The computer program GEAR is intended for design of toothed gears with flank pitch line (GEAR_PH with the pitch helix). This program allows a multi-criterion gear optimization with respect to various combinations of criteria (for example: minimal mass, minimal stress and maximal life). The program - through the suitable structure of criterial functions - provides optimum load distribution for individual pairs of gears. The use of efficient optimization procedures allows for effective search for the best solutions.

Due to the enormous number of parameters and factors necessary to perform the calculations, it was assumed that in almost all dialog boxes, the initial values are preliminarily set (proposed by the program). Of course, it is possible to change any of the initial values in the corresponding dialog box. The load values and optimization parameters could be modified by the user in appropriate dialog boxes. There would be also possibility to create animation of gearbox, with interactive view in virtual space and with possibility to watch the elements of gearbox in motion.

The user has to determine the structure of the gearbox, what is performed in a very simple manner. The structure data for each transmission must be saved, just by using the dialog box, under the full control of the program (no accidental input errors) and then, the initial data for the gears will be generated from the templates. There is also possibility to present in appropriate window the scheme of an analyzed gearbox, during the entering input data of the transmission structure.
Dialog box of gear structure
Gear structure and scheme
The software includes a module which allows setting initial parameters of toothed gears when a need to create new gearboxes arises. Particularly, the module adjusts the number of teeth to assumed number of gear ratios for all gears. Therefore, the initial gearbox design phase is significantly simpler. Adjustment of the number of teeth for a complex gearbox can be difficult because there is a great amount of available combinations. Thanks to this module, a user who wants to begin calculations of a gearbox only needs to define its structure and indicate gear ratios for individual gears.
Determination wheels parameters - start
Determination wheels parameters-calculations
Determination wheels parameters-results
Results of calculation
Depending on applied modifications to particular gear parameters, an appropriate type of a gear is generated (three types of a toothed gear have been assumed). Appropriate dialog box serves for modifying the type of a gear in a very convenient way. The modification automatically adjusts parameters of the gear. The software validates correctness of applied parameters on the stage of data preparation – verifies the possibility of creating actual toothed gear – and suggests automatic modification of data. A user can allow automatic data modification, can modify the data manually, or ignore the warning. During optimization, the software on each of the processing steps also checks the possibility of creating an actual toothed gear. If data generated by an optimization procedure do not fulfill the requirements, then such a procedure will not launch. As a result, the calculations take less time.

Calculations of the strength parameters are updated in accordance with the standard ISO 6336. Parameters: sigmaFlim - unlimited fatigue endurance of a tooth root and sigmaHlim - unlimited fatigue endurance of a tooth side were determined experimentally. Experiments were run on toothed gears made from five grades of carburising steel, finished by the two treatment methods: grinding and gear shaving. Within the software, it is possible to enter parameters for a given material and conduct respective calculations. Modification of a material results in immediate modification of all parameters of materials used in the given toothed gear. Moreover, selecting appropriate option in the dialog box allows setting similar parameters of materials applied in all gears of a gearbox automatically.

Changes of input parameters are also controlled by the program - for example the program won't allow to enter the parameter value out of allowable range. A user, preferably an experienced user, can also modify the parameters within a specified range. A user with little experience in designing toothed gears can take advantage of pre-set parameters and conveniently launch and complete the calculations.
Wheel type
Parameters 1
A module can be expressed in [mm] or [1/cal] (DP - Diametral-Pitch). It can also be selected in three different ways: as any module of the particular range, as any of the series of standardized modules types, or selected from among the series of types. A modification to a module for the given toothed gear results in automatic modification of all associated gears. During edition of a given toothed gear data, it is also possible to select the ‘same module for all gears’ option and then, all gears of a gearbox will be associated with a module that is expressed with the same units and they will be selected according to the pre-defined selection schedule.
Module m
Module DP
Multi-criterion optimization allows the user to consider any arbitrary combination of partial criteria and their respective weights, enabling a more flexible approach to the design of gear boxes. The program utilizes effective optimization procedures (NNLPF, BCONF, BCPOL - IMSL library, NLPQLP - Prof. K. Schittkowski and the SSW_MM - M. Martyna procedure written based on article [1]). When local minimums are found, the program automatically re-starts the calculations, providing the necessary modification of the starting point (predetermined or random). This allows for continuous browse of enormous space of solutions (small tasks contains tens and bigger ones even hundreds of decision variables and an even greater number of limitations - mostly non-linear). Optimization procedures can be automatically switched by the program or manually by the user.
Parameters of partial criteria
Optimization parameters
Calculation results can be observed in a special dialog box. User can also enable or disable the additional window, which shows the variability of the optimization criteria as a function of the number of optimal steps. The graph shows plots for all selected sub-criteria and for global criterion. The X-axis scale is changing dynamically and it depends on the current number of optimal solutions. Data and results of calculations are saved to text files. Every such a text file with calculation results can be immediately used as a starting point for subsequent calculations.
Optimization calculation
Calculation and plot
Current results
The program can run under any 32-bit or 64-bit Windows operating system, but also it can be specially compiled and optimized for specific processors. It has an advanced multi-language installer, help documentation in various formats (HTML, CHM, and PDF) and multimedia demo. Program also updates automatically or on user demand.

The GEAR program has reached a certain stage already and its many features here discussed shall be gradually implemented, but even now most complicated and useful computations are fully possible. By using the GEAR program, it is possible to get a much shorter project cycle, optimized parameters of components and the optimized parameters of the whole gearbox.

[1] Molina D., Lozano M., Sanchez A. M., Herrera F.: Memetic algorithms based on local search chains for large scale continuous optimization problems: MA-SSW-Chains. Springer-Verlag 2010.