Abstract
A generalized system of relationships corresponding to different quality indices during machining of surfaces is developed. A general characteristic for assessing the surface quality of manufacturing products is derived.
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Manufacturing is characterized by constant improvement in product quality. That is associated with progressive methods of assessing product performance. In this context, it is of interest to develop general (typical) and specific (local) relations between production characteristics (quality indices) and operational characteristics of the product [1–8]. Therefore, we need to investigate the relations between production characteristics and to develop criteria for their assessment.
Characteristics of surface quality—such as the dimensional precision, shape precision, and roughness—in machining largely depend on a set of technological (industrial) factors and the relations between them. Numerous studies have attempted to establish functional relations between the indices of machining quality and significant technological factors [6, 9–12]. As yet, however, no generalized system of relationships has been formulated, taking account of the specifics of all types of machining. Such a system would permit effective control of the quality characteristics and the determination of optimal machining conditions.
In the present work, we develop a generalized system of relationships between the input and output parameters of an machining system in which components are machined, and we derive generalized quality criteria for the manufacturing products and their methods of utilization.
To formulate a generalized system of technological relationships in machining, we analyze research and production experience at manufacturing enterprises relating to the shaping of surfaces by different methods, with different quality indices [5, 13–16]. The relations between the input and output parameters are systematized.
On the basis of the generalized system of relationships, we develop a model of the machining quality. Since the set of quality parameters for each component of the part determines its overall quality, the analytical model of the quality takes the form
where Mi, Wj, Pk are the sets of quality characteristics of the material, the workpiece, and the finished part, respectively; An is the set of quality indices for the assembly units and products; m1, m2, … mi are the relations corresponding to the quality characteristics of the material; Fw1 and Fp1 are the relations corresponding to the geometric shape characteristics of the workpiece and part; Dw2 and Dp2 are the relations corresponding to the dimensional characteristics of the workpiece and part; Ow3, Op3 and Onw4, Onp4 are the relations corresponding to the positional and orientational characteristics of the surfaces of the workpiece and part; Cg.w5, Cg.p5 and Cs.w5, Cs.p5 are the relations corresponding to the geometric and surface layer characteristics of the workpiece and part; \({{Y}_{1}}\) denotes the relations corresponding to the quality of the connections between individual elements; \({{Y}_{2}}\) denotes the relations corresponding to the quality of the elements that are connected; \({{Y}_{3}}\) denotes the relations corresponding to the quality of the mutual position of the assembly units (components); and \({{Y}_{4}}\) denotes the relations corresponding to the quality of the mutual position of the individual elements of the products.
We now formulate a model of each design-quality subsystem of the product, and compare the two models.
Thus, we have developed a generalizing system of technological relationships reflecting the formation of the surface-quality characteristics in all types of machining (Fig. 1). On that basis, we may develop a systematic model of the quality in machining.
The resulting generalized system of technological relationships permits the solution of any technological problem associated with surface generation. For example, by taking account of the static, kinematic, and dynamic components of the technological relationships in removing material from the surface of involute gear teeth for the case of grinding the teeth by coping method, we recieved formulas for the minimum and maximum allowance for in grinding [17].
GENERALIZED CHARACTERISTIC OF MANUFACTURING QUALITY
We have developed a mathematical model of a quality characteristic Kq for comprehensive assessment of the manufacturing quality on the basis of the individual output parameters of the manufacturing system. In developing the characteristic Kq, it is assumed that the upper standard (actual) limit of any quality index is one, while the lower limit is zero [7, 18].
The characteristic of manufacturing quality must assess the output parameters of the part, with limits on the operating parameters of the product, including its working life.
The product quality is determined by its dimensional and shape precision and also by the surface quality and roughness after machining [19–23].
If the rated dimension А is maintained with permissible deviations es and ei in the manufacture of a batch of parts, while the maximum dimension with deviation es ensures the best performance, then the quality characteristic Kq = 1. Correspondingly, for the minimum permissible dimension, Kq = 0.5. For parts with intermediate dimensions, such that (А + ei) ≤ (A + х) ≤ (А + es), the relation between Kq and (А + х) will be parametric.
Taking account of the influence of each parameter on the life of the part, we obtain a model for comprehensive assessment of the product quality, generalizing all the individual quality characteristics.
The analytical relation between Kq and (A + хi) takes the form
where t is the number of parameters of the same type that limit the product quality; n, m, and k are the numbers of parameters of the same type (dimensions, shapes, surface roughness) affecting product performance; xi is the permissible deviation for characteristic i (ei ≤ x ≤ es); ITi, ITj, and ITy are the tolerances on the size, shape, and surface roughness, respectively [24]; esi, esj, and esy are the upper limits on the deviation; xi, xj, and xy are the permissible values of the size, shape, and surface irregularity, respectively, for a specific part; \({{\alpha }_{i}}{\text{,}}\) \({{\beta }_{i}}{\text{,}}\) and \({{\gamma }_{i}}\) are significant factors (weights) for the corresponding parameters in determining the product life; and i, γ, and y are the numbers of dimensional, shape, and surface-quality indices for the part.
Thus, we have obtained a generalized characteristic Kq of machining quality. If this general characteristic is used in combination with automated determination of the output surface parameters, product performance may be improved.
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Rasulov, N.M., Nadirov, U.M. & Alekberov, M.Z. Generalized Assessment of Machined Surfaces Quality. Russ. Engin. Res. 40, 822–825 (2020). https://doi.org/10.3103/S1068798X20100202
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DOI: https://doi.org/10.3103/S1068798X20100202