Base Tangent Length Calculation for Helical Gears




Application of guideline Base tangent length required for gear tooth inspection

Introduction: Base tangent length  (Wk)  is generallly used to determine gear tooth thickness by measuring length across a certain no. of teeth (k) and unit correction factor.

To determine optimum no.of teeth there is two methods-

  1. It can be determined by refering to graph in CMTI  handbook pg 268 'Optimum number of teeth'

  2. From following calculation method

    NOTE : Compulsory follow both method for verification of optimum no. of teeth

Calculation Reference

Gear Design

CMTI handbook

The base tangent length, also known as the span measurement, is an essential parameter for the accurate manufacturing and inspection of helical gears. The base tangent length is the distance between two points on the base circle where the tangent to the base circle is parallel to the tooth profile at the pitch point. This measurement is used to determine the tooth thickness and evaluate the accuracy of the tooth profile.

To calculate the base tangent length (Wt) for helical gears, you can use the following formula:

Wt = π * D * m * cos(β) / Z


  • Wt is the base tangent length (span measurement)
  • D is the pitch diameter of the gear
  • m is the module of the gear (the ratio of pitch diameter to the number of teeth)
  • β is the helix angle (the angle between the helix and an axial line on the gear)
  • Z is the number of teeth on the gear

In the case of an involute gear profile, it is important to note that the base tangent length calculated using this formula is an approximation, as the true base tangent length is influenced by the shape of the involute curve. However, the approximation is generally accurate enough for most practical purposes.

Remember to use consistent units when performing the calculation (e.g., millimeters or inches for dimensions). Also, make sure to convert the helix angle (β) to radians if your calculator uses radians for trigonometric functions.

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jigar (hdcdesign)
28 Apr 2023
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Comments: 1
hdcdesign 14 years ago
Sorry for the delay been tied up with accounts: its tax time.Whilst my formal eductaion is manufacturing and mechanical engineering, I haven't had much experience in that area except as it interfaces with structural design, which is what I am mostly involved with.So I cannot comment on the accuracy or validity of the calculation. It would be helpful if there was a reference to say Shigley, or the Machinerys handbook, or Marks Handbook of Mechanical Engineering, and national standard which requires such calculation (BS 436 ?), along with recommended/favorate gear design handbook.That way those not overly familiar with the calculation but may need to carry it out can do some research into its background and get proper understanding of its purpose before doing so.Also after nearly 20 years of creating spreadsheets without the benefit of XLC I am not into rushing into converting spreadsheets over to using XLC. However the base tangent length calculation does look like a simple enough workbook to quickly convert over to using XLC.Also do you have any more gear design workbooks which you can contribute. They are useful to students and provide building blocks for more advanced and complete design workbooks.Think of it this way Euler and Bernoulli wrote papers on bending, Coulomb expanded on this and then so did Navier: these papers were largely theoretical mathematics. In the modern world with the use of computer software, each generation can build on the practical application of the theory. Simplistically every minute spent interacting with a computer is 59 seconds of wasted time, because the computer can complete the task in less than 1 second. So the more software building blocks we have to plug together the more time we can save.So the more parametric design models made available under the design science license (DSL), or general public license (GPL) or similar, the faster technological progress can be and also the more stable and consistent the development of established technologies based on established science.Also note that google and other search engines are more likely to search the ExcelCalcs website rather the contents of the Excel Workbooks. Therefore the more commentary and discussion about the workbook, the greater the potential for a larger audience viewing the workbook.So for example more description about the point and purpose of the calculation would attract a greater audience and group of supporters for the workbook. Thus increasing the number of gear designers contributing to ExcelCalcs making more gear design calculations readily available.Not every manufacturer employs design personnel on staff, they simply make the product and only employ technical consultants should they encounter a problem with what they make. So analytical design and assessment is still relatively new concept compared to the thousands of years of building by trial and error. So the scientific method of design still needs to be promoted and expanded in its use to produce higher quality products. That requires sharing of knowledge and experience.Generally speaking it takes as long to create an Excel worksheet as it does to write the calculations out by hand, unless really want to get the diagrams into the workbook, then it takes longer. Formal instrument drawings take longer than freehand sketches: and the instruments for drawing in Excel are cumbersome. Searching with google takes longer than creating a worksheet for simple calculations.So there has to be a reason to create an Excel worksheet rather than push the numbers through a calculator, and a still greater reason to choose to search for an existing worksheet rather than simply create one from scratch.So for example make the workbook a more complete gear design workbook: not immediately but do so with the passage of time, and promote ExcelCalcs as a source of tools for gear design.Participate in the forums and dicussions. Also use the contributions by John Doyle and Alex Tomanovich as a guide to the heights of contribution to be aimed for. Also take a look at David Hunters contributions, only a few workbooks, but on relatively common place calculations with a consequential high download rate: not what I would go looking for. But still if here at ExcelCalcs already, and haven't got such workbooks, can save a lot of time if these are useful building blocks to something more complex.Otherwise seems a useful worksheet and if can contribute more like that and provide expertise on gear design and manufacture that would be still better.
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