Allowable deflection analysis of the most popular

The allowable deflection analysis of modern machine tool spindle

preface

the rigidity of the components injected into the chamber of modern machine tool spindle is the main index reflecting the structural performance of spindle components. It comprehensively reflects the deformation of spindle and bearing, which is directly related to the machining accuracy of machine tool. The high-speed spindle is one of the key components of machine tools, so when designing the spindle components of high-precision CNC machine tools, it should meet the requirements of high stiffness. The stiffness of the spindle components is usually measured by the displacement in the direction of the force exerted by a certain force on the front end of the spindle. This displacement, called "deflection" at the end, is an important parameter in the design of spindle components. The allowable deflection has a decisive impact on the stiffness of spindle components, so it determines the service performance of machine tools

I. [y]=0.0002l source

at present, there is no unified regulation on the allowable value of the stiffness of the spindle components. Most of them take the displacement at the end of the main shaft, the rotation angle at the front bearing, the rotation angle at the gear mesh and the maximum cutting width without chatter, etc., which are often controlled by some empirical data and formulas. Among them, at the end of the main shaft, the overall prosperity of the mobile industry continues to decline, and the following contents are often used to control [2][3]:

1 The displacement of the spindle end of the finishing machine tool shall not exceed one third of the allowable radial runout of the spindle

2. The end deflection of spindle for general machine tools [y]=0.0002l

allowable deflection is widely used in China. At present, this empirical formula is also quoted in various school textbooks. As we all know, the teaching content of most relevant textbooks in China comes from the former Soviet Union, and almost all of them adopt the early discussions on the allowable deflection of shafts and spindles by liechetov and Archer Kang, the authorities of machine tool research in the former Soviet Union

literature [5] states: "for most shafts in machine tools (this section does not include the spindle), the ratio of the maximum deflection to the length between bearings is in the range of 0.0001---0.0005. Generally, it does not exceed 0.0002."

literature [6] also introduces: "the general criteria for determining the allowable deflection of machine tool spindles and shafts have not been studied. Therefore, in machine tool manufacturers, these test data that can be applied to machine tools without causing waste are still used. At present, the widely used data: the maximum deflection of the main shaft or shaft is 0.0002 times the distance between shaft seats." It can be seen from the above two documents that they did not specify the end deflection, and the scope of the discussions of the two authorities is different. Liechetov's statement does not include the main shaft, while Archer Kang's statement includes the main shaft

some textbooks in China, such as literature [1], introduce: "some factories believe that under rated load, the maximum deflection of the spindle ymax3. Requirements for fixture structure: it shall not exceed 0.0002l." There are also documents [2], [3], [7] "at present, there is no unified standard for the allowable value of the deflection y at the end of the spindle, and some materials recommend that for general machine tools, the maximum displacement ymax at the end of the spindle is required to be ≤ 0.0002l" or avoid explanation: "at present, there is no unified stiffness standard for spindle components." There is also a table in the 2006 edition of the mechanical design manual [8], which recommends "metal cutting machine tool spindle ymaxp=0.0002l". It can be seen that the latter indicates the deflection of the spindle end, while the former does not. But it can be judged that they are all quoted from Archer Kang's discussion

second, the deflection calculation value of typical machine tools

because there are many types of spindle of machine tools, in order to select typical examples of structure and performance to illustrate the problem, we use the deflection calculation of spindle end of several typical lathes as an example

in the calculation process, according to the different forms of support, it is divided into three calculation forms. On the computer (the calculation source program is abbreviated):

1 Two support structure forms: as shown in sketch 1,

the deflection of the spindle end is:

y=p[a3/(3ej) + la2/(3ej) + (1+a/l) 2/c1+ (a2/l2)/c2]

2 Three support structure, the front middle support is the main support: as shown in Figure 2,

is simplified to the front middle two supports, and the deflection of the end of the main shaft is:

y=pa2 (l+a)/(3ej) -rcal/(6ej) +ra (1+a/l)/c1+rb (a/l)/c2

where RA, Rb, RC are the support reactions, which can be obtained according to engineering mechanics

3. Three support structure, taking the front and rear supports as the main supports: the

shown in Figure 3 is simplified to the front and rear supports. After the mold at the end of the main shaft is installed, the mechanical action deflection of each part of the mold should be carefully checked as follows:

y=pa2 (l+a)/(3ej) -rca (L)/(6ejl) +ra (1+a/l)/c1+rb (a/l)/c2

among which RA, Rb and RC are support reactions, which can be obtained according to engineering mechanics

where p is the acting force at the head end of the main shaft (n)

e --- elastic modulus of spindle material (n/mm2)

j --- average moment of inertia of the main shaft section (mm 4)

c1 and C2 --- front and rear bearing stiffness (n/mm2)

a --- front end overhang of main shaft (mm)

l --- span between main supports (mm)

--- span between auxiliary supports (mm)

see Table 1 for the calculation results of typical spindle end deflection, and compare with the allowable value of [y]=0.0002l

Table 1 Comparison between calculated value and allowable value &nbs