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Advanced Design Assistance

Finite Element Analysis at Arrow Gear
Arrow uses Finite Element Analysis and other advanced technology to predict gear performance.

Arrow's advanced technologies reach beyond machine tools alone. Arrow is equipped with design and development assistance capabilities that are on the leading edge of the industry.

Through the use of the latest technology, Arrow's engineers utilize a computer-based analysis system that offers substantial savings for customers, both in time and expense. This technology is particularly beneficial in the process of design assistance and manufacture of critical and complex gearing in applications like aerospace systems.

Equipped with Gleason CAGE, G-AGE, MINIGAGE, Finite Element and Fully Loaded TCA software, the critical process of tooth contact pattern development can be performed more efficiently than with conventional methods. This technology for gear design assistance is routinely utilized on demanding aerospace and commercial applications.

Features of the software include:

• Design assistance and analysis of spiral bevel and hypoid gears
• Produces data for Gleason gear cutting and grinding machines
• Produces data for Gleason blade grinding machines

• Generates nominal data for gear tooth inspection
• Calculates Gleason machine corrections

Finite Element Analysis
• Analysis of gear strength and life
• Calculates peak pinion and gear fillet stresses
• Calculates contact, fillet, and bending stress contours
• Simulates influence of gear deflections
• Estimates bending and contact stress fatigue life

For More Information
The following is a detailed overview of Arrow's advanced design and development assistance capabilities.  For more information, please refer to the Design Assistance Article in our Publications Section and the Design Assistance Video in our Video Gallery.

Detailed Overview of Arrow's Design and Development Assistance Capabilities

Understanding Contact Pattern and Gear Displacement
A critical attribute of a spiral bevel gear’s performance is its contact pattern. Simply stated, the contact pattern is the area in which the gear teeth come in contact as they engage and disengage during their rotation. [Fig.1] 

Tape Transfer of Contact Pattern
Fig.1 - Marking compound on a tape transfer of a pinion tooth (convex side)  showing the area of contact pattern.

When a gear is installed in a gearbox and is powering the designated application, there are varying degrees of pressure, or loads, on the gear teeth. These loads are affected by box deflections, bearing movement, and temperature changes. When the gear teeth are subjected to these variables, the contact pattern will change.  

For a gear to perform properly under load, the contact pattern must be a certain shape and at a certain location. Typically, an ideal tooth contact pattern under load should encompass the bulk of the tooth surface while avoiding any contact with the edges of the tooth surface or the radius in the root of its mating part. [Fig.2] 

Ideal Tooth Contact Pattern Under Load
Fig.2 - Ideal tooth contact pattern while under load - encompassing the bulk of the tooth surface while avoiding contact with the edges.

Another critical issue to consider when assessing how the contact pattern will perform in an operating gearbox is gear displacement. In the operation of many gearboxes, the gears and their shafts do not remain in a fixed orientation. Thermal forces and stress from being under load can cause significant movement of the gearbox components from their original positions.  

Conventional Methods for Contact Pattern Development
The conventional method of achieving an ideal contact pattern is performed in the following way. First, an engineer will make an educated guess at the gear tooth geometry required to provide a correct contact pattern. Typically this is a 40-60 percent central toe, non-loaded contact pattern. Next, the part is fabricated and the gear teeth are machined to an undeveloped summary of machine settings.

When the gear and its mating pinion are finished they are run together in a tester. More often than not, the contact pattern will not be correct in this first attempt. This requires going back and changing the settings on the gear tooth grinder, then producing a new pinion. The parts are checked again. This trial-and-error process can continue through many cycles until the best educated guess for contact pattern location is achieved. But how will the gear perform under load in a gearbox, and what will the contact pattern look like then? Answering this question leads to more steps in the trial-and-error process.  

First, the gears are mounted in the gearbox and run under light to medium load to determine the contact pattern movement. Then the gears are visually inspected to check the contact pattern, which is indicated by a light wear pattern on the mating tooth surfaces. If the pattern is not correct, which is commonly the case, the gear tooth grinder has to be set up again with new machine settings, and another pinion is ground. This cycle continues until a suitable contact pattern is developed when run under full load.  

For a new gear design this process can take several months to complete. And while this is a time-consuming and costly process, it was just the way it had to be done—or it was, until new computer-based technologies for gear development became available.  

A New Method for Contact Pattern Development To address the traditional limitations of conventional methods, Arrow Gear implemented a highly advanced system for performing contact pattern development, a system that provides a dramatic reduction in the time and expense of the process when compared to conventional methods. This system uses a combination of state-of-the-art development software and machine tools.  

Using the development software, engineers can build virtual models to predict how the gear will perform in actual operation. This in turn generates the settings to be used by the machine tools. In addition, these settings for the machine adjustments are automatically downloaded to the machine tools, greatly reducing the time spent on setup. Perhaps the most dramatic aspect of this system is that ideal settings of the machine tools—which are required to produce the desired contact pattern—are typically achieved in the first or second attempt on the gear manufacturer’s shop floor.  

In essence, this system eliminates the two step trial-and-error process that was once required to first perform the initial development on the gear grinding machines, and secondly to achieve an acceptable full load contact pattern on the final product. The bottom line is that development time is reduced, and the gear producer is able to provide a significant cost savings to the customer.  

Developing the Contact Pattern through Computer Modeling The process of developing a contact pattern with this system is very complex. However, to provide a clear understanding of how the system works, the conceptual highlights of a typical development will first be presented.  

The process begins by receiving the customer’s design requirements. This would include drawings of the part detailing the critical geometry, such as ratio, diametral pitch, and so on. In addition, it is helpful if the customer can supply specifications on operating torque and the gear displacements.  

Gear Displacement Conditions
Fig.3 - The TCA study takes into account all displacement conditions that will be experienced when the gears are under full load.

Engineers begin the process of contact pattern development by establishing a working file for the part based on its geometry. Using the CAGE software, a tooth contact analysis study, or TCA study is performed. This indicates the location of the contact pattern without load.  

Finally, a loaded TCA is performed, taking into account all the displacement conditions. [Fig.3]  Once the TCA study is performed for all displacement conditions, the ideal contact pattern is identified. [Fig.4]  With this information, a finite element analysis is performed that predicts real stress on the tooth surface as well as the root fillet. 

Gear Displacement Conditions Calculated by TCA Study
Fig.4 - The load zone or ideal contact pattern is determined from the TCA study.



In today’s competitive manufacturing environment customer demands for fast delivery and lower costs are prevalent. The computerized closed-loop approach to gear production is ideally suited to this climate. In addition, by reducing development time, this technique allows the product to be released to the market much sooner, substantially reducing costs to the OEM.  

In view of the numerous benefits of this technology, the closed-loop methodology promises to become the standard development technique in the gear industry for years to come.