The Ultimate Guide to Industrial V-Belt Drives: Selection & Tensioning Figure 1: Not all black rubber bands are the same. Choosing the wrong profile is the #1 cause of slip. If you walk into a plant and hear a high-pitched "chirp" or smell burning rubber, you are witnessing wasted money. The industrial V-belt drive is the most common power transmission method, yet it is often the most misunderstood. Engineers often specify "A-Section" belts out of habit, ignoring modern, high-efficiency options. This guide covers Profile Selection , Length Calculation (with VBA) , and the critical belt tensioning method to eliminate belt squeal and premature failure. 1. The "Wedge" Effect: How it Works A flat belt relies purely on friction. A V-Belt relies on the Wedge Effect . As tension pulls the belt into the sheave groove, the side walls push outward, multiplying the normal force. Critical Rule: The belt should NEVE...
Machine designers have to deal with several equations in their design projects. There are a number of ways to solve for roots of algebraic and transcendental equations. Sometimes, the roots could be obtained by direct methods. However, there are many more that could not.
The classical equation such as f(x) = e-x - x cannot be solved analytically. For this case, the only alternative is an approximate solution technique.
There are several methods available to solve the root finding problem, generally categorized as "Bracketing methods" and "Open methods".
1. Bracketing Methods
The bracketing methods require two initial guesses for the root. These guesses must "bracket" the root (one positive, one negative relative to the root). The numerical methods using bracketing methods consist of the following techniques:
- The Bisection Method: The idea of this technique is an incremental search related to the sign change. Sometimes, this technique is called binary chopping, or Bolzano's method.
- The False-Position Method: It's the improved technique from the bisection methods. It replaces the curve f(x) by a straight line and gives a false-position of the root. The false-position method is also called the linear interpolation method.
2. Open Methods
However, my favorite technique in root finding is not the bracketing methods but the open methods.
The bracketing methods are said to be convergent (they always find the root). In contrast, the open methods are based on formulas that require a single starting value of x. They sometimes diverge (fail to find the root). However, when the open methods converge, they usually do so much more quickly than the bracketing methods.
The following are the root finding techniques using open methods:
- Simple One-Point Iteration
- The Newton-Raphson Method: The most widely used of all root-locating formulas. The Newton-Raphson method uses the slope (first derivative) of the function to find the root. It's my favorite one because of its speed.
- The Secant Method: Instead of using the first derivative of the function to find the slope as in The Newton-Raphson Method, the first derivative in the secant method can be approximated by a finite divided difference.
In the next post, let's see how we can use Microsoft Excel VBA again to solve the root finding problems using the Newton-Raphson Method. I'll show you the simple VBA code that you can copy & paste into your excel file and use it as the module to calculate for the root of your equation.
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