not to be the order with the highest amplitude level LAi. This fact is illustrated in figure 5 with the specific coefficient of magnification Vi
31、/ Vmwhere Vmis the maximum of magnification in the natural frequency: Figure 5: Specific coefficient of magnification V i / Vmdepending on the resonance ratio (=1.5, D=0.05) The specific coefficient of magnification Vi / Vm becomes 1 at the natural frequency and 0 in the extreme state n- 0. Normally
32、 gear stages are operated in the under critical speed range 00.8 seems to be favorable. Gears with an integer overlap ratio show the lowest levels. Thats based on the fact that the mesh stiffness in first assumption is proportional to the length of the line of contact. In practical use, gears have t
33、o be modified for load carrying reasons (Hertzian pressure and tooth root stresses can be reduced by tooth modifications). Gears have normally manufacturing deviations also. Every modification or deviation influences the length of the line of contact and therefore also the course of the mesh stiffne
34、ss. Figure 7 shows the results that correspond to figure 6 by modifying the gears for optimal load carrying capacity. Figure 7: Force level LFdepending on both contact ratio and overlap ratio (N=1) modified In this example, gear modifications shift the noise minimum from overlap ratio =1 (unmodified
35、) to a overlap ratio of =1.5 (modified). The result depends basically on the effective overlap ratio. It is important to point out that these calculations done for another speed ratio look totally different. The following two pictures show the force level of a helical gear with and without modificat
36、ion. Figure 8: Force level LFdepending on both load and resonance ratio unmodified gear Figure 9: Force level LFdepending on both load and resonance ratio modified gear Figures 8 and 9 illustrate the influence of modifications depending on the load and on the running speed. In this 4case the modific
37、ation was designed for approximately 40% of the nominal load and for a running speed corresponding to a resonance ratio N=0.75. While in the specific operating point the force level could be reduced significantly in other operating ranges the force level increases. A few recommendations: To determin
38、e the main gear data the modifications have to be considered already. In the calculation possible production deviations have to be considered also - the feedback from the production to the design department is essential. The determination of the natural gear frequency is elementary. Constant operati
39、ng conditions make the design of a noise optimized tooth modification easier, variable load and speed conditions make it more difficult. If a gear is operated over a large load range an integer overlap ratio can be recommended for load carrying capacity reasons. The gears with integer overlap ratio
40、should be modified as little as possible, otherwise the basic dynamic advantage of the constant contact line would not be realized. Generally, a high transverse contact ratio can be recommended. The basic feature of the modern gear calculation programs is the exact determination of the mesh stiffnes
41、s which influences the dynamic behavior in the under critical speed range. All the secondary influences like shaft bending and deflection in the bearings have also to be considered. For the load distribution calculation a static view is often sufficient. The dynamic analysis is much more complicated
42、 and requires a much higher calculation accuracy. Numerical simulations lead often to complex modifications which can not be realized with normal standard modifications like crowning and root or tip relief. Topological modifications are required. Noise optimization: Many companies have discovered th
43、e high improvement potential of topological modifications: Gears can be modified only where they need to be modified. The generating engagement relief of a helical gear corresponds to the normal tip and root relief of a spur gear. With the generating engagement relief, the teeth are modified in the
44、area of highest pressure (at the beginning and at the end of the mesh). Contact areas with lower Hertzian pressure can transmit more load. Topological modifications show substantial advantages for noise and vibration behavior also due to the much higher variability in direction of contact pattern. U
45、nfortunately a load optimized tooth flank modification is not always a noise optimized modification; a compromise between optimized load distribution and low noise has to be found. For the following, real gear transmission the method and the possibilities for a noise optimization of the tooth flank
46、modifications are shown. The basic gear data of the gear stage of interest are shown in table 1. gear stage center distance a mm 435 helix angle degrees 17 normal module mnmm 4,0 ratio i - 169/36 contact ratio- 1,93 overlap ratio - 3,0 Table 1: main gear data The drive is a multi stage industrial ge
47、ar transmission in which the high speed gear needs a special optimization. Due to the main gear data, the gear stage with high contact ratio and integral overlap ratio should have low dynamic response in the first mesh order. In the actual case with tooth modifications the tonal levels exceed the re
48、quired limits. Figure 10 shows the results of a sound intensity measurement by maximum load. The higher level of the first harmonic can easily be distinguished. Figure 10: Sound intensity measurement results of the original gear transmission (gear mesh frequency approx. 900 Hz) To exclude a natural
49、frequency problem the running speed is compared with the natural frequency of the system. With a relative resonance ratio of N=0,3 a under critical running speed can be assumed. 5Figure 11: Comparison of the original and the optimized modifications and the corresponding load carrying calculation results In the optimization of the modification the load carrying capacity can not be neglected. Figure 11 shows a comparison between the classic original modification and the optimized one. Many calculation va
