Determination of Process Dimensions and Tolerances
In the field of manufacturing, and particularly for plastic injection moulders, the accurate determination of process dimensions and tolerances is crucial for ensuring product quality, functionality, and interchangeability. This comprehensive guide explores the fundamental concepts, calculations, and practical applications of process dimensions and tolerances, with specific relevance to plastic injection moulders who rely heavily on these principles to produce consistent, high-quality parts.
1. Concepts Related to Process Dimensions
Process Dimensions
Process dimensions refer to the dimensions that should be guaranteed after each processing step. For plastic injection moulders, these dimensions are critical as they determine the final fit and function of injection-moulded components. Each stage of the manufacturing process, from initial mould design to final finishing, requires precise dimension control to ensure that the end product meets specifications.
Plastic injection moulders must pay special attention to process dimensions because the injection moulding process involves complex interactions between material properties, mould design, and processing parameters. Even minor variations in any of these factors can affect the final dimensions of the part, making accurate process dimension determination essential for consistent production.
Dimension Chains
A dimension chain refers to a closed group of interconnected dimensions formed by linking related dimensions in a specific sequence for the purpose of analyzing and calculating process dimensions during part manufacturing. For plastic injection moulders, understanding dimension chains is vital for designing moulds that produce parts with correct geometric relationships.
Figure 2-12: Process Dimension Chain
As shown in Figure 2-12, dimension A₂ can be derived from dimensions Aₙ and A₁. When dimensions A₁ and A₂ are obtained through processing, dimension Aₙ is indirectly determined simultaneously. Obviously, the size and accuracy of dimension Aₙ will be affected by the size and accuracy of dimensions A₁ and A₂. This closed dimension group consisting of Aₙ, A₁, and A₂ constitutes a process dimension chain, which is particularly important for plastic injection moulders to ensure part interchangeability.
Each dimension that forms a dimension chain is called a link of the chain. Dimensions directly obtained through processing are called component links, while dimensions obtained indirectly are called closed links. Component links can be further classified as increasing links or decreasing links based on their impact on the closed link.
For plastic injection moulders, correctly identifying these links in the dimension chain is crucial for mould design and process optimization. When other component links remain unchanged, if the closed link increases as a particular component link increases, this component link is called an increasing link. Conversely, if the closed link decreases as a particular component link increases, this component link is called a decreasing link.
Practical Example: Chute Pressure Block Dimension Chain
Let's consider a practical example relevant to plastic injection moulders: the chute pressure block dimension chain shown in Figure 2-13. If surface C is first machined with surface A as the reference, obtaining dimension A₁, and then the step surface B is machined using the adjustment method with surface A as the reference, obtaining dimension A₂, the requirement is to ensure the dimension A₀ between surface B and surface C.
Figure 2-13: Chute Pressure Block Dimension Chain
These three dimensions A₁, A₂, and A₀ form a closed dimension group, which is a dimension chain. For plastic injection moulders, recognizing such chains in part designs helps in determining the correct mould dimensions and processing parameters. A₀ is the indirectly obtained dimension, so it is the closed link of the dimension chain. A₁ is an increasing link, and A₂ is a decreasing link.
Understanding this relationship allows plastic injection moulders to establish appropriate tolerances for each directly machined dimension (A₁ and A₂) to ensure that the indirectly controlled dimension (A₀) falls within its specified tolerance range. This is particularly important in injection moulding where multiple dimensions interact to create the final part geometry.
2. Calculation of Dimension Chains
① Formula Calculation Method
For plastic injection moulders, accurate calculation methods are essential for determining appropriate dimensions and tolerances in mould design and part production. The formula calculation method provides a systematic approach to dimension chain analysis.
Nominal Size of Closed Link
Aₙ = ΣAᵢ⁺ - ΣAⱼ⁻
Where:
- Aₙ - Nominal size of the closed link
- Aᵢ⁺ - Nominal sizes of each increasing link
- Aⱼ⁻ - Nominal sizes of each decreasing link
- m - Number of increasing links in the dimension chain
- n - Total number of links in the dimension chain including the closed link
Upper and Lower Limit Sizes
Aₙₘₐₓ = ΣAᵢₘₐₓ⁺ - ΣAⱼₘᵢₙ⁻
Aₙₘᵢₙ = ΣAᵢₘᵢₙ⁺ - ΣAⱼₘₐₓ⁻
Where:
- Aₙₘₐₓ - Upper limit size of the closed link
- Aₙₘᵢₙ - Lower limit size of the closed link
- Aᵢₘₐₓ⁺ - Upper limit sizes of each increasing link
- Aᵢₘᵢₙ⁺ - Lower limit sizes of each increasing link
- Aⱼₘₐₓ⁻ - Upper limit sizes of each decreasing link
- Aⱼₘᵢₙ⁻ - Lower limit sizes of each decreasing link
Tolerance of Closed Link
Tₙ = ΣTᵢ
Where:
- Tₙ - Tolerance of the closed link
- Tᵢ - Tolerances of each component link
② Vertical Calculation Method
The vertical calculation method for process dimension chains avoids memorizing cumbersome formulas and is less error-prone, making it an excellent method for calculating and verifying dimension chains, especially valuable for plastic injection moulders who need efficient and accurate calculations in their daily work.
The mnemonic for vertical calculation of process dimension chains is as follows: For increasing links, copy the upper and lower limit deviations as they are; for decreasing links, swap and reverse the signs of the upper and lower limit deviations; the closed link is the algebraic sum.
| Item | Calculation |
|---|---|
| Nominal size of increasing links (A⁺) | Sum of all increasing link nominal sizes |
| Nominal size of decreasing links (A⁻) | Sum of all decreasing link nominal sizes |
| Nominal size of closed link (Aₙ) | Sum of increasing links - Sum of decreasing links |
| Upper limit deviation of increasing links (Es⁺) | Sum of upper limit deviations of increasing links |
| Lower limit deviation of decreasing links (Ei⁻) | Sum of lower limit deviations of decreasing links |
| Upper limit deviation of closed link (Esₙ) | Sum of increasing upper deviations - Sum of decreasing lower deviations |
| Lower limit deviation of increasing links (Ei⁺) | Sum of lower limit deviations of increasing links |
| Upper limit deviation of decreasing links (Es⁻) | Sum of upper limit deviations of decreasing links |
| Lower limit deviation of closed link (Eiₙ) | Sum of increasing lower deviations - Sum of decreasing upper deviations |
Plastic injection moulders often prefer this vertical method because it provides a structured, tabular approach that minimizes calculation errors. By following the simple mnemonic, even complex dimension chains can be solved systematically, ensuring that the mould designs and process parameters result in parts that meet all dimensional requirements.
3. Calculation of Process Dimensions and Tolerances
For plastic injection moulders, the calculation of process dimensions and tolerances follows specific principles depending on whether the datums coincide or not. These calculations are fundamental to producing high-quality injection-moulded parts that meet design specifications and function correctly in their intended applications.
Case 1: Datum Coincidence
When the processing datum coincides with the design datum, the calculation sequence is as follows: first determine the nominal dimensions of each process, then推算 them one by one from the last process backward. The tolerances of process dimensions are determined according to the economic accuracy of each process and the upper and lower limit deviations are determined according to the "human body principle."
The "human body principle" is particularly important for plastic injection moulders, as it helps ensure consistent part quality and interchangeability. This principle states that for dimensions without special requirements:
- For hole dimensions, the basic size is the lower limit, and the upper limit is the basic size plus tolerance
- For shaft dimensions, the basic size is the upper limit, and the lower limit is the basic size minus tolerance
- For length dimensions, the basic size is generally taken as the lower limit for external dimensions and the upper limit for internal dimensions
Case 2: Datum Non-Coincidence
When the datums do not coincide, it is necessary to analyze and calculate using process dimension chains. This situation is common in plastic injection moulding where mould design constraints may require using different datums for manufacturing than those specified in the part design.
Figure 2-14: Guide Bushing Dimension Chain
As shown in Figure 2-14(a), for a guide bushing, Aₙ = 15⁺⁰·⁰¹ mm, A₂ = 8⁻⁰·⁰³₀ mm. When machining three end faces, it is necessary to calculate dimension A₁ and its deviations. This example is particularly relevant to plastic injection moulders who frequently produce such precision components.
First, draw the dimension chain diagram as shown in Figure 2-14(b). According to the processing process, we know that Aₙ is the closed link, A₁ is the increasing link, and A₂ is the decreasing link. This analysis helps plastic injection moulders determine the correct mould dimensions to achieve the desired final part dimensions.
Step 1: Calculate the nominal size of A₁
Using the formula for the nominal size of the closed link:
Aₙ = A₁⁺ - A₂⁻
15 = A₁ - 8
A₁ = 15 + 8 = 23 (mm)
Step 2: Calculate the tolerance of Aₙ
The tolerance of the closed link is the sum of the tolerances of each component link:
Tₙ = T₁ + T₂
0.01 = T₁ + 0.03
T₁ = 0.01 + 0.03 = 0.04 (mm)
Step 3: Calculate the upper and lower limit deviations of A₁
For upper limit deviation:
Esₙ = Es₁ - Ei₂
+0.01 = Es₁ - (-0.03)
Es₁ = +0.01 - 0.03 = -0.02 (mm)
For lower limit deviation:
Eiₙ = Ei₁ - Es₂
0 = Ei₁ - 0
Ei₁ = 0 (mm)
Therefore, the dimension A₁ with its deviations is:
A₁ = 23⁰₋₀.₀₂ mm
Practical Considerations for Plastic Injection Moulders
In actual processing, especially for plastic injection moulders, due to the non-coincidence between the measurement datum and the design datum, it is necessary to convert the measurement dimensions. If the converted measurement dimension of a part is out of tolerance, as long as the out-of-tolerance amount is less than or equal to the tolerance of another component link, the part may be a false reject.
This concept of "false rejects" is particularly important for plastic injection moulders as it can significantly reduce production costs. When a measurement dimension appears to be out of tolerance, plastic injection moulders should reinspect the part, measure each dimension individually, and calculate the actual dimension of the closed link to determine if the part is truly acceptable.
By understanding and applying these dimension chain principles, plastic injection moulders can optimize their mould designs, set appropriate processing parameters, and establish effective inspection procedures. This leads to improved part quality, reduced waste, and increased efficiency in the injection moulding process. Whether dealing with simple or complex part geometries, the systematic approach to dimension and tolerance calculation ensures that plastic injection moulders can consistently produce parts that meet all design requirements.
Conclusion
The determination of process dimensions and tolerances is a fundamental aspect of manufacturing engineering, with particular significance for plastic injection moulders. By understanding the concepts of process dimensions, dimension chains, and mastering both formula and vertical calculation methods, manufacturers can ensure that their products meet design specifications consistently.
For plastic injection moulders, accurate dimension and tolerance calculations are essential for mould design, process optimization, and quality control. These principles allow plastic injection moulders to anticipate dimensional variations, establish appropriate tolerances, and minimize production of defective parts. By applying the systematic approach outlined in this guide, plastic injection moulders can improve efficiency, reduce costs, and enhance the quality of their injection-moulded products.
Whether dealing with simple or complex components, the ability to correctly analyze and calculate dimension chains ensures that plastic injection moulders can produce parts that fit together properly, function as intended, and meet all performance requirements. As manufacturing processes continue to evolve, these fundamental principles remain essential for achieving precision and consistency in plastic injection moulding.