JPH0989703A - Method for eliminating dynamic unbalance - Google Patents

Abstract

PROBLEM TO BE SOLVED: To judge whether or not correction should be executed before the correction and to determine an adequate quantity of the correction by a method wherein four simultaneous basic equations that have unknown values of correction quantities are obtained in order to offset dynamic unbalance of a rotary body obtained by measuring. SOLUTION: On set five correction faces #1-#5, correction angle positions V1-V12 are limited in respective maximum correctable quantities. Initial dynamic unbalance vectors measured on the correction faces #1, #5 are U1, U5 and the balancing of them is executed such that each of them is respectively corrected in an adequate quantity on the positions V1-V12. In order to offset dynamic unbalance obtained by measuring, four simultaneous basic equations that have unknown values of correction quantities on the positions V1-V12 are obtained. Next, the basic equations are expanded on the basis of the maximum correctable quantities. After that, when solutions exist in the equations, the correction quantity is determined such that estimation function as a sum of values that a weight coefficient is multiplied to the correction quantities with respect to the positions V1-V12 is minimized.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a dynamic unbalance of a rotating body such as a crankshaft of an engine, and particularly to a correction amount for the balance after determining whether or not the balance is possible. Regarding the way I was asked.

[0002]

2. Description of the Related Art In order to balance the dynamic imbalance of a rotating body, the position and amount of the dynamic imbalance on any two correction surfaces of the rotating body are measured and corrected. However, in general, depending on the shape and properties of the rotating body, the correction surface position to be corrected, the angular position or range within the correction surface,
And there are often restrictions on the maximum modifiable amount. For example, an engine crankshaft has a correction surface position and an angle range that can be corrected in its counterweight portion, and the maximum correction amount is also limited.

A model of a crankshaft for a 6-cylinder engine as shown in FIG. 1 will be described. In the figure, # 1 to # 5 are correction planes, and correction angular positions are V1 to V on each correction plane.
There are 12 of 12, and the maximum modifiable amount is limited for each. U
1 and U5 are initial dynamic unbalance vectors measured on the two surfaces # 1 and # 5, and this balancing is performed by correcting an appropriate amount at the correction angular positions V1 to V12. Also, all correction radii are the same.

In the balancing by the conventional method, since two correction surfaces are considered, two surfaces out of # 1 to # 5 are selected, U1 and U5 are converted into the selected two correction surfaces, and conversion is performed. With respect to the unbalances U1 'and U5', vector decomposition is performed on the correction angular position on each correction surface, and the vector decomposed amount is used as the correction amount of the correction angular position. If the correction amount is negative, no correction is performed. If the correction amount exceeds the maximum correction amount, the maximum correction amount is set as the correction amount. If the balance is insufficient,
Select two surfaces from the correction surface that have not been used yet, measure the residual imbalance, and repeat the above steps. Further, if the balance is insufficient, the correction surface that is not used yet is only one surface, and therefore the correction of the dynamic imbalance is impossible.

[0005]

In the conventional method as described above, when the number of correction surfaces is odd, only one surface remains at the end, and it becomes impossible to correct the dynamic imbalance. However, in general, the conventional technology does not take into account the influence of all the correction force components of other correction surfaces, so it is not possible to accurately determine whether or not the dynamic imbalance is possible, and it is impossible to achieve the balance. Even for defective products such as crankshafts, which have a bad rotating body, there is a problem that the balancing work is unnecessarily advanced. Further, even if the balance is successful, there is a problem that it is not necessarily a rational balance with a small total correction amount. The present invention is intended to solve such problems,
It is an object of the present invention to provide a method capable of appropriately determining each correction amount for the above-mentioned balance after determining whether or not the dynamic unbalance of the rotating body is balanced.

[0006]

In order to achieve the above-mentioned object, the dynamic unbalance balancing method of the present invention sets two or more correction surfaces for the dynamic unbalance of the rotating body, and makes a total correction. In the case of dynamic unbalance when making corrections on at least 5 correction places on the surface,
The dynamic unbalance of the rotating body is obtained by measuring the dynamic unbalance of the rotating body, and then four mutually simultaneous basic equations in which the correction amount at the correction place for canceling the dynamic unbalance is an unknown number are obtained. Then, after expanding the basic equation based on the maximum modifiable amount at the correction place, if there is a solution of the equation, the evaluation function as the sum of the product of each correction amount at the correction place and the weighting coefficient. The feature is that each correction amount is determined at the same correction location so as to minimize.

Further, in the dynamic unbalance balancing method of the present invention, the rotating body is a crankshaft for a 6-cylinder engine, and the distance from the origin on the rotation axis of the crankshaft in the axial direction (Z-axis direction) is respectively determined. L ₁ , L ₂ , ... L ₅
And five correction surfaces are set, and the X and Y coordinate systems orthogonal to the Z axis are set, and the absolute values of the initial imbalances U1 and U5 obtained by the dynamic imbalance measurement are u ₁ , u ₅ and the angles formed with the X axis are θu ₁ and θu ₅ , and the correction component forces at the correction angle positions V1, V2 ... V12 are D1, D.
2, ... As D12, each amount of these modified component forces is d ₁ ,
Let d ₂ , ... d _{12 be} the angles formed with the X-axis be θ ₁ , θ ₂ , ... θ ₁₂ , then use the above basic equations [Equation 1], [Equation 2] for the condition of zero static imbalance. expressed by the formula, the moment equation (3) for unbalance is zero condition, with expressed by [expression 4] where the D1 as only cutting correction is performed, D2, a maximum correctable amount of ...... D12 d _m1 ，
When d _m2 , ... D _m12 , each correction component force is non-negative and is equal to or less than the maximum correctable amount.
Adding the conditions of the equations, when there are solutions d ₁ , d ₂ , ..., D ₁₂ that simultaneously satisfy the above equations when U1 and U5 are given, for the correction amount d _i The weighting coefficient C _i is introduced to determine the correction amount d _i so as to minimize the evaluation function ΣC _i · d _i .

[0008]

BEST MODE FOR CARRYING OUT THE INVENTION An embodiment of the present invention will be described below with reference to the drawings. FIG. 1 is a schematic explanatory view when the present invention is applied to a crankshaft for a 6-cylinder engine.

In FIG. 1, # 1 to # 5 indicate correction surfaces, and two or more correction surfaces (five in this embodiment) are set. There are 12 correction angular positions V1 to V12 on each correction surface, and the maximum correctable amount is limited. U1 and U5 are 2 of # 1 and # 5
This is an initial dynamic unbalance vector measured on the surface, and this balancing is performed by correcting each by an appropriate amount at the correction angular positions of V1 to V12. Also, all correction radii are the same.

The distances from the origin on the rotation axis of the crankshaft in the axial direction (Z-axis direction) of the respective correction surfaces # 1 to # 5 are set to L ₁ , L _2, ... L ₅ , respectively, and the Z-axis is set. The X and Y coordinate systems orthogonal to each other are set, the absolute values of the initial imbalances U1 and U5 obtained by the dynamic imbalance measurement are u ₁ and u ₅ , and the angles formed with the X axis are θu ₁ and θu ₅ , Corrected component forces at the corrected angular positions V1, V2 ... V12 are D1, D
2 ... D12, and the amount of each of these modified component forces is d ₁ , d ₂ ,
.. d ₁₂ , and the angles formed with the X axis are θ ₁ , θ ₂ , ... θ ₁₂ , the amount d ₁ of each correction component force at the correction angular position for canceling the dynamic imbalance U1, U5. d ₂ , …… d
Four basic equations with ₁₂ unknowns are
Regarding the condition that static imbalance is zero [Equation 6], [Equation 7]
It is expressed by a formula and expressed by the formulas [8] and [9] under the condition that the moment imbalance is zero.

(Equation 6)

(Equation 7)

(Equation 8)

[Equation 9] However, L _i = L ₁ i = 1,2 = L ₂ i = 3,4,5 = L ₃ i = 6,7 = L ₄ i = 8,9,10 = L ₅ i = 11,12 .

Assuming that only cutting correction is performed for dynamic imbalance, the above D1, D2 ,.
_Assuming that the maximum modifiable amount of 12 is d _m1 , d _m2 , ... D _m12 , each modified component force is non-negative and is equal to or less than the maximum modifiable amount. Is added.

[Equation 10] When 0 ≦ d _i ≦ d _mi i = 1, 2 ... 12 U1 and U5 are given, [Equation 6] to [Equation 9] expressions,
The set of solutions d ₁ , ..., D ₁₂ that simultaneously satisfy the equation (10) is divided into the following three cases. (1) No solution {impossible} ……………… Balancing is impossible (2) There is a single solution ……………… Limitation of equilibrium (3) There is an infinite number of solutions {undefined}… … There are endless ways of balancing.

By the way, in order to judge whether or not there is a solution in the above three cases and to perform the most rational balance when there is a solution, Σd _i (this is, in the present embodiment,
It means the total amount of shavings scraped from the counterweight for balancing). Further, in order to give priority to the use of the modified component force, a weighting coefficient C _i (which is a positive number) is introduced to d _i , and ΣC _i ·
It suffices to minimize d _i . By giving a large weighting coefficient to the correction component force having a low priority (preferably not to be used), a condition can be set so that the correction component is corrected only when it is unavoidable. Also, when the correction radii of the respective correction component forces are not the same, it can be set by multiplying the weighting coefficient by a coefficient inversely proportional to each correction radius. If all the correction places are treated equally, C _i = 1 may be set. Therefore, the formula [11] is introduced as the evaluation function.

[Equation 11] As described above, the meaning of this equation is that a small value of Z is treated as a better solution.

First, the extension of the above basic equation will be described step by step. Rewrite the expression [10] into the expression [12].

[Formula 12] d _i + d _{i + 12} = d _mi 0 ≦ d _i i = 1 ...
12 Since the coefficient of d _i in each equation of [Equation 6] to [Equation 9] is a constant,
Let the coefficients be A _i , _j (i = 1 ... 4, j = 1 ... 12), and the right side of each equation of [Equation 6] to [Equation 9] is the measurement of initial dynamic imbalance U1 and U5. It is a value, and it can be regarded as a constant at the stage of solving this equation. Therefore, by rewriting [Equation 6] to [Equation 9] and [Equation 10] as B _i (i = 1 ... 4), [Equation 13], [Equation 14] Expression is obtained.

[Equation 13] A₁,₁・ D₁＋ ………… ＋ A₁,₁₂・ D₁₂= B₁  A₂,₁・ D₁＋ ………… ＋ A₂,₁₂・ D₁₂= B₂ A_Three,₁・ D₁＋ ………… ＋ A_Three,₁₂・ D₁₂= B_Three A_Four,₁・ D₁＋ ………… ＋ A_Four,₁₂・ D₁₂= B_Four

D ₁ + d ₁₃ = d _m1 d ₂ + d ₁₄ = d _{m2 ::} d ₁₂ + d ₂₄ = d _m12

In order to combine the equations (13) and (14) into a set of simultaneous equations, A _i , _j are (i = 1 ... 16, j = 1 ...
… Extended to 24). Also, B ₅ = d _m1 , B ₆ = d _m2 , ...
…, B ₁₆ = d _m12 , the equation in question is [Equation 15]
Is a formula, and Z of [Formula 11] is obtained under the condition of [Formula 15].
It is a better solution to minimize.

[Equation 15]

Here, E ₁ , E ₂ , E ₃ , and E ₄ are respectively added to the _four left-hand sides of the equation [15] to obtain the equation [15].
Let [Equation 16] be the expression.

[Formula 16] A ₁ , ₁ · d ₁ ＋ ………… ＋ A ₁ , ₂₄・ d ₂₄ + E ₁ = B ₁ A ₂ , ₁・ d ₁ + ………… ＋ A ₂ , ₂₄・ d ₂₄ + E ₂ ＝ B ₂ A ₃ , ₁・ d ₁ ＋ ………… ＋ A ₃ , ₂₄・ d ₂₄ + E ₃ = B ₃ A ₄ , ₁・ d ₁ ＋ ………… + A ₄ , ₂₄・ d ₂₄ + E ₄ = B ₄ A ₅ , ₁・ d ₁ ＋ ………… ＋ A ₅ , ₂₄・ d ₂₄ = B ₅ :: A ₁₅ , ₁・ d ₁ ＋ ………… ＋ A ₁₅ , ₂₄・ d ₂₄ = B ₁₅ A ₁₆ , ₁・ D ₁ ＋ ………… ＋ A ₁₆ , ₂₄・ d ₂₄ = B ₁₆ d _i ≧ 0 If the right side of [Equation 16] is a negative number, then both sides of the equation −
Multiply by one. Since the general form of [Equation 16] is invariant, it will not be rewritten here.

Further, the equation (11) is transformed into the equation (17).

[Expression 17] C ₁ · d ₁ + ... + C ₁₂ · d ₁₂ −Z = 0 Further, the sum W of E ₁ , E ₂ , E ₃ , and E ₄ is introduced. That is, E ₁ + E ₂ + E ₃ + E ₄ = W. Also, if the four expressions above [Equation 16] are added and W is used to create a new expression, [Equation 18] is obtained.

[Expression 18] − (A ₁ , ₁ + A ₂ , _1, + A ₃ , _1, + A ₄ , _1, ) · d ₁ −
-(A ₁ , ₂₄ + A ₂ , ₂₄ + A ₃ , ₂₄ + A ₄ , ₂₄ ) d ₂₄ -W =-
(B ₁ + B ₂ + B ₃ + B ₄ ) The coefficients of d _{i in} the equations [17] and [18] and the right side are all constants. In addition, regarding -Z and -W as variables, the equation [16] is taken in and A _i , _j , and B _i are expanded to obtain the following equation [19].

[Formula 19] A₁,₁・ D₁＋ ………… ＋ A₁,_{twenty four}・ D_{twenty four}+ E₁ = B₁ A₂,₁・ D₁＋ ………… ＋ A₂,_{twenty four}・ D_{twenty four} + E₂ = B₂  A_Three,₁・ D₁＋ ………… ＋ A_Three,_{twenty four}・ D_{twenty four} + E_Three = B_Three A_Four,₁・ D₁＋ ………… ＋ A_Four,_{twenty four}・ D_{twenty four} + E_Four= B_Four A_Five,₁・ D₁＋ ………… ＋ A_Five,_{twenty four}・ D_{twenty four} = B_Five :: A_Fifteen,₁・ D₁＋ ………… ＋ A_Fifteen,_{twenty four}・ D_{twenty four} = B_Fifteen A₁₆,₁・ D₁＋ ………… ＋ A₁₆,_{twenty four}・ D_{twenty four} = B₁₆ A₁₇,₁・ D₁＋ ………… ＋ A₁₇,_{twenty four}・ D_{twenty four}-Z = B₁₇ A₁₈,₁・ D₁＋ ………… ＋ A₁₈,_{twenty four}・ D_{twenty four} -W = B₁₈ d_i≧ 0

As a preparatory step for solving the problem, the expressions [6] to [9] and [10] are expanded to the expression [19]. Further, since E _i , -Z, -W are treated as variables in a unified manner, d ₂₅ = E ₁ , d ₂₆ = E ₂ , d ₂₇ = E ₃ , d ₂₈ =
E ₄ , d ₂₉ = −Z, d ₃₀ = −W, and A _i , _j
To extend. (I = 1 ... 18, j = 1 ... 30). That is, the above-mentioned basic equation is extended as the following [Equation 20].

[Formula 20] A ₁ , ₁ · d ₁ + A ₁ , ₂ · d ₂ + ……………… + A ₁ , ₃₀ · d ₃₀ = B ₁ : :: ： A ₁₈ , ₁ · d ₁ + A ₁₈ , ₂ · d ₂ ＋ ………… ＋ A ₁₈ , ₃₀・ d ₃₀ ＝ B ₁₈

The determination as to whether or not there is a solution will be described step by step. In the first step, the minimum value of the coefficients A ₁₈ , _j (j = 1 ... 24) in the above formula for W is searched for, and G _s =
Let s be j, which gives Min (A ₁₈ , _j ). If more than one A
_{If 18} and _j give the same minimum, then choose randomly. Here, if G _s ≧ 0, there are no solutions d ₁ , d ₂ , ... D ₁₂ . At the second stage, A _i , _s (i = 1 ... 16, A _i , _s >>
Among 0), _let i be r that gives B _r / A _r , _s = Min · (B _i / A _i , _s ). If multiple A _i , _s give the same minimum value, then choose randomly. At this time, i in the above condition
There is no solution d ₁ , d ₂ , ... D ₁₂ without. In the third stage, sweeping out according to [Equation 19] is performed using A _r and _s as pivot elements. That is, A _r , _j = A _r , _j / A _r , _s B _r = B _r / A _r , _s P _i , _s = A _i , _s / A _r , _s as A _i , _j = A _i , _j −A _r , _j · P _i , _s (i = 1 ... 18,
However, i = r is excluded.) B _i = B _i −B _r · P _i , _s (j = 1 ... 30). Then, in the fourth stage, B ₁₈ is evaluated. If B
_{If 18} = 0, proceed to the fifth stage. From the fifth stage onward, a solution is sought to minimize the evaluation function Z. If B ₁₈ ≠ 0, the process returns to the first stage based on the calculation result of the third stage.

In this way, it is judged that the dynamic imbalance of the crankshaft cannot be corrected only when the solution of the expanded equation does not exist. Then, if it is determined that the above solution exists and can be corrected,
Move to the next stage. That is, in the fifth stage,
Search for the minimum value of the coefficients A ₁₇ , _j (j = 1 ... 24) in the equation relating to Z. Let _{s be j,} which gives C _s = Min (A ₁₇ , _j ).
If C _s ≧ 0, d ₁ ... D ₁₂ at this stage is the solution to be obtained and gives the minimum value of ΣC _i · d _i . Otherwise,
It shows that there is a better solution and goes to the sixth stage. In the sixth stage, A _i , _s of the s column (i = 1 ... 16, A _i , _s > 0)
I of which B _r / A _r , _s = Min · (B _i / A _i , _s )
Be r. If multiple A _i , _s give the same minimum, then choose randomly. In the seventh step, A _r, performs sweep-out of the number 19] Equation _s as pivot elements. That is, A _r , _j = A _r , _j / A _r , _s B _r = B _r / A _r , _s P _i , _s = A _i , _s / A _r , _s as A _i , _j = A _i , _j −A _r , _j · P _i , _s (i = 1 ... 17,
However, i = r is excluded.) B _i = B _i −B _r · P _i , _s (i = 1 ... 29) Based on the calculation result, the process returns to the fifth step.

By using the method described in detail above, it becomes possible to appropriately judge whether or not the dynamic imbalance is caused by the multi-correction surface / multi-correction component force, and the total correction amount of the imbalance balance is minimized. It is possible to make a match. In this way, by determining whether or not imbalance correction is possible, defective rotating parts that cannot be balanced are
Not only will the balance work not be wasted, but also the balance can be made reasonably accurately with a minimum total correction amount. Furthermore, by introducing a weighting factor, rational balance can be achieved even under the condition that priority is added to the correction place.

[0021]

As described above in detail, according to the dynamic unbalance method of the present invention, prior to the correction of the dynamic unbalance of the rotating body such as the crankshaft of the engine,
Whether or not the correction can be made is accurately determined, and in the case of the correction, the correction amounts at all the correction locations are appropriately determined so that the correction amount becomes small. In addition, by using the sum of products obtained by multiplying the correction amount by the weighting coefficient as the evaluation function,
It is also possible to accurately determine the balance correction amount under the condition in which the priority of each correction place and the correction radius are also taken into consideration.
In particular, according to the method of the present invention, it becomes possible to appropriately correct the dynamic imbalance of the crankshaft of a 6-cylinder engine, and to limit the depth of drilling when only the cutting correction is performed, and to set the weighting factor as a weighting factor. There is an effect that it can be treated by the introduction.

[Brief description of drawings]

FIG. 1 is an explanatory view schematically showing a correction place on each correction surface of a crankshaft for a 6-cylinder engine having five correction surfaces.

[Explanation of symbols]

 # 1-5 Correction surface V1-V12 Correction angle position U1, U5 Initial dynamic unbalance vector

Claims (2)

[Claims] 1. A dynamic imbalance in the case where two or more correction surfaces are set for the balance of the dynamic imbalance of a rotating body, and the correction is carried out at at least five correction locations on all the correction surfaces. After obtaining the dynamic unbalance of the rotating body by measuring the dynamic unbalance of the rotating body, four mutually simultaneous equations in which the correction amount at the correction place for canceling the dynamic unbalance is an unknown number are obtained, Then, after expanding the basic equation based on the maximum modifiable amount at the correction location, if there is a solution of the equation, the evaluation function as the sum of those obtained by multiplying each correction amount at the correction location by a weighting coefficient is calculated. A dynamic imbalance balancing method, characterized in that each correction amount is determined so as to minimize the correction amount. 2. The dynamic imbalance balancing method according to claim 1, wherein the rotating body is a crankshaft for a 6-cylinder engine, and an axial direction (Z-axis direction) from an origin on a rotation axis of the crankshaft. The distance of L ₁ , respectively
Set 5 correction planes, L ₂ , ... L ₅ ,
Initial imbalances U1 and U obtained by the dynamic imbalance measurement by setting an X and Y coordinate system orthogonal to the Z axis.
The absolute values of 5 are u ₁ , u ₅ , the angles formed with the X axis are θu ₁ , θu _5, and the respective corrected component forces at the corrected angular positions V1, V2 ... V12 are D1, D2 ,. The corrected component forces are d ₁ , d ₂ , ... D ₁₂ , and the angles formed with the X axis are θ ₁ , θ ₂ ,
...... When the theta _12, the basic equation, static imbalance is about zero condition Equation 1, Equation 2] represents the formula for moment imbalance is zero condition equation (3),
Together expressed by [Expression 4] where the D1, D2 as only cutting modification is performed, the maximum correctable amount of ...... D12 d _m1, d _m2, when the ...... d _m12, each modification amount competence Based on being non-negative and less than or equal to the maximum modifiable amount,
By adding the condition of the formula [5], solutions d ₁ , d ₂ , ... D which simultaneously satisfy the above formulas when U1 and U5 are given
_{When 12} is present, by introducing a weighting coefficient C _i relative to the amount of correction d _i, and determining the amount of correction d _i so as to minimize an evaluation function .SIGMA.C _i · d _i , Dynamic unbalanced balancing method. [Equation 1] [Equation 2] (Equation 3) [Equation 4] However, L _i = L ₁ i = 1,2 = L ₂ i = 3,4,5 = L ₃ i = 6,7 = L ₄ i = 8,9,10 = L ₅ i = 11,12 5] 0 ≦ d _i ≦ d _mi i = 1,2 ... 12