**Basic concepts of basing theory**

Machining accuracy, complexity and design of fixtures, processing performance largely depend on the workpiece location.

**Basing** is called giving the workpiece or product the required position in the selected coordinate system.

**Consolidation.** The application of forces and pairs of forces to the workpiece to ensure the constancy of their position achieved during basing.

**Installation** . The process of basing and fixing the workpiece.

**Basing error.** Deviation of the actually achieved position of the workpiece during basing from the required one.

**Installation error.** Deviation of the actual position of the workpiece during installation from the required one.

When processing on metal-cutting machines, basing is understood as giving the workpiece the required position relative to the machine elements that determine the movement of feeds and the cutting tool.

A free rigid body has six degrees of freedom (displacements along the coordinate axes **X, Y, Z** and three rotations around these axes). The required position or motion of a rigid body relative to the selected coordinate system is achieved by imposing geometric or kinematic constraints. In order to deprive the body of the possibility of movement in the listed six directions, it is necessary to impose six geometric constraints.

To base a prismatic workpiece (Fig. 1), it is advisable to use its three surfaces, which can be replaced by reference points of a theoretical nature. The reference point symbolizes one of the connections of the workpiece with the selected coordinate system. For the complete orientation of the workpiece in the fixture, it is necessary and sufficient to have six reference points located in a certain way relative to the base surfaces of the workpiece. Points *A1* **,** *A2* and *A3* not lying on the same straight line are in the *XY* plane. Points *B1* and *B2* are in the *XZ* plane and point *C* is in the *YZ* plane.

**A base** is a surface or a combination of surfaces performing the same function, an axis, a point belonging to a workpiece or product and used for basing.

Bases are classified according to several criteria:

- by appointment;
- by deprived degrees of freedom;
- according to the nature of the manifestation.

Basing is used at different stages of product creation: design, manufacture and measurement, therefore bases are divided into three types according to their purpose: design, technological and measuring.

Rice. 1. Scheme of basing a prismatic blank

**Design base** – the base used to determine the position of a part or assembly unit in a product.

*The main design base* is the design base that belongs to this part or assembly unit and is used to determine its position in the product.

*Auxiliary datum* is a datum that belongs to a given part or assembly unit and is used to determine the position of the product attached to it.

**Technological base** – the base used to determine the position of the workpiece or product in the manufacturing or repair process (Fig. 2).

Rice. 2. Technological base: 1 – prism (an element of adaptation to a milling machine); 2 – key cutter; 3 – shaft blank; TB – technological base

**Measuring base** – the base used to determine the relative position of the workpiece or product and measuring instruments (Fig. 3).

Rice. 3. Measuring base: 1 – indicator stand; 2 – product; 3 – indicator (measuring instrument). *A* – measuring base of the part

According to the deprived degrees of freedom, installation, guide and support bases are distinguished.

**The mounting base** deprives the workpiece of three degrees of freedom (movement along the Z axis, and rotations about the X and Y axes). There are points *A1* **,** *A2* and *A3* on it.

**The guide base** deprives the workpiece of two degrees of freedom (movement along the Y axis and rotation about the Z axis). It contains reference points *B1* **,** *B2* .

**The support base** point *C* deprives the workpiece of one degree of freedom (movement along the X axis).

According to the nature of the manifestation, explicit (real) and hidden (conditional) bases are distinguished.

The explicit base is the base of the workpiece in the form of a real surface, marking marks or the point of intersection of the marks, and the hidden base is in the form of an imaginary plane, axis or point.

Reference points are used in technological documentation. They are placed to determine the layout of the part or workpiece.

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The following signs are accepted for symbolic designation of reference points: – reference points on the front and side view of the part; – anchor points top view of the part; – Anchor points bottom view.

The layout of the prismatic blank is as follows (Fig. 2).

Rice. 4. Scheme of basing a prismatic blank

Rice. 5. Scheme of basing a body of revolution. Set of bases: double guide (points *1* , *2* , *3* , *4* ); reference (points *5* , *6* ): *a* – isometric image; *b* – projection

**Base selection**

When choosing bases, they are guided by the following provisions:

1. The mounting base is usually the largest surface of the workpiece, which allows you to place three reference points that do not lie on one straight line and at a great distance from each other.

2. For the guide base, use the longest surface with two reference points as far apart as possible.

3. For the support base, any surface is used, provided that there are no sprues, burrs, casting and stamping seams on it.

- The choice of a set of bases depends on the number of dimensions maintained in a given operation. For example, when processing a plane by milling or grinding (Fig. 6 a), when it is necessary to maintain only one dimension L, it is enough

determine the installation base. If two sizes L _{1} and L _{2} are maintained (Fig. 4, b), it is required to determine the installation and guide base. If three or more sizes are maintained, it is required to determine the entire set of bases (Fig. 6 c).

Rice. 6. Processing of parts using one ( *a* ) two ( *b* ) and three ( *c* ) bases

5. When choosing bases, they are guided by the principles of combination and constancy of bases.

*The principle of combining bases* lies in the desire to combine technological bases with design and measurement ones. If this principle is not observed, then the technologist has to change the dimensioning of the parts, putting them down from the technological bases. This is due to the need to recalculate dimensions and tighter tolerances on dimensions, which increases the cost of processing.

*The principle of constancy of technological bases* is the desire to use the same bases for different processing operations. This is due to the fact that changing the bases leads to additional errors in the relative position of the surfaces.

6. Technological bases are also assigned to perform the first operation (draft technological bases). The draft base is used only once and serves to process the main (finishing) technological bases used in further TP operations. As a draft base, you should choose a surface with respect to which finishing technological bases can be processed. It is desirable that there are no sprues, casting and stamping seams on it.

7. The accuracy of processing the finishing bases must be higher than the accuracy of the surfaces processed on these bases.

**Schemes of basing and installation of parts in fixtures**

The choice of workpiece installation schemes is inextricably linked with the type of operation being performed. The initial data are the working drawings of the part and workpiece, as well as the technical requirements for their manufacture. Initially, technological bases and a schematic diagram of the installation are assigned, which are determined by the geometric shape of the part, the location of the surfaces to be processed and their coordinate (dimensional) linkage with each other. This takes into account the following circumstances:

1) the convenience of approaching the cutting tool to the surfaces to be machined;

2) ease of installation and removal of the workpiece;

3) reliability and convenience of its fastening in the selected places of application of the fastening forces;

4) exclusion of deformation of the bending of the workpiece from the selected scheme of its fastening.

The choice of the basing and installation method is made by the technologist developing the technological processing route. They are shown on operational sketches using a system of symbols defined by GOST 3.1107-81. The chosen schemes of basing and installation are used by the designers of technological equipment when designing fixtures.

Depending on the geometric shape of the workpiece, various installation schemes are used, differing in the shape and location of the technological bases, the number of reference points on each of them, the number of degrees of freedom deprived and the fastening scheme. The following are examples of common ways of locating and mounting workpieces.

For workpieces processed on lathes and cylindrical grinding machines and rotating about the longitudinal axis, installation in chucks is used (Fig. 7).

Parts with a center hole can be mounted on tapered internal chamfers or in centers. In this case, corrugated centers or driving chucks are used to transmit torque (Fig. 8). For parts of small diameters, reverse centers are used.

Using these installation methods, a wide range of parts such as “body of revolution” is processed: shafts, axles, rods, plungers, etc.

Installation on the inner surface of rotation and a plane perpendicular to its axis is performed when processing workpieces of parts with a main central hole (bushings, sleeves,

cups, discs with holes, rings, etc.). When processing rotating workpieces, they are installed in chucks with cams in a thrust over the hole (Fig. 9), on cylindrical (Fig. 10) and conical mandrels or mandrels with sliding elements.

Rice. 7. Installing the part in a three-jaw chuck. Set of bases: double guide (points *1* , *2* , *3* , *4* ); reference (points *5* , *6* ): *a* – structural diagram; *b* – theoretical basing scheme; *c* – installation scheme

Rice. 8. Installing the part in the centers with a driving chuck. Set of bases: double guide (points *1* , *2* , *3* , *4* ); reference (points *5* , *6* ): *a* – structural diagram; *b* – theoretical basing scheme; *c* – installation scheme

Workpieces that do not have rotation during processing are based on the outer surfaces of rotation in prisms (Fig. 11) or in bushings.

Rice. 9. Installing the part in the three-jaw parton in the unclamp. Set of bases: installation (points *1* , *2* , *3* ); reference (points *4* , *5* , *6* ): *a* – structural diagram; *b* – theoretical basing scheme; *c* – installation scheme

Rice. 10. Installation of the workpiece on a cylindrical mandrel. Set of bases: double guide (points *1* , *2* , *3* , *4* ); reference (points *5* , *6* ): ; *b* – theoretical basing scheme; *c* – installation scheme

Installation on a plane is used in the processing of blanks for housings, brackets and other parts that have surfaces or elements that it is advisable to use as installation and guide bases. For parts with holes

parallel axes often use installation on a plane, round and cut fingers (Fig. 12).

Rice. 11. Installation of a cylindrical workpiece in a prism. Set of bases: double guide (points *1* , *2* , *3* , *4* ); reference (points *5* , *6* ): ; *a* – theoretical basing scheme; *b* – installation scheme

Rice. 12. Installing the part on a plane, round and cut fingers with vertical axes. Set of bases: installation (points *1* , *2* , *3* ); reference (points *4* , *5* , *6* ): *a* – structural diagram; *b* – theoretical basing scheme; *c* – installation scheme

Installation on the gear surfaces and the end is carried out when grinding the axial holes of the blanks of cylindrical and bevel gears (Fig. 13). As setting elements, three rollers are used for spur gears and six balls (two in each cavity) for cylindrical gears with a spiral tooth and bevel gears. For the same purpose, devices with three gears are used.

Rice. 13. Installing the part on a plane and a jagged surface. Set of bases: installation (points *1* , *2* , *3* ); reference (points *4* , *5* , *6* ): *a* – structural diagram; *b* – theoretical basing scheme

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