We present the fifth contributed volume on the theory and practice of gearing and transmissions within the MMS series. This book traditionally unites publications of gear scientists from Belarus, Bulgaria, China, Germany, Italy, Japan, Kazakhstan, Russia, and Spain. As time has shown, this gearing series with such a vast geography contributes to the popularization of both the mechanisms and machine science, in general, and its component gearing science, in particular.
The series of contributed volumes on gearing and transmissions was initiated in 2014 by Prof. Marco Ceccarelli and implemented by Prof. Veniamin Goldfarb (1941-2019) and his followers in the scientific school "Institute of Mechanics" at Kalashnikov Izhevsk State Technical University. This activity is supported by Small Innovative Enterprise "Mechanik" (Izhevsk, Russia). In 2024 the Institute of Mechanics named after Professor Veniamin Goldfarb celebrated its 30th anniversary and the Small Innovative Enterprise "Mechanik" celebrated its 25th anniversary. Institute of Mechanics named after Professor Veniamin Goldfarb is one of the leading national scientific schools in the field of gears, a leader in Russia and abroad in the study, development, and implementation of worm-type gears and gearboxes in various engineering fields. Six Dr. Sc. in Engineering and more than 20 Ph.D. graduates have been raised there and involved in its activity in different periods. Among the most significant international achievements of Izhevsk scientific school on gears are cooperation of Russian and foreign scientists and specialists in the field of gearing and gearbox engineering, organization and holding of scientific and practical conferences and symposia at national and international level "Theory and practice of gearing and gearbox engineering" in Izhevsk State Technical University in 1993, 1994, 1996, 1998, 2001, 2004, 2008, 2014, 2017, 2021, 2024; active international activities within the framework of ISO and IFToMM (Technical Committee on Gearing); publication of the international bilingual journal "Gearing and Transmissions" (1991-2004); organization of the First International Student Olympiad on the Theory of Mechanisms and Machines (Izhevsk, 2011); and development and maintenance of a specialized website about gears ogears.ru with the history of the scientific branch development, personalities, current events, and library. The scientific school "Institute of Mechanics named after Professor Veniamin Goldfarb" is inextricably and mutually connected with the scientific, innovative, and implementation activities of the Small Innovative Enterprise "Mechanik". It is the largest Russian manufacturer of various types of gearboxes, in particular, for control of pipeline valves, with the full set of modern equipment and tools for design, research, production, testing, and control of gears and gearboxes. So, a part of the contributions in this volume is authored by the staff of these two organizations focusing on results of long-term studies of various issues of design, engineering, testing, implementation, and series production of gears and gearboxes.
The reader familiar with the previous books on gears will also find relevant themes that, in essence, continue the work previously done by the authors of the contributed volumes to follow and assess their further achieved development. We would like to greet traditional and new issues discussed in the present book related to various types of gears, their geometry, analysis, progressive methods of their heat treatment, and so on. The editors also applaud to the outstanding historical review resulting in the handbook of machinery with geared systems that circulate since Renaissance.
By tradition, we want to express our deep gratitude to Springer publishers, especially to the chief editor of the MMS series Prof. Marco Ceccarelli for the constant support of this series of books.

1 Wear Simulation of Tooth Profile During Gear Operation 1

Akio Ueda and Masakazu Nakasako

2 Methodology for Calculation of Contact Loading Meshing Spur and Barrel-Shaped Teeth Gears in the Presence of a Skew Angle 41

Vladimir Syzrantsev

3 Analysis of the Possibility of Manufacturing Loaded Gears from Structural Steels with Subsequent Laser Hardening 57

Mark M. Kane, Oleg G. Devoino, and Irina V. Shvets

4 An Early Handbook with Geared Machines at Renaissance Time 75

Marco Ceccarelli

5 Computer-Aided System SPDIAL+ for Design and Research of Worm-Type Gears 85

Evgeniy S. Trubachev

6 Analysis of the Teeth Constraints of Internal Spur Gears Considering Teeth Flexibility, Backlash Allowance, and Tip Relief 101

Jose I. Pedrero, Miguel Pleguezuelos, and Miryam B. Sanchez

7 Design of Gears with Involute-Bevel Gearwheels 117

Boris A. Lopatin, Svetlana V. Plotnikova, Dmitry B. Lopatin, and Viktor A. Plotnikov

8 Definable Adaptive Gear Differential 135

Konstantin Ivanov

9 Undercutting Phenomenon of Flat-Faced Worm Gearing 149

Yaoting Yu and Yaping Zhao

10 A New Approach to Estimation of Machine Parts Strength Reliability 167

Ksenia Syzrantseva and Alina Beloborodova

11 Geometrical Design Conditions for Feed Channels of Planetary-Rotor Hydraulic Machines 183

Gleb Yu. Volkov, Denis V. Fadyushin, and Yulia V. Alekseeva

12 Mathematical Modelling Oriented to the Synthesis of Globoid Worm Gears of Type Wildhaber 195

Emilia Abadjieva and Valentin Abadjiev

13 Some Results of Physical Modeling of Point Contact in Steel Spiroid Gears 213

Evgeniy S. Trubachev, Valery N. Anferov, Andrey S. Kuznetsov, and Aleksandr S. Korobeinikov

14 Toothed Mechanisms as Objects of Structural Analysis in MMS Study Course 231

Eduard G. Krylov

15 Residual Stresses Determination in Gear Teeth Subsurface Layers 243

Michael Storchak

16 Analysis of the Arc Teeth Self-Adjusting Cylindrical Gear 257

Vladimir Syzrantsev and Aleksandr Starikov

17 Design and Technological Preproduction of Straight Bevel Gears with Forged Teeth 277

Andrey E. Volkov and Sergey S. Biryukov

18 Machining of Worm Threads by Face-Type Tool 293

Evgeniy S. Trubachev, Kirill V. Bogdanov, Anton A. Mitroshin, and Gleb K. Grigoryev

19 Developing a Computerized Model for the Longitudinal Localization of a Straight Bevel Gear with a Small Shaft Angle with a Non-generated Gear and a Generated Pinion 309

Andrey Pazyak and Vladimir Syzrantsev

20 Design and Experimental Testing of a Planetary Gear Drive for Space Purposes 327

Gani Sergazin and Balzhan Bakhtiyar

21 Control of Automated Manufacturing Operations for Tooth Cutting by Running-In Cutter Heads 337

Kirill V. Bogdanov and Tatiana A. Pushkareva

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