Dimensional Tolerances PDF

# Tolerancias dimensionales - It is impossible to realize a piece with exact dimensions, adopt pieces within a range of measurements as correct pieces. - Tolerance is the admissible difference of measures that is allowed from a nominal value. - The unit used, when referring to tolerances, will be th...

# Tolerancias dimensionales - It is impossible to realize a piece with exact dimensions, adopt pieces within a range of measurements as correct pieces. - Tolerance is the admissible difference of measures that is allowed from a nominal value. - The unit used, when referring to tolerances, will be the micron (μm). ## Basic Concepts - Understand certain concepts in order to interpret tolerances correctly. - **Axis:** An element that can be lodged or inserted into another element, regardless of whether its shape is cylindrical or prismatic. - **Hole:** The area capable of containing the shaft. - **Nominal measure (Mn):** The value that is represented in the quotas of the plans. - It is the basis for the subsequent calculation of tolerances. - The line that represents this value is called the nominal line (In). ## Tolerances - **Effective measure:** Is the dimension obtained from the measurement processes of the pieces. - **Maximum measure (Mmax):** The maximum value that the dimension can acquire to consider the piece as good. - **Minimum measure (Mmin):** The minimum value that the dimension can acquire to consider the piece as good. - **Superior difference (ds):** The difference between the maximum measure and the nominal measure. - **d = M max - Mn**. ## Understanding Tolerances: Example - **Inferior difference (d;):** The difference between the minimum measure and the nominal measure. - **d₁ = M min - Mn**. - The superior and inferior differences can have positive or negative values. - **Tolerance:** The total range of error that can be exceeded when performing a piece. - **T = M max - M min = d - d₁**. - **Example:** A shaft whose diameter must be 40 ± 31 that will fit into a hole whose dimensions are 40 ± 35. - **Values of the shaft:** - Nominal measure = 40 - Maximum measure = 40.011 - Minimum measure = 30.995 - Superior difference = 0.011 - Inferior difference = -0.005 - Tolerance = 0.016 - **Values of the hole:** - Nominal measure = 40 - Maximum measure = 40.025 - Minimum measure = 40 - Superior difference = 0.025 - Inferior difference = 0 - Tolerance = 0.025 ## Adjustments - Depending on the combination of the tolerances of the shaft and the hole, different types of adjustments can occur. ## Fit with Play - Occurs when there is always a space between the shaft and the hole. - The union of both elements occurs without difficulty because the hole is always larger than the shaft. - The following can be calculated: - **Maximum play (Jmax):** The difference between the largest dimension that the hole can take and the smallest possible measure of the shaft. - *Jmax = Mmax(hole) - Mmin(shaft)*. - **Minimum play (Jmin):** The difference between the smallest dimension that the hole can take and the largest possible measure of the shaft. - *Jmin = Mmin(hole) - Mmax(shaft) *. ## Fit with Tightness - The diameter of the shaft is larger than that of the hole. - The union will be forced and the coupling will be made with a sledgehammer or press. - The following cases are possible: - **Maximum tightness (Amax):** The difference between the largest dimension that the shaft can take and the smallest possible measure of the hole. - *Amax = Mmax(shaft) - Mmin(hole)*. - **Minimum tightness (Amin):** The difference between the smallest dimension that the shaft can take and the largest possible measure of the hole. - *Amin = Mmin(shaft) - Mmax(hole)*. ## Undetermined Fit - Tolerance allows for the coupling between the parts to have a play or tightness. - The fit between the shaft and the hole is not determined. ## ISO System of Tolerances - Tolerances are standardized according to an international system. - Need to know certain parameters: - **Tolerance quality**: Established 20 tolerance qualities which indicate the range of measurements that a given dimension can take, which represents the tolerance width. - The qualities are classified from IT01, IT0, IT1, to IT18. - Higher quality tolerances indicate larger dimensions. ## Quality of Tolerance - The quality of the tolerance will be higher the larger the dimensions of the pieces. - The tolerance unit i is calculated: - **i = 0.45 x √D + 0.001 x D**, where D is the geometric average of the extreme values of the groups of diameters. - Tolerance units must be multiplied by a constant depending on the quality of tolerances. ## Position of the Tolerance - Specifies the position of the difference closest to the reference line, whether it is superior or inferior. - The position closest to the reference line is called the difference of reference. - The ISO system uses 27 different positions for tolerances, which are identified by letters. - **Axis:** Uppercase letters are used. - **Holes:** lowercase letters are used. ## Visual Representation of Tolerances - Tolerances can be represented in two ways: - **Numerically**: Tolerance numbers and their signs (positive or negative) are shown, indicating the tolerance width. The sign shows the location of the tolerance zone with respect to the nominal diameter. - **Symbolically**: Tolerance is expressed with a letter and a number. - Uppercase for holes. - Lowercase for shafts. - The size of the tolerance depends on the size of the piece, increasing as the dimension increases. ## Systems of Fit - The combination of axis and hole tolerances fully determines any fit. Different combinations are created with different tolerances, increasing the complexity of manufacturing. - To reduce the complications of manufacturing and check the systems, there are two types of tolerance systems: - **Hole base system** - **Shaft base system** ## Hole Base System - The tolerance of the hole always occupies the position defined by the letter "H." - The minimum measure that the hole can take coincides with its nominal measure, which implies that the inferior difference is equal to the reference, which is zero. - Choose the tolerance zone of the shaft to obtain the desired fit. - **Fits with play:** Positions "a" to "h" are used. - **Fits with tightness:** Positions "p" to "zc" are used. - **Undetermined fit:** Positions "j", "k", "m", and "n" are used. - The complete designation of the fit is written as: 24H7/k6. - It is indicated by the nominal measure, followed by the hole tolerance (letter "H"), and finally the shaft tolerance. ## Shaft Base System - The tolerance of the shaft always occupies the position defined by the letter "h." - The maximum measure that the shaft can take coincides with its nominal measure, which implies that the superior difference is equal to the reference, which is zero. - Choose the tolerance zone of the hole to obtain the desired fit. - **Fits with play:** Positions "A" to "H" are used. - **Fits with tightness:** Positions "P" to "ZC" are used. - **Undetermined fit:** Positions "J", "K", "M", and "N" are used. - The complete designation of the fit is written as: 24h7/K6. - It is indicated by the nominal measure, followed by the shaft tolerance (letter "h"), and finally the hole tolerance. ## Comparison of Systems - The hole base system is more common because the tolerance of the hole has a wider range and the shaft tolerance is generally smaller. - The shaft tolerance is usually the most difficult to manufacture, so it is easier to work with the external measures. ## Tables | Tolerance | Nominal Measure | Hole Superior | Hole Inferior | Hole Tolerance | Shaft Superior | Shaft Inferior | Shaft Tolerance | |---|---|---|---|---|---|---|---| | A11 | 1 | 0.009 | -0.006 | 0.015 | 0.014 | -0.010 | 0.024 | | A12 | 3 | 0.012 | -0.009 | 0.021 | 0.018 | -0.013 | 0.031 | | A13 | 6 | 0.018 | -0.013 | 0.031 | 0.025 | -0.018 | 0.043 | | A14 | 10 | 0.025 | -0.018 | 0.043 | 0.034 | -0.025 | 0.059 | | B8 | 1 | 0.003 | -0.003 | 0.006 | 0.005 | -0.004 | 0.009 | | B9 | 3 | 0.005 | -0.004 | 0.009 | 0.008 | -0.006 | 0.014 | | B10 | 6 | 0.008 | -0.006 | 0.014 | 0.011 | -0.008 | 0.019 | | B11 | 10 | 0.011 | -0.008 | 0.019 | 0.016 | -0.011 | 0.027 | | C8 | 1 | 0.001 | -0.001 | 0.002 | 0.002 | -0.002 | 0.004 | | C9 | 3 | 0.002 | -0.002 | 0.004 | 0.004 | -0.003 | 0.007 | | C10 | 6 | 0.004 | -0.003 | 0.007 | 0.006 | -0.005 | 0.011 | | C11 | 10 | 0.006 | -0.005 | 0.011 | 0.009 | -0.007 | 0.016 | | D8 | 1 | 0 | -0 | 0 | 0.001 | -0.001 | 0.002 | | D9 | 3 | 0 | -0 | 0 | 0.002 | -0.002 | 0.004 | | D10 | 6 | 0 | -0 | 0 | 0.003 | -0.003 | 0.006 | | D11 | 10 | 0 | -0 | 0 | 0.005 | -0.004 | 0.009 | | E7 | 1 | 0 | -0 | 0 | 0 | -0 | 0 | | E8 | 3 | 0 | -0 | 0 | 0 | -0 | 0 | | E9 | 6 | 0 | -0 | 0 | 0 | -0 | 0 | | E10 | 10 | 0 | -0 | 0 | 0.001 | -0.001 | 0.002 | | F7 | 1 | 0 | -0 | 0 | 0| -0 | 0| | F8 | 3 | 0 | -0 | 0 | 0 | -0 | 0 | | F9| 6 | 0 | -0 | 0 | 0 | -0 | 0 | | F10 | 10 | 0 | -0 | 0 | 0 | -0 | 0 | | G7 | 1 | 0 | -0 | 0 | 0 | -0 | 0 | | G8 | 3 | 0 | -0 | 0 | 0 | -0 | 0 | | G9 | 6 | 0 | -0 | 0 | 0 | -0 | 0 | | G10 | 10 | 0 | -0 | 0 | 0 | -0 | 0 | | H7 | 1 | 0 | -0 | 0 | 0 | -0 | 0 | | H8 | 3 | 0 | -0 | 0 | 0 | -0 | 0 | | H9 | 6 | 0 | -0 | 0 | 0 | -0 | 0 | | H10 | 10 | 0 | -0 | 0 | 0 | -0 | 0 | | J6 | 1 | 0.001 | 0 | 0.001 | 0.002 | 0.001 | 0.003 | | J7 | 3 | 0.002 | 0.001 | 0.003 | 0.004 | 0.002 | 0.006 | | J8 | 6 | 0.004 | 0.002 | 0.006 | 0.006 | 0.003 | 0.009 | | J9 | 10 | 0.006 | 0.003 | 0.009 | 0.009 | 0.005 | 0.014 | | K5 | 1 | 0 | 0 | 0 | 0.001 | 0 | 0.001 | | K6 | 3 | 0 | 0 | 0 | 0.002 | 0.001 | 0.003 | | K7 | 6 | 0 | 0 | 0 | 0.004 | 0.002 | 0.006 | | K8 | 10 | 0 | 0 | 0 | 0.006 | 0.003 | 0.009 | | M5 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | | M6 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | | M7 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | | M 8 | 10 | 0 | 0 | 0 | 0.001 | 0 | 0.001 | | N 5| 1 | 0 | 0 | 0 | 0 | 0 | 0 | | N6 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | | N7 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | | N8 | 10 | 0 | 0 | 0 | 0 | 0 | 0 | - **Tolerances of Holes** - Nominal measure is expressed in mm. - The table shows the superior and inferior tolerances for holes and shafts. - The tables are expressed in 1/1000 mm. - The difference of reference is indicated by the letter used in the table