# equations - Search Results

## Articles About equations

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**1 General Equations for Gear Cutting Tool Calculations** *(November/December 1985)*

*The proper design or selection of gear cutting tools requires thorough and detailed attention from the tool designer. In addition to experience, intuition and practical knowledge, a
good understanding of profile calculations is very important.*

**2 Investigation of the Strength of Gear Teeth** *(November/December 1992)*

*To mechanical engineers, the strength of gear teeth is a question of constant recurrence, and although the problem to be solved is quite elementary in character, probably no other question could be raised upon which such a diversity of opinion exists, and in support of which such an array of rules and authorities might be quoted. In 1879, Mr. John H. Cooper, the author of a well-known work on "Belting," made an examination of the subject and found there were then in existence about forty-eight well-established rules for horsepower and working strength, sanctioned by some twenty-four authorities, and differing from each other in extreme causes of 500%. Since then, a number of new rules have been added, but as no rules have been given which take account of the actual tooth forms in common use, and as no attempt has been made to include in any formula the working stress on the material so that the engineer may see at once upon what assumption a given result is based, I trust I may be pardoned for suggesting that a further investigation is necessary or desirable.*

**3 1992 Marks Important Gear Design Milestone: Lewis Bending Strenth Equations Now 100 Years old** *(November/December 1992)*

*Columbus' first voyage to the Americas is not the only anniversary worthy of celebration this year. In 1892, on October 15, Wilfred Lewis gave an address to the Engineer's Club of Philadelphia, whose significance, while not as great as that of Columbus' voyage, had important results for the gearing community. In this address, Lewis first publicly outlined his formula for computing bending stress in gear teeth, a formula still in use today.*

**4 The Geometry of Helical Mesh** *(September/October 1997)*

*In 1961 I presented a paper, "Calculating Conjugate Helical Forms," at the semi-annual meeting of the American Gear Manufacturers Association (AGMA). Since that time, thousands of hobs, shaper cutters and other meshing parts have been designed on the basis of the equations presented in that paper. This article presents the math of that paper without the formality of its development and goes on to discuss its practical application.*

**5 Load Distribution in Planetary Gears ** *(May/June 2001)*

*Two-shaft planetary gear drives are power-branching transmissions, which lead the power from input to output shaft on several parallel ways. A part of the power is transferred loss-free as clutch power. That results in high efficiency and high power density. Those advantages can be used optimally only if an even distribution of load on the individual branches of power is ensured. Static over-constraint, manufacturing deviations and the internal dynamics of those transmission gears obstruct the load balance. With the help of complex simulation programs, it is possible today to predict the dynamic behavior of such gears. The results of those investigations consolidate the approximation equations for the calculation of the load factors...*

**6 Effect of Extended Tooth Contact on the Modeling of Spur Gear Transmissions ** *(July/August 1994)*

*In some gear dynamic models, the effect of tooth flexibility is ignored when the model determines which pairs of teeth are in contact. Deflection of loaded teeth is not introduced until the equations of motion are solved. This means the zone of tooth contact and average tooth meshing stiffness are underestimated, and the individual tooth load is overstated, especially for heavily loaded gears.
This article compares the static transmission error and dynamic load of heavily loaded, low-contact-ratio spur gears when the effect of tooth flexibility has been considered and when it has been ignored. Neglecting the effect yields an underestimate of resonance speeds and an overestimate of the dynamic load.*

**7 Balancing: Smoke and Mirrors No Longer** *(January/February 2013)*

*By virtue of collected anecdotal accounts, equations and problem solving, balancing is discussed as more math and common sense, and less smoke and mirrors.*

**8 Adding Up Gear Spheres** *(March/April 2016)*

*Paul Nylander is something between an entrepreneur and a Renaissance man. He has degrees in engineering and physics, but he’s also a creative artist who’s put together sketches and 3D renderings alike. His website, bugman123.
com, features everything from an in-depth explanation of a Tesla coil to 3D renderings of physics equations to an extensive library of fractal-based artwork. At first glance, one
might find Nylander’s many pursuits to be somewhat scattershot, but at their core, his works are tied together by his love for all things mathematical.*

**9 Minimizing Backlash in Spur Gears** *(May/June 1994)*

*simplified equations for backlash and roll test center distance are derived. Unknown errors in measured tooth thickness are investigate. Master gear design is outlined, and an alternative to the master gear method is described. Defects in the test radius method are enumerated. Procedures for calculating backlash and for preventing significant errors in measurement are presented.*

**10 Measuring Profile and Base Pitch Error with a Micrometer** *(September/October 2002)*

*In this article, equations for finding profile and base pitch errors with a micrometer are derived. Limitations of micrometers with disc anvils are described. The design of a micrometer with suitable anvils is outlined.*

**11 Systematic Approach to Designing Plastic Spur and Helical Gears** *(November/December 1989)*

*Plastic gears are being used increasingly in applications, such as printers, cameras, small household appliances, small power tools, instruments, timers, counters and various other products. Because of the many variables involved, an engineer who designs gear trains on an occasional basis may find the design process to be somewhat overwhelming. This article outlines a systematic design approach for developing injection molded plastic spur and helical gears. The use of a computer program for designing plastic gears is introduced as an invaluable design tool for solving complex gearing equations.*

**12 Scoring Load Capacity of Gears Lubricated with EP-Oils** *(October/November 1984)*

*The Integral Temperature Method for the evaluation of the scoring load capacity of gears is described. All necessary equations for the practical application are presented. The limit scoring temperature for any oil can be obtained from a gear scoring test.*

**13 The Effect of Manufaturing Microgeometry Variations on the Load Distribution Factor and on Gear Contact and Root Stresses** *(July 2009)*

*Traditionally, gear rating procedures consider manufacturing accuracy in the application of the dynamic factor, but
only indirectly through the load distribution are such errors in the calculation of stresses used in the durability and gear strength equations. This paper discusses how accuracy affects the calculation of stresses and then uses both statistical
design of experiments and Monte Carlo simulation techniques to quantify the effects of different manufacturing and
assembly errors on root and contact stresses.*

**14 Efficient Methods for the Synthesis of Compound Planetary Differential Gear Trains for Multiple Speed Ratio Generation** *(July/August 1990)*

*This article presents an efficient and direct method for the synthesis of compound planetary differential gear trains for the generation of specified multiple speed ratios. It is a train-value method that utilizes the train values of the integrated train components of the systems to form design equations which are solved for the tooth numbers of the gears, the number of mating gear sets and the number of external contacts in the system. Application examples, including vehicle differential transmission units, rear-end differentials with unit and fractional speed ratios, multi-input functions generators and robot wrist joints are given.*

**15 Helical Gear Mathematics Formulas and Examples** *(May/June 1988)*

*The following excerpt is from the Revised Manual of Gear Design, Section III, covering helical and spiral gears. This section on helical gear mathematics shows the detailed solutions to many general helical gearing problems. In each case, a definite example has been worked out to illustrate the solution. All equations are arranged in their most effective form for use on a computer or calculating machine.*

**16 Dynamic Loads in Parallel Shaft Transmissions - Part 2** *(May/June 1990)*

*Solutions to the governing equations of a spur gear transmission model, developed in a previous article are presented. Factors affecting the dynamic load are identified. It is found that the dynamic load increases with operating speed up to a system natural frequency. At operating speeds beyond the natural frequency the dynamic load decreases dramatically. Also, it is found that the transmitted load and shaft inertia have little effect upon the total dynamic load. Damping and friction decrease the dynamic load. Finally, tooth stiffness has a significant effect upon dynamic loadings the higher the stiffness, the lower the dynamic loading. Also, the higher the stiffness, the higher the rotating speed required for peak dynamic response.*

**17 Helical Gear Mathematics, Formulas and Examples Part II** *(July/August 1988)*

*The following excerpt is from the Revised Manual of Gear Design, Section III, covering helical and spiral gears. This section on helical gear mathematics shows the detailed solutions to many general helical gearing problems. In each case, a definite example has been worked out to illustrate the solution. All equations are arranged in their most effective form for use on a computer or calculating machine.*

**18 Viewpoint** *(March/April 1986)*

*I received a letter from Mr. G. W. Richmond, Sullivan Machinery Company, N.H., in which in addition to correcting
mistyping, he made several suggestions
concerning my article "General Equations
for Gear Cutting Tool Calculations."*