DIMENSIONAL ANALYSIS OF CONSTRUCTIVE UNITS ( Basic Equations of Dimension Chains. Definition of Dimension Chains) Lecturer Egor Efremenkov Tomsk - 2015.

Slides:

Advertisements

Similar presentations

1/16/ : Coordinates in 3 Dimensions 6.4: Coordinates in Three Dimensions Expectations: G1.1.5: Given a segment in terms of its endpoints, determine.

Advertisements

Remember: Derivative=Slope of the Tangent Line.

Applied Informatics Štefan BEREŽNÝ

1 Computational Methodology for the Prediction of Functional Requirement Variations Across the Product Life-Cycle Guillaume Mandil Alain Desrochers Alain.

Mathematics1 Mathematics 1 Applied Informatics Štefan BEREŽNÝ.

Recovery of affine and metric properties from images in 2D Projective space Ko Dae-Won.

OR Simplex method (algebraic interpretation) Add slack variables( 여유변수 ) to each constraint to convert them to equations. (We may refer it as.

SYSTEM OF FITS AND TOLERANCES

DIMENSIONAL ANALYSIS OF CONSTRUCTIVE UNITS (Methods for accuracy is achieved of closing links) Lecturer Egor Efremenkov Tomsk

Heat Transfer Chapter 2.

1. Substitute Eq. (3) under expectation sign and use addiditve property of expectation 2. All expectations are equal (3) 4. Use the results of the first.

Basic Math Vectors and Scalars Addition/Subtraction of Vectors Unit Vectors Dot Product.

Mathematical Modeling of Assembly Coordinate frames –each part has a base coordinate frame Relationships between parts are expressed as 4x4 matrix transforms.

Arithmetic Operations on Matrices. 1. Definition of Matrix 2. Column, Row and Square Matrix 3. Addition and Subtraction of Matrices 4. Multiplying Row.

Integration in polar coordinates involves finding not the area underneath a curve but, rather, the area of a sector bounded by a curve. Consider the region.

DIMENSIONAL ANALYSIS OF CONSTRUCTIVE UNITS (Links like position deviations of surfaces) Lecturer Egor Efremenkov Tomsk

Equations of Circles 10.6 California State Standards 17: Prove theorems using coordinate geometry.

CHE/ME 109 Heat Transfer in Electronics LECTURE 9 – GENERAL TRANSIENT CONDUCTION MODELS.

Chapter 13 Section 13.1 Rectangular Space Coordinates.

Section 11.6 Pythagorean Theorem. Pythagorean Theorem: In any right triangle, the square of the length of the hypotenuse equals the sum of the squares.

Section 4.7 Slope-Intercept Form. Coordinated Plane.

Functions and their Operations Integrated Math 4 Mrs. Tyrpak.

This presentation shows how the tableau method is used to solve a simple linear programming problem in two variables: Maximising subject to two  constraints.

3-7 Equations of Lines in the Coordinate Plane

Vector Spaces RANK © 2016 Pearson Education, Inc..

1 STRESS STATE 2- D. 2 It is convenient to resolve the stresses at a point into normal and shear components. The stresses used to describe the state of.

Ahmed M. El-Sherbeeny, PhD Industrial Engineering Department

Mechanical Drawing (MDP 115)

4 © 2012 Pearson Education, Inc. Vector Spaces 4.4 COORDINATE SYSTEMS.

When designing a gauge to check a piece of work you need to remember that like the item itself it is impossible to manufacture it to the exact size and.

4.1 Using Matrices Warm-up (IN) Learning Objective: to represent mathematical and real-world data in a matrix and to find sums, differences and scalar.

MATH – High School Common Core Vs Kansas Standards.

Similar Solids definition Similar Solids Two solids in which their corresponding linear measures form equal ratios

DIMENSIONAL ANALISIS OF CONSTRUCTIVE UNITS ( Main Conceptions and Statements ) Lecturer Egor Efremenkov Tomsk

Handout 10a1 TOLERANCES - Introduction Nearly impossible to make the part to the exact dimension by any means of manufacturing approach  tolerances of.

Section 2.6 Inverse Functions. Definition: Inverse The inverse of an invertible function f is the function f (read “f inverse”) where the ordered pairs.

 When drawing 3-dimensional objects, you have to pay attention to the length, width, and height or depth of the object you are interested in drawing.

Table of Contents Ellipse - Definition and Equations Consider two fixed points in the plane, F 1 and F 2, which we shall call foci... Select a point in.

10.3 Ellipses Foci Major Axis / Minor Axis Vertices / Co- Vertices Eccentricity.

Reference Book is. Introduction mechanical waves electromagnetic wavesMechanical waves Waves are two main types : mechanical waves and electromagnetic.

Fundamentals of Data Analysis Lecture 10 Correlation and regression.

MTH108 Business Math I Lecture 20.

Midpoint and Distance in the Coordinate Plane

MATRIX MULTIPLICATION

Circuit Theorems Represented by Md. Feroz Ali (M. F. Ali) Lecturer, Dept. of EEE, PUST.

Lecture 7: Z-Transform Remember the Laplace transform? This is the same thing but for discrete-time signals! Definition: z is a complex variable: imaginary.

11.2 Arithmetic Sequences.

STRESS STATE 2- D.

Matrix Operations SpringSemester 2017.

ME 251 Anupam Saxena Professor Mechanical Engineering

دانشگاه شهیدرجایی تهران

Mathematical Modeling of Assembly

Notes with Whiteboard LEARNING OBJECTIVE Definition 1 figure out

A function f is increasing on an open interval I if, for any choice of x1 and x2 in I, with x1 < x2, we have f(x1) < f(x2). A function f is decreasing.

تعهدات مشتری در کنوانسیون بیع بین المللی

5.7: THE PYTHAGOREAN THEOREM (REVIEW) AND DISTANCE FORMULA

Mathematical Modeling of Assembly

PLASTIC ANALYSIS OF STRUCTURES

Notes for Analysis Et/Wi

Standardized Test Practice

12.4 Box-and-Whisker Plots

Chapter7 Dimensional Chain尺寸链

Tolerances Flóra Hajdu B406

Similar Triangles Review

Simplex method (algebraic interpretation)

Matrix Operations SpringSemester 2017.

Use the Chain Rule to find {image} {image}

Vector Spaces RANK © 2012 Pearson Education, Inc..

Presentation transcript:

DIMENSIONAL ANALYSIS OF CONSTRUCTIVE UNITS ( Basic Equations of Dimension Chains. Definition of Dimension Chains) Lecturer Egor Efremenkov Tomsk

Basic Equations of Dimension Chains There is Dependency between basic performances of closing link and simple links of plane dimensional chain with dimension links. Determinate this dependency for simple dimensional chain

Basic Equations of Dimension Chains You see that nominal meaning of closing link А  is In common case there is equation which called Nominal Equation (1)(1)

Using transfer ratio  i which is equal to +1 for increase links and -1 for decrease links that the Nominal Equation was transformed Basic Equations of Dimension Chains Maximum and minimum meanings of closing link is equal (2)(2)

Basic Equations of Dimension Chains In common case After transformation we obtained So closing link’s tolerance is equal sum of tolerances of formative links (3)(3) (4)(4)

wher Δ в А i, Δ в А Δ – is top deviations of formative links and closing link; Δ н А i, Δ н А Δ – low deviations of them The Dependency is found between limit deviations of closing link and deviations of formative links Basic Equations of Dimension Chains

If equations put into (2) we obtain Basic Equations of Dimension Chains After transformation we obtained So top deviation of closing link is diminution of sums of top deviations of increase links and low deviations of decrease links. But for low deviation of closing link vice versa. (5)(5)

These equation put into (5) and after transformation we obtained Basic Equations of Dimension Chains So middle coordinate of tolerance zone of closing link is diminution of sums of middle coordinate of tolerance zone of increase links and decrease links. (6)(6) The Dependency is found between middle coordinate of tolerance zone of closing link (Δ 0 А Δ ) and middle coordinate of tolerance zone of formative links (Δ 0 А i )

Make sum (1) and (6) as a result: Basic Equations of Dimension Chains But we now that Then obtained So middle meaning of closing link is diminution of sums of middle meaning of increase links and decrease links.

The method is using these equations (3) – (5) we calling The Method of Maximum and Minimum Basic Equations of Dimension Chains or (7)(7)

Basic Equations of Dimension Chains By theorem where t Δ – risk factor, find by Laplace’s function Ф(t); λ i – relative standard deviation. And remember about (7) we obtain in common case

Basic Equations of Dimension Chains or Risk Р,% ,62,10,940,510,270,1 Risk factor t  11,21,41,722,32,62,833,3 Таблица 1 relative standard deviation find like Risk (P, %) correspond to Ф(t) by equation Risk (P, %) is took from row

Basic Equations of Dimension Chains Таблица 1

Definition of Dimension Chains Assembly example

Definition of Dimension Chains Temperature elongation of the shaft may be find like where t 1 –temperature of environment; t 2 – working temperature of the shaft; l – length of the shaft.

Thanks for Your attention