The effect of the teeth profile shape on polymer gear pair properties

U radu se predstavlja opsežno istraživanje dviju različitih geometrija boka zuba t.j. evolventnih i S-zupčanika. Zapažena je značajna razlika između te dvije analizirane geometrije tijekom ispitivanja njihovog vijeka trajanja. Ispitivanja su provedena na posebnoj opremi za ispitivanje s udaljenošću vratila od 20 mm. Materijal ispitivanih zupčanika bio je POM za pogonski zupčanik i PA6 za pogonjeni zupčanik. Rabljene su iste veličine pogonskog i pogonjenog zupčanika (m = 1 mm, z = 20). Zupčanici te veličine su naročito pogodni za mikro zupčanični prijenos. Ispitivanja su provedena uz različite brzine vrtnje i okretne momente, između 0,8 N·m i 1,5 N·m. Tijekom ispitivanja toplinskom se kamerom mjerilo toplinsko stanje zupčanika. Analize naprezanja i deformacije ispitivanih zupčanika provedene su numeričkom simulacijom primjenom metode konačnih elemenata.The paper presents an extensive research on two different tooth-flank geometries, i.e. involute and S-gears. A significant difference between the two analyzed geometries was observed during the lifetime testing. The tests were conducted on special test equipment with an axis distance of 20 mm. The material used for the tested gears was POM for the driver gear and PA6 for the driven gear. The same sizes of driver and driven gears were used (m = 1 mm, z = 20). Gears of this size are particularly suitable for micro-gear transmissions. The tests were carried out using different rotational speeds and torques, between 0,8 N·m and 1,5 N·m. During testing the thermal state of the gears was measured with a thermal camera. The stress and deformation analyses of the tested gears were undertaken using numerical simulations employing the finite-element method

Effect of process parameters on the crystallinity and geometric quality of injection molded polymer gears and the resulting stress state during gear operation

The quality of gear manufacturing significantly influences the way load is distributed in meshing gears. Despite this being well-known from practical experience, gear quality effects were never systematically characterized for polymer gears in a manner able to account for them in a standard calculation process. The present study employs a novel combination of numerical and experimental methods, leading to a successful determination of these effects. The findings of the study enhance existing gear design models and contribute to a more optimized polymer gear design. The study first explores the effect of injection-molding parameters on the gear quality and secondly the effect of resulting gear quality on the stress conditions in a polymer gear pair. For the gear sample production, different combinations of process parameters were investigated, and a classic injection-molding and the Variotherm process were utilized. Gear quality and crystallinity measurements were conducted for all produced gears, providing insights into the correlation between them. Based on the evaluated gear quality of produced samples, the effect of gear quality was further studied by numerical means within a meaningful range of quality grades and transmitted loads. Special attention was dedicated to lead and pitch deviations, which were found to exert a noteworthy influence on the stress state (both root and flank) of the gear. The effect of lead deviation was most pronounced when improving the gear quality from grade Q12 to grade Q10 (30% to 80% stress reduction, depending on the load). However, enhancing the quality grade from Q10 to Q8 yielded less improvement (5% to 20% stress reduction, depending on the load). A similar pattern was evident also for pitch deviations

Engineering design of polymer gears with S form of teeth

V doktorskem delu je obravnavana problematika konstruiranja polimernih zobnikov. Predlagan je model za preračun polimernih zobnikov s progresivno ukrivljeno ubirnico, t. i. S-ozobjem. Pri postavitvi modela za S-ozobje smo izhajali iz uveljavljenih modelov za preračun kovinskih in polimernih zobnikov z evolventnim ozobjem. Ti modeli so bili dopolnjeni tako, da omogočajo dimenzioniranje zobnikov s S-ozobjem. Model zajema kontrolni preračun temperature pri obratovanju in kontrolo korenske in bočne trdnosti. Specifični vplivi oblike S-ozobja na temperaturo pri obratovanju so bili okarakterizirani s preizkušanjem zobniških dvojic. Izvedenih je bilo večje število trajnostnih preizkusov polimernih zobniških dvojic, kjer smo merili temperaturo v ustaljenem stanju. Testirane materialne kombinacije pogonskega in gnanega zobnika so bile POM/PA66, POM/POM, jeklo/POM, jeklo/PA66, jeklo/PEEK in jeklo/PA6.10. Vpliv specifične oblike profila zoba na korensko in bočno trdnost je v modelu za dimenzioniranje upoštevan z vplivnimi koeficienti, ki so bili določeni s pomočjo sistematičnega izvajanja numeričnih simulacij. Model za trdnostni preračun je dopolnjen s koeficienti, ki upoštevajo vpliv izdelovalnih natančnosti razdelka in bočne slednice, na napetostno stanje v zobniku. Določena je bila tudi dinamična korenska trdnost za testirane polimerne materiale.The doctoral thesis deals with the problem of designing polymer gears. A model for the conversion of polymer gears with a progressively curved path of contact, i.e. S-gears, was proposed. The basis of the proposed model are the established models for the conversion of metal and polymer gears with involute tooth form. These models have been complemented in the way that they enable a reliable design of polymer S-gears. The proposed model includes a temperature control calculation and fatigue control. Fatigue control includes root and flank load carrying capacity calculation. Specific effects of S-gears that affect the operating temperature were characterized with gear testing. A large number of life time tests were performed, where the steady state operating temperature was measured. Material combinations POM/PA66, POM/POM, steel/POM, steel/PA66, steel/PEEK and steel/PA6.10 were tested. The influence of the specific tooth shape on the root and flank strength is taken into account with shape factors, which were defined by employing a series of numerical simulations. The load capacity calculation model is complemented with influencial factors, which take into account the effect of pitch and lead deviation on the stress state of the gear. Fatigue strength of tested polymer materials was determined

A method for enhanced polymer spur gear inspection based on 3D optical metrology

Accurately manufactured gears require a reliable, holistic, and fast inspection method. Standardised geometrical parameters enable a consistent and regulated inspection of gearshowever, current inspection methods include only a limited set of measurements for gears at specific locations. Therefore, a method to obtain holistic three-dimensional (3D) measurements with an optical inspection was thoroughly investigated. The measurement data were acquired via 3D optical scanning. The data were then processed and evaluated using the developed software. This was first tested on a simulated scan of an ideal shape with different mesh resolutions and subsequently on a simulated scan with synthetic deviations. The method was finally validated by measuring the gears using a coordinate-measuring machinethe results obtained were compared with those obtained using the developed optical method. A good agreement between the methods was observed. The optical method offers a more holistic measurement approach with many important advantages being identified compared with the tactile method

Tooth bending strength of gears with a progressive curved path of contact

The article presents a comprehensive study on the tooth bending strength of spur gears with a progressive curved path of contact, or so-called S-gears. Systematic gear meshing simulations were conducted to study the effects of S-gear geometry parameters on tooth bending strength. Different S-gear geometries were analysed in a systematically organized manner, and a comparison was made against a standard 20° pressure angle involute shape. Furthermore, different material combinations, e.g. polymer/polymer, steel/polymer, and steel/steel, of both drive and driven gear were analysed within a meaningful range of loads. The gear profile shape, material combination of the drive and the driven gear, and the transmitted load were found as the main parameters affecting gear tooth bending stress. Complex, non-linear relations between the recognized effects and the corresponding root stress were observed. Based on the numerical results, a shape factor, which considers the above-mentioned effects, was introduced, and a model for root strength control of S-gears was proposed and verified employing the finite element method (FEM)

Tooth bending strength of gears with a progressive curved path of contact

The article presents a comprehensive study on the tooth bending strength of spur gears with a progressive curved path of contact, or so-called S-gears. Systematic gear meshing simulations were conducted to study the effects of S-gear geometry parameters on tooth bending strength. Different S-gear geometries were analysed in a systematically organized manner, and a comparison was made against a standard 20° pressure angle involute shape. Furthermore, different material combinations, e.g. polymer/polymer, steel/polymer, and steel/steel, of both drive and driven gear were analysed within a meaningful range of loads. The gear profile shape, material combination of the drive and the driven gear, and the transmitted load were found as the main parameters affecting gear tooth bending stress. Complex, non-linear relations between the recognized effects and the corresponding root stress were observed. Based on the numerical results, a shape factor, which considers the above-mentioned effects, was introduced, and a model for root strength control of S-gears was proposed and verified employing the finite element method (FEM)

An investigation on the potential of bio-based polymers for use in polymer gear transmissions

The potential for replacing the fossil-based Polyoxymethylene (POM) and Polyamide 66 (PA 66) in polymer gear applications with a bio-based Polyamide 6.10 (PA 6.10) was studied and is presented in the article. The use of bio-based plastics is increasing but mostly in undemanding applications like packaging. High-performance plastics are needed in polymer gear transmissions since their operational conditions are far more severe. The potential of bio-based PA 6.10 was studied by means of gear lifespan testing. Additional insights into the process of polymer gear meshing were garnered by simulating all the tested cases with a FEM model of meshing gears. Test gears were manufactured from commercially available materials, making the results useful for gear designers. Encouraging results were observed since the PA 6.10 gears exhibited a 3.5-times longer lifespan than POM gears and a 10-times longer lifespan than PA 66 gears when tested under identical test conditions. The results indicate great potential for replacing fossil-based plastics in polymer gear applications with bio-based polymer materials. The fatigue strength, coefficient of friction, and wear coefficient were determined and compared for the tested materials, facilitating the reliable design of polymer gears

Machine learning based nominal root stress calculation model for gears with a progressive curved path of contact

The study aims to investigate the possibility of employing machine learning models in the design of non-involute gears. Such a model would be useful for design calculations of non-standard gears, where there are no available guidelines. The aim is to create a decision-support model accompanying the Finite Element Method (FEM) simulations, from which the data for training was collected. Multiple models for numerical prediction were tested, i.e. linear regression, Support Vector Machine, K-nearest neighbour, neural network, AdaBoost, and random forest. The models were firstly validated with N-fold cross-validation. Further validation was done with new FEM simulations. The results from the simulations and the models were in good agreement. The best-performing ones were random forest and AdaBoost. Based on the validation results, a machine learning constructed model for calculating nominal root stress in gears with a progressive curved path of contact is proposed. The model can be used as an alternative to FEM simulations for determining the nominal root stress in real-time, and is able to calculate the stress for gears with different number of teeth, widths, modules, paths of contact, materials, and loads. Therefore, many combinations of gear geometries can be analysed and the most suitable can be chosen

Durability and design parameters of a steel/PEEK gear pair

The parameters necessary for the reliable design of PEEK gears were determined. The effect of a steel gear\u27s surface on the polymer gear\u27s wear was investigated. Values for the wear coefficient of a steel/PEEK gear pair in dry and lubricated conditions are proposed. Testing showed that, on average, grease lubrication extends the lifespan of PEEK gears by a factor of 1.23, while the additional treatment of steel gears with trovalisation and lubrication extends the lifespan by a factor of 2.54. Temperature measurements were used to determine the coefficient of friction that is required to compute the operating temperature of a steel/PEEK gear pair. Using numerical simulations it was found that a proper tooth tip relief can improve the meshing and results in a further extension of the gear\u27s lifespan