The relationship between dimensional tolerances, form and position tolerances, and surface roughness is understood only by those in the field of mechanics

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I. The numerical relationships between dimensional tolerances, form and position tolerances, and surface roughness: 1 b" f0 Q4 g& L+ g1 G5 ^ 1. Numerical relationship between form tolerances and dimensional tolerances: Once the precision of the dimensional tolerance is determined, there is a corresponding appropriate value for the form tolerance; generally, this value is approximately 50% of the dimensional tolerance value； In the instrumentation industry, approximately 20% of the dimensional tolerances are used as form tolerances ； The heavy industry uses a dimension tolerance of around 70% as the form tolerance. It can be seen that the higher the precision of the dimensional tolerance, the smaller the proportion of the form tolerance relative to the dimensional tolerance. Therefore, when specifying dimensional and form tolerance requirements in design, unless under special circumstances, once the dimensional precision is determined, a value equal to 50% of the dimensional tolerance is generally used as the form tolerance value; this approach is beneficial both for manufacturing processes and for ensuring quality. - n% A% I2 ]1 r) t; o" N* L 2. The numerical relationship between form tolerances and positional tolerances There is also a certain relationship between form tolerances and positional tolerances. In terms of the causes of errors, shape errors are caused by factors such as machine tool vibration, tool vibration, and spindle runout ； Position error is caused by factors such as the non-parallelism of the machine tool’s guide rails, the non-parallel or non-perpendicular alignment of the tool holder, and the force applied for clamping. From the perspective of tolerance zone definitions, position error includes the shape errors of the surface being measured; for example, parallelism error encompasses flatness error. Therefore, position error is much greater than shape error. Therefore, under normal circumstances and in the absence of further requirements, once a positional tolerance is specified, no shape tolerance is given. When there are special requirements, shape and position tolerance specifications can be indicated simultaneously, but the value of the shape tolerance specified must be less than that of the position tolerance; otherwise, it will not be possible to manufacture the parts in accordance with the design requirements. 3 b/ N7 a0 B$ V$ t 3. The relationship between shape tolerance and surface roughness: % }/ i2 H2 Y# M* B, n. Although there is no direct numerical or measurement-based connection between shape errors and surface roughness, under certain machining conditions, a certain proportional relationship exists between them. According to experimental studies, at normal precision levels, surface roughness accounts for 1/5 to 1/4 of the shape tolerance. It can be seen that, to ensure shape tolerances, the maximum allowable value of the corresponding surface roughness height parameter should be appropriately limited. : o6 U: i! F4 _# } Under normal circumstances, there is the following relationship among the tolerances for dimension tolerance, form tolerance, position tolerance, and surface roughness: Dimension tolerance > Position tolerance > Form tolerance > Surface roughness. It is clear from the numerical relationships between dimensions, form and position characteristics, and surface roughness that it is necessary to properly balance these values during design. When specifying tolerances on drawings, it should be ensured that the value assigned to surface roughness for a given surface is less than its form tolerance value ； And the shape tolerance value should be less than its position tolerance value ； The differences in position should be less than their dimensional tolerances. Otherwise, it will cause various problems in manufacturing. However, what is most involved in design work is how to handle the relationship between dimensional tolerances and surface roughness, as well as the relationship between various fit precisions and surface roughness. 　　Under normal circumstances, it is determined according to the following relationship: 1. When the form tolerance is 60% of the dimensional tolerance (moderate relative geometric accuracy), Ra ≤ 0.05IT ； 2. When the form tolerance is 40% of the dimensional tolerance (higher relative geometric accuracy), Ra ≤ 0.025IT ； 3. When the form tolerance is 25% of the dimensional tolerance (high relative geometric accuracy), Ra ≤ 0.012IT ； 4. When the form tolerance is less than 25% of the dimension tolerance (very high relative geometric accuracy), Ra ≤ 0.15Tf (form tolerance value). ; ]$ F( L! G# H Z! H1 g8 V3 H The simplest reference value: the dimension tolerance should be 3-4 times that of the surface roughness, as this is the most cost-effective approach. ( U* u, L7 h3 v/ ~; T) o6 U II. Selection of form and position tolerances 2 S; k" i8 F9 w& a# @ 1. Selection of form and position tolerance criteria: G& n2 K9 H4 v$ S The function of comprehensive control criteria should be fully utilized in order to reduce the number of form and position tolerance criteria specified in the drawings, as well as the corresponding tests for detecting such tolerances. 　　While meeting the functional requirements, items that are easy to measure should be selected. For example, the coaxiality tolerance is often replaced by the radial runout tolerance. It should be noted, however, that radial runout is a combination of coaxiality error and cylindrical surface shape error; therefore, when substituting it, the specified runout tolerance should be slightly greater than the coaxiality tolerance, otherwise the requirement will be too strict. 2. Selection of tolerance principle: 0 h- A R5 g6 k! {' \ The tolerance principle should be chosen based on the functional requirements of the element being measured, taking into account the effectiveness of that tolerance principle as well as its feasibility and economic viability. 　　The independence principle is applied in situations where there are significant differences between the requirements for dimensional accuracy and form and position accuracy, where these requirements need to be met separately, or when there is no connection between them; it helps ensure motion accuracy, sealing performance, and in cases where no tolerances are specified. 　　Inclusivity requirements are mainly used in situations where a strict guarantee of compatibility is necessary. 　　The maximum entity requirement is used for central features, and is generally applied in situations where the requirement for accessories is accessibility (without any fit-related requirements). 　　The minimum entity requirement is mainly used in situations where it is necessary to ensure the strength of parts and a minimum wall thickness. 　　The reversibility requirement, used in combination with the maximum (minimum) entity requirement, allows for full utilization of the tolerance zone, expands the range of the actual dimensions of the feature under inspection, and improves efficiency. It can be chosen without affecting performance. 2 Z7 n2 F( x. Z' A% ~$ ?0 Y d 3、Selection of reference elements 1）Selection of the reference point% M7 O2 y9 ^% `$ G/ k" U: e 　　(1) The mating surface used for positioning the part within the machine is selected as the reference point. For example, the bottom plane and sides of a housing, the axis of disc-shaped parts, the bearing journals or bearing holes of rotating parts, etc. 　　(2) The reference elements should have sufficient size and stiffness to ensure stable and reliable positioning. For example, it is more stable to use two or more axles that are far apart to form a common reference axis than to use just one reference axis. 　　(3) Select a surface with high precision in machining as the reference area. 　　(4) Strive to standardize the assembly, machining, and inspection references. In this way, errors resulting from inconsistent benchmarks can be eliminated ； It can also simplify the design and manufacturing of fixtures and measuring tools, making measurements easier. " j Q& W$ P+ S 2）. Determination of the number of references Generally speaking, the number of references should be determined based on the geometric requirements for orientation and positioning of the toleranced features. Orientation tolerances generally require only one datum, whereas positioning tolerances need one or more datums. For example, for tolerance criteria such as parallelism, perpendicularity, and coaxiality, generally only one plane or one axis is used as the reference element ； For position tolerance requirements, in order to determine the positional accuracy of a hole system, two or three datum features may be required. / m’ r6 l2 @& I4 P( N8 Q8 J’ B3 x 3). Arrangement of reference elements When two or more reference elements are used, it is necessary to determine their order, and they should be indicated in the tolerance fields as first, second, third, etc. The first reference element is the most important, followed by the second one. 4. Selection of form and position tolerance values General principle: Select the most economical tolerance values while ensuring that the part’s functions are met. ◆Based on the functional requirements of the part, taking into account the economic efficiency of manufacturing as well as the structure and stiffness of the part, the tolerance values for the various elements are determined according to the table. And consider the following factors: ◆The shape tolerance specified for the same element should be less than the position tolerance value ； ◆The form tolerance value of cylindrical parts (except for the straightness of the axis) should be less than their dimensional tolerance value ； Just as in a plane, the flatness tolerance should be less than the parallelism tolerance of that plane with respect to the datum. ◆The parallelism tolerance value should be less than the corresponding distance tolerance value. ◆The approximate proportional relationship between surface roughness and form tolerance: generally, the Ra value for surface roughness can be taken as 20% to 25% of the form tolerance value. ◆In the following cases, taking into account the difficulty of machining and the influence of factors other than the main parameters, the grade can be appropriately reduced by 1–2 levels as long as the functional requirements of the part are met: ○ Hole relative to the shaft ； ○Relatively long and large shafts and holes ； Axes and holes with a large distance between them ； ○Surface of parts with a large width (greater than 1/2 of the length) ； ○Tolerances for parallelism and perpendicularity between line pairs and between line pairs and faces. 5. Provisions for tolerances of form and position not specified: 8 g- l8 C/ K1 v# u. To simplify drawing, for those form and position precisions that can be ensured by ordinary machine tool processing, it is not necessary to specify tolerances for form and position on the drawings; such tolerances shall be applied in accordance with the provisions of GB/T1184-1996. The main contents are as follows: 1 M% \( I) @1 @- A9 A( W: (1) Three tolerance grades, H, K, and L, are specified for straightness, flatness, perpendicularity, symmetry, and circular runout when these properties are not specified. (2) The tolerance value for roundness, when not specified, is equal to the diameter tolerance value, but it cannot be greater than the unspecified tolerance value for radial circular runout. (3) If no tolerance value for cylindricity is specified, it is controlled by the specified or unspecified tolerances for the roundness of the element, the straightness of the generatrix, and the parallelism of the generatrices. (4) The unspecified parallelism tolerance value is equal to the larger of the dimensional tolerance between the feature under inspection and the reference feature, and the unspecified tolerance for the shape tolerance (straightness or flatness) of the feature under inspection; the longer of the two features is taken as the reference. (5) If no coaxiality tolerance value is specified, it is not defined. If necessary, a coaxiality unmarked tolerance equal to the unmarked tolerance for circular runout can be used. (6) The tolerance values for unmarked linear profile accuracy, surface profile accuracy, inclination, and positional accuracy are all controlled by the tolerances of the linear dimensions or angular tolerances of the respective elements, whether they are marked or not. (7) The full runout tolerance value, where not specified, is not defined. 5 6. Representation of drawings for which tolerances are not specified# D/ U" K8 l/ L' `& L 　　If the unspecified tolerances defined in GB/T1184-1996 are to be used, the standard and grade codes should be indicated in the title block or in the technical requirements. :“GB/T1184—K”. 　　If the working tolerances are not specified in the drawing as follows \"Tolerance principles shall comply with GB/T 4249\", they shall be implemented in accordance with the requirements of GB/T 1800.2-1998.