TWI791343B - Obtaining method and obtaining apparatus for geometric error of rotation axis - Google Patents
Obtaining method and obtaining apparatus for geometric error of rotation axis Download PDFInfo
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Description
本發明是有關於一種幾何誤差的獲取方法與獲取設備,且特別是有關於一種旋轉軸的幾何誤差的獲取方法與獲取設備。 The present invention relates to a geometric error acquisition method and acquisition device, and in particular to a rotational axis geometric error acquisition method and acquisition device.
旋轉軸被廣泛應用在各種動力機械、工具機中。尤其在精密機械中,旋轉軸的精確度更加重要。為此,開發出旋轉軸的幾何誤差的獲取方法與獲取設備是很重要的課題。 Rotary shafts are widely used in various power machinery and machine tools. Especially in precision machinery, the accuracy of the rotating axis is even more important. Therefore, it is an important subject to develop a method and equipment for obtaining the geometric error of the rotating shaft.
本發明提供一種旋轉軸的幾何誤差的獲取方法與獲取設備,可獲取旋轉軸的幾何誤差。 The invention provides a method and equipment for obtaining the geometric error of the rotating shaft, which can obtain the geometric error of the rotating shaft.
本發明的一種旋轉軸的幾何誤差的獲取方法包括下列步驟。安裝環型編碼器於旋轉軸上,並於環型編碼器的周圍安裝第一光學讀取頭與第二光學讀取頭。以旋轉軸旋轉環型編碼器,並由第一光學讀取頭與第二光學讀取頭同時讀取旋轉軸旋轉至多個角度時對應的環型編碼器上的多個角度值。根據第一光學讀取頭 讀取的角度值而獲取旋轉軸旋轉0度時環型編碼器的中心點相對旋轉軸的中心軸線的偏差距離與方位角。根據第一光學讀取頭與第二光學讀取頭讀取的角度值而獲取第一光學讀取頭的第一組裝角度偏差與第二光學讀取頭的第二組裝角度偏差。根據角度值、第一組裝角度偏差與第二組裝角度偏差而獲取旋轉軸在旋轉至各個角度時的旋轉角度誤差。根據角度值、環型編碼器的半徑、旋轉角度誤差、第一組裝角度偏差與第二組裝角度偏差而獲取旋轉軸在旋轉至各個角度時的旋轉偏擺誤差。 A method for obtaining the geometric error of the rotating shaft in the present invention includes the following steps. The ring encoder is installed on the rotating shaft, and the first optical pickup head and the second optical pickup head are installed around the ring encoder. The ring encoder is rotated by the rotating shaft, and the first optical reading head and the second optical reading head simultaneously read multiple angle values on the ring encoder when the rotating shaft rotates to multiple angles. According to the first optical read head The read angle value is used to obtain the deviation distance and azimuth angle of the center point of the ring encoder relative to the central axis of the rotary shaft when the rotary shaft rotates 0 degrees. The first assembly angle deviation of the first optical pickup head and the second assembly angle deviation of the second optical pickup head are obtained according to the angle values read by the first optical pickup head and the second optical pickup head. According to the angle value, the first assembly angle deviation and the second assembly angle deviation, the rotation angle error when the rotating shaft rotates to each angle is obtained. According to the angle value, the radius of the ring encoder, the rotation angle error, the first assembly angle deviation and the second assembly angle deviation, the rotation deflection error when the rotation shaft rotates to each angle is obtained.
本發明的一種旋轉軸的幾何誤差的獲取設備包括一環型編碼器以及一第一光學讀取頭與一第二光學讀取頭。環型編碼器用以安裝於一旋轉軸上。第一光學讀取頭與第二光學讀取頭安裝於環型編碼器的周圍。其中,以旋轉軸旋轉環型編碼器,並由第一光學讀取頭與第二光學讀取頭同時讀取旋轉軸旋轉至多個角度時對應的環型編碼器上的多個角度值。根據第一光學讀取頭讀取的角度值而獲取旋轉軸旋轉0度時環型編碼器的一中心點相對旋轉軸的一中心軸線的一偏差距離與一方位角。根據第一光學讀取頭與第二光學讀取頭讀取的角度值而獲取第一光學讀取頭的一第一組裝角度偏差與第二光學讀取頭的一第二組裝角度偏差。根據角度值、第一組裝角度偏差與第二組裝角度偏差而獲取旋轉軸在旋轉至各個角度時的一旋轉角度誤差。根據角度值、環型編碼器的半徑、旋轉角度誤差、第一組裝角度偏差與第二組裝角度偏差而獲取旋轉軸在旋轉至各個角度時的一旋轉偏擺誤差。 A device for obtaining the geometric error of the rotating shaft of the present invention includes a ring encoder, a first optical pickup head and a second optical pickup head. Ring encoders are used for mounting on a rotating shaft. The first optical pickup head and the second optical pickup head are installed around the ring encoder. Wherein, the ring encoder is rotated by the rotating shaft, and the first optical reading head and the second optical reading head simultaneously read multiple angle values on the ring encoder when the rotating shaft rotates to multiple angles. According to the angle value read by the first optical reading head, a deviation distance and an azimuth angle of a center point of the ring encoder relative to a central axis of the rotation shaft when the rotation shaft rotates 0 degrees are obtained. A first assembly angle deviation of the first optical pickup head and a second assembly angle deviation of the second optical pickup head are acquired according to the angle values read by the first optical pickup head and the second optical pickup head. According to the angle value, the first assembly angle deviation and the second assembly angle deviation, a rotation angle error when the rotating shaft rotates to each angle is obtained. According to the angle value, the radius of the ring encoder, the rotation angle error, the first assembly angle deviation and the second assembly angle deviation, a rotation yaw error when the rotating shaft rotates to each angle is obtained.
基於上述,在本發明的旋轉軸的幾何誤差的獲取方法與獲取設備中,可獲取旋轉軸的旋轉角度誤差與旋轉軸的旋轉偏擺誤差。 Based on the above, in the acquisition method and acquisition device of the geometric error of the rotating shaft in the present invention, the rotational angle error of the rotating shaft and the rotational yaw error of the rotating shaft can be obtained.
50:旋轉軸 50: axis of rotation
100:旋轉軸的幾何誤差的獲取設備 100: Obtaining equipment for the geometric error of the rotary axis
110:環型編碼器 110: ring encoder
R1:第一光學讀取頭 R1: the first optical read head
R2:第二光學讀取頭 R2: Second optical read head
R3:第三光學讀取頭 R3: The third optical read head
R4:第四光學讀取頭 R4: The fourth optical read head
R5:第五光學讀取頭 R5: fifth optical read head
S110~S160:步驟 S110~S160: steps
θ:標稱旋轉角度值 θ : nominal rotation angle value
e:偏差距離 e : deviation distance
φ:方位角 φ : Azimuth
R:中心軸線與第一光學讀取頭的距離 R : the distance between the central axis and the first optical reading head
O’:中心點 O' : center point
O:點 O : point
ρ:環型編碼器的半徑 ρ: radius of the ring encoder
圖1是依照本發明的一實施例的旋轉軸的幾何誤差的獲取設備的示意圖。 FIG. 1 is a schematic diagram of a device for acquiring geometric errors of a rotating shaft according to an embodiment of the present invention.
圖2是依照本發明的一實施例的旋轉軸的幾何誤差的獲取方法的流程圖。 FIG. 2 is a flow chart of a method for obtaining a geometric error of a rotating shaft according to an embodiment of the present invention.
圖3是說明環型編碼器的中心點相對旋轉軸的中心軸線的偏差距離與方位角。 Fig. 3 illustrates the deviation distance and azimuth angle of the center point of the ring encoder relative to the central axis of the rotating shaft.
圖4是各個光學讀取頭在旋轉軸旋轉至各個角度時所讀取的角度值與旋轉角度的差值。 FIG. 4 shows the difference between the angle value read by each optical pickup head and the rotation angle when the rotation axis rotates to various angles.
圖5是旋轉軸旋轉至各個角度時實際的旋轉角度與理想的旋轉角度的差值。 Fig. 5 shows the difference between the actual rotation angle and the ideal rotation angle when the rotation shaft rotates to various angles.
圖6是旋轉軸旋轉至各個角度時的偏擺誤差在X軸與Y軸的分量。 FIG. 6 shows the components of the yaw error on the X-axis and the Y-axis when the rotating shaft rotates to various angles.
圖1是依照本發明的一實施例的旋轉軸的幾何誤差的獲取設備的示意圖。請參照圖1,本實施例的旋轉軸的幾何誤差的獲
取設備100包括一環型編碼器110以及一第一光學讀取頭R1與一第二光學讀取頭R2。環型編碼器110用以安裝於一旋轉軸50上。第一光學讀取頭R1與第二光學讀取頭R2安裝於環型編碼器110的周圍。藉由旋轉軸50帶動固定在其上的環型編碼器110旋轉,並搭配第一光學讀取頭R1與第二光學讀取頭R2讀取環型編碼器110上的角度值,可以分析並獲取旋轉軸50多種幾何誤差。因此,可用於檢測旋轉軸50的品質是否合乎要求,並且可以做為後續應用旋轉軸50時的校正依據。
FIG. 1 is a schematic diagram of a device for acquiring geometric errors of a rotating shaft according to an embodiment of the present invention. Please refer to Fig. 1, the acquisition of the geometric error of the rotating shaft of the present embodiment
The
在本實施例的旋轉軸的幾何誤差的獲取設備100中,更包括一第三光學讀取頭R3、一第四光學讀取頭R4與一第五光學讀取頭R5,安裝於該環型編碼器110的周圍。第一光學讀取頭R1、第二光學讀取頭R2、第三光學讀取頭R3、第四光學讀取頭R4與第五光學讀取頭R5的預設安裝角度分別為0度、72度、144度、216度與288度。藉此,使用第一光學讀取頭R1、第二光學讀取頭R2、第三光學讀取頭R3、第四光學讀取頭R4與第五光學讀取頭R5而獲取旋轉軸50在旋轉至各個角度時的旋轉角度誤差與旋轉偏擺誤差。需說明的是,雖然以下是以使用了五個光學讀取頭的狀態作說明,但在本發明的旋轉軸的幾何誤差的獲取方法與獲取設備中,也可僅使用兩個光學讀取頭而獲取相同項目的幾何誤差。在使用兩個光學讀取頭時,兩個光學讀取頭的預設安裝角度可以分別為0度與90度,但本發明不以此為限。
In this embodiment, the
圖2是依照本發明的一實施例的旋轉軸的幾何誤差的獲
取方法的流程圖。請參照圖1與圖2,本實施例的旋轉軸的幾何誤差的獲取方法包括下列步驟。首先,安裝環型編碼器110於旋轉軸50上,並於環型編碼器110的周圍安裝第一光學讀取頭R1與第二光學讀取頭R2,步驟S110。
Fig. 2 is the acquisition of the geometric error of the rotating shaft according to an embodiment of the present invention
Flowchart of the method. Please refer to FIG. 1 and FIG. 2 , the method for obtaining the geometric error of the rotating shaft in this embodiment includes the following steps. Firstly, install the
接著,以旋轉軸50旋轉環型編碼器110,也就是環型編碼器110被旋轉軸50帶動而跟著旋轉。在轉動的過程中,由第一光學讀取頭R1與第二光學讀取頭R2同時讀取旋轉軸50旋轉至多個角度時對應的環型編碼器110上的多個角度值,步驟S120。由於第一光學讀取頭R1與第二光學讀取頭R2的組裝角度不同,所以本實施例的第一光學讀取頭R1與第二光學讀取頭R2讀取的角度值在理論上就存在著72度的差異。
Next, the
圖3是說明環型編碼器的中心點相對旋轉軸的中心軸線的偏差距離與方位角。請參照圖2與圖3,接著根據第一光學讀取頭R1讀取的角度值而獲取旋轉軸50旋轉0度時環型編碼器110的中心點O’相對旋轉軸50的中心軸線(圖3中以中心軸線通過的點O做說明)的偏差距離e與方位角φ,步驟S130。在此,是以旋轉軸50的中心軸線通過的點O與第一光學讀取頭R1的連線方向做為X軸,並以X軸及點O為參考基準來定義方位角φ。
Fig. 3 illustrates the deviation distance and azimuth angle of the center point of the ring encoder relative to the central axis of the rotating shaft. Please refer to FIG. 2 and FIG. 3, then according to the angle value read by the first optical reading head R1, the central point O' of the
圖4是各個光學讀取頭在旋轉軸旋轉至各個角度時所讀取的角度值與旋轉角度的差值。請參照圖3與圖4,舉例來說,是將第一光學讀取頭R1讀取的角度值減去對應的旋轉軸50的多個標稱旋轉角度值而獲取多個量測角度誤差值。例如,旋轉軸50旋
轉0度時,也就是旋轉軸50未旋轉時,第一光學讀取頭R1讀取的角度值是359度59分52秒。將359度59分52秒減去此時的標稱旋轉角度值0度即獲得-8秒的量測角度誤差值,也就是圖4中縱軸為-8秒且橫軸為0度的資料點。以此方式,完成圖4中第一光學讀取頭R1所對應的曲線。然後,將此表示量測角度誤差值與對應的標稱旋轉角度值的關係的曲線進行曲線擬合,以獲取與標稱旋轉角度值相關的一第一三角函數。根據所得到的第一三角函數與如下的式一而聯立求解,即可獲取偏差距離與方位角。本實施例中,進行曲線擬合的步驟是使用最小平方法。在如下的式一中,是第一光學讀取頭讀取的角度值,θ是標稱旋轉角度值,e是偏差距離,φ是方位角,R是中心軸線與第一光學讀取頭的距離,
在本實施例中,根據圖4中的第一光學讀取頭R1所對應的曲線而曲線擬合得到的第一三角函數為,因此得出偏差距離e是14.39微米,方位角是0.089度。 In this embodiment, the first trigonometric function obtained by curve fitting according to the curve corresponding to the first optical pickup head R1 in FIG. 4 is , so the deviation distance e is 14.39 microns, and the azimuth angle is 0.089 degrees.
接著,請參照圖1與圖2,根據第一光學讀取頭R1與第二光學讀取頭R2讀取的角度值而獲取第一光學讀取頭R1的第一組裝角度偏差與第二光學讀取頭R2的第二組裝角度偏差,步驟 S140。 Next, please refer to FIG. 1 and FIG. 2 , according to the angle values read by the first optical pickup R1 and the second optical pickup R2, the first assembly angle deviation and the second optical pickup R1 of the first optical pickup R1 are obtained. Second assembly angular deviation of read head R2, step S140.
舉例來說,請參照圖1與圖4,與前述步驟相同,將第一光學讀取頭R1讀取的角度值減去對應的旋轉軸50的多個標稱旋轉角度值而獲取多個第一量測角度誤差值。然後,將第一量測角度誤差值與對應的標稱旋轉角度值的關係(也就是圖4中第一光學讀取頭R1所對應的曲線)進行曲線擬合而獲取與標稱旋轉角度值相關的一第一三角函數。
For example, please refer to FIG. 1 and FIG. 4 , the same as the previous steps, the angle value read by the first optical pickup head R1 is subtracted from the multiple nominal rotation angle values of the
此外,將第二光學讀取頭R2讀取的角度值減去對應的旋轉軸的多個標稱旋轉角度值及第一光學讀取頭R1與第二光學讀取頭R2的一預設角度差值而獲取多個第二量測角度誤差值。例如,旋轉軸50旋轉0度時,也就是旋轉軸50未旋轉時,第二光學讀取頭R2讀取的角度值是73度59分35秒。將73度59分35秒減去此時的標稱旋轉角度值0度及第一光學讀取頭R1與第二光學讀取頭R2的預設角度差值72度即獲得95秒的量測角度誤差值,也就是圖4中縱軸為95秒且橫軸為0度的資料點。以此方式,完成圖4中第二光學讀取頭R2所對應的曲線。
In addition, the angle value read by the second optical pickup head R2 is subtracted from a plurality of nominal rotation angle values of the corresponding rotation axis and a preset angle between the first optical pickup head R1 and the second optical pickup head R2 Obtain a plurality of second measurement angle error values based on the difference values. For example, when the rotating
然後,將此表示第二量測角度誤差值與對應的標稱旋轉角度值的關係的曲線進行曲線擬合,以獲取與標稱旋轉角度值相關的一第二三角函數。在此,以0度做為第一光學讀取頭R1的實際安裝角度,則第二光學讀取頭R2的實際安裝角度為使第二三角函數與第一三角函數重合的一偏移角度值,在此例如是72.07度。並且,以0度做為第一光學讀取頭R1的第一組裝角度偏差,並將 偏移角度值(例如是72.07度)減去第二光學讀取頭R2的預設安裝角度(例如是72度)以取得第二組裝角度偏差(例如是0.07度)。舉例來說,第三光學讀取頭R3的第三組裝角度偏差是0.01度,第四光學讀取頭R4的第四組裝角度偏差是0.03度,第五光學讀取頭R5的第五組裝角度偏差是0.07度。 Then, curve fitting is performed on the curve representing the relationship between the second measured angle error value and the corresponding nominal rotation angle value, so as to obtain a second trigonometric function related to the nominal rotation angle value. Here, taking 0 degree as the actual installation angle of the first optical pickup R1, the actual installation angle of the second optical pickup R2 is an offset angle value that makes the second trigonometric function coincide with the first trigonometric function , for example 72.07 degrees here. And, take 0 degree as the first assembly angle deviation of the first optical pickup head R1, and The second assembly angle deviation (for example, 0.07 degrees) is obtained by subtracting the default installation angle (for example, 72 degrees) of the second optical pickup head R2 from the offset angle value (for example, 72.07 degrees). For example, the third assembly angle deviation of the third optical pickup head R3 is 0.01 degrees, the fourth assembly angle deviation of the fourth optical pickup head R4 is 0.03 degrees, and the fifth assembly angle deviation of the fifth optical pickup head R5 is 0.01 degrees. The deviation is 0.07 degrees.
圖5是旋轉軸旋轉至各個角度時實際的旋轉角度與理想的旋轉角度的差值。請參照圖2與圖5,根據角度值、第一組裝角度偏差與第二組裝角度偏差而獲取旋轉軸50在旋轉至各個角度時的旋轉角度誤差,步驟S150。
Fig. 5 shows the difference between the actual rotation angle and the ideal rotation angle when the rotation shaft rotates to various angles. Referring to FIG. 2 and FIG. 5 , according to the angle value, the first assembly angle deviation and the second assembly angle deviation, the rotation angle error when the rotating
舉例來說,在旋轉軸旋50轉至各個角度時,將第二光學讀取頭R2讀取的角度值減去第二光學讀取頭R2的預設安裝角度以及第二組裝角度偏差後與第一光學讀取頭R1讀取的角度值取平均,以獲取旋轉軸50在旋轉至各個角度時的旋轉角度誤差。實際上,第一光學讀取頭R1讀取的角度值也會減去第一光學讀取頭R1的預設安裝角度以及第一組裝角度偏差,但因為第一光學讀取頭R1的預設安裝角度以及第一組裝角度偏差都是0,所以是直接以第一光學讀取頭R1讀取的角度值與第二光學讀取頭R2讀取的角度值減去第二光學讀取頭R2的預設安裝角度以及第二組裝角度偏差後的值做平均。本實施例中,因為安裝了五個光學讀取頭,所以除了第一光學讀取頭R1讀取的角度值與第二光學讀取頭R2讀取的角度值減去第二光學讀取頭R2的預設安裝角度以及第二組裝角度偏差後的值之外,還加上第三光學讀取頭R3讀取的角度
值減去第三光學讀取頭R3的預設安裝角度以及第三組裝角度偏差後的值、第四光學讀取頭R4讀取的角度值減去第四光學讀取頭R4的預設安裝角度以及第四組裝角度偏差後的值與第五光學讀取頭R5讀取的角度值減去第五光學讀取頭R5的預設安裝角度以及第五組裝角度偏差後的值,然後取平均值。此平均值就是旋轉軸50的旋轉角度誤差,而旋轉軸50在旋轉至各個角度時的旋轉角度誤差與旋轉軸50的旋轉角度的關係就如圖5中的曲線所示。
For example, when the rotation axis rotates 50° to various angles, the angle value read by the second optical pickup R2 is subtracted from the preset installation angle of the second optical pickup R2 and the second assembly angle deviation, and The angle values read by the first optical reading head R1 are averaged to obtain the rotation angle error when the
圖6是旋轉軸旋轉至各個角度時的偏擺誤差在X軸與Y軸的分量。請參照圖3與圖6,根據角度值、環型編碼器的半徑、旋轉角度誤差、第一組裝角度偏差與第二組裝角度偏差而獲取旋轉軸50在旋轉至各個角度時的旋轉偏擺誤差,步驟S160。
FIG. 6 shows the components of the yaw error on the X-axis and the Y-axis when the rotating shaft rotates to various angles. Please refer to FIG. 3 and FIG. 6, according to the angle value, the radius of the ring encoder, the rotation angle error, the first assembly angle deviation and the second assembly angle deviation to obtain the rotation deflection error of the
舉例來說,將第一光學讀取頭R1讀取的角度值減去環型編碼器110的中心點O’相對旋轉軸50的中心軸線的方位角以及對應的旋轉角度誤差後,乘以2πρ除以360度並乘以第一光學讀取頭R1的實際安裝角度的正弦值以獲取在旋轉軸50旋轉至各個角度時的一第一X軸偏擺誤差,乘以2πρ除以360度並乘以第一光學讀取頭R1的實際安裝角度的餘弦值以獲取在旋轉軸50旋轉至各個角度時的一第一Y軸偏擺誤差。其中,ρ是環型編碼器的半徑。
For example, after subtracting the azimuth angle of the center point O' of the
此外,將第二光學讀取頭R2讀取的角度值減去環型編碼器110的中心點O’相對旋轉軸50的中心軸線的方位角以及對應的旋轉角度誤差後,乘以2πρ除以360度並乘以第二光學讀取頭R2
的實際安裝角度的正弦值以獲取在旋轉軸50旋轉至各個角度時的一第二X軸偏擺誤差,乘以2πρ除以360度並乘以第二光學讀取頭R2的實際安裝角度的餘弦值以獲取在旋轉軸50旋轉至各個角度時的一第二Y軸偏擺誤差。同時,也以相同方式獲取第三光學讀取頭R3、第四光學讀取頭R4與第五光學讀取頭R5各自的X軸偏擺誤差與Y軸偏擺誤差。
In addition, after subtracting the azimuth angle of the center point O' of the
然後,將所有讀取頭的X軸偏擺誤差(例如只有兩個讀取頭時的第一X軸偏擺誤差與第二X軸偏擺誤差)根據對應的旋轉軸50的旋轉角度而取平均,並將所有讀取頭的Y軸偏擺誤差(例如只有兩個讀取頭時的第一Y軸偏擺誤差與第二Y軸偏擺誤差)根據對應的旋轉軸50的旋轉角度而取平均,以獲取在旋轉軸旋轉至各個角度時的旋轉偏擺誤差的X軸分量與Y軸分量,例如是如圖6所示。
Then, the X-axis yaw errors of all read heads (for example, the first X-axis yaw error and the second X-axis yaw error when there are only two read heads) are obtained according to the rotation angle of the
綜上所述,在本發明的旋轉軸的幾何誤差的獲取方法與獲取設備中,首先獲取環型編碼器的中心點的偏差距離與方位角以及光學讀取頭的組裝角度偏差,然後可以獲取旋轉軸的旋轉角度誤差與旋轉軸的旋轉偏擺誤差。因此,可檢測旋轉軸的品質,並可做為後續應用此旋轉軸時的校正依據。並且,因為先獲取環型編碼器的組裝偏差,所以獲取的旋轉軸的旋轉角度誤差與旋轉軸的旋轉偏擺誤差更為精確。 To sum up, in the acquisition method and acquisition device of the geometric error of the rotating shaft of the present invention, the deviation distance and azimuth angle of the center point of the ring encoder and the assembly angle deviation of the optical reading head are first acquired, and then the deviation can be obtained Rotational angle error of the rotary axis and rotational yaw error of the rotary axis. Therefore, the quality of the rotating shaft can be detected, and can be used as a calibration basis for the subsequent application of the rotating shaft. Moreover, because the assembly deviation of the ring encoder is acquired first, the acquired rotational angle error of the rotary shaft and the rotational yaw error of the rotary shaft are more accurate.
S110~S160:步驟 S110~S160: steps
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| CN101405840A (en) * | 2006-08-31 | 2009-04-08 | 株式会社尼康 | Moving body driving method and moving body driving system, pattern forming method and apparatus, exposure method and apparatus, and device manufacturing method |
| CN106164779A (en) * | 2014-04-01 | 2016-11-23 | 株式会社尼康 | Substrate processing apparatus, device manufacturing method, and adjustment method of substrate processing apparatus |
| CN106979766A (en) * | 2016-01-15 | 2017-07-25 | 宝山钢铁股份有限公司 | The measurement apparatus and method of pole material parameter |
| CN110375694A (en) * | 2019-08-30 | 2019-10-25 | 合肥工业大学 | Method for self-calibrating based on portable articulated coordinate machine Circular gratings angle error |
| CN112781496A (en) * | 2021-01-20 | 2021-05-11 | 湘潭大学 | Measuring head pose calibration technology of non-contact measuring system |
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| CN101405840A (en) * | 2006-08-31 | 2009-04-08 | 株式会社尼康 | Moving body driving method and moving body driving system, pattern forming method and apparatus, exposure method and apparatus, and device manufacturing method |
| CN106164779A (en) * | 2014-04-01 | 2016-11-23 | 株式会社尼康 | Substrate processing apparatus, device manufacturing method, and adjustment method of substrate processing apparatus |
| CN106979766A (en) * | 2016-01-15 | 2017-07-25 | 宝山钢铁股份有限公司 | The measurement apparatus and method of pole material parameter |
| CN110375694A (en) * | 2019-08-30 | 2019-10-25 | 合肥工业大学 | Method for self-calibrating based on portable articulated coordinate machine Circular gratings angle error |
| CN112781496A (en) * | 2021-01-20 | 2021-05-11 | 湘潭大学 | Measuring head pose calibration technology of non-contact measuring system |
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