Telecurso 2000 - Metrologia - 24 Controle Trigonométrico

Understanding Measurement with Complementary Parts

Introduction to the Lesson

• The session begins with a greeting and an introduction to the topic of measurement using complementary parts.

• The lesson aims to teach how to measure using complementary pieces and the formulas involved in these measurements.

Scientific Approach to Measurement

• The instructor compares their approach to that of scientists, emphasizing control over variables like temperature during experiments.

• A specific example is introduced: measuring a piece that cannot be measured directly due to its shape, necessitating the use of complementary parts.

Importance of Complementary Parts

• An analogy is made about measuring oil levels in a car, highlighting that direct access is often impractical.

• It’s noted that certain shapes, such as prismatic or revolution pieces, require indirect measurement methods.

Types of Complementary Instruments

• Various instruments used for indirect measurement are introduced: cylinders, spheres, and hemispheres.

• These instruments are made from tempered steel and are known for their durability and precision in measuring angles.

Application of Trigonometric Relationships

• The instructor explains that measurements with complementary parts rely on two basic trigonometric relationships.

• A right triangle is presented where sine (sin α = opposite/hypotenuse) and tangent (tan α = opposite/adjacent) functions are defined.

Calculating Measurements Using Formulas

Step-by-Step Calculation Process

• Students are encouraged to calculate values based on given dimensions (a = 20mm, b = 40mm).

• The calculation for hypotenuse 'c' involves applying the Pythagorean theorem: c = √(a² + b²).

Results from Calculations

• After calculations, it’s found that c ≈ 44.7 mm; sine of alpha is approximately 0.4472; tangent of alpha equals 0.5.

Practical Applications in Engineering

• The process discussed is particularly useful for measuring components like rabodandurinha fittings using calibrated cylinders.

Advanced Calculations Involving Specific Dimensions

Formula Derivation for Fitting Measurements

• Height calculations involve specific formulas relating internal/external widths and angles.

Example Calculation Scenario

• An example problem requires calculating 'X' based on provided dimensions (L-minúscula = 60.418H, H = 10).

Final Calculation Insights

Mathematical Measurements in Engineering

Understanding the Main Formula

• The primary formula discussed is Y = L - (D + d/tan(alpha/2)) , where D approx 9mm and H = 11 . The goal is to find the value of L using this equation.

Calculation of X in Rabodandurinha Fitting

• Given values: L = 80mm, H = 20mm, alpha = 60^circ . The calculation leads to finding X based on these parameters.

• Using the formula, it was determined that L = 56.906mm and D approx 18mm . This step is crucial for further calculations.

Applying the Main Formula

• The main formula is applied as follows:

• Calculate: Y = 56.906 + (18 / (tan(60^circ)/2)) + 18.

• Resulting in a final value of approximately X = 106mm, Y = 83mm. This demonstrates how to derive measurements from given parameters.

Measuring Reina and Reina Interna

• To measure reina and reina interna, two formulas are introduced:

• For reina:

• X = A + R + (R/tan(alpha))/2 - (H/tan(alpha))

• or alternatively,

• X = B + (R/tan(alpha))/2 + R.

These formulas help in determining specific dimensions within fittings.

Additional Formulas for Specific Cases

• Several additional formulas are provided for different types of rabodandurinha fittings:

• For one type:

• A = X - (D + R)

• and subsequently,

• B = A + H.

This highlights the need for various approaches depending on fitting configurations.

• Other variations include:

• Adjustments based on Z values or other parameters leading to different equations such as:

• For another fitting type:

• A = X + D + R

• with corresponding adjustments for B.

Each variation emphasizes adaptability in measurement techniques.

Importance of Standard Axes Selection

• It’s essential to choose standard axes so that contact points align correctly with piece specifications at half height of flanks, ensuring accurate measurements according to design specifications.

Summary and Review

• The session concludes with a review emphasizing that today's lesson focused heavily on mathematical principles related to complementary pieces and trigonometric relationships necessary for calculating rabodandurinha fittings accurately.