Precision machinery and instruments are composed of thousands of components. Under the action of external forces, the size and shape of the components will always have a different degree of change, this change is called deformation. Deformation can be divided into elastic deformation and plastic deformation. After the withdrawal of the external force, the deformation will disappear is called elastic deformation; when the external force exceeds a certain limit, after the withdrawal of the external force is still residual deformation is called plastic deformation. The strength and stiffness of the part refers to the ability of the material to resist damage and deformation under the action of external forces. This chapter is mainly a few simple and commonly used components as an example, for the principle of deformation and its impact, the introduction of precision machinery in the component strength, stiffness, stress analysis of the basic concepts and methods.
1. Strength
The so-called strength refers to the ability of the component to resist damage, to ensure that the parts will not break or have significant plastic deformation. If the machine tool spindle by the load is too large and fracture, the entire machine tool cannot be used, therefore, the strength calculation is a very important part of the design of precision machinery parts.
2. Rigidity
The so-called stiffness refers to the ability of the component to resist deformation to ensure that the elastic deformation of the parts in the force produced is within the permissible limits, so that the parts can work properly. Components in the external force caused by the deformation cannot exceed the scope of engineering permission. If the spindle of the machine tool and the body of the stiffness is not enough, will affect its machining accuracy, but also produce excessive noise; if the house components of the stiffness are not enough, will make the residents lack of security.
3. Stress and deformation
3.1 Classification of force
When a mechanism or precision mechanical part works, its parts are subject to force and transfer it between each other. These act on the component. The force on it is also called the load. There are several main ways to classify force.
(1). According to the source of force, it can be divided into main power and constraint reaction. In general, the main force is the load, the constraint reaction is the force, and its role is to prevent the movement of the object caused by the load.
(2) According to the scope of force, it can be divided into concentrated force and distributed force.
If the external force distribution range is far less than the surface size of the object, or the distribution range along the axis of the rod is far less than the axis length of the rod, the external force can be simplified into a concentrated force acting on a point, such as the pressure of the train wheel on the rail, the reaction force of the ball bearing on the shaft, etc., the dimension is [force], the international unit is N (N).
The so-called distribution of force, refers to the force acting on the surface of the object or at various points within the object, can be further divided into line distribution of force, surface force and volume force. Some of the distribution of force is along the axis of the rod, such as such as the force of the floor on the roof beam, which can be simplified to the line distribution force distributed on the axis of the beam, the outline is simplified to [force] / [length], the international unit is N / m (N per metre); surface force refers to the continuous action on the surface of the object in a wider range of force, for example, the liquid on the pressure of the container; the outline is [force] / [length] 2, the international unit is N / m2 (N per square metre); so-called distribution of force, is acting on the surface of objects or points within the object, can be further divided into line distribution of force, surface force and volume force.m2 (cattle per square metre); the so-called volumetric force, refers to the continuous distribution of forces at various points within the object, for example, the object’s self-gravity and inertial forces, etc., the outline is [force]/[length]*, the international unit is N/m3 (cattle per cubic metre).
(3) According to the relationship between force and time, can be divided into static load and dynamic load. The so-called static load, refers to the load from zero slowly increased to the final value, and then remain unchanged or insignificant changes in the load. For example, when an instrument is placed slowly on a base, a static load is applied to the base. Dynamic loads are loads that change significantly over time. According to its change can be divided into alternating load, impact load. Alternating load refers to the load with time is a periodic change, such as gear rotation, each tooth on the meshing force is a periodic change with time; impact load refers to the instantaneous load applied to the object, such as forging, the hammer and the workpiece contact is completed in an instant, the workpiece and the hammer are subject to the impact of the load.
(3) The assumption of isotropy is that elastomers have mechanical properties orientated in different directions. Most engineering materials, although not isotropic in the microscopic, such as metal materials, the mechanical properties of its individual grains have directionality, but the elastomer contains a very large number of grains, and random orientation, and thus in the macroscopic performance of isotropy. With this isotropic elastomer is called isotropic elastomer. Along different directions with different physical and mechanical properties of the elastomer, called anisotropic elastomer.
3.2 Elastomer
When studying the statics of rigid bodies, people ignore the deformation of objects and abstract them as rigid bodies. But in fact, any object will change its size and shape after being stressed, and this change includes elastic deformation and plastic deformation. In engineering applications, the deformation of most objects is limited to the elastic range, and the object is called elastic deformable, referred to as elastic body.
In order to establish the mechanical model of elastomer, the following assumptions are made about elastomer.
(1) The continuity hypothesis holds that the materials composing the elastomer fill the entire geometrical space of the elastomer without any gaps. In fact, there are gaps between the particles that make up the elastomer, but these gaps are extremely small and negligible compared to the size of the elastomer. Thus, the matter in the elastomer can be considered continuous. In this way, both the mechanical quantity and the deformation in the elastomer can be expressed as a continuous function of coordinates.
(2) The homogeneity hypothesis holds that the mechanical properties at all points in the elastic body are the same. According to this assumption, the microunits cut from any part of the interior of the elastomer have exactly the same mechanical properties. At the same time, the material properties measured by large size samples can also be used in any part of the elastomer.
(3) The isotropy hypothesis assumes that elastomers have opposite mechanical properties along different directions. Although most engineering materials are not isotropic in the micro level, such as metal materials, the mechanical properties of their individual grains are directional, but the number of grains contained in the elastomer is very large, and the random orientation, so it is isotropic in the macro level. An elastomer with this isotropy is called an isotropic elastomer. Elastomers with different physical and mechanical properties in different directions are called anisotropic elastomers.
3.Elastic deformation
In engineering applications, the deformation should be controlled within the range required and allowed when the part is designed, and the deformation of the part is generally elastic deformation. According to the characteristics of deformation, elastic deformation can be divided into: tensile and compressive deformation, such as the deformation of chain, belt, truss rod (or pressure rod), column, etc.; Shear deformation, such as the deformation of screws and rivets under shearing force; Torsional deformation, such as that of a drive shaft; Bending deformation, as of various beams. These kinds of deformation are simple deformation, is the basic form of deformation. Some parts work under more complex loads, such as the combined action of stretching (or compression) and bending, the combined action of bending and torsion, etc., may produce two or more kinds of deformation at the same time, such deformation is called complex deformation.
