EES KISSsoft GmbH ++41 41 755 09 54 (Phone) P.O. Box 121 ++41 41 755 09 48 (Fax) Weid 10 ++41 79 372 64 89 (Mobile) 6313 Menzingen h.dinner@ees-kisssoft.ch Switzerland www.ees-kisssoft.ch Gear Optimisation for Reduced Noise Levels 1 Gear, shaft, bearing design for low noise transmissions 1.1 Executive summary While gear noise is not a topic to be covered in a single paper, effective strategies to reduce noise and vibration by optimized gear (macro and micro), shaft and bearing design are shown below. Reducing noise and vibration is most efficient if tackled at its source, that is, on the gear, shaft and bearing level. Proper design of gears and shaft-bearing systems ensures that the excitation of the transmission housing is minimized. The below mentioned strategies may be applied during an early design phase of the transmission, before detailed and time consuming investigation through e.g. FEM or multiphysics dynamic analysis are performed. This ensures that from the earliest possible stage in the transmission design, components are designed such that lowest possible noise level will be achieved on system level. 1.2 Permissible noise level, noise sources Limit noise levels in Europe for accelerated pass by along DIN ISO 362 as a function of time is shown below. It is obvious that demands on lower noise levels, despite continuously increasing vehicle mass and power have risen dramatically, see Table 1-1. Gear noise may be classified in five categories as shown in the table below. The order of the table reflects the importance of the respective category, see Table 1-2. Vehicle type 1970 [db] 1980 [db] 1990 [db] Since 1995 [db] Passenger car 82 80 77 74 LCV 84 81 78-79 76-77 Truck 89-91 86-88 81-84 77-80 Bus 89-91 82-85 80-83 78-80 Table 1-1 Permissible noise levels in Europe for different types of vehicles Category of noise Source Whining: Vibration of gears - meshing impact under load - transmission error - meshing noise Rattle: Vibration of - idler gears elements without load - synchronizer rings Clonking: Engagement of - gears elements with application of - joints load - shaft-hub connections Shifting noise Synchronizer gear noise in case of suboptimal working condition Bearing noise Noise from running bearings, e.g. in case of damaged bearings Table 1-2 Noise categories in order of relevance Public EES KISSsoft GmbH Weid 10 / P.O. Box 6313 Menzingen Switzerland www.ees-kisssoft.ch Title: SIAT EXPO 09 No.: Date: 21.1.09 Manager: HD Email: h.dinner@ees-kisssoft.ch Revision: 1 Autor: HD Date: 21.11.08 Approved: HD Date: 21.11.08 C:\Dokumente und Einstellungen\HD\Desktop\ARAI\SIAT-EXPO-09-EEES-KISSsoft-Rev-2.doc 1 of 10
1.3 KISSsoft and KISSsys KISSsoft: The KISSsoft design program was specifically developed for engineers and designers in the field of gearing and transmission development. It simplifies and accelerates the sizing, optimisation and rating of machine elements under the application of valid standards like ISO, DIN, AGMA, etc.. KISSsoft s versatility is used in the most different areas, such as, industrial gearboxes, fine pitch and plastic gearing, wind turbine gearboxes, energy production, automotive actuators and vehicle transmissions. Some sixty companies use KISSsoft specifically for vehicle transmission design while the worldwide overall user base exceeds 1300 installations. Users of KISSsoft design transmissions for - Motorcycles (including three wheelers) - Cars (MT, AT, DCT, ) - Racing (Formula 1, sports cars) - Commercial vehicles (trucks, buses, LCV) - Tractors (including CVT transmissions) - Defence (armoured personnel carriers, tracked tanks) - Components (differentials, wheel drives, axles, transfer cases) Standard packages for various areas form the basis of the extensive software. Expert add-ons to the standard packages expand the system there where needed. Refined sizing and optimization algorithms and most different interfaces to CAD platforms simplify the entire design process and guarantee obtaining the required component safety. Advanced level features for the transmission designer include bearing analysis considering inner geometry, gear micro geometry definition and load sharing analysis as well as transmission error calculation. Figure 1-1 Transmission error, gear geometry, shaft system in KISSsoft KISSsys: With KISSsys, a software commercially available since five years, the power flow in the power trains can be calculated and linked to a strength calculation of the power train s machine elements. It is thus possible to parameterize entire gearboxes / power trains and analyse them concerning strength and life time. Among other things, KISSsys allows the user to quickly carry out elaborate parameter studies of entire gearboxes / power trains and efficiently compare different design variants. KISSsys uses KISSsoft for the strength and lifetime calculation of the various machine elements. KISSsoft is a CAE software for a fast and secure sizing, optimization and verification of machine elements such as gear wheels, shafts, bearings, screws, shaft-hub connections and springs. KISSsoft is aimed at the user in the transmission construction area and is well known for its varied optimization possibilities. C:\Dokumente und Einstellungen\HD\Desktop\ARAI\SIAT-EXPO-09-EEES-KISSsoft-Rev-2.doc 2 of 10
Figure 1-2 Parallel shaft manual transmission modelled in KISSsys KISSsys, as system add-on to KISSsoft offers following features: Kinematics Calculation: power flow / speed with spur, bevel, worms and face gear stages, modelling of rotational mechanisms (planetary, Ravigneaux, Wolfrom, ), differentials, (with bevel or spur gears), chain and belt transmissions, couplings can be activated and deactivated, slippage taken into account, outer loads applied to the system taken into account. Integrated strength and lifetime calculation: to do this, KISSsys accesses KISSsoft, bearing stiffness, transmission error, profile modification, efficiencies. 3D-models: automatic 3D-display (based upon the data defined in KISSsoft), 3D-model export to CAD platforms, gearbox housing import, (-step / -iges), checking for collisions. Special features: calculations with load spectra for all machine elements in the model, different mechanisms variants in the same model, automatic documentation (proof of strength) for the entire mechanism integrated programming language for implementation of special functions Use of KISSsoft & KISSsys in the vehicle industry: KISSsoft and KISSsys are used in different areas of vehicle industry like - tractor - defence - automotive - two and three wheelers - commercial vehicles C:\Dokumente und Einstellungen\HD\Desktop\ARAI\SIAT-EXPO-09-EEES-KISSsoft-Rev-2.doc 3 of 10
Figure 1-3 Tractor transmission, armoured personel carrier drive line, front wheel drive, super sports car, double clutch transmission and automatic transmissions, all modelled in KISSsys. 2 Optimizing gear geometry 2.1 Number of teeth After having decided on a suitable centre distance for the transmission, selecting the appropriate number of teeth for a gear pair is a next, crucial step. An FEM modal analysis of the housing including its elastic support quickly yields critical frequencies. Comparing the meshing speeds with the natural frequencies of the housing allows for an efficient design of housing stiffness and mass distribution. Alternatively, changing the number of teeth (while maintaining centre distance and strength properties) to either side is possible as well. C:\Dokumente und Einstellungen\HD\Desktop\ARAI\SIAT-EXPO-09-EEES-KISSsoft-Rev-2.doc 4 of 10
Figure 2-1 Gear meshing frequency for engaged and idling gears, including harmonics, as a function of engine speed. Vertical red line indicates current operational speed. Example shown for a manual six speed transmission with reverse. In the below table, different solutions for a gear pairs with ration i=2.10 +-1.5%, a=70mm, P=40kW, constant face width and n1=2200rpm is shown. As shown below, the ratio between maximum to minimum number of teeth per gear allows for the meshing frequency to be moved by about 10% in either direction without affecting torque capacity. This is typically sufficient to place exciting and natural frequency apart to avoid excitation. z1max/z1min=19/16=1.19 Span= 1.19=1.09 z2max/z2min=40/34=1.18 Span= 1.18=1.09 Figure 2-2 Possible combinations of teeth number for a given design problem. While module and profile shift is varied, ratio and centre distances is maintained accurately. 2.2 Gear macro geometry 2.2.1 Module and helix angle Measurements prove that smaller module will result in lower noise level. Furthermore, higher helix angle will result into higher overlap contact ratio εβ, resulting in lower noise levels. The increase in transverse module due to helix angle compared to normal module is of lesser relevance. Typically, helix angle are designed such that εβ is larger than 1.00. In the figure below, different possible gearing solutions were found by variation of module, profile shift and number of teeth combinations., face width and centre distance were maintained for given values. It can be seen that for a required overlap contact ratio (horizontal axis), different mass of the gear set may result as a function of helix angle. For example, for a desire overlap ratio of εβ=2.00, some 5% in gear mass may be saved by choosing an optimum gear macro geometry (all solutions achieve the same required strength values). Note that with the Technical Corrigendum 1 of the ISO6336-2:2006, the influence of the helix angle on the flank strength has been modified. Zβ is now calculated as follows Zβ=1/ cosβ, resulting in considerably lower flank strength values for higher helix angles. C:\Dokumente und Einstellungen\HD\Desktop\ARAI\SIAT-EXPO-09-EEES-KISSsoft-Rev-2.doc 5 of 10
Figure 2-3 Gear mass for a required overlap ratio as a function of helix angle. Variation of gear macro geometry (module, profile shift, number of teeth). Explanation on above figure Vertical line: Overlap contact ratio εβ=2.00 Lower horizontal line: Mass of gearing solution No. 64, gear-set with lowest mass for εβ=2.00 Upper horizontal line: Mass of gearing solution No. 220, gear-set with highest mass for εβ=2.00 2.2.2 Tooth height The tooth height determines the contact ratio which is defined as AE:BD, which in turn is calculated considering gear geometry only, not considering load applied. Therefore while the contact ratio is an easy to calculate and understand value, it is not the best means to assess a mesh. More suitable is the transmission error, which does consider the deflection of the teeth, resulting in a higher contact ratio under load. Below, it is shown that in fact a transverse contact εα ratio slightly below 2.00, εα=1.90(61) results in a lower peak to peak transmission error compared to εα=2.00(05). C:\Dokumente und Einstellungen\HD\Desktop\ARAI\SIAT-EXPO-09-EEES-KISSsoft-Rev-2.doc 6 of 10
1.25/0.38/1.00 Transverse contact ratio 1.6052 1.40/0.20/1.20 Transverse contact ratio 1.9061 1.464/0.20/1.264 Transverse contact ratio 2.0005 Figure 2-4 Influence of tooth height on transverse contact (visualised as theoretical contact stiffness) ratio and transmission error 2.2.3 Profile shift Selecting the profile shift such that a lowest possible amount of sliding occurs is a highly efficient way to optimize gears in terms of high frequency noise. The below figure shows that even though an increased tooth height does lead to higher sliding speeds, the detrimental effect can easily be compensated by selecting an appropriate profile shift. 1.25/0.38/1.00, V-0 Gearing, x1*=0.00, x2*=0.00 1.25/0.38/1.00, Balanced specific sliding, x1*=0.27, x2*=-0.27 Figure 2-5 Specific sliding as a function of tooth height and profile shift. 2.3 Gear micro geometry 1.41/0.38/1.16, Balanced specific sliding, x1*=0.35, x2*=-0.35 2.3.1 Profile modifications Profile modifications like profile crowning, pressure angle correction, tip and root relief are applied to improve the load distribution (to decrease the lubricant film distress) and to reduce the impact at start of meshing. C:\Dokumente und Einstellungen\HD\Desktop\ARAI\SIAT-EXPO-09-EEES-KISSsoft-Rev-2.doc 7 of 10
Without profile correction Meshing shock is visible Short, linear tip relief of 45um Long, progressive tip relief of 45um. Highly regular curves Figure 2-6 Transmission error / meshing shock as a function of profile modification at tip of gears. 2.3.2 Gear quality One of the most critical issues in gear noise is gear quality, typically errors in the pitch. This error can be considered in the transmission error calculation as shown below. A typical gear pair as found in a vehicle transmission with a reference profile 1.40/0.20/1.20 is analysed in three conditions as described: It can be shown that the difference between condition 1 and condition 2 is minimal. However, it can be shown that condition 3 gives completely different results. Condition 1: No profile modification, not considering pitch error C:\Dokumente und Einstellungen\HD\Desktop\ARAI\SIAT-EXPO-09-EEES-KISSsoft-Rev-2.doc 8 of 10
Condition 2: Long, progressive tip relief, not considering pitch error. Peak to peak transmission error ( ) has somewhat increased. Condition 3: Long, progressive tip relief, considering pitch error based on DIN quality 6. The peak to peak transmission error ( ) has increased dramatically Figure 2-7 Transmission error and torque variation with / without modification, with / without pitch error 3 Optimising shaft systems 3.1 Vibration behavior of shaft systems For vehicle transmissions where gears are supported by needle bearing between the gear body and the shaft (see Figure 3-1), the tilting stiffness of the needle bearing may be a critical value for controlling natural modes where a single gear stage is excited in tilting (see right side of Figure 3-2). Gear body mass properties or bearing stiffness may be adjusted. Figure 3-1 Input shaft, five speeds, needle bearings. Shaft is driven from left side, supported by two taper roller bearings in X arrangement. Figure 3-2 Eigenmodes of shaft system (input shaft and five gears) as per left side of Figure 3-1 Left: 10th natural frequency: bending of shaft @ 1346Hz Middle: 7th nat. frequency: tilting, 5th speed gear (needle bearing 5th speed: d=30, D=34, b=29) @784Hz Middle: 7th nat. frequency: tilting, 3th speed gear (needle bearing 5th speed: d=30, D=45, b=30) @561Hz C:\Dokumente und Einstellungen\HD\Desktop\ARAI\SIAT-EXPO-09-EEES-KISSsoft-Rev-2.doc 9 of 10
The above shows that by adjusting bearing stiffness of the 5 th gear, the natural mode (tilting of 5 th gear) @ 784Hz could not be found anymore if calculated up to 5774Hz. Instead, the 7 th natural mode now became tilting of 3 rd gear instead @ 561Hz. This shows how unwanted natural modes / natural frequencies may easily be avoided as long as different bearing sizes may be used. 3.2 Bearing pre-tension Using a simple shaft system (see right side of Figure 3-1) containing a pilot bearing and two tapered roller bearing, the influence of the axial pre-tension of the tapered roller bearings can be shown. Figure 3-3 Shaft arrangement with pilot bearing. Calculation without bearing clearance. f3=209hz dy=0.05 (positive clearance in axial direction) f3=147hz dy=-0.05 (negative clearance in axial direction) f3=216hz Figure 3-4 3 rd natural frequency / bearing load distribution, as a function of bearing clearance. C:\Dokumente und Einstellungen\HD\Desktop\ARAI\SIAT-EXPO-09-EEES-KISSsoft-Rev-2.doc 10 of 10