Acta Polytechnica doi:10.14311/AP.2017.57.0316 Acta Polytechnica 57(5):316–320, 2017 © Czech Technical University in Prague, 2017 available online at http://ojs.cvut.cz/ojs/index.php/ap STRENGTH AND DYNAMIC ANALYSIS OF A STRUCTURAL NODE LIMITING THE MULTI-OUTPUT GEAR MECHANISM Mária Kačalováa, ∗, Slavko Pavlenkob a Department of Technological Systems Design, Bayerova 1, 080 01 Prešov, Slovak Republic b Faculty of Manufacturing Technologies, Bayerova 1, Prešov 080 01, Slovak Republic ∗ corresponding author: maria.kacalova@tuke.sk Abstract. The rapidly advancing technological development leads to designing and researching a new multi- output gear mechanism. The investigated new double-output gear mechanism has two output coaxial shafts located against the input shaft on the other side of the gearbox. The gear mechanism achieves high gear ratios. Its limiting structural node is the output stage, to which the gears belong. The problem is addressed through the analysis of the stress resistance of tooth flanks in contact and bending. The content of the paper is a comparison of analytical computations with the modal analysis on the model. We expect that new findings will be beneficial for further optimization of the gear mechanism. Keywords: double-output gear mechanism; gears; strength and dynamic analysis. 1. Introduction From continuing trends of current developments, it is believed that in the 21st century, there will be a rise in production to meet higher customer de- mands for products. It puts a strain on the flex- ible response to customer requirements, and also on the construction machinery of the manufactur- ing technology that is related to the concept with the required technical parameters. In the develop- ment process, you can include the search for new principles of construction of the gear mechanism. It has been developed with efforts to increase the carrying capacity and lifespan, with the possibility of creating a gear mechanism with a wide range of gear ratios with one or multiple outputs. The nearest area of the current state of the principles of comparability solutions and possibilities of ap- plication in production engineering have been cho- sen high-precision gears. The term “high-precision gears” or “gears of high accuracy” have been in- vented by producers of their respective products. The producer declared a high accuracy of the transfer of their characteristic precision. In this regard, it should be noted that this kind of reducers has a relatively short history of development and imple- mentation. Currently, the world’s leading compa- nies producing these reducers include Japanese com- pany Tein Seiki, Sumitomo Cyclo and Harmonic Drive. High-precision gears are predestined for ap- plications in machinery and equipment, which re- quire virtually zero clearance, high positioning ac- curacy and repeatability of accomplishing its high stiffness with the requirement of a higher gear ra- tio. Figure 1. Functional model of double-output gear mechanism 2. Materials and methods The Department of Technical Systems design on Fac- ulty of Manufacturing Technologies in Prešov of the Technical University in Košice has designed the high- precision gears multi-output transmission gear mech- anism shown in Figure 1, Designed from an existing utility model number 3937 Harmonic double-output gear mechanism, authors: Ing. Jozef Haľko, PhD., prof. Ing. Vladimír Klimo, CSc. The gear mechanism achieves small and large ratios at the same time. The limiting output stage is a hollow shaft with an internal gearing at the end that needs an investigation from the strength and dynamics point of view. Figure 2 shows the basic scheme of a double-output gear mechanism that has two output coaxial shafts II and III located against the input shaft I on the other side of the gearbox. The output stage of the double-output gear mechanism shown in Figure 2 under number II was researched. 316 http://dx.doi.org/10.14311/AP.2017.57.0316 http://ojs.cvut.cz/ojs/index.php/ap vol. 57 no. 5/2017 Analysis of Structural Node Limiting Multi-Output Gear Mechanism Figure 2. Principal scheme of double-output gear mechanism: I – input shaft, II – output shaft, III – output shaft, S – central axis, E – eccentricity, z1–z6 – numbers of teeth, 1 – frame, 2 – gear wheel Figure 3. Output stage of gear mechanism Diameter Hertz pressure under ideal load Coefficient of the additional forces Hertz allowable pressure Hertz stress in contact d [mm] σHO [MPa] kH [–] σhp [MPa] σH [MPa] Gear 101 180.41 2.486 281.15 284.46 Pinion 101 99.52 2.486 281.15 156.91 Table 1. The results of strength analysis for fatigue in contact. Circumferential force corresponding to the first degree of load Allowable stress in contact Maximum load Coefficient of the dynamic external forces Hertz stress in contact Ft1 [N] σHP,max [MPa] σH,max [MPa] kAS [–] σH [MPa] Gear 3376.7 620 348.39 1.5 284.46 Pinion 419.69 620 192.17 1.5 156.91 Table 2. The results of strength analysis for disposable load in contact. 2.1. Strength analysis of the output stage The output stage shown in Figure 3 is the most stressed and loaded with high torques. It is a hol- low shaft with an internal gearing at the end. This internal gearing has been analysed by a strength anal- ysis. Strength analysis was performed on the gear: • fatigue in contact Table 1; • disposable load in contact Table 2; • bending fatigue Table 3; • disposable retraced bending Table 4. Strength calculations of the investigated gear were carried out according to the standard STN 01 4686 based on the basic input parameters for a given gear. 2.2. Dynamic analysis of the output stage The output stage of the gear mechanism shown in Fig- ure 3 was analysed by a dynamic analysis for fatigue. The following condition have to be fulfilled: kc < k, where kc is the minimum dynamic safety and k is the overall safety margin. While the minimum dynamic safety for a less accu- rate calculation without any experimental verification is kc = 1.5–1.8. The overall safety margin is calculated as: k = kσ · kτ√ k2σ · k2τ , (1) where kτ is a safety against a fatigue failure under a torsion loading and kσ is a safety against a fatigue failure under a bending stress. 2.3. Modal analysis of the output stage A modal analysis method can solve many technical problems encountered in the design, manufacture and operation of mechanical systems or parts. In this 317 Mária Kačalová, Slavko Pavlenko Acta Polytechnica Coefficient of the additional load Bending stresses in the dangerous section of dedendum Permissible bending stress Safety factor against fatigue fracture in the dedendum kF [–] σF [MPa] σFP [MPa] SF,min [–] Gear 2.465 260.71 254.29 1.4 Pinion 2.465 33.74 254.29 1.4 Table 3. The results of strength analysis for bending fatigue. The biggest local bending stresses in the dedendum Permissible bending stress at maximum load Bending stress at maximum load σF,max [MPa] σFP,max [MPa] σF,St [MPa] Gear 391.07 712 890 Pinion 50.06 712 890 Table 4. The results of strength analysis for disposable retracted bending. Figure 4. Finite element mesh created on the model of the output stage. A B kσ 5.23 9.79 kτ 21.25 23.34 k 5.08 9.03 Table 5. The results of dynamic analysis of output stage. work the Finite Element Method (FEM), which is a frequently used numerical method, was used. The analysed output stage of the double-output gear mech- anism has been created in ANSYS Workbench 14.5. The calculation model was created with the defined ex- act geometry, high-quality finite element mesh model and a corresponding load. Figure 4 shows the fi- nite element mesh of the output stage of the double- output gear mechanism, and the Figures 5 and 6 show the stress in the meshing of the mating teeth. On the wheel, the maximum tension value 335.66 MPa is reached at the point of contact with the teeth and the maximum tension value reached on the pinion is 187.50 MPa. 3. Discussion Using a finite element method on the output stage of the double-output gear mechanism, it has been found out that the greatest stress 335.66 MPa is on the wheel gear, opposed to 187.50 Pa on the pinion. The an- alytical solution values of the tension calculated for the wheel and pinion are 284.46 MPa and 156.91 MPa respectively. The verification of the results of the calculated values of the tension differs from the values generated by the ANSYS analysis. Probably due to rounding of the results and the distribution of the fi- nite element mesh. The finite element method (FEA) is widely used to optimize the gearing. Workplaces, such as Collage of Information and Control Engineer- ing in China, Department of Mechanical Engineering, Curtin University, Bentle & Western Australia, also use this method in their work. In a similar way, by comparing calculated and generated values, the School of Mechanical Engineering, Department of Design and Automation, University, Vellore, Tamil Nadu, India followed these principles. They used this experiment to analyse the gear system for the turboshaft aero engine reduction gearbox. 318 vol. 57 no. 5/2017 Analysis of Structural Node Limiting Multi-Output Gear Mechanism Figure 5. Analysis of pinion teeth at contact. Figure 6. Analysis of the gear at the point of contact of teeth. 4. Conlusion The main task of this paper was to find the limit states of the output stage of the double-output gear mechanism. Based on these results, we can continue to optimize the entire double-output gear mechanism. The authors will continue their work in research, de- velopment, testing and diagnosis of these newly devel- oped transmission mechanisms at the Department of Technical Systems Design, Faculty of Manufacturing Technologies. We can say that the Finite element method (FEA) is a reliable method for optimizing in- dividual parts of the gear mechanism as well as other components of the manufacturing technologies. References [1] J. Haľko, V. Klimo. Dvojstupňový viacvytupový harmonický prevod, Úžitkový vzor zaregistrovaný Úradom priemyselného vlastníctva SR č. 3937, 2004. [2] J. Haľko, I. Vojtko. Simulácia prevodovky vo virtuálnom prostredí. Acta Mechanica Slovaca, roc. 11, c. 4-A, s. 89-94, ISSN 1335-2393, 2007. [3] J. 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ISSN 16609336, 2014. 320 Acta Polytechnica 57(5):316–320, 2017 1 Introduction 2 Materials and methods 2.1 Strength analysis of the output stage 2.2 Dynamic analysis of the output stage 2.3 Modal analysis of the output stage 3 Discussion 4 Conlusion References