KR20030050469A - Method for measuring shape error of spiral bevel gear - Google Patents
Method for measuring shape error of spiral bevel gear Download PDFInfo
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- KR20030050469A KR20030050469A KR1020010080900A KR20010080900A KR20030050469A KR 20030050469 A KR20030050469 A KR 20030050469A KR 1020010080900 A KR1020010080900 A KR 1020010080900A KR 20010080900 A KR20010080900 A KR 20010080900A KR 20030050469 A KR20030050469 A KR 20030050469A
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- 230000001186 cumulative effect Effects 0.000 claims abstract description 5
- 238000005259 measurement Methods 0.000 claims description 15
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- 238000000691 measurement method Methods 0.000 claims description 5
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/20—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring contours or curvatures, e.g. determining profile
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/02—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
- G01B21/04—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness by measuring coordinates of points
- G01B21/042—Calibration or calibration artifacts
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/30—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring roughness or irregularity of surfaces
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/32—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring the deformation in a solid
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Abstract
본 발명은 스파이럴 베벨기어의 형상오차 측정방법에 관한 것으로서, 더 상세하게는 기존의 방법으로 측정하기 어려운 치형오차(tooth profile error) 및 옆줄오차(tooth trace error)를 전용측정기가 아닌 범용 3차원 측정기(CMM; Coordinate Measuring Machine)를 이용하여 컴퓨터 상에서 알고리즘에 의해 측정하도록 하는 스파이럴 베벨기어의 형상오차 측정방법에 관한 것이다. 한편, 본 발명은 기존의 방법으로 측정되었던 스파이럴 베벨기어의 피치오차(인접피치오차 및 누적피치오차)를 더 정확하게 측정할 수 있는 스파이럴 베벨기어의 형상오차 측정방법에 관한 것이다.The present invention relates to a method for measuring a shape error of a spiral bevel gear, and more particularly, it is a general three-dimensional measuring device for tooth profile errors and tooth trace errors that are difficult to measure by conventional methods. The present invention relates to a method for measuring a shape error of a spiral bevel gear, which is measured by an algorithm on a computer using a Coordinate Measuring Machine (CMM). Meanwhile, the present invention relates to a method for measuring a shape error of a spiral bevel gear, which can more accurately measure a pitch error (adjacent pitch error and cumulative pitch error) of a spiral bevel gear, which has been measured by a conventional method.
Description
본 발명은 스파이럴 베벨기어의 형상오차 측정방법에 관한 것으로서, 더 상세하게는 기존의 방법으로 측정하기 어려운 치형오차(tooth profile error) 및 옆줄오차(tooth trace error)를 전용측정기가 아닌 범용 3차원 측정기(CMM; Coordinate Measuring Machine)를 이용하여 컴퓨터 상에서 알고리즘에 의해 측정하도록 하는 스파이럴 베벨기어의 형상오차 측정방법에 관한 것이다.The present invention relates to a method for measuring a shape error of a spiral bevel gear, and more particularly, it is a general three-dimensional measuring device for tooth profile errors and tooth trace errors that are difficult to measure by conventional methods. The present invention relates to a method for measuring a shape error of a spiral bevel gear, which is measured by an algorithm on a computer using a Coordinate Measuring Machine (CMM).
한편, 본 발명은 기존의 방법으로 측정되었던 스파이럴 베벨기어의 피치오차를 더 정확하게 측정할 수 있는 스파이럴 베벨기어의 형상오차 측정방법에 관한 것이다.Meanwhile, the present invention relates to a method for measuring a shape error of a spiral bevel gear, which can more accurately measure a pitch error of a spiral bevel gear, which has been measured by a conventional method.
당업자에게 잘 알려진 바와 같이, 스파이럴 베벨 기어(Spiral Bevel Gear; SBG)는 소형으로 높은 토오크를 전달하기 위한 목적으로 사용되며 직선 베벨 기어에 비하여 스파이럴 곡선을 따라 치형이 형성된다. 스파이럴 베벨 기어의 기어형상은 기어형상 중에서 가장 복잡한 형상으로서 정밀한 칫수공차를 요구하며, 이의 측정방법 또한 매우 중요하다.As is well known to those skilled in the art, Spiral Bevel Gears (SBGs) are used for the purpose of delivering high torque in a compact form and are toothed along spiral curves as compared to straight bevel gears. The gear shape of the spiral bevel gear is the most complicated shape among the gear shapes and requires precise tolerances, and its measuring method is also very important.
도 1a 내지 도 1c에 스파이럴 베벨기어의 형상오차의 종류를 개략적으로 나타내 보였는데, 도 1a는 치형오차(Tooth Profile Error)를 나타내고, 도 1b는 옆줄오차(Tooth Trace Error)를 나타내고, 도 1c는 피치오차(Pitch Error)를 나타낸다.1A to 1C schematically illustrate the types of shape errors of spiral bevel gears, FIG. 1A shows tooth profile errors, FIG. 1B shows tooth trace errors, and FIG. 1C shows Pitch Error
그러나 도 1에 도시한 스파이럴 베벨기어의 형상오차를 측정하기 위한 측정방법의 부재로 인하여 현재 측정에 사용되는 방법은 상기 피치오차에 국한되고 있는 문제점이 있다.However, due to the absence of a measuring method for measuring the shape error of the spiral bevel gear shown in FIG. 1, the method currently used for measurement has a problem that is limited to the pitch error.
본 발명은 상기와 같은 문제점을 해결하기 위하여 창출된 것으로서, 기존의 방법으로 측정하기 어려운 치형오차 및 옆줄오차를 전용측정기가 아닌 범용 3차원 측정기(CMM; Coordinate Measuring Machine)를 이용하여 컴퓨터 상에서 알고리즘에 의해 측정하도록 하는 스파이럴 베벨기어의 형상오차 측정방법을 제공하는데 그 목적이 있다.The present invention was created in order to solve the above problems, and it is difficult to measure the tooth error and the side line error by the conventional method using an algorithm on a computer using a universal coordinate measuring machine (CMM; It is an object of the present invention to provide a method for measuring a shape error of a spiral bevel gear.
본 발명의 또 다른 목적은 기존의 방법으로 측정되었던 스파이럴 베벨기어의 피치오차를 더 정확하게 측정할 수 있는 스파이럴 베벨기어의 형상오차 측정방법을 제공하는데 있다.Still another object of the present invention is to provide a method for measuring a shape error of a spiral bevel gear, which can more accurately measure a pitch error of a spiral bevel gear, which has been measured by a conventional method.
도 1a 내지 도 1c는 일반적인 스파이럴 베벨기어(SBG)의 형상오차를 도시한 개념도.1A to 1C are conceptual views illustrating a shape error of a general spiral bevel gear (SBG).
도 2는 3차원 좌표측정기(CMM)를 이용한 스파이럴 베벨기어의 좌표 측정 실시예도.Figure 2 is an embodiment of the coordinate measurement of the spiral bevel gear using a three-dimensional coordinate measuring machine (CMM).
도 3은 소프트웨어 기준 모델(SMM) 생성을 위한 구형 인볼루트 좌표계의 일실시예도.3 illustrates one embodiment of a spherical involute coordinate system for generating a software reference model (SMM).
도 4a 내지 도 4c는 본 발명에 따른 해당 측정항목에서 SMM에 대한 버추얼 기어 모델(VGM)의 회전량 관계를 각각 도시한 개념도.4a to 4c are conceptual views showing the relationship between the rotation amount of the virtual gear model (VGM) for the SMM in the corresponding measurement item according to the present invention.
도 5는 본 발명 방법에 의한 치형오차의 측정 예시도.Figure 5 is an exemplary view of the measurement of the tooth error according to the method of the present invention.
도 6은 본 발명 방법에 의한 옆줄오차의 측정 예시도.Figure 6 is an exemplary view of the measurement of the side line error by the method of the present invention.
도 7은 본 발명 방법에 의한 인접피치오차 및 누적피치오차의 측정 예시도.Figure 7 is an exemplary measurement of the adjacent pitch error and cumulative pitch error by the method of the present invention.
도 8은 본 발명 방법의 구성 단계를 도시한 개념도.8 is a conceptual diagram showing the construction steps of the method of the present invention.
상기 목적을 달성하기 위하여 본 발명에 따른 스파이럴 베벨기어의 형상오차 측정방법은,Shape error measurement method of the spiral bevel gear according to the present invention to achieve the above object,
소정의 3차원 좌표측정기를 이용하여 가공된 스파이럴 베벨기어 형상의 불연속점에 대한 3차원 좌표를 측정하는 단계와; 측정된 3차원 좌표값을 이용하여 소정의 피팅(fitting) 방법으로 3차원 공간에서의 곡선 수식인 아래 공식의 버추얼 기어 모델(Virtual Gear Model; VGM)을 구성하는 단계와;Measuring three-dimensional coordinates of the discontinuous point of the spiral bevel gear shape processed using a predetermined three-dimensional coordinate measuring machine; Constructing a virtual gear model (VGM) of the following formula, which is a curve equation in three-dimensional space, by using a predetermined fitting method using the measured three-dimensional coordinate values;
여기서,here,
u: 인볼루트(Involute) 치형 방향에 대한 매개변수 u : Parameter for the direction of involute teeth
w: 스파이럴(Spiral) 곡선 방향에 대한 매개변수 w : Parameter for the spiral curve direction
P i,j : n×m개의 제어 포인트에 대한 미지수 P i, j : Unknown for n × m control points
R i,p (u), R j,q (w): u, w 방향에 대한 피팅 보간 함수 R i, p (u), R j, q (w) : fitting interpolation function for u, w direction
주어진 기어설계 데이터 및 사양으로부터 소정의 구형(Spherical) 인볼루트 좌표에서 아래의 공식과 같은 소프트웨어 기준 모델(Software Master Model; SMM)을 구성하는 단계와;Constructing a Software Master Model (SMM) such as the following formula at given spherical involute coordinates from the given gear design data and specifications;
여기서,here,
: u 방향 좌표 변환 행렬 : u-direction coordinate transformation matrix
: w 방향 좌표 변환 행렬 : w direction coordinate transformation matrix
상기 소프트웨어 기준 모델(SMM)과 상기 버추얼 기어 모델(VGM)을 비교하여 아래의 공식이 최소가 되도록 해당 측정항목에 대하여 회전변환하는 단계; 및Comparing the software reference model (SMM) with the virtual gear model (VGM) and rotationally converting the corresponding measurement items to minimize the following formula; And
여기서,here,
Rot(X,θ) : X, θ방향에 대한 회전 변환 행렬Rot (X, θ): Rotation transformation matrix for the X and θ directions
V(i) : 회전 변환 중심좌표V (i): rotation coordinate center coordinate
상기 소프트웨어 기준 모델과 버추얼 기어 모델과의 차이로부터 해당 측정 항목에서 치형 오차 및 옆줄 오차를 최대 오차 및 최소 오차의 합으로 아래 공식,From the difference between the software reference model and the virtual gear model, the tooth error and side line error in the corresponding measurement items are calculated as the sum of the maximum error and the minimum error.
- 치형 오차(Tooth Profile Error) : Tooth Profile Error
- 옆줄 오차(Tooth Trace Error) : Tooth Trace Error
으로 구하는 단계를 포함하는 것을 특징으로 한다.It characterized by including the step of obtaining.
본 발명의 바람직한 실시예에 있어서, 스파이럴 베벨기어의 단일 피치오차를 아래의 공식,In a preferred embodiment of the present invention, the single pitch error of the spiral bevel gear is
여기서,here,
: i번째 이(teeth)의 단일 피치오차 : single pitch error of the i th tooth
: w=0.5에서의 피치 원형 직경(PCD; Pitch Circle Diameter) : Pitch Circle Diameter at w = 0.5
: i번째 이의 정렬 각도 : alignment angle of the i th tooth
n: 이 갯수 n : this number
i: 이 인덱스 i : this index
에 의해 구하는 단계를 더 포함한다.It further includes the step of obtaining.
본 발명의 바람직한 실시예에 있어서, 상기는또는로 대체될 수 있다.In a preferred embodiment of the present invention, the Is or Can be replaced with
본 발명의 바람직한 실시예에 있어서, 상기 스파이럴 베벨기어의 소정의 i번째 치면의 인접피치오차()와 누적피치오차()를 상기 단일 피치오차값을 이용한 공식,In a preferred embodiment of the present invention, the adjacent pitch error of the predetermined i-th tooth of the spiral bevel gear ( ) And cumulative pitch error ( ) Using the single pitch error value,
을 이용하여 구하는 단계를 더 포함한다.It further includes the step of obtaining using.
이하, 첨부한 도면을 참조하면서 본 발명에 따른 스파이럴 베벨기어의 형상오차 측정방법의 바람직한 실시예를 상세하게 설명한다. 본 발명을 설명함에 있어서 관련된 공지기술 또는 구성에 대한 구체적인 설명이 본 발명의 요지를 불필요하게 흐릴 수 있다고 판단되는 경우에는 그 상세한 설명은 생략할 것이다. 그리고, 후술되는 용어들은 본 발명에서의 기능을 고려하여 정의된 용어들로서 이는 사용자, 운용자의 의도 또는 관례 등에 따라 달라질 수 있다. 그러므로 그 정의는 본 명세서 전반에 걸친 내용을 토대로 내려져야 할 것이다.Hereinafter, with reference to the accompanying drawings will be described in detail a preferred embodiment of the method for measuring the shape error of the spiral bevel gear according to the present invention. In the following description of the present invention, when it is determined that detailed descriptions of related well-known technologies or configurations may unnecessarily obscure the subject matter of the present invention, the detailed description will be omitted. In addition, terms to be described below are terms defined in consideration of functions in the present invention, which may vary according to the intention or custom of a user or an operator. Therefore, the definition should be made based on the contents throughout the specification.
먼저, 본 발명의 방법에 있어서 3차원 좌표 측정기을 이용하여 가공된 스파이럴 베벨기어 형상의 불연속점에 대한 3차원 좌표를 측정하여야 하는데, 이 실시예의 구현예를 도 2에 나타내 보였다.First, in the method of the present invention, three-dimensional coordinates of discontinuous points of a spiral bevel gear shape processed using a three-dimensional coordinate measuring machine should be measured. An embodiment of this embodiment is shown in FIG.
도 2에 도시한 바와 같은 실시예에 의해서 측정된 3차원 좌표값을 이용하여 소정의 피팅방법, 예를 들면 NUBS 피팅 방법으로 3차원 공간에서의 곡선 수식인 아래 공식 1의 버추얼 기어 모델(Virtual Gear Model; VGM)을 구성한다.The virtual gear model of Equation 1 below, which is a curve equation in a three-dimensional space using a three-dimensional coordinate value measured by the embodiment as shown in FIG. 2, for example, a NUBS fitting method. Model (VGM).
공식 1 Formula 1
상기 공식 1에서,In Formula 1 above,
u: 인볼루트(Involute) 치형 방향에 대한 매개변수이고; u : parameter for Involute tooth direction;
w: 스파이럴(Spiral) 곡선 방향에 대한 매개변수이고; w is a parameter for the spiral curve direction;
P i,j : n×m개의 제어 포인트에 대한 미지수이고; P i, j : unknown for n × m control points;
R i,p (u), R j,q (w): u, w 방향에 대한 피팅 보간 함수이다. R i, p (u), R j, q (w) : Fitting interpolation function for u, w directions.
상기와 같이 버추얼 기어 모델을 구성한 후, 주어진 기어설계 데이터 및 사양으로부터 도 3에 도시한 바와 같이 정의되는 구형 인볼루트 좌표에서 아래 공식 2와 같은 소프트웨어 기준 모델을 구성한다.After constructing the virtual gear model as above, a software reference model is constructed as shown in Equation 2 below in the spherical involute coordinates defined as shown in FIG. 3 from the given gear design data and specifications.
공식 2 Formula 2
상기 공식 2에서,In Formula 2 above,
: u 방향 좌표 변환 행렬이고; : u direction coordinate transformation matrix;
: w 방향 좌표 변환 행렬이다. : w direction coordinate transformation matrix.
상기와 같이 해서 소프트웨어 기준 모델과 버추얼 기어 모델을 구성한 후, 이들을 비교하여 아래 공식 3의 값이 최소가 되도록 도 4에 도시한 바와 같이 해당측정항목에 대하여 회전변환시킨다. 도 4a는 치형 프로파일 변환(alignment) 회전량을 나타내고, 도 4b는 스파이럴 커브 프로파일 변환 회전량을 나타내고, 도 4c는 피치점의 변환 회전량을 나타낸다.After the software reference model and the virtual gear model are constructed as described above, they are compared and rotated for the corresponding measurement item as shown in FIG. FIG. 4A shows the tooth profile alignment rotation amount, FIG. 4B shows the spiral curve profile conversion rotation amount, and FIG. 4C shows the conversion rotation amount of the pitch point.
공식 3 Formula 3
상기 공식 3에서,In Formula 3 above,
Rot(X,θ) : X, θ방향에 대한 회전 변환 행렬이고;Rot (X, θ): rotation transformation matrix for the X, θ directions;
V(i) : 회전 변환 중심좌표이다.V (i): rotation coordinate center coordinate.
상기한 소프트웨어 기준 모델(SMM)과 회전변환된 버추얼 기어 모델(VGM)과의 차이로부터 각 해당 측정 항목에서 치형오차와 옆줄오차는 최대오차 및 최소오차의 합으로 아래의 공식 4, 5에 의해 구해진다.From the difference between the software reference model (SMM) and the rotated virtual gear model (VGM), the tooth and side line errors in each relevant measurement are obtained by the following formulas 4 and 5 as the sum of the maximum and minimum errors: Become.
공식 4 Formula 4
공식 5 Formula 5
상기 공식 4는 치형 오차(Tooth Profile Error)를 구하는 바람직한 공식이고, 공식 5는 옆줄 오차(Tooth Trace Error)를 구하는 바람직한 공식이다.Equation 4 is a preferable formula for calculating tooth profile error, and Equation 5 is a preferable formula for calculating tooth trace error.
한편, 상기한 바와 같은 방법으로 PCD(Pitch Circle Diameter) 상에서 프로파일 방향으로의 단일 피치오차 값을 구하는 방식을 살펴보면 다음과 같다. 즉, 상기 단일 피치오차 값은 다양한 단면(예;w-parameter로 정의됨)에서 구할 수 있으며, 중간단면인w=0.5를 기준으로 정의하면 단일 피치오차는 아래 공식 6과 같이 구할 수 있다.Meanwhile, a method of obtaining a single pitch error value in the profile direction on the pitch circle diameter (PCD) as described above is as follows. That is, the single pitch error value can be obtained from various cross sections (eg, defined by w -parameter), and the single pitch error can be obtained as shown in Equation 6 below by defining the intermediate section w = 0.5.
공식 6 Formula 6
상기 공식 6에서,In Formula 6 above,
: i번째 이(teeth)의 단일 피치오차이고; : single pitch error of the i th tooth;
: w=0.5에서의 피치 원형 직경(PCD; Pitch Circle Diameter)이고; : Pitch Circle Diameter (PCD) at w = 0.5;
: i번째 이의 정렬 각도이고; is the alignment angle of the i th tooth;
n: 이 갯수이고; n : this number;
i: 이 인덱스이다. i : This index.
다른 한편, 스파이럴 베벨기어의 i번째 치면의 인접피치오차()와 누적피치오차()는 상기 단일 피치오차값을 이용하여 아래 공식 7과 같이 구할 수 있다.On the other hand, the adjacent pitch error of the i th tooth of the spiral bevel gear ( ) And cumulative pitch error ( ) Can be obtained using Equation 7 below using the single pitch error value.
공식 7 Formula 7
상술한 본 발명에 따른 스파이럴 베벨기어의 형상오차 측정방법의 각 단계를 도 8에 일목요연하게 나타내 보였다.Each step of the method for measuring the shape error of the spiral bevel gear according to the present invention described above is clearly shown in FIG. 8.
한편, 도 5는 본 발명 방법에 의한 치형오차의 측정예를, 도 6은 옆줄오차의 측정예를, 도 7은 피치오차의 측정예를 나타내 보인다.On the other hand, Figure 5 shows a measurement example of the tooth error according to the method of the present invention, Figure 6 shows a measurement example of the side row error, Figure 7 shows a measurement example of the pitch error.
이상에서 설명한 바와 같이 본 발명에 따른 스파이럴 베벨기어의 형상오차측정방법은, 기존의 방법으로 측정하기 어려운 치형오차 및 옆줄오차를 전용측정기가 아닌 범용 3차원 측정기를 이용하여 컴퓨터 상에서 알고리즘에 의해 측정하도록 하는 이점을 제공한다.As described above, the shape error measuring method of the spiral bevel gear according to the present invention is to measure the tooth error and side line error, which are difficult to measure by the conventional method, by using an algorithm on a computer using a general-purpose three-dimensional measuring device rather than a dedicated measuring device. To provide an advantage.
또한, 본 발명은 기존의 방법으로 측정되었던 스파이럴 베벨기어의 피치오차를 더 정확하게 측정할 수 있는 이점을 제공한다.In addition, the present invention provides an advantage of more accurately measuring the pitch error of a spiral bevel gear, which has been measured by conventional methods.
이상 본 발명의 바람직한 실시예에 대해 상세히 기술하였지만, 본 발명이 속하는 기술분야에 있어서 통상의 지식을 가진 사람이라면, 첨부된 청구 범위에 정의된 본 발명의 정신 및 범위를 벗어나지 않으면서 본 발명을 여러 가지로 변형 또는 변경하여 실시할 수 있음을 알 수 있을 것이다. 따라서 본 발명의 앞으로의 실시예들의 변경은 본 발명의 기술을 벗어날 수 없을 것이다.Although a preferred embodiment of the present invention has been described in detail above, those skilled in the art to which the present invention pertains may make various changes without departing from the spirit and scope of the invention as defined in the appended claims. It will be appreciated that modifications or variations may be made. Therefore, changes in the future embodiments of the present invention will not be able to escape the technology of the present invention.
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| CN1036417C (en) * | 1988-01-29 | 1997-11-12 | 国家机械工业委员会成都工具研究所 | Method & implement of gearing error measuring by mating and separating |
| JP2554157B2 (en) * | 1989-01-24 | 1996-11-13 | 三菱重工業株式会社 | Tooth profile error measurement method |
| JP3527565B2 (en) * | 1995-06-27 | 2004-05-17 | 三菱マテリアル神戸ツールズ株式会社 | Gear measuring method and NC gear cutting machine |
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