Researches Regarding Determination of Sliding Velocity Between Two Xylan 1052-coated Homologous Flanks at Helical Gear Wheels ION-CORNEL MITULETU, ION VELA, GILBERT-RAINER GILLICH, DANIEL AMARIEI, MARIUS TUFOI Center of Advanced Research, Design and Technology CARDT Eftimie Murgu University of Resita Piata Traian Vuia 1-4, 320085, Resita ROMANIA i.mituletu@uem.ro, i.vela@uem.ro, gr.gillich@uem.ro, d.amariei@uem.ro, m.tufoi@uem.ro Abstract: - Sliding speed determination of helical wheels is required for load capacity analysis of Xylan 1052- coated helical gears. The actual paper presents a find-out modality of sliding velocity which manifests between two homologous flanks of helical wheels. Three rotational speeds, which are considered very important, were chosen to perform this investigation. In order of previously mentioned sliding velocity determination, a mathematical analysis method and a numerical motion analysis using Motion Study module of Solid Works software platform, were considered. The results have been compared and validated afterwards. Key-Words: - helical wheel, mathematical analysis, motion analysis, simulation, sliding velocity, teeth meshing, Xylan 1052-coated 1 Introduction Plastic-metal materials association in cylindrical toothed wheels construction has various forms: metal toothed wheel engaging plastic toothed wheel and plastic toothed wheel fixed to a metal shaft, plastic crown gear fixed to metal support and, more recently, a film coating made of stress resistive fluoropolymer material applied to the surface of a metal toothed wheel. Last version is a new concept used in manufacturing of cylindrical toothed wheels. This concept has been studied in terms of vibration damping and mechanical efficiency, results being encouraging. Fluoropolymerised toothed wheels behave like having a class processing accuracy which decreases from VIII to VI and improves its efficiency by 10% after latest performed experiments. Fluoropolymerisation treatment is equally applicable to new or used cylindrical gears. If standards provide detailed information about metallic materials, regarding plastics, standards are extremely poor in technical specifications and no experimental research reveal full results. In particular, Xylan 1052 is a fluoropolymer material that shows high stress contact and very low friction. Using manufacturing features of Xylan 1052- coating we defined material characteristics in Solid Works software platform. Permissible contact stress is about 343 N/mm 2 and coefficient of friction 0,2. Also, by coating teeth flank with Xylan 1052, other advantages can be obtained such as: better protection to corrosive agents, Xylan 1052-film can be used as wear-layer, Xylan 1052 can operate with poor or no lubrication, increasing class precision up to VI (related to DIN), can be applied with easy and is not expensive. Thickness of Xylan 1052-film is another significant advantage, each applied layer having 12 μm to 25 μm, meaning that the heat accumulated in fluoropolymer-film is very fast absorbed by metallic support of toothed wheel. In current research a film made by two superposed layers was investigated. Resulted film was approximately 47 μm thick. 2 Problem Formulation Testing on stand a gear equipped with such a pair of helical toothed wheels, it was observed that the flank surfaces wear appeared at the start and the end of meshing. Obviously, in those points sliding friction is higher than rolling friction. Pure rolling is achieved at pitch point, sliding increases along surface of flank and reaches maximum value at the end of meshing. Reciprocally, maximum sliding velocity appears at start of meshing, decreasing to the pitch point. ISBN: 978-1-61804-099-2 243
Figure 1 shows the gear pinion. Xylan 1052- coating film has a green color and gives the wheel a clean aspect. It is important to specify that the gear box contains lubrication oil. Gear was tested for 16 to 38 Nm torque and 500 at 1500 RPM. Testing time was established at one hour for each set of measurement values for torque and rotational speed. v S = v Q1 t - v Q2 t (3) v S = ρ 1 ω 1 - ρ 2 ω 2 (4) Fig.1. Toothed pinion with Xylan 1052-coating Starting from the idea that sliding velocity is very important in load capacity and wear study, two methods of determination were furthermore performed. 2.1 Mathematical analysis method In order to obtain accurate results on sliding velocity, a mathematical analysis method is described below. In Fig.2, K 1 K 2 - action line sector belongs to normal surface of flank teeth in contact point Q and in all successive meshing points between A and E, as well. Absolute velocity of the Q point: v Q1 = O 1 Q ω 1 si v Q2 = O 2 Q ω 2. For a correct meshing, velocity projection on normal have to be equal v Q1 n = v Q2 n, on the contrary, tangential components are different (v Q1 t v Q2 t ). Therefore, a relatively sliding appears. Tangential components: v Q1 t = K 1 Q ρ 1 = ρ 1 ω 1 (1) v Q2 t = K 2 Q ρ 2 = ρ 2 ω 2 (2) In K 1 and K 2 points, the tangential velocity components reach the maximum value. That means t that in C, v Q2 = v t Q2, relative sliding is zero. In all the other points along action line, the difference between velocity tangential components, v Q1 and v Q2, lead to a sliding velocity: Fig. 2 Analytic diagram r f root radius; r a tip radius; r w pitch radius; r linear pitch radius; r b base radius; ω 1,2 angular velocity for wheel (1) and (2); O 1,2 rotational axis for wheel (1) and (2); C pitch point; A to E path of action; K 1 K 2 - action line sector. Taking in consideration the fact that ρ 1 = K 1 C + CQ and ρ 2 = K 2 C - CQ and, also K 1 C ω 1 = K 2 C ω 2, the final analytical expression of sliding velocity can be calculated: v S = ± q (ω 1 + ω 2 ) (5) where: q = CQ. The (±) indicates that, sliding velocity changes sign in respect of pitch point action side. At the edges of action line, where the sliding velocity has maximum value, the gripping phenomena, due to wear action, could appear. Friction force changes the direction after the C-pitch point is reached. ISBN: 978-1-61804-099-2 244
2.1 Numerical motion analysis First two wheels were built-up with the following geometrical dimensions. Characteristics Pinion Driven Wheel α - pressure angle ( o ) 20 o 20 o β - helix angle ( o ) 9 o 9 o a - centre distance (mm) 125 125 m n - normal module (mm) 4 4 m t - frontal module (mm) 4.05 4.05 z 1/2 - teeth number 17 43 d a 1/2 - tip diameter (mm) 80.04 185.28 d 1/2 - pitch diameter (mm) 68.85 174.14 d f 1/2 - root diameter (mm) 61.73 166.9 d b 1/2 - base diameter (mm) 64.601 163.402 h 1/2 - tooth height (mm) 9.156 9.19 h a 1/2 /h f 1/2 - tip/root tooth height 5.6/3.56 5.57/3.62 h ny 1/2 - tooth height on cord 5.808 5.649 s ny 1/2 - tooth thickness on cord 7.679 7.668 j t 1/2 - gear backlash (mm) 0.15/0.27 0.15/0.27 The reference profiles / tolerances were made in accord to DIN 967 / DIN 3967 25 CD. The quality features according to DIN 3961-63 quality 8. Drawing helical wheels is not simple as it can be seen bellow, in figure 3, many features of SolidWorks platform have been used to result an accurate design performing. After the wheels were built, sustaining simple shafts were achieved. Second step consists in mates establishing. Concentric, coincident and gear mates were requested for accurate gear meshing accomplishing. The model was performed to reach all the geometrical and functional requirements of such a test. Fig. 3 Model of gear mashing 3 Problem Solution Once the maximum value for q-segment was geometrically determined and the value being verified by on-site measurements, the sliding velocity is easy to be calculated considering formula (5) given above. Table 1 indicates values for rotational speed of input shaft (n 1 ), calculated angular velocities of input (ω 1 ) and output (ω 2 ) shafts, resulted from mathematical method sliding velocity calculation (v s/m ) and achieved by numerical simulation sliding velocity (v s/s ). For q = 13.3 (mm), column 5 of table 1 shows the mathematical results. Table 1 n 1 (RPM) ω 1 ω 2 ω 1 + ω 2 v s/m (mm/s) v s/s (mm/s) 500 52.4 20.7 73.1 972.2 963.4 750 78.5 31 109.5 1456.3 1428.6 1000 104.7 41.4 146.1 1903.2 1897.2 1250 130.9 51.7 182.6 2428.6 2412.7 1500 157.1 62.1 219.2 2915.4 2892.9 ISBN: 978-1-61804-099-2 245
Fig. 4 Motion Analysis 500 RPM Performing Motion Analysis in Motion Study module of SolidWorks platform, accurate values for sliding velocities have resulted. It was attached a motor to the pinion and set at constant rotational speeds: 500, 750, 1000, 1250 and 1500. A resistive torque gives the contact stress between homologous flanks and keeps the permanent contact, as well. Testing time base was set at 0.5 s, enough to read the correct values. Results are set for sliding velocity in mm / s to time in seconds and are also presented as graphs. In figure 4 is indicated the characteristic evolution of sliding velocity along time axis, considering 500 RPM as input shaft. Figures 5 and 6, picture the characteristic diagrams afferent for 1000 and 1500 RPM. Fig. 6 Motion Analysis 1500 RPM Fig. 5 Motion Analysis 1000 RPM To see more accurate the difference between cases, the mathematical analysis and the numerical analysis, in figure 7 a graphic diagram of the results obtained was also performed. This graphical representation shows the small differences between the result sets. ISBN: 978-1-61804-099-2 246
Vs (mm/s) 3500 3000 2500 2000 1500 1000 500 0 Sliding Velocity 500 750 1000 1250 1500 n1 (RPM) Vs-mathematical Vs-numerical Fig. 7 Sliding velocity to RPM 4 Conclusion In load capacity and wear researches, sliding velocity takes an important place along with contact stress. In this paper performing two sets of methods, precise results for sliding velocity have been determined. As observed in figure 7, both methods reveal satisfying results and the results similarity underlines that they are correct and efficient. These values will be taken for further more consideration as well as the methods used in this research. In the same time, numerical algorithm can be modified to reach and determine different parametrical values, if these will show interest. References: [1] L. Andrei, G. Andrei, Al. Epureanu, N. Oancea, D. Walton, Numerical simulation and generation of curved face width gears, 20th International Danube Adria Association for Automation and Manufacturing Symposium, Int. J. Machine Tools Manufact., 2002. [2] G. R. Gillich, Gh. Samoilescu, F. Berinde, Experimental determination of the rubber dynamic rigidity and elasticity module by timefrequency measurements, Materiale Plastice, Vol. 44, No. 1, 2007, pp. 18-21. [3] G. R. Gillich, E. D. Birdeanu, N. Gillich, Detection of Damages in Simple Elements, 20th International Danube Adria Association for Automation and Manufacturing Symposium, Annals of DAAAM and Proceedings, Vol. 20, 2009, pp. 623-624. [4] G. Mogan, E. V. Buti, Expert System for the Total Design of Mechanical Systems with Gears, Product Engineering, Springer, 2004, pp. 143 162. [5] W. Seong-woo, M. Pecht e, Failure analysis and redesign of a helix upper dispenser, Elsevier Ltd., Vol. 15, 2008, pp. 642 653. [6] L. Tudose, O. Buiga, C. Stefanache, A. Sóbester, Automated optimal design of a twostage helical gear reducer, Struct Multidisc Optim, Springer-Verlag, Vol. 42, No. 1, 2010, pp. 429 435. ISBN: 978-1-61804-099-2 247