Method for determining pose parameters of centerline laser sensor in gear detection

Abstract

The invention provides a method for determining pose parameters of a centerline laser sensor in gear detection. Through the coupling relationship among the pose parameters of the line laser sensor, the fast determination of the pose of the gear line laser sensor is realized. Determining the range of the rotation angle of the sensor around the Zs axis based on the initial pose of the sensor in order to ensure that the laser plane is always in the upper and lower end surfaces of the measured gear; further determining the range of the rotation angle of the sensor around the Xs axis; then, based on the rotation angle of the sensor around the three-coordinate axis, the offset of the sensor coordinate origin 0s relative to the gear coordinate origin 0c in the Zc and Yc axis directions is determined; finally, based on the incident angle of the laser plane and a shading model, the offset of the coordinate origin 0s of the sensor relative to the gear coordinate origin 0c in the Xc axis direction is determined; through the technical method provided by the invention, the pose parameters of the line laser sensor can be determined, and the three-dimensional information of the tooth surface can be quickly acquired.

Description

Technical Field

[0001] The present invention relates to the technical field of on-line gear detection in gear processing, and particularly to a method for calibrating the pose of a line laser in three-dimensional measurement of a gear line laser. Background Art

[0002] With the continuous improvement of the demand for gear quality inspection, the traditional gear inspection methods have the following defects: 1. Advanced gear processing technologies can achieve the processing of arbitrarily complex tooth surface modification shapes, but the current gear inspection technologies only obtain local tooth surface information (a small number of local points or lines on the gear tooth surface), and are not suitable for characterizing and evaluating gear tooth surfaces with complex shapes. 2. The measurement efficiency is too low to meet the quantity of thousands or even tens of thousands of pieces produced per day on average in a gear production workshop. 3. Problems such as wear and radius compensation are likely to occur during contact measurement. Comparatively speaking, non-contact measurement methods are more suitable for current gear inspection. Non-contact measurement methods can greatly improve the inspection speed and can obtain all the information of the entire tooth surface.

[0003] As an efficient non-contact detection means, line laser detection has characteristics such as digital modeling, full-size analysis, real-time feedback, and non-destructive detection. The intelligent integrated system of this technology significantly improves the automation level of the detection process. Its modular design simplifies the operation process, reduces the professional requirements for operators, and can quickly and accurately obtain the three-dimensional data information of complex surfaces, and can realize more convenient and comprehensive precision measurement of entities.

[0004] Line laser measurement is a comparison measurement technology. To obtain the complete three-dimensional information of the measured gear, it is particularly important to determine the relative pose relationship between the line laser sensor and the measured gear. In addition, for different specifications of gear models, when parameters such as the helix angle, base circle radius, and tooth width length of the measured gear change, the spatial pose of the line laser sensor needs to be re-determined, which greatly affects the speed of gear detection.

[0005] Based on the above status quo and problems, a method for calibrating the pose of a line laser in three-dimensional measurement of a gear line laser is proposed. This patent can quickly locate the range of six pose parameters when parameters such as the helix angle, base circle radius, and tooth width length of the measured gear change for different types of cylindrical gears. Summary of the Invention

[0006] The main purpose of the present invention is to provide a method for determining the pose parameters of a line laser sensor in gear detection, aiming to quickly determine the pose of the gear line laser sensor and improve the speed of on-line gear detection.

[0007] To achieve the above object, the present invention provides a method for determining the pose parameters of a line laser sensor in gear detection, and the method for determining the pose parameters of a line laser sensor in gear detection includes:

[0008] S1. Set the initial pose of the line laser sensor. Taking the measurement range of the laser plane on the upper and lower end faces of the gear to be measured as the boundary condition, establish a geometric function of the rotation angle β of the sensor around the Z s axis through spatial projection analysis; s

[0009] S2. Under the condition of fixing β s =β0, solve the value range of the rotation angle γ of the sensor around the X s axis; On this basis, establish a relationship function between the offset c of the origin 0 of the sensor coordinate system relative to the origin 0 of the gear coordinate system on the Z s axis and β s , γ c and α c through spatial geometric analysis; s , γ s and α s ;

[0010] S3. Combining the quadrilateral region formed by the depth of field range and the field of view boundary of the line laser sensor, determine the value range of the offset b of the origin 0 of the sensor coordinate system relative to the origin 0 of the gear coordinate system in the Y s axis direction; c axis direction; c ;

[0011] S4. Based on the incident angle of the laser plane and the occlusion model of adjacent teeth on the laser plane, determine the mathematical model of the offset a of the origin 0 of the sensor coordinate system relative to the origin 0 of the gear coordinate system in the X s axis direction; c axis direction; c ;

[0012] Furthermore, the gear coordinate system and the line laser sensor coordinate system are:

[0013] Establish a gear coordinate system δ c : O c -X c Y c Z c ; It is a fixed coordinate system; δ c is the label of the gear coordinate system; O c is the origin of the gear coordinate system; X c Y c Z c are the three coordinate axes of the gear coordinate system; The origin of the gear coordinate system is at the geometric center of the gear; Establish a sensor coordinate system δ s : O​s -X s Y s Z s ; is a moving coordinate system; changes with the movement of the sensor; δ s is the label of the sensor coordinate system; O s is the origin of the sensor coordinate system; X s Y s Z s are the three coordinate axes of the sensor coordinate system; the sensor is arranged circumferentially on the calibration part; the origin of the sensor coordinate system is located at the center of the laser emission port; at the initial position of the sensor, the three coordinate axes of the sensor coordinate system are parallel to the three coordinate axes of the gear coordinate system.

[0014] Furthermore, the initial pose of the set line laser sensor is set with the measurement range of the laser plane on the upper and lower end faces of the measured gear as the boundary condition, and the geometric function of the rotation angle β s of the sensor around the Z s axis is established through spatial projection analysis;

[0015] Z1 = tan(θ)·X1

[0016]

[0017] (-β, β)

[0018] Z1 is the coordinate value of the projection line of the upper end face of the gear on the X c O c Z c plane;

[0019] X1 is the abscissa value of the intersection point of the upper end of the laser line and the projection line of the upper end face of the gear on the X c OZ c plane;

[0020] X o1 is the X-axis coordinate value of the midpoint O1 of the projection line of the laser plane at the initial position of the sensor on the X c O c Z c plane in the δ c coordinate system;

[0021] Z o1 is the Z-axis coordinate value of the midpoint O1 of the projection line of the laser plane at the initial position of the sensor on the X c O c Z c plane in the δ c coordinate system; X o2 is the X-axis coordinate value of the laser plane when the sensor rotates around the Zs axis until the laser plane intersects with the upper end face of the gear on the X c O c Zc The X-axis coordinate value of the midpoint O2 of the projection line on the plane in the δ c coordinate system;

[0022] Z o2 is the X-axis of the laser plane when the sensor rotates around the Zs axis until the laser plane intersects with the upper end face of the gear c O c Z c The Z-axis coordinate value of the midpoint O2 of the projection line on the plane in the δ c coordinate system;

[0023] L0 is the straight-line distance between point O1 and point O2;

[0024] L1 is the straight-line distance between the coordinate origin O s and point O1 when the sensor is in the initial position;

[0025] L2 is the straight-line distance between the coordinate origin O s and point O2 when the laser plane intersects with the upper end face of the gear.

[0026] Furthermore, under the condition that the fixed β s = β0, solve for the range of the rotation angle γ s of the sensor around the X s axis; On this basis, establish the relationship function between the offset c of the sensor coordinate origin 0 s relative to the gear coordinate origin 0 c on the Z c axis and β s , γ s and α s ;

[0027] The calculation formula for the rotation angle γ s of the sensor around the X s axis is:

[0028] When the sensor rotates upward around the X s axis, the magnitude of λ is:

[0029] Z1 = tan(θ)·X1 + b0

[0030]

[0031] When the sensor rotates downward around the X s axis, the magnitude of λ is:

[0032]

[0033] (-λ min , λ max )

[0034] Sensor Zc The calculation formula for the offset c on the axis is:

[0035] H1 = L·sin(θ)

[0036] (-(H + H2 - H1), (H - H2 - H1))

[0037] X o3 is the X-axis coordinate value of the midpoint O3 of the projection line of the laser plane on the XOZ plane when the sensor rotates by an angle β0 around the Z-axis; s axis when the laser plane intersects the upper end face of the gear. c O c Z c plane at the midpoint O3 of the projection line on the XOZ plane in the δ coordinate system; c coordinate system;

[0038] Z o3 is the Z-axis coordinate value of the midpoint O3 of the projection line of the laser plane on the XOZ plane when the sensor rotates by an angle β0 around the Z-axis; s axis when the laser plane intersects the upper end face of the gear. c O c Z c plane at the midpoint O3 of the projection line on the XOZ plane in the δ coordinate system; c coordinate system;

[0039] X o4 is the X-axis coordinate value of the midpoint O4 of the projection line of the laser plane on the XOZ plane when the sensor rotates around the X-axis until the laser plane intersects the upper end face of the gear; s axis until the laser plane intersects the upper end face of the gear. c O c Z c plane at the midpoint O4 of the projection line on the XOZ plane; c axis coordinate value;

[0040] Z o4 is the Z-axis coordinate value of the midpoint O4 of the projection line of the laser plane on the XOZ plane when the sensor rotates around the X-axis until the laser plane intersects the upper end face of the gear; s axis until the laser plane intersects the upper end face of the gear. c O c Z c plane at the midpoint O4 of the projection line on the XOZ plane; c axis coordinate value;

[0041] L3 is the straight-line distance between point O3 and point O4;

[0042] L4 is the straight-line distance between the coordinate origin O and point O3 when the sensor rotates by an angle β0 around the Z-axis; s axis; s and point O3;

[0043] L5 is the straight-line distance between the coordinate origin O and point O4 when the sensor rotates around the X-axis until the laser plane intersects the upper end face of the gear; L6 is the straight-line distance between point O3 and point O5; s axis until the laser plane intersects the upper end face of the gear; s and point O4;

[0044] L7 is the straight-line distance between the coordinate origin O and point O5 when the sensor rotates around the X-axis; sThe coordinate origin O when the axis rotates until the laser plane intersects with the lower end face of the gear s The straight-line distance between the point O5; L is the length of the projection line of the laser plane on the X c O c Z c Half of the length of the projection line on the plane;

[0045] H1 is the vertical distance between the end point of the projection line of the laser plane on the X c O c Z c plane and the X-axis when the sensor is in the initial position;

[0046] H is 1 / 2 of the tooth width length;

[0047] H2 is the Z-axis coordinate value of the midpoint of the projection line of the laser plane on the X c O c Z c plane in the δc coordinate system after the sensor rotates around the three coordinate axes.

[0048] Furthermore, combining the quadrilateral area formed by the depth of field range and the field of view boundary of the line laser sensor, determine the coordinate origin 0 of the sensor s relative to the gear coordinate origin 0 c in the Y c axis direction offset b value range:

[0049] b1 + Kh = L min

[0050] b2 = L max

[0051] (b1, b2)

[0052] h is the tooth height of the gear to be measured;

[0053] K is the extension coefficient;

[0054] L min is the minimum allowable measurement distance of the selected line laser sensor;

[0055] L max is the maximum allowable measurement distance of the selected line laser sensor.

[0056] Furthermore, based on the incident angle of the laser plane and the occlusion model of adjacent teeth on the laser plane, determine the mathematical model of the offset a of the coordinate origin 0 of the sensor s relative to the gear coordinate origin 0 c in the X c axis direction is:

[0057] The line laser sensor in the X cThe calculation formula for the minimum value of the offset a0 in the axial direction is:

[0058] Φ ∈ [Φ1, Φ2]

[0059]

[0060] Z = (x - a0)·tan(θ)

[0061]

[0062] The line laser sensor is offset in the X c axis direction, and the calculation formula for the maximum value of the offset a0 is:

[0063] X = r b ·cosФ + ζ·r b ·sinФ | ζ = -ζ a , τ = τ L

[0064] X = r b ·cosФ + ζ·r b ·sinФ | ζ = ζ f , τ = τ r

[0065] Z = (x - a0)·tan(θ)

[0066] Z = Z down = -0.5·L7·sin(ζ)

[0067]

[0068] M s (x s , z s ) = P(x down , z down )

[0069] From the above equations, a max

[0070] (a min + a1, a max + a1)

[0071] Φ1 is the starting rotation angle of the measured tooth surface;

[0072] Φ2 is the ending rotation angle of the measured tooth surface;

[0073] r b is the base cylinder radius of the measured gear;

[0074] τ is the position angle corresponding to the involute helix surface of the measured gear;

[0075] ζ is the sum of the involute expansion angle and the pressure angle at a certain point on the gear under test;

[0076] δ is the comprehensive rotation angle of a certain point on the tooth surface under test;

[0077] a0 is the X-axis coordinate value of the midpoint of the projection line of the laser plane on the X c O c Z c plane at the initial position of the sensor;

[0078] B b is the helix angle of the gear under test;

[0079] Ψ p is the measurement angle size of the tooth surface under test;

[0080] Ψ pmax is the maximum value of the measurement angle of the tooth surface under test;

[0081] Ψ r is the measurement angle size allowed by the selected line laser sensor;

[0082] a0 is the search step size of the minimum offset;

[0083] a min is the coordinate origin O of the line laser sensor in the initial pose s relative to the coordinate origin O of the gear c in the X c axis direction of the minimum offset:

[0084] ζ a is the sum of the involute expansion angle and the pressure angle at the tooth tip of the gear under test;

[0085] ζ f is the sum of the involute expansion angle and the pressure angle at the tooth root of the gear under test;

[0086] τ L is the position angle corresponding to the involute helicoid of the left tooth surface of the gear under test;

[0087] τ r is the position angle corresponding to the involute helicoid of the right tooth surface of the gear under test;

[0088] Z down is the ordinate value of the lower endpoint of the projection of the laser plane on the X c O c Z c plane;

[0089] L7 is the length of the projection line of the laser plane on the X c O c Z c plane;

[0090] Ms is the light-shielding starting point of the tooth surface to be measured;

[0091] P is the coordinate of the lower endpoint of the projection of the laser plane on the X c O c Z c plane;

[0092] a max is the coordinate origin O of the line laser sensor in the initial pose s relative to the coordinate origin O of the gear c in the X c axis direction;

[0093] a1 is the coordinate origin O of the line laser sensor after rotating around the three coordinate axes s relative to the coordinate origin O of the gear c in the X c axis direction;

[0094] Furthermore, as described in S1, the initial pose of the line laser sensor is:

[0095] α s = θ, β s = 0, λ s = 0, a = 0, b = L, c = 0

[0096] α0 is the rotation angle of the sensor around the Y s axis;

[0097] Furthermore, as described in S4, the incident angle of the laser plane is:

[0098] In the three-dimensional measurement of the gear line laser, the angle (acute angle) between the measurement light of the line laser sensor and the normal direction of the tooth surface to be measured is called the incident angle of the laser plane.

[0099] Furthermore, as described in S4, the light-shielding model of adjacent teeth for the laser plane is:

[0100] In actual measurement, the line laser sensor remains stationary, and the gear rotates around the rotation center. When the offset of the sensor in the X C direction is too large, it will cause the line laser to be blocked by the adjacent teeth of the tooth surface to be measured during the measurement process. According to the principle of parallel projection in projective geometry, the three-dimensional model is transformed into a two-dimensional model, and a corresponding mathematical model is established based on the light-shielding situation of adjacent teeth for the laser plane.

[0101] So far, all the pose parameters of the line laser sensor have been determined.

[0102] Compared with the prior art, the beneficial effects of the present invention are:

[0103] For different types of gears, based on the coupling relationship between the pose parameters of the line laser sensor, the pose parameters of the line laser sensor in gear measurement can be quickly determined through simple calculations. This is beneficial to quickly obtaining the three-dimensional information of the tooth surface and improving the detection speed of gears. BRIEF DESCRIPTION OF THE DRAWINGS

[0104] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0105] Figure 1 It is a schematic flow chart of a method for determining the pose parameters of a line laser sensor in gear detection provided by the present invention;

[0106] Figure 2 It is a schematic diagram of the coordinate system of the line laser sensor and the gear coordinate system provided by the present invention;

[0107] Figure 3(a) is a schematic diagram of the projection of the laser plane on the X s O c Z c plane when the line laser sensor rotates around the Z c axis;

[0108] Figure 3(b) is a schematic diagram of the variation range of the angle β s when the line laser sensor rotates around the Z s axis;

[0109] Figure 4(a) is a schematic diagram of the projection of the laser plane on the X s O c Z c plane when the line laser sensor rotates around the X c axis;

[0110] Figure 4(b) is a schematic diagram of the variation range of the angle λ s when the line laser sensor rotates around the X s axis;

[0111] Figure 5 It is a schematic diagram of the projection of the laser plane on the X c O c Z c plane when the line laser sensor moves along the Z c axis;

[0112] Figure 6 It is a schematic diagram of the laser plane after the line laser sensor rotates around the three coordinate axes;

[0113] Figure 7 Schematic diagram of the incident angle of the laser plane changing with the offset a

[0114] Figure 8(a) shows the projection of the light-shielding model on the X c O c Z c plane when the tooth surface to be measured has not entered the scanning area with the offset of the line laser sensor being a0

[0115] Figure 8(b) shows the projection of the light-shielding model on the X c O c Z c plane when the tooth surface to be measured has entered the scanning area with the offset of the line laser sensor being a0

[0116] Figure 8(c) shows the projection of the light-shielding model on the X max when the offset of the line laser sensor is a c O c Z c plane

[0117] Figure 6 In the figure: 1 is the proximal distance; 2 is the distal distance; 3 is the proximal field of view; 4 is the distal field of view;

[0118] In Figure 8(a): 1 is the tooth surface to be measured; 2 is the tooth surface of the adjacent tooth Specific implementation manner

[0119] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention

[0120] The following further details the present application in conjunction with Figure 1 -8

[0121] Please refer to Figure 1 , Embodiment 1 of the present invention provides a method for determining the pose parameters of a line laser sensor in gear detection. The method for determining the pose parameters of a line laser sensor in gear detection includes:

[0122] S1. Set the initial pose of the line laser sensor. Taking the measurement range of the laser plane on the upper and lower end faces of the gear to be measured as the boundary condition, establish a geometric function of the rotation angle β s of the sensor around the Z s axis through spatial projection analysis

[0123] S2. Fix β sUnder the condition of = β0, solve for the range of the rotation angle γ of the sensor around the X-axis s ; On this basis, establish the offset c of the origin 0 of the sensor coordinate system relative to the origin 0 of the gear coordinate system on the Z-axis through spatial geometric analysis s ; and the relational function with β s , γ c and α c ; s s s

[0124] S3. Combine the quadrilateral area formed by the depth of field range and the field of view boundary of the line laser sensor to determine the range of the offset b of the origin 0 of the sensor coordinate system relative to the origin 0 of the gear coordinate system in the Y-axis direction

[0125] s ; c c s c c

[0126] S4. Based on the incident angle of the laser plane and the occlusion model of adjacent gear teeth on the laser plane, determine the mathematical model of the offset a of the origin 0 of the sensor coordinate system relative to the origin 0 of the gear coordinate system in the X-axis direction s s c c c c

[0126] Please refer to Figure 1 ; In the initial pose of the line laser sensor, the rotation angle of the line laser sensor around the Y-axis is generally determined to be perpendicular to the helix angle of the measured gear. If the measured gear is a cylindrical gear, then the rotation angle of the line laser sensor around the Y-axis is generally defined as 30° s s

[0127] Figure 2 c Please refer to Figure 2 to establish the gear coordinate system δ c : O c -X c Y c Z c ; which is a fixed coordinate system; δ c is the label of the gear coordinate system; O c is the origin of the gear coordinate system; X c Y c Z c are the three coordinate axes of the gear coordinate system; the origin of the gear coordinate system is at the geometric center of the gear; establish the sensor coordinate system δ s : O s -X s Y s Z s ; which is a moving coordinate system; it changes as the sensor moves; δ s is the label of the sensor coordinate system; O sis the origin of the sensor coordinate system; X s Y s Z s are the three coordinate axes of the sensor coordinate system; the sensor is arranged circumferentially on the calibration piece; the origin of the sensor coordinate system is located at the center of the laser emission port; at the initial position of the sensor, the three coordinate axes of the sensor coordinate system are parallel to the three coordinate axes of the gear coordinate system.

[0128] Please refer to Figure 3. Figure 3 is the projection of the measured gear and the laser plane on the X c O c Z c plane. It is stipulated that the β s angle formed by the sensor rotating upward around Z s is positive. At the initial position, the midpoint O1 of the laser line coincides with O c ; when the line laser sensor rotates around the Z S axis, the laser plane intersects with the upper end face of the gear, and the projection line of the laser plane on the X c O c Z c plane moves from the initial position to position 1 in Figure 3(a), and at this time the β s angle is the maximum value. Since the measured gear is a cylindrical gear, the gear is symmetric about the X c O c Y c plane, so the maximum value and the minimum value of the β angle are opposite to each other. Figure 3(b) is a triangle formed by the straight-line distance between point O s and the midpoint of the laser line before and after rotation, and the straight-line distance between the midpoints of the laser lines at the two positions. The β angle in the figure is the angle of the sensor rotating around the Z S axis.

[0129] Therefore, set the initial pose of the line laser sensor, and take the measurement range of the laser plane on the upper and lower end faces of the measured gear as the boundary condition. Through spatial projection analysis, establish the geometric function of the rotation angle β s of the sensor around the Z s axis as:

[0130] Z1 = tan(θ)·X1

[0131]

[0132] (-β, β)

[0133] Z1 is the coordinate value of the projection line of the upper end face of the gear on the X c O c Z c plane;

[0134] X1 is the coordinate value of the upper end of the laser line and the upper end face of the gear on the X c OZc The abscissa value of the intersection point of the projection lines on the plane;

[0135] X o1 is the X-axis coordinate value of the midpoint O1 of the projection line of the laser plane at the initial position of the sensor on the c O c Z c plane in the δ c coordinate system;

[0136] Z o1 is the Z-axis coordinate value of the midpoint O1 of the projection line of the laser plane at the initial position of the sensor on the X c O c Z c plane in the δ c coordinate system; X o2 is the X-axis coordinate value of the midpoint O2 of the projection line of the laser plane when the sensor rotates around the Zs axis until the laser plane intersects with the upper end face of the gear on the X c O c Z c plane in the δ c coordinate system;

[0137] Z o2 is the Z-axis coordinate value of the midpoint O2 of the projection line of the laser plane when the sensor rotates around the Zs axis until the laser plane intersects with the upper end face of the gear on the X c O c Z c plane in the δ c coordinate system;

[0138] L0 is the straight-line distance between point O1 and point O2;

[0139] L1 is the straight-line distance between the coordinate origin O s and point O1 at the initial position of the sensor;

[0140] L2 is the straight-line distance between the coordinate origin O s and point O2 when the laser plane intersects with the upper end face of the gear.

[0141] Please refer to Figure 4. Figure 4 is the projection of the measured gear and the laser plane on the X c O c Z c plane. It is stipulated that the λ angle formed by the sensor rotating upward around the X s axis is positive. The determination of the λ angle range is affected by the β s angle. According to the range of β s , a specific value β0 of β is determined. At this time, the projection of the laser plane is at position 1 in Figure 4(a). When the sensor rotates around the X sRotate to move the laser line in Fig. 4(a) from position 1 to position 2, where the laser plane intersects with the upper end face of the gear. At this time, the obtained λ s angle reaches the maximum value. When the sensor rotates around the X s axis to move the laser line in Fig. 4(a) from position 1 to position 3, the laser plane intersects with the lower end face of the gear, and the obtained λ s angle reaches the minimum value. Fig. 4(b) shows the triangle formed by the straight-line distance between point O s and the midpoint of the laser line before and after rotation, and the straight-line distance between the midpoints of the laser lines at the two positions. The λ angle in the figure is the angle of the sensor's rotation around the X s axis.

[0142] Please refer to Figure 5 , Figure 5 which is the projection of the gear under test and the laser plane on the X c O c Z c plane. The determination of the offset of the line laser sensor in the Z c axis direction depends on the rotation angles of the gear around the three axes. According to the ranges of the sensor's rotation around the three coordinates obtained above, the rotation angles of the sensor around the three coordinate axes are determined to be α0, β0, and λ0 respectively. At this time, the projection of the laser plane is at Figure 5 position 1. When the sensor moves along the Z c axis to move the laser line to Figure 5 position 2, the laser plane intersects with the upper end face of the gear. At this time, the offset C of the sensor in the Z c axis direction reaches the maximum value. When the laser line moves to Figure 5 position 3, the laser plane intersects with the lower end face of the gear. At this time, the offset C of the sensor in the Z C axis direction reaches the minimum value.

[0143] Therefore, under the condition of fixing β s = β0, solve for the range of the rotation angle γ s of the sensor around the X s axis; on this basis, establish the relationship function between the offset c of the origin 0 s of the sensor coordinate system relative to the origin 0 c of the gear coordinate system on the Z c axis and β s , γ s and α s as:

[0144] The calculation formula for the rotation angle γ s of the sensor around the X s axis is:

[0145] The rotation angle γ sWhen rotating axially, the magnitude of λ is:

[0146] Z1 = tan(θ)·X1 + b0

[0147]

[0148] When the sensor rotates downward about the X s axis, the magnitude of λ is:

[0149]

[0150] (-λ min , λ max )

[0151] The offset c of the sensor on the Z c axis is calculated by the formula:

[0152] H1 = L·sin(θ)

[0153] (-(H + H2 - H1), (H - H2 - H1))

[0154] X o3 is the X-axis coordinate value of the midpoint O3 of the projection line of the laser plane on the X s O c Z c plane when the sensor rotates by an angle β0 about the Z c axis in the δ c coordinate system;

[0155] Z o3 is the Z-axis coordinate value of the midpoint O3 of the projection line of the laser plane on the X s O c Z c plane when the sensor rotates by an angle β0 about the Z c axis in the δ c coordinate system;

[0156] X o4 is the X-axis coordinate value of the midpoint O4 of the projection line of the laser plane on the X s plane when the sensor rotates about the X c O c Z c plane until the laser plane intersects the upper end face of the gear; c axis coordinate value;

[0157] Z o4 is the Z-axis coordinate value of the midpoint O4 of the projection line of the laser plane on the X s plane when the sensor rotates about the X c O c Z c plane until the laser plane intersects the upper end face of the gear; c axis coordinate value;

[0158] L3 is the straight-line distance between point O3 and point O4;

[0159] L4 is the straight-line distance between the origin O of coordinates and point O3 when the sensor rotates by an angle of β0 around the Z s axis; s and point O3;

[0160] L5 is the straight-line distance between the origin O of coordinates and point O4 when the sensor rotates around the X s axis until the laser plane intersects with the upper end face of the gear; s L6 is the straight-line distance between point O3 and point O5;

[0161] L7 is the straight-line distance between the origin O of coordinates and point O5 when the sensor rotates around the X s axis until the laser plane intersects with the lower end face of the gear; L is half of the length of the projection line of the laser plane on the X s O c Z c plane; c H1 is the vertical distance between the end point of the projection line of the laser plane on the X

[0162] O c Z c plane in the initial position of the sensor and the X axis; c H is 1 / 2 of the tooth width;

[0163] H2 is the Z-axis coordinate value of the midpoint of the projection line of the laser plane on the X

[0164] O c Z c plane in the δc coordinate system after the sensor rotates around the three coordinate axes. c Please refer to

[0165] and Figure 5 When the rotation angles of the sensor around the three coordinate axes are α0, β0, and λ0, the projection of the laser plane is in Figure 6 position 1 in Figure 5 At this time, the laser plane is as shown in Figure 6 The maximum value of the offset d of the sensor in the Y C axis direction is the maximum value allowed by the sensor. The minimum value should ensure that the measured tooth surface is within the measurement range of the laser plane. When the rotation angles of the sensor around the Z S and Y S axes are equal to zero, K is taken as zero.

[0166] Therefore, combining the quadrilateral area formed by the depth of field range and the field of view boundary of the line laser sensor, the origin 0 of the sensor coordinates is determined s relative to the origin 0 of the gear coordinates c in the Y cThe value range of the offset b in the axial direction is as follows:

[0167] b1 + Kh = L min

[0168] b2 = L max

[0169] (b1, b2)

[0170] h is the tooth height of the measured gear;

[0171] K is the extension coefficient;

[0172] L min is the minimum allowable measurement distance of the selected line laser sensor;

[0173] L max is the maximum allowable measurement distance of the selected line laser sensor.

[0174] Please refer to Figure 7 , the angle (acute angle) between the measurement light of the line laser sensor and the normal direction of the measured tooth surface is called the incident angle of the laser plane. During the actual measurement process, when the incident angle is relatively large, the tooth surface data will be distorted due to the inability to receive the measurement light reflected back to the sensor, affecting the integrity of the tooth surface data. The magnitude of the incident angle increases as the offset a of the sensor in the X c axis direction increases. Therefore, according to the relationship between the incident angle and the offset a and the maximum allowable incident angle of the line laser sensor, a mathematical model is established to determine the minimum value of the offset.

[0175] Please refer to Figure 8. In the actual measurement, the line laser sensor remains stationary, and the gear rotates around the rotation center. When the offset of the sensor in the X c axis direction is too large, during the measurement process, the laser plane will be blocked by the adjacent teeth of the measured tooth surface. According to the principle of parallel projection in projective geometry, the three-dimensional model is transformed into a two-dimensional model. The laser plane emitted by the line laser sensor is projected onto the X c O c Z c plane and is a straight line; the tooth surface and adjacent tooth surface of the measured gear are projected onto the X c O c Z c plane and can be regarded as a quadrilateral region surrounded by the projection of the tooth tip helix and the projection of the tooth root helix. The three are in the X c O c Z cThe projection on the plane is shown in Fig. 8(a). As shown in Fig. 8(b), when the offset a0 of the line laser sensor is too large, the laser plane will be blocked by adjacent teeth. As shown in Fig. 8(c), when the measurement of the tooth surface to be measured is completed, the top line of the adjacent tooth surface and the root line of the tooth surface to be measured intersect, and at this time, the offset a0 of the sensor is the maximum value.

[0176] Therefore, based on the incident angle of the laser plane and the occlusion model of adjacent teeth on the laser plane, the coordinate origin 0 of the sensor is determined s Relative to the gear coordinate origin 0 c In the X c axis direction, the mathematical model of the offset a is:

[0177] The minimum value of the offset a0 of the X-axis of the line laser sensor is:

[0178] Φ ∈ [Φ1, Φ2]

[0179]

[0180] Z = (x - a0) · tan(θ)

[0181]

[0182] The line laser sensor in the X c axis direction, the calculation formula for the maximum value of the offset a0 is:

[0183] X = r b · cosФ + ζ · r b · sinФ | ζ = -ζ a , τ = τ L

[0184] X = r b · cosФ + ζ · r b · sinФ | ζ = ζ f , τ = τ r

[0185] Z = (x - a0) · tan(θ)

[0186] Z = Z down = -0.5 · L7 · sin(ζ)

[0187]

[0188] M s (x s , z s ) = P(x down , z down )

[0189] From the above equations, a can be obtainedmax

[0190] (a min +a1, a max +a1)

[0191] Φ1 is the starting rotation angle of the tooth surface to be measured;

[0192] Φ2 is the ending rotation angle of the tooth surface to be measured;

[0193] r b is the base cylinder radius of the gear to be measured;

[0194] τ is the position angle corresponding to the involute helicoid of the gear to be measured;

[0195] ζ is the sum of the developed angle and the pressure angle at a certain point on the involute of the gear to be measured;

[0196] δ is the composite rotation angle of a certain point on the tooth surface to be measured;

[0197] a0 is the X-axis coordinate value of the midpoint of the projection line of the laser plane on the X c O c Z c plane when the sensor is at the initial position;

[0198] B b is the helix angle of the gear to be measured;

[0199] Ψ p is the measurement angle size of the tooth surface to be measured;

[0200] Ψ pmax is the maximum value of the measurement angle of the tooth surface to be measured;

[0201] Ψ r is the measurement angle size allowed by the selected line laser sensor;

[0202] a0 is the search step size of the minimum offset;

[0203] a min is the coordinate origin O of the sensor in the initial pose of the line laser sensor s relative to the coordinate origin O of the gear c in the X c axis direction minimum offset:

[0204] ζ a is the sum of the developed angle and the pressure angle at the tooth tip of the involute of the gear to be measured;

[0205] ζ f is the sum of the developed angle and the pressure angle at the tooth root of the involute of the gear to be measured;

[0206] τ L is the position angle corresponding to the involute helicoid of the left tooth surface of the gear to be measured;

[0207] τ r is the position angle corresponding to the involute helicoid of the right tooth surface of the gear to be measured;

[0208] Z down is the ordinate value of the lower endpoint of the projection of the laser plane on the X c O c Z c plane;

[0209] L7 is the length of the projection line of the laser plane on the X c O c Z c plane;

[0210] M s is the starting point of light shielding of the tooth surface to be measured;

[0211] P is the coordinate of the lower endpoint of the projection of the laser plane on the X c O c Z c plane;

[0212] a max is the coordinate origin O of the line laser sensor in the initial pose relative to the coordinate origin O of the gear s in the maximum offset in the X c axis direction; c

[0213] a1 is the offset of the coordinate origin O of the line laser sensor relative to the coordinate origin O of the gear after the line laser sensor rotates around the three coordinate axes s in the X c axis direction. c

[0214] The above are only the specific embodiments of the present application, enabling those skilled in the art to understand or implement the present application. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to these embodiments shown herein, but rather to the widest scope consistent with the principles and novel features claimed herein.​​

Claims

1. A method for determining the pose parameters of a line laser sensor in gear detection, characterized in that Including: S1. Set the initial pose of the line laser sensor. Taking the measurement range of the laser plane on the upper and lower end faces of the gear under test as the boundary condition, establish the geometric function of the rotation angle β of the sensor around the Z s axis. s ​ S2. Under the condition of fixing β s = β0, solve for the range of values of the rotation angle γ s of the sensor about the X s axis; On this basis, establish, through spatial geometric analysis, the offset c of the origin 0 s of the sensor coordinate system relative to the origin 0 c of the gear coordinate system on the Z c axis and the relational function of β s、 γ s and α s . S3. Determine the origin 0 of the sensor coordinates by combining the quadrilateral area formed by the depth of field range and the field of view boundary of the line laser sensor s Relative to the origin 0 of the gear coordinates c In the Y c Axis direction, the value range of the offset b; S4. Determine the coordinate origin 0 of the sensor based on the incident angle of the laser plane and the occlusion model of adjacent gear teeth with respect to the laser plane. s With respect to the gear coordinate origin 0 c In the X c Mathematical model of the axial offset a.

2. The method for determining the pose parameters of the line laser sensor for gear detection according to claim 1, wherein The gear coordinate system and the line laser sensor coordinate system are as follows: Establish the gear coordinate system δ c : O c -X c Y c Z c ; is the fixed coordinate system; δ c is the label of the gear coordinate system; O c is the origin of the gear coordinate system; X c Y c Z c are the three coordinate axes of the gear coordinate system; the origin of the gear coordinate system is at the geometric center of the gear; Establish the sensor coordinate system δ s : O s -X s Y s Z s ; is the moving coordinate system; changes with the movement of the sensor; δ s is the label of the sensor coordinate system; O s is the origin of the sensor coordinate system; X s Y s Z s are the three coordinate axes of the sensor coordinate system; the sensor is arranged circumferentially on the calibration piece; the origin of the sensor coordinate system is located at the center of the laser emission port; At the initial position of the sensor, the three coordinate axes of the sensor coordinate system are parallel to the three coordinate axes of the gear coordinate system.

3. The method for determining the pose parameters of the line laser sensor in gear detection according to claim 1, characterized in that, Set the initial pose of the line laser sensor. Taking the measurement range of the laser plane on the upper and lower end faces of the gear to be measured as the boundary condition, establish the geometric function of the rotation angle β of the sensor around the Z s axis as follows: s : Z1 = tan(θ)·X1 (-β,β) Z1 is the coordinate value of the projection line of the upper end face of the gear on the X c O c Z c plane; X1 is the abscissa value of the intersection point of the projection line of the upper end of the laser line and the upper end face of the gear on the X c OZ c plane; X o1 The X-axis coordinate value of the midpoint O1 of the projection line of the laser plane at the initial position of the sensor on the X c O c Z c plane in the δ c coordinate system; Z o1 The X-axis coordinate value of the midpoint O1 of the projection line of the laser plane at the initial position of the sensor on the X c O c Z c plane in the δ c coordinate system; X o2 The X-axis coordinate value of the midpoint O2 of the projection line of the laser plane when the sensor rotates around the Zs axis until the laser plane intersects the upper end face of the gear on the X c O c Z c plane in the δ c coordinate system; Z o2 When the sensor rotates around the Zs axis until the laser plane intersects with the upper end face of the gear, the Z-axis coordinate value of the midpoint O2 of the projection line of the laser plane on the X c O c Z c plane in the δ c coordinate system; L0 is the straight-line distance between point O1 and point O2; L1 is the coordinate origin O when the sensor is at the initial position s The straight-line distance between it and point O1; L2 is the straight-line distance between the origin O when the upper end of the laser line intersects with the upper end face of the gear s and point O2.

4. The method for determining the pose parameters of the line laser sensor in gear detection according to claim 1, characterized in that, Under the condition that the fixed β s = β0, solve for the range of the rotation angle γ s of the sensor about the X s axis; On this basis, establish the offset c of the origin 0 s of the sensor coordinate system with respect to the origin 0 c of the gear coordinate system on the Z c axis and the relational function of β s、 γ s and α s : The rotation angle γ of the sensor around the X s axis is calculated by the following formula: s ​ The sensor rotates axially about the X s axis, and the magnitude of λ is as follows: Z1 = tan(θ)·X1 + b0 When the sensor rotates downward about the X s axis, the magnitude of λ is: (-λ min ,λ max ) Sensor Z c The calculation formula for the offset c on the axis is as follows: H1 = L·sin(θ) (-(H + H2 - H1), (H - H2 - H1)) X o3 When the sensor rotates around the Z s axis by an angle of β0, the X c O c Z c coordinate value of the midpoint O3 of the projection line of the laser plane on the c X-axis in the δ coordinate system; Z o3 When the sensor rotates around the Z s axis by an angle of β0, the Z-axis coordinate value of the midpoint O3 of the projection line of the laser plane on the X c O c Z c plane in the δ c coordinate system; X o4 When the sensor rotates around the X s axis until the laser plane intersects with the upper end face of the gear, the X c O c Z c coordinate value of the midpoint O4 of the projection line of the laser plane on the c X plane; Z o4 When the sensor rotates around the X s axis until the laser plane intersects with the upper end face of the gear, the Z c O c Z c coordinate value of the midpoint O4 of the projection line on the c plane; L3 is the straight-line distance between point O3 and point O4; L4 is the straight-line distance between the origin O of coordinates and point O3 when the sensor rotates by an angle of β0 around the Z s axis; s ​ L5 is the straight-line distance between the coordinate origin O and point O4 when the sensor rotates around the X-axis until the laser plane intersects with the upper end face of the gear; s L6 is the straight-line distance between point O3 and point O5; s ​ L7 is the linear distance between the origin O of coordinates and point O5 when the sensor rotates around the X-axis until the laser plane intersects with the lower end face of the gear; s L is half of the length of the projection line of the laser plane on the XOZ plane. s When the laser plane intersects with the lower end face of the gear, the linear distance between the origin O of coordinates and point O5; c O c Z c half of the length of the projection line of the laser plane on the XOZ plane; H1 is the vertical distance between the end point of the projection line of the laser plane on the X plane when the sensor is in the initial position and the X-axis; c O c Z c plane and the X-axis; H is half of the tooth width length; H2 is the Z-axis coordinate value of the midpoint of the projection line of the laser plane on the X plane after the sensor rotates around the three coordinate axes in the δc coordinate system. c O c Z c plane.

5. The method for determining the pose parameters of the line laser sensor in gear detection according to claim 1, characterized in that Determine the origin 0 of the sensor coordinates based on the quadrilateral region formed by the depth of field range and the field of view boundary of the combined line laser sensor s Relative to the origin 0 of the gear coordinates c In the Y c Axis direction, the value range of the offset b: Point 0 s in the Y c axis direction, the calculation formula for the offset is as follows: b1 + Kh = L min b2 = L max (b1, b2) h is the tooth height of the measured gear; K is the extension coefficient; L min The minimum measurement distance allowed for the selected line laser sensor; L max Is the maximum measurement distance allowed for the selected line laser sensor.

6. The method for determining the pose parameters of the line laser sensor in gear detection according to claim 1, characterized in that The mathematical model of the offset a in the X-axis direction is determined based on the incident angle of the laser plane and the occlusion model of adjacent gear teeth on the laser plane with respect to the coordinate origin 0 of the sensor s with respect to the gear coordinate origin 0 c In the X c axis direction offset a mathematical model;: The minimum value calculation formula for the offset a0 of the line laser sensor in the X C axis direction is as follows: Φ ∈ [Φ1, Φ2] Z = (x - a0)·tan(θ) The maximum value of the offset a0 of the line laser sensor in the X c axis direction is calculated by the formula: X = r b ·cosФ + ζ·r b ·sinФ | ζ = -ζ a ,τ = τ L X = r b ·cosФ + ζ·r b ·sinФ|ζ = ζ f ,τ = τ r Z = (x - a0)·tan(θ) Z = Z down = -0.5·L7·sin(ζ) M s (x s ,z s ) = P(x p ,z p ) We can obtain a from the above equation max (a min +a1, a max +a1) Φ1 is the starting rotation angle of the measured tooth surface; Φ2 is the ending rotation angle of the measured tooth surface; r b is the base cylinder radius of the gear under test; τ is the position angle corresponding to the involute helix surface of the measured gear; ζ is the sum of the developed angle and the pressure angle at a certain point on the involute of the measured gear; δ is the comprehensive rotation angle of a certain point on the measured tooth surface; The X-axis coordinate value of the midpoint of the projection line of the laser plane on the X-plane when a0 is the initial position of the sensor c O c Z c plane B b is the helix angle of the gear under test; Ψ p is the measurement angle size of the tooth surface to be measured; Ψ pmax is the maximum value of the measuring angle of the tooth surface to be measured; Ψ r The measurement angle size allowed for the selected line laser sensor; a0 is the search step size of the minimum offset; a min The coordinate origin O of the line laser sensor in the initial pose s Relative to the coordinate origin O of the gear c In the X c Axis direction minimum offset: ζ a is the sum of the involute expansion angle and the pressure angle at the tooth tip of the gear under test; ζ f is the sum of the involute expansion angle and the pressure angle at the tooth root of the gear under test; τ L is the position angle corresponding to the involute helicoid of the left tooth surface of the gear under test; τ r is the position angle corresponding to the involute helicoid of the right tooth surface of the gear under test; Z down is the ordinate value of the lower endpoint of the projection of the laser plane on the X c O c Z c plane projection; L7 is the length of the projection line of the laser plane on the X c O c Z c plane; M s is the light-shielding starting point of the tooth surface to be measured; P is the coordinate of the lower endpoint of the projection of the laser plane on the X c O c Z c plane; a max is the coordinate origin O of the line laser sensor in the initial pose s relative to the coordinate origin O of the gear c in the X c axis direction maximum offset; a1 is the coordinate origin O of the line laser sensor after rotating around the three coordinate axes s relative to the coordinate origin O of the gear c in the X c axis direction offset.

7. The method for determining the pose parameters of the line laser sensor in gear detection according to claim 2, wherein The initial pose of the line laser sensor is: α = α0, β = 0, λ = 0, a = 0, b = L, c = 0 α0 is the rotation angle of the initial pose of the sensor about the Y s axis.

8. The method for determining the pose parameters of the line laser sensor in gear detection according to claim 5, wherein The incident angle of the laser plane is: In the three-dimensional measurement of gear line laser, the angle (acute angle) between the measurement light of the line laser sensor and the normal direction of the measured tooth surface is called the incident angle of the laser plane.

9. The method for determining the pose parameters of the line laser sensor in gear detection according to claim 5, characterized in that The light-shielding model of the laser plane is: In actual measurement, the line laser sensor remains stationary while the gear rotates around the center of rotation. When the offset of the sensor in the X C direction is too large, it will cause the line laser to be blocked by adjacent teeth on the tooth surface to be measured during the measurement process. According to the principle of parallel projection in projective geometry, the three-dimensional model is transformed into a two-dimensional model, and a corresponding mathematical model is established based on the occlusion of the laser plane by adjacent teeth.

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