JP7312427B2 - Dynamic vibration absorber for suppressing stick-slip and method for suppressing the same - Google Patents

Description

The present invention relates to a dynamic vibration reducer that suppresses stick-slip and a method for suppressing the same.

Design formulas for suppressing stick-slip have been published in past studies. According to the design formula, methods for suppressing stick-slip that occurs on the sliding surface generally include reducing the difference between static friction and dynamic friction, making the relative velocity dependence of the dynamic friction coefficient positive, and increasing the rigidity of the system. The former method of controlling the coefficient of friction is based on improving the roughness of the sliding surface and the lubricating oil. The latter, which focuses on rigidity, is often difficult in terms of system functionality (for example, the jig that supports the sliding surface is a cantilever beam and there is no space).

On the other hand, there is a dynamic vibration absorber as a general technique for suppressing or reducing vibration. A dynamic vibration absorber is a technology that reduces the vibration of both the main vibration system and the secondary vibration system by attaching an additional mass (secondary vibration system) to a vibrating object (main vibration system), and the design method of the dynamic vibration absorber is already known.

Patent Document 1 describes a frictional vibration, which is vibration excited by friction generated by the sliding of a driving portion and a driven portion that slide relative to each other, and describes a "structure having a sliding surface with lateral slip" that gives a driving angle φ where φ≠0 as an angle between the driving direction of the driving portion 110 and the deformation direction of the driven portion 120, preferably an angle equal to or greater than the critical driving angle φc, in the "driving direction of the driving surface of the driving portion 110" and the "direction in which the supporting portion of the driven portion 120 deforms." , and that the critical drive angle φc is defined by the relative speed Vrel between the drive portion 110 and the driven portion 120 and the friction coefficient μ (Vrel) with this relative speed Vrel as a parameter, and that the noise caused by the frictional vibration can be suppressed. Further, Patent Document 2 describes the natural frequency of the dynamic vibration absorber with respect to the spring constant of the parallel leaf spring type dynamic vibration absorber.

JP 2013-007737 A JP 2015-094384 A

However, in the prior art, the technology of the dynamic vibration reducer is not applied to the stick-slip phenomenon. Therefore, an object of the present invention is to propose a design formula for suppressing stick-slip by using a dynamic damper.

(1) A dynamic vibration absorber that acts by contacting a vibrating body having a sliding surface on which stick-slip occurs and suppresses stick-slip.
（２）（１）に記載の作用は、動吸振器の取り付けモデルを適用した設計式が、式（９）により定まるダンピング比ζ _ｅqと、式（６）により定まる無次元パラメータλとによって定義される式（１０）の不等式が成立するように、質量比率μ _ｏｐｔが決定される質量比率決定ステップと、決定された質量比率μ _ｏｐｔにより式（１１）、（１２）及び（１３）によってそれぞれ定まる動吸振器の最適な付加質量ｍ _ａｏｐｔ 、動吸振器のばね定数ｋ _ａｏｐｔ 、動吸振器の減衰係数ｃ _ａｏｐｔが決定される動吸振器特性決定ステップと、を備える手順によって発現することを特徴とするスティックスリップを抑制する動吸振器の設計方法である。
(3) A stick-slip suppression method using the dynamic vibration absorber designed by the design method described in (2).

A dynamic vibration absorber designed according to a design formula for suppressing stick-slip can suppress stick-slip that occurs.

1 is a diagram schematically showing a specific example in which a dynamic vibration reducer according to one embodiment of the present invention is attached to a stick-slip vibrating body; FIG. FIG. 10 is a diagram showing an example in which a work material is fixed to a stick-slip vibrating body; FIG. 2A is a diagram schematically showing (A) a model of a stick-slip vibrating body, and (B) a model in which a dynamic vibration reducer according to one embodiment of the present invention is attached to a stick-slip vibrating body. FIG. 4 is a diagram showing that the effective damping ratio ζ _eq =0.10 when μ=0.0833 in the formula representing the stick-slip generation condition determined by the design formula. FIG. 10 is a diagram showing regions where stick-slip occurs (Stick-Slip) and where no stick-slip occurs (Damped vibration); FIG. 6 is a diagram showing (a)-I (stick-slip), (a)-II (stick-slip), and (a)-III (damped vibration) in FIG. 5;

BEST MODE FOR CARRYING OUT THE INVENTION Hereinafter, embodiments of the present invention will be described with reference to the drawings. The present invention is not limited to the following embodiments, and changes, modifications, and improvements can be made without departing from the scope of the invention.

FIG. 1 shows a cutting apparatus (1) as a specific example in which a stick-slip vibrating body (4) (hereinafter sometimes referred to as "vibrating body") is attached with a dynamic vibration reducer (10) (hereinafter sometimes referred to as "dynamic vibration reducer") that suppresses the stick-slip. A cutting device (1) comprises a dynamic vibration reducer (10), a vibrating body (4), a power mechanism (2) and a work material (4). A vibrating body (4) is connected to the power mechanism (2) by a support mechanism (3), an additional mass (11), which is a component of the dynamic vibration absorber (10), is attached to the vibrating body (4), and a workpiece (20) is fixed on the vibrating body (4) in contact therewith. The vibrating body (4) is sometimes referred to as a sliding guide surface from the viewpoint of the function that it exhibits. A work material (20) is a part to be machined by a machine tool.

When the vibrating body (4) is driven by the support mechanism (3), it is driven in contact with the friction surface (7) of the guide (6) of the power mechanism (2). The friction surface (7) formed by contact between the vibrator (4) and the guide (6) is particularly called a sliding surface (8).

A ball screw or the like is used as the power mechanism (2). Regarding the size of the vibrating body (4), the longitudinal dimension L1 is 1000 to 2000 mm and the lateral dimension L2 is 500 to 1000 mm from the viewpoint of the size of the workpiece to be fixed.
On the other hand, the mass of the additional mass (11) is preferably several % to 10% of the vibrating body (4) from the viewpoint of reducing the weight of the machine tool as a whole and effect of reducing vibration.

FIG. 2 shows an example of fixing the work piece to the vibrating body, where the work piece member (21) is placed fixedly on the vibrating body (14). Note that the device 22 is used when a processing tool such as a grindstone is attached. The role of the dynamic vibration absorber is to suppress the vibration generated in the vibrating body (4) by attaching it to the vibrating body (4), and does not limit the driving of the device 22 or the like.

The dynamic vibration reducer (12) will be described based on the model of FIG. As shown in FIG. 3A, the vibrating body has a mass m (kg), a static friction coefficient μ _s and a kinetic friction coefficient μ _k , and is fixed to a rigid base via a spring constant k (N/m). Stick-slip occurs when the lower surface of the vibrator 14 is driven at a speed V (m/s, driving speed) while a load (Normal load) W(N) is applied.
On the other hand, the dynamic vibration absorber (12) (DVA system) is given by its design formula to have a mass _ma (kg), a spring constant _ka (N/m) of the dynamic vibration absorber, and a damping constant _ca (Nsm) of the dynamic vibration absorber, and is connected to the vibrator as shown in FIG. 3(B). The driving speed V (m/s) for the lower surface is the same.

The static friction coefficient _μs is generated by the stick-slip vibrating body (14) having a sliding surface (18, not shown), and the dynamic vibration damper (12) is coupled to the stick-slip vibrating body (14), thereby suppressing the stick-slip of the vibrating body (14). Combining is one aspect of contacting, and the dynamic vibration absorber acts on the dynamic vibration absorber that sticks and slips.

The equation of motion of the vibrator (14) and the dynamic vibration absorber (12) in FIG. 3(B) is represented by the following equation (1).

However, F is the frictional force acting on the sliding surface (18) of the vibrating body (14) and is expressed by the following formula according to the sliding direction.

Here, x (dot) is the velocity of the vibrator (14). In the case of x (dot)=V (stick state), the velocity of the vibrator (14) and the lower surface are equal and the two are stuck together. In this case, the static friction force _Fs acts. The range of the static friction force _Fs is expressed by the following formula.

Moreover, when x (dot) and V (stick state) are different, a slip acts between the vibrating body (14) and the lower surface, and a dynamic friction force _Fk acts. Note that the dynamic friction force _Fk is represented by the following formula.

Note that the static friction coefficient μ _s and the kinetic friction coefficient μ _k in this model are assumed to be constant independent of the speed of the sliding surface, as described below.

FIG. 6 is obtained by numerically calculating the governing equations consisting of the above equations (1) to (5). The vertical axis in FIG. 6 is the displacement x of the vibrator (14), and the horizontal axis is time.

Here, if a dimensionless parameter λ defined by the following equation (6) is introduced, the stick-slip non-occurrence condition can be expressed by the equation (7). The validity of Equation (7) is verified by reference 1 (design guidelines for avoiding stick-slip, Takeshi Nakano, Japan Rubber Association, 2007).

Furthermore, by introducing a dimensionless parameter μ defined by Equation (8), ζ _eq included in Equation (7) is expressed by Equation (9). In addition, the validity of Formula (9) is proved by the reference document 2 (Dynamic vibration absorber and its application, Kazuto Seto, Coronasha, 2010). Note that FIG. 5 shows the relationship between μ and ζ _eq given by equation (9).

Combining equations (7) and (9), equation (10) is obtained as a design equation for avoiding stick-slip.

From the above, the following is obtained as a design guideline for stick-slip avoidance. First, for the stick-slip vibrating body shown in FIG. 3A, mass m (kg), static friction coefficient μ _s , kinetic friction coefficient μ _k , spring constant k (N/m), load W (N), and speed V (m/s, driving speed) are estimated to determine the dimensionless parameter λ. Next, after substituting the obtained λ, a dimensionless parameter μ for establishing the expression (10) is set (μ adjusted so that the expression (10) holds is called μ _opt ). From the finally obtained μ _opt , optimum values of mass _ma (kg), spring constant _ka (N _/ m) _of the dynamic vibration absorber, and damping constant _ca (N sm) of the dynamic vibration absorber in the model shown _in FIG. Get more. In summary, stick-slip can be suppressed by determining μ _opt from equation (10), determining m _aopt , k _aopt , _and caopt from equations (11) to (13), and attaching a dynamic vibration reducer having these dynamic vibration reducer parameters to the vibrating body.

FIG. 5 shows the result of applying the analysis result of FIG. 6 to the inequality of formula (10). It can be seen from the figure that stick-slip is suppressed only in a-(III) of FIG. 5, and stick-slip is suppressed if the inequality is satisfied (if the damped vibration region in the figure is entered). It can be seen that stick-slip cannot be avoided in a-(I) and a-(II), which do not satisfy the inequality (in the stick-slip region in the figure). From the above, the validity of Expression (10) is confirmed.

Stick-slip can be suppressed for vibrating bodies that cause stick-slip.

1: Cutting device 2: Power mechanism 3: Support mechanism 4, 14: Vibrating body 5: Vibrating body with dynamic vibration absorber 6: Guide 7: Friction surface 8, 18: Sliding surface 10, 12: Dynamic vibration absorber 11: Added mass 20: Work material 22: Apparatus L1: Longitudinal dimension of vibrating body L2: Transverse dimension of vibrating body

Claims (3)

A dynamic vibration absorber that acts by contacting a vibrating body having a sliding surface on which stick-slip occurs and suppresses stick-slip ,
A dynamic vibration absorber having the added mass m _aopt of the optimum dynamic vibration absorber parameters, the optimum dynamic vibration absorber spring constant k aopt , and the optimum dynamic vibration absorber damping coefficient c aopt obtained from the formulas (11), (12) and (13) using the mass ratio μ opt for μ adjusted so that the formula (10) holds for the dimensionless λ determined by the _formula ( _{6 )} .

(In formula (6), μ _s : static friction coefficient of vibrating body, μ _k : dynamic friction coefficient of vibrating body, W: load (N) applied to vibrating body, V: driving speed (m/s) of lower surface of vibrating body with load W applied, m: mass of vibrating body (kg), k: spring constant k (N/m), respectively)



The operation described in claim 1 includes a mass ratio determination step in which the mass ratio μ _opt is adjusted so that the inequality of equation (10) holds true for the dimensionless parameter λ determined by equation (6), and the optimum additional mass m _aopt of the dynamic vibration absorber and the dynamic absorber determined by equations (11), (12) and (13) based on the determined mass ratio μ _opt , respectively. A dynamic vibration absorber characteristic determining step in which the optimum spring constant k _aopt of the vibration absorber _and the optimum damping coefficient caopt of the dynamic vibration absorber are determined. A method for suppressing stick-slip using a dynamic vibration absorber designed by the design method according to claim 2.