Development of Custom Gear Design and Modelling Software Solution

Transcription

1 Development of Custom Gear Design and Modelling Software Solution Robert Basan*, Marina Franulović and Božidar Križan Department of Mechanical Engineering Design Faculty of Engineering, University in Rijeka Republic of Croatia Although significant number of commercial software packages for calculation, analysis and design of wide variety of mechanical elements are available today, development of own, custom software solutions remains very important. Usualy in the framework of scientific work, custom applications with novel techniques and solutions get developed but often remain in form which is unsuitable for wider, practical use. Additional development of user-friendly environment, user-interface and necessary documentation often reveals itself to be the critical step in achieving wider acceptance of such tools and solutions. Such custom developed solutions offer good control over implemented methodology and procedures and the way calculations are performed, greater flexibility and easy subsequent implementation of neccessary improvements and modifications. An example of own, customdeveloped software application for gear design and modelling with its possibilities and options is presented. Keywords: gear design, software, geometry, efficiency, load carrying capacity 1. Introduction With significant number of available commercial software packages for calculation, analysis and design of wide variety of mechanical elements, development of own, custom software solutions very often seems to be superfluous and unnecessary. There is always the question of time and effort which must be invested in development of such specialized computer applications. In certain cases - usualy in the framework of scientific work, when custom applications which implement novel techniques and solutions get developed, they often remain in "research" form which is highly unsuitable for widespread, practical use. Additional development of user-friendly environment, user-interface and necessary documentation which would make such solutions more widely applicable in industrial environment, often reveals itself to be the critical step. Despite the fact that commercially available, out-of-the-box-ready-to-use solutions are usually attractive and convenient to use, they very often have not so obvious, but serious deficiencies that the user should be aware of. One of the more dangerous down-sides to such solutions, especially when they are implemented in scientific work, is the fact that some of them incorporate certain simplifications which are sometimes omitted from the documentation. Such simplifications may be justified from the practical point of view but are unacceptable for highly specialized work in fields of research and development. In terms of such specialized applications, development of own, custom software solutions remains indispensable. Custom developed solutions offer good control over implemented methodology and procedures and the way calculations are performed, greater flexibility and easy subsequent implementation of neccessary improvements and modifications. As an example of custom-developed application, own software solution for gear design and modelling which is developed at Department of Mechanical Engineering Design which is part of Faculty of Engineering in Rijeka is presented. In its current version, Geargraph 3.0 incorporates different options for gears geometry definition and generation through accurate analytical procedures. Furthermore, detailed analytical calculations of tooth load distribution during the mesh, tip factor values according to various calculation methods as well as estimation of gear efficiency rating based on power losses due to sliding friction are also available. Geometry of every calculated gear can be modelled and previewed in desired level of accuracy and detail according to values given to the set of governing parameters. All calculated parameters can be saved for subsequent calculations. Gears' geometry can be

2 exported in formats suitable for use in CAD and/or software for structural numerical analysis later in the design process. Said application is constantly under development and new calculation methods and procedures are being added as certain research work at our Department progresses. 2. Gearing parameters and calculation of geometry Current version of the software supports calculation of geometrical parameters for standard (LCR) and non-standard (HCR) involute spur gears. As a method of gear profile generation, standard rack generation method in accordance with [1] and [2] standards can be chosen. In order to fully define gears geometry, a set of governing parameters of both basic profile and final gear pair must be given. This input is performed through the interface presented on Fig. 1. A number of checks are performed and bracketed values are calculated in order to prevent generation of faulty geometry. Fig. 1 Part of the program and its interface for input of gears basic geometrical parameters Apart from the number of parameters and values which are calculated according to well-known formulas and expressions, additional parameters which define generation of gears tooth profile comprising of set number of points, are also calculated. Procedure of generation of tooth profile simulates and closely follows actual generation process which is used in production of real gears. Basic principles and underlying mathematical expressions which are employed in calculation of points defining result-

3 ing gear profile are presented and explained in more detail in [3]. Afterwards, values of certain variables (transverse contact ratio and position of characteristic points along the path of contact etc.) calculated analyticaly and values acquired using generated geometry are compared and validated. 3. Tip factor values as indicators of tooth root stress level Employing gears effective tip factor Y FS values alone, level of relative tooth root stresses and their dependency on value of gears geometrical parameters can be estimated very quickly and efficiently. Due to the existence of number of said tip factors, attention must be paid so that compatible values are compared. Apart from the calculation of standard tip factors Y F which are well documented in national [4] and international [5] standards, non-standard calculation procedure [6] is also implemented in Geargraph 3.0 (Fig. 2). For this purpose, iterative method which searches for maximum value is used. Previously determined data of tooth root geometry (ie. points coordinates) are used. Maximum value of obtained effective tip factor Y FS, proves to be the relevant one when compared to the values calculated according to procedures given in [4] and [5]. Fig. 2 Calculation of various geometrical parameter and tip factor values according to different methods Tip factor values can be calculated, exported and then presented in form of a diagram for series of gear pairs (Fig. 3) which facilitates both their presentation and subsequent analysis and comparison. Y FS Method C [4] B [4] B [6] B mod [6] log (z 1 ) Fig. 3 Example diagram containig effective tip factors values calculated according to different methods

4 4. Tooth load distribution and sharing during the mesh In order to accurately determine values of loading which act on tooth during the mesh, the overall tooth deformation and deflection comprising tooth bending, tooth foundation deformation and local deformation in the vicinity of contact must be taken into account. Due to its non-regular shape, gear tooth can be regarded as non-uniform cantilever beam loaded with normal force in points which correspond to points of contact during the mesh. In this case tooth deflection depends on gears tooth geometry as well as on location on point of contact considered. Tooth also deflects due to the deformation of the material in fillet region and due to the foundation flexibility (for the case of thickrimmed gears). Local deformation of the material caused by the contact of two flanks is made up of Hertzian contact deformation and the compression of the tooth' material between contact point and the tooth centreline. For the calculation of mentioned components of tooth deflection and deformation, calculation procedure proposed in literature [7] is used. Due to the complexity of these calculations, a simplified, empiricaly based analytical calculation method proposed in [8] is also used. Although it offers somewhat reduced level of accuracy, information it provides is usually sufficient. For final calculation of values of total normal tooth force F bti in series of mesh points along the tooth flank procedure explained in [9] which was adapted to HCR-gears in [10] was used. Example of resulting load sharing history of the single gear teeth pair along with coordinates of characteristic points on path of contact and corresponding percentile values of F bti is shown on Fig. 4. Fig. 4 Change of total normal tooth force F bti along the path of contact for sample HCR gears gearing 5. Estimation of gears efficiency regarding sliding frictional losses during the mesh For achieving successful gearbox design, a number of design criteria must be satisfied (i.e. load capacity, power transmission efficiency, uniform torque transmission, low-noise and vibration emission). Efficiency with which power is transmitted in gearbox continuosly gains in importance and so does the ability to estimate its' level early in gears design process. Among power losses that occur in gearbox, the losses owing to gear meshing are directly related to gears geometry and are influenced by choice of various gearing parameters. Sliding friction losses are a consequence of the frictional forces which develop as two gear teeth slide across each other and they are most dominant at low and moderate velocities. For the purpose of comparing different spur gears regarding their sliding losses i.e. efficiency, the sliding friction loss geometrical factor G f0 has been introduced [11] and is, as such, implemented in presented software. In this way large number of gear pairs and combinations of their parameters can be compared and analyzed quickly and efficiently. On Fig. 5, a diagram representing values of the sliding friction loss geometrical factor G f0 calculated for sample gear pair which had its addendum modification coefficient x 1 and addendum modification coefficients sum x 1 +x 2 varied over certain range [12].

5 G f0 x 1 +x 2 x 1 Fig. 5 Calculated influence of x 1 and x 1 +x 2 on value of the sliding friction loss geometrical factor G f0 6. Calculations and determination of contact conditions and parameters during the mesh In order to determine multiple points of contact along the path of contact during the mesh, detailed geometry of mating teeth flanks has to be calculated. However, it is not sufficient to calculate mentioned geometry for each flank individually. Pairs of corresponding points must be formed so that additional parameters which characterize teeth contact and for which this relation is neccessary, can be calculated. In Geargraph 3.0, this can be done in folowing manner: by defining number or length of segments on tooth flank of each gear, by defining total number of segments along the line of contact Minor adjustments of given parameters are usually needed and are performed automatically since uniform distribution of segments on tooth flank is performed which is not possible for every given value. With recalculated number of segments on each flank, geometry of gear tooth is adjusted and is as such available for previewing (Fig. 6 and Fig. 7) and later, for eventual use in CAD/CAE software. Fig. 6 Tooth profile of pinion Fig. 7 Tooth profile of wheel

6 Value of coefficient of friction between contacting teeth flanks as well as state of strain/stress which is anticipated to take place can also be defined. After geometry of mating teeth flanks and contact points has been determined and the neccessary gear loading data given, values of stress components on and under teeth flanks can be calculated and evaluated. This calculation is possible for every point of contact so that evolution of stresses for any given point up to a reasonable depth can be found. Fig. 8 Program interface and options for characterisation of tooth contact during the mesh 7. Generation and export of gears geometry After all the calculations and check-ups of the gear pair and definition of geometry details, generated data can be prepared for export in order to be used in external CAD/CAE software. To do this, additional information such as number of teeth of pinion and wheel, their relative and absolute position and orientation must be inputed into the program by selecting and checking apropriate options. Auxiliary geometry as gearing axes, and different circles (base diameter, tooth tip diameter, root diameter, pitch diameter, etc.). Prior to export, generated gear pair can again be previewed and finally saved in desired file format (Fig. 9).

7 Fig. 9 Various options for previewing and exporting of generated gear geometry Geometry of sample HCR pinion and wheel which was generated with previous version of Geargraph is presented on figure 10. Upon export it was imported in CAD software, further modified and finaly meshed in software for FE structural analysis where it was used for nonlinear contact analysis of gears in mesh [13]. Fig. 10 Generated geometry and finite element mesh of sample HCR gear pair

8 8. Conclusion In this paper some of the most important arguments for development of own software were pointed out. As an example of such custom application, own software solution for gear design and modelling which is an ongoing project at Department of Mechanical Engineering Design at Faculty of Engineering in Rijeka is presented. In its current version it incorporates different options for gears' geometry definition and generation through accurate analytical procedure. Detailed analytical calculations of tooth load distribution during the mesh, tip factor values according to various methods as well as estimation of gear efficiency rating based on power losses due to sliding friction are also available. Geometry of every calculated gear can be modelled and previewed in desired level of accuracy and detail. All calculated parameters can be saved for subsequent calculations. Gears' geometry can be exported in formats suitable for use in CAD/CAE software later in the design process. 9. References [1] DIN 867-Standard, Bezugsprofile für Evolventenverzahnung an Stirnrädern (Zylinderrädern) für den allgemeinen Maschinenbau und den Schwermaschinenbau, Deutschland, [2] DIN 3972-Standard, Bezugsprofile von Vetzahnwerkzeugen für Evolventenverzahnung nach DIN 867, Deutschland, [3] OBSIEGER, B.: Analitički prikaz profila ozubljenja dobivenih odvaljivanjem proizvoljnog osnovnog profila, Svjetski simpozijum o zupčanicima i zupčastim prenosnicima, Zbornik radova Vol. A, Rad A-22, str , Dubrovnik Kupari [4] DIN 3990-Standard, Tragfaehigkeitsberechnung von Stirnraedern, Beuth-Verlag, Berlin, Deutschland, [5] ISO Standard, Calculation of tooth bending strength, International Organization for Standardization, Geneve, Switzerland, [6] OBSIEGER, J., OBSIEGER B.: Analitičko određivanje faktora oblika zuba evolventnog ozubljenja, Svjetski simpozijum o zupčanicima i zupčastim prenosnicima, Zbornik radova Vol. A, Rad A-23, str , Dubrovnik Kupari [7] WEBER C., BANASCHEK. K.: Formänderung und Profilrücknahme bei gerad- und schrägverzahnten Rädern, Schriftenreihe Antriebstechnik, Vieweg&Sohn, Braunschweig, [8] TERAUCHI, Y., NAGAMURA, K.: On Tooth Deflection Calculation and Profile Modification of Spur Gear Teeth, Proceedings of International Symposium on Gearing & Power Transmissions, Vol. II, pp C-27, , Tokyo [9] FRONIUS, S. : Maschinenelemente Antriebselemente, Berlin:Verlag Technik, [10] FRANULOVIĆ, M. : Influence of Base Pitch Deviation on Stresses in Involute Gearing (in Croatian), Master's thesis, Faculty of Engineering, University of Rijeka, Rijeka [11] KRIŽAN, B.: Contribution to the Research of Friction Losses in Involute Gear Mesh (in Croatian), Thesis, Faculty of Engineering, University of Rijeka, Rijeka [12] KRIŽAN B., BASAN R., LOVRIN N.: A Contribution to the Optimal Choice of the HCR-Gears Regarding Frictional Losses, International Journal of Applied Mechanics and Engineering, 2002, 7. [13] BASAN R., LOVRIN N., KRIŽAN B.: A Contribution to The Analytical Determination of Tooth Root Stresses in High Transverse Contact Ratio Gears, The Eleventh International Conference on Machine Design and Production, Conference Proceedings, Antalya : Middle East Technical University, Ankara, [14] Borland Delphi, User s Manual