NORMAS PARA LA REGULACION DEL SUELO

The main factor to the success of any machining operation is the clamping the workpiece in the best state condition. A serious design factor with regard to fixturing the workpiece is the selection of the clamping force.

Practically, the clamping loads are mostly setting to more 10 times than that need to prevent the slipping of the workpiece. This is due to the inaccessibility of the analytical tools to evaluate and computing the minimum clamping load. Therefore, more flexible and higher performance fixturing systems are required to improve the accuracy of machined components [40]. However, there has been little research reported with regard to the development of models to predict minimum required clamp pre-loads in light of fixture-workpiece system. Therefore, reference [41] presents a linear clamp pre-load model to compute the minimum required pre-loads needed to avoid the workpiece slip at the fixture-workpiece joints opposite to a variety of external loads.

The minimum clamping forces to secure a workpiece are changed continuously during the machining processes. Therefore, the reference [42] attempted to design an Intelligent Fixturing System (IFS) to provide dynamic clamping forces during the entire machining and fixturing process. The clamping force distribution between a jaw chuck and a cylindrical workpiece had been measured by references [43, 44]. Measuring techniques for the contact pressure between elastic bodies are developed. For instance, ultrasonic method has been used to measure the contact pressure in bolted joints, in which it is extended up to 50MPa [45]. However, it is difficult to find a small ultrasonic transducer which can be built in a tool shank. A new technique [46] using strain gauge is designed to detect the contact pressure in the collet chuck holder by using cylindrical bar similar to a hob to cut spur gear teeth.

2.5.4.2 Coefficient of Friction

To assist the selection of proper clamping forces, analytical methods [47] have been developed to predict fixture-workpiece reaction forces and/or determine the minimum clamping forces necessary to keep the workpiece from slipping within the fixture during machining. These models assumed that the forces at the joints of fixture-workpiece observe Coulomb's law of friction. This law states that the friction force is proportional to the normal load, the force perpendicular to the sliding surface which presses the two solids together. The proportionality factor is called friction coefficient.

Furthermore, the predictions provided by these models are very sensitive to the assumed coefficients of friction. Consequently, in order for these models to be used

with confidence, the coefficients of friction for the fixture-workpiece joints modelled must be identified further with their expected ranges of variation.

Typically, the main source of the coefficient of friction data is handbooks. In general, accurate values of coefficients of friction for fixture-workpiece joints can be obtained through experimentation that investigates the geometric-tribological- loading conditions of the joints.

2.5.4.3 Number of Contact Point

The machining and clamping forces significantly affect the workpiece location accuracy and hence the machined part quality, therefore the workpiece motion arising from localised elastic deformation at the contact point of the workpiece- fixture. Generally, the contact problems with friction are complex in terms of the contact surface can encourage slipping, sliding, and rolling or tension relief depending on the amount of the normal and tangential forces at the contact interface. Although, the literature is significant of research on friction and its application, but it lacks research that investigates the contact between workpiece-fixture systems. However, it is noticed that many joints in machine tools and their characteristics have direct effect upon the static and dynamic performance of the machine tool. Reference [45] classified the joints into three kinds according to the joints stiffness including open, semi closed and closed type. A bolted joint and a sliding joint belong to an open type, and a tapered joint is a closed type. A joint between a workpiece and three jaw chuck is a semi-closed type. The form of closure grasp is needed to constrain a rigid workpiece by surrounding the part surface with mechanical fingers. Reference [48] reported a new and convenient synthetic procedure to develop an efficient algorithm for examining the form closure grasp conditions by applying linear programming techniques. Fingertip locations are determined to achieve the form of closure grasp specified the geometry of a workpiece as illustrated in Figure 2.7.

x

y

z

Constraint

0

Rigid Body

Figure 2.7: Rigid body and constraint points [48].

For simple workpiece geometries, designers mostly depend on the self-experience to ensure that constraint requirements are implemented. Nevertheless, for complex workpieces, it is virtually incredible to validate total restraint without prototyping the fixture. An alternative to prototyping is full constraint analysis if a workpiece is totally clamped by contact area geometry. Reference [49] demonstrated that algebraic analysis has been providing that a minimum of seven points of contact are needed to form close a workpiece in three dimensions, and as extended to this analysis, by adding friction.

2.5.4.4 Modelling

To ensure the dynamic stability of a fixtured workpiece during machining, reference [50] presented a model-based structure for determining the minimum required clamping forces. As shown in Figure 2.8, three types of contact status are possible including full stick, macro-slip, and lift-off. Since full constraint of the workpiece by the fixture must be satisfied during the machining operation, lift-off of the workpiece from any fixture element and macro-slip of the workpiece at any contact at any instant are indicators of an unstable workpiece. The developed approach exposes that the minimum required clamping forces for dynamically stable fixturing are significantly affected by the fixture-workpiece system dynamics. The main limitation with this explanation is that it does not explain what the role of the clamping force to keep the stability between the matting surfaces of workpice and the fixture.

Macro-slip

Full stick Lift-off

Fixture element Workpiece Gap yi xi xi xi yi _yi zi zi zi

Figure 2.8: Dynamic contact interaction between the workpiece and fixture.. Figure 2 .

2.5.4.5 Slip

Reference [51] addressed the influence of the partial slip phenomenon on the dynamic motion of a spherical workpiece held in a fixture with application to machining fixture design. The model studies the effect of interfacial slip damping arising from partial slip at a spherical-planar frictional contact exposed to a constant normal load and oscillating tangential load. The model designed to search both single and multiple contact probabilities. Experimental results agree with those predicted by the model, and the effect of the partial slip phenomenon on workpiece dynamic motion is significant and should not be ignored.

2.5.4.6 Force/deformation

Deformation of the workpiece may cause dimensional problems in machining. Supporters and locators are used in order to reduce the error caused by elastic deformation of the workpiece. The optimization of support, locator and clamp locations is a critical problem to reduce the geometric error in workpiece machining. A genetic algorithm based approach is developed to optimize fixture layout through integrating a finite element code to compute the objective function values for each generation [52]. Based on the fixturing principle there are two locating planes for accurate location containing two and one locators shown in Figure 2.9. Therefore, there are two sides clamping against each locating plane. The results show that the optimized designs do not have any apparent similarities although they provide very similar performances. One of the explanations tends to overlook all the effected parameters in the design of the model, such as the friction between the locators and the surface of the workpiece. .

Clamp 1 Clamp 2

Locator 1 Locator 2

Locator 3

Workpiece

Figure 2.9: Locating layout for 2D prismatic workpiece.