The computation of stiffness of deputy drive of feed ball guide screw
- source:HOTA CNC Machining
The Result Supplies A Basis To Determine Positioning Accuracy And Driving Accuracy In Design Of NC Machine Tools And Precision Machines.
Key Words: Ballscrew, the Rigidity development as modern science and technology, mechanical manufacturing industry is facing the new challenge such as high rate, high accuracy ceaselessly. And the ball guide screw of low stiffness deputy it is one of main reasons that bring about motion to lose. Reach precision of the fixed position precision of accurate machinery and drive to raise numerical control machine tool, besides each proper design, parts that select feed system, mathematical calculation outside its intensity, stability and driving moment, even deputy to accurate ball guide screw in bear the stiffness below load undertakes checking computations, work in order to ensure its are safe, reliable, stable. The article with respect to feed ball guide screw deputy stiffness calculation method undertakes discussion, explain with example its apply actually. Xiang Gang of deputy layshaft of guide screw of ball of axial stiffness feed spends guide screw of 1 feed ball express ball guide screw deputy reach its bearing component to resist ability of metabolic of its axial flexibility. With bedspring constant K1 expresses, press type is calculated the K1 in 1 type of K1=F/ δ -- stiffness of axial of system of deputy transmission of feed ball guide screw, f of of of of N/ μ M -- bring to bear on the axial at feed guide screw is laden, δ of of N 1 -- displacement of flexibility of deputy axial of feed ball guide screw, KS of of of μ M -- stiffness of guide screw axial, KN of of of of N/ μ M -- stiffness of nut component axial, KB of of of of N/ μ M -- stiffness of bearing bearing axial, KH of of of of N/ μ M -- nut bracket and stiffness of bearing bracket axial, n/ μ M1.
Because installation kind is different and the axial stiffness of guide screw of computation of stiffness of axial of 1 guide screw is different. 1.
1 pair is pushed, the axial stiffness of bearing installation guide screw is used double push, when bearing means installs guide screw, the axial stiffness of guide screw comes along with load action point pair of distances that choose bearing end change and change. Its are the smallest stiffness KS presses type is calculated the A in type -- the section of guide screw is accumulated, of of of of Mm2 (D is whorl trail, mm) E of -- the stretch model quantity of guide screw material, to E=2 of of of of of rolled steel .
La of of of 07 × 105MPa -- load action point is apart from pair of the largest spaces that push bearing, the standard ball guide screw that A of Mm attached drawing produces for Japanese essence machine double push, the axial stiffness graph when bearing is installed. Stiffness of axial of ball guide screw pursues 1.
2 pairs are pushed, double the axial stiffness that turns installation guide screw is used double push, double when turning installation guide screw, formula of computation of its axial stiffness is the L in type -- two pairs push bearing to carry a distance, mm by on type can see, guide screw is used double push, double when pushing means to install, stiffness also is change, and be worth in place axial stiffness the smallest, its are the smallest value. The standard ball guide screw that attached drawing B produces for Japanese essence machine double push, double the axial stiffness graph when pushing installation. 1.
The stiffness of 2 nut is united to produce title of manufacturer trade catalogue with majority, the article still stiffness of nut of continue to use this one name. Nut stiffness fact is the stiffness of nut component, include the axial stiffness of raceway of whorl of ball and guide screw, nut. Contact theory according to hertz, the axial between ball and whorl raceway is stretch deflection δ N presses type is calculated (μ M) the α in type -- the osculatory horn of ball, (° ) F of -- axial load, d0 of of N -- ball diameter, z of of Mm -- φ of Dm/(d0cos of π of Z= of of of number of ball of every effective load) Dm of -- nut nominal diameter, φ of of Mm -- helix promotes role, (° ) 1.
Guide screw of ball of feed of stiffness of axial of 1 odd nut when the deputy nut that it is sheet, if axial work load is equal to 30 ％ to move rated load Ca, its stiffness KN=0.
8K ′ 1 (the 1 stiffness that in be being expressed for trade catalogue dimension, gives out is worth K ′ ) ; When if axial load is not equal to 30 ％ ,moving rated load Ca, its axial stiffness presses type is calculated 1.
2 belts press the stiffness of double nut axial of load to should press load Fao=0 beforehand beforehand.
When 1Ca, its stiffness KN presses type is calculated KN=0.
1 of 8K ′ is become Fao ≠ 0.
When 1Ca, formula of stiffness KN computation is the Fao in type -- press load beforehand, n1.
When does not add the stiffness KB of 3 bearing bearing to press load beforehand, bearing axial stiffness presses type is calculated the F in type of KB=F/ δ B -- axial load, b of δ of of N -- quantity of displacement of bearing axial flexibility, when μ M brings to bear on to press load beforehand, formula of computation of bearing axial stiffness is the Fao in type of KB=3Fao/ δ Ao -- axial presses load beforehand, ao of δ of of N -- in press load action to fall beforehand, axial flexibility displacement, the axial flexibility displacement of all sorts of bearing of μ M measures formula of δ B computation to be as follows: ① moves a heart automatically ② of ball bearing is conic ③ of roller bearing stops the α in turning ball bearing pattern -- osculatory horn, (° ) Q of -- add at bearing the load on body of a scroll, d0 of of N -- the diameter of bearing scroll body, l of of Mm -- the effective contact length of bearing roller, z of of Mm -- bearing scroll body several 1.
The stiffness of the bracket of nut of stiffness KH of 4 nut and bearing bearing component, already multiplied when nut stiffness is calculated with coefficient 0.
8 plan into. Bearing installs the stiffness of the component to be able to spend bearing component to solve through using Gao Gang. Guide screw of 2 feed ball turns round stiffness deputily to affect feed ball guide screw deputy the main factor that seizes change form is guide screw. Below only with respect to guide screw turn round stiffness to undertake discussion. Of guide screw turning round stiffness is to show guide screw resistance turns round metabolic ability, its computation formula is the KT in type -- guide screw turns round stiffness, n.
θ of of Mm/rad -- reverse part, m of of Rad -- torque, n.
G of of Mm -- guide screw material is fought cut stretch model amount, to G=8 of of rolled steel .
JP of of of 24 × 104MPa -- sectional and inertial quadrature, to sincere guide screw, deputy transmission stiffness is in guide screw of Mm43 feed ball below load action, feed ball guide screw deputy axial flexibility is out of shape be guide screw twist change form to become ball guide screw for this horn convert deputy axial deflection is the T in type -- lead of ball guide screw, guide screw of ball of Mm reason deputy total axial is out of shape for can get (μ M) the K in type -- stiffness of deputy drive of feed ball guide screw, of N/ μ M because 2 δ of δ 1, when so computational guide screw turns round stiffness KT, x takes the following numerical value system of deputy transmission of guide screw of one feed ball uses 4 computation example double push, bearing means. Foregone data is: La=1800mm, double the automatic attune heart that promotes bearing to carry bearing to be decorated to carry back of a chair on the back ball bearing, ball bearing diameter 5.
556mm, ball bearing several Z=15, contact ° of horny α =30, bearing tightens force Fao=3kN beforehand; Model of ball guide screw is BNFN3612, 2.
5GO, dp=37 of ball center round diameter.
5mm, ball diameter is 7.
144mm, move rated load Ca=27 basically.
2kN, tighten force Fao=0 beforehand.
1Ca, the requirement is calculated stiffness of its system drive. Computational move is as follows: (1) of computation of stiffness of guide screw axial (2) computational nut stiffness presses foregone condition, check from inside watch of trade catalogue dimension M of μ of K ′ 1=750N/ , KN=0.
8K ′ 1=0.
M of μ of 8 × 750=600N/ . (3) bearing of bearing of stiffness of computational bearing bearing is automatic attune heart ball bearing and tighten beforehand, because of this (4) nut bracket and bearing advanced already face calculates stiffness of bracket of stiffness KH nut nut stiffness with coefficient 0.
8 plan into, do not grant to consider here. Set bearing stiffness is very big, namely → 0, then, deputy axial stiffness K1 can pass guide screw of this system ball the following computation is gotten for (5) guide screw turns round stiffness by model of ball guide screw knowable its lead T=12mm, check from inside watch of trade catalogue dimension D=30 of trail of guide screw whorl.