Aero face gear in-situ measurement error compensation method based on pre-travel driving

Abstract

The application discloses an aero face gear in-situ measurement error compensation method based on pre-travel driving and relates to the technical field of gear machining, which comprises the following steps: step one, calculating the error caused by data transmission delay of a measuring head at different measuring speeds; step two, establishing a model of pre-travel error caused by the mechanical structure of the measuring head; and step three, referring to the pre-travel error model of the measuring head, completing the measurement of a standard ball and the calibration of the measuring head, and calculating the pre-travel size of the measuring head along each measuring direction through the interpolation mode to calculate the pre-travel size corresponding to the measuring point of the face gear tooth surface. The application can improve the in-situ measurement accuracy and make the in-situ measurement accuracy consistent with the offline measurement accuracy as much as possible.

Description

Technical Field

[0001] This invention relates to the field of gear processing technology, and in particular to an in-machine measurement error compensation method for aerospace surface gears based on pre-stroke drive. Background Technology

[0002] For high-precision gears, achieving the required accuracy in a single machining operation is difficult. Often, one or more adjustments based on previous measurements are needed to produce a product that meets the precision requirements. Compared to offline measurement, in-machine measurement systems operate in harsher environments. Besides the machine tool positioning accuracy being lower than that of a dedicated coordinate measuring machine, in-machine measurement accuracy is also affected by machine tool vibration, ambient temperature, and workpiece oil contamination. The main source of error in in-machine measurement is the probe system error. During the measurement process, the acquisition and transmission of measurement data rely on the probe system, and the probe system's errors will inevitably be reflected in the measurement results. Probe system errors mainly include probe pre-stroke error, anisotropy, probe eccentricity, and hysteresis errors. These errors lead to low in-machine measurement accuracy, affecting the final machining quality of the gears. Summary of the Invention

[0003] This invention aims to at least solve one of the technical problems existing in the prior art. To this end, this invention proposes an in-machine measurement error compensation method for aircraft surface gears based on pre-stroke drive, which can improve the in-machine measurement accuracy and make it as consistent as possible with the offline measurement accuracy.

[0004] According to a first aspect of the present invention, an in-machine measurement error compensation method for aircraft surface gears based on pre-stroke drive includes the following steps: Step 1: Calculate the error caused by data transmission delay at different measurement speeds of the probe; Step 2: Establish a model for the pre-stroke error caused by the mechanical structure of the probe; Step 3: Referencing the probe pre-stroke error model, complete the measurement of the standard ball and the calibration of the probe, calculate the pre-stroke size of the probe along each measurement direction, and calculate the pre-stroke size corresponding to the test point on the gear tooth surface by interpolation.

[0005] According to an embodiment of the present invention, an in-flight measurement error compensation method for aircraft face gears based on pre-stroke drive has at least the following beneficial effects: A full-process model of probe triggering is established, and each stage of probe triggering is analyzed. Errors caused by signal transmission delay are separated by calculating data transmission time. Based on the structural characteristics of the mechanical probe, a mechanical model of the probe structure is performed to predict the distribution law of the probe pre-stroke. Furthermore, based on the geometric tooth surface characteristics of face gears, a method for calibrating a probe using a standard ball is proposed, and a corresponding model is established, enabling in-flight measurement error compensation.

[0006] According to some embodiments of the present invention, step one specifically includes the following steps: controlling the probe to measure the same point to be measured along the same measurement direction at different speeds, recording different measurement data corresponding to different measurement speeds, and then calculating the error caused by data transmission delay at different measurement speeds.

[0007] According to some embodiments of the present invention, step two specifically includes the following steps: based on the symmetrical structure of the mechanical probe, the motion mode of the support rod under different triggering force directions is analyzed, and the distribution law of the pre-stroke changing with the triggering force direction is calculated.

[0008] According to some embodiments of the present invention, the mechanical probe includes a probe rod, three support rods, and three support balls. The probe rod is vertically arranged, with a probe ball connected to its lower end. The three support rods are symmetrically connected to the upper end of the probe rod, and each support rod is connected to a balance spring. The balance spring pushes the support rod to contact the support ball. When in the untriggered state, current flows through the probe, and the support rods and support balls form a closed circuit. Under the action of a triggering force, the probe rod shifts, and the support rod of the probe disengages from one of the support balls, interrupting the current inside the probe and generating a trigger signal.

[0009] According to some embodiments of the present invention, the analysis of the motion mode of the support rod under different triggering force directions specifically includes the following steps: different triggering force directions are divided into three types. The first type is that the triggering force causes the support rod to rotate around a specific axis. The triggering force and pre-stroke are derived by using the Hertz contact deformation and the balance spring torque equation. The second type is that the triggering force causes the support rod to rotate around an axis perpendicular to the triggering force. The deformation of the balance spring is calculated by combining the displacement of the support point, and the triggering force is calculated from the deformation of the spring. The third type is that the triggering force causes the support rod to translate upwards. The triggering force is equal to the preload of the balance spring and the gravity.

[0010] According to some embodiments of the present invention, the calculation of the distribution law of the pre-stroke as a function of the triggering force direction specifically includes the following steps: based on the obtained triggering force, the bending effect of the triggering force on the probe is calculated, thereby obtaining the probe pre-stroke.

[0011] According to some embodiments of the present invention, step three specifically includes the following steps: calculating the center position of the standard sphere, planning multiple test points on the standard sphere based on the center position of the standard sphere, calculating the pre-travel of the probe along the normal of each test point on the standard sphere, determining the magnitude of the pre-travel of the probe along each measurement direction, and using bilinear interpolation to map the pre-travel data of discrete calibration points to arbitrary tooth surface measurement directions.

[0012] According to some embodiments of the present invention, the calculation of the position of the center of the standard ball relative to the center point of the machine tool A-axis specifically includes the following steps: manually triggering the probe to contact multiple points of the standard ball, initially calculating the position of the center of the standard ball through least squares optimization, establishing an optimization model, planning multiple test points on the standard ball, and accurately calculating the position of the center of the standard ball.

[0013] According to some embodiments of the present invention, the step of planning multiple test points on a standard sphere specifically includes the following steps: the angular interval between adjacent test points in the same cross section along the Z-axis is 60°.

[0014] According to some embodiments of the present invention, the planning of multiple test points on a standard sphere specifically includes the following steps: in order to avoid interference during the measurement process due to inaccurate preliminary calculation of the center position of the standard sphere, the planned test points are offset inward by a certain distance along their normal vector direction.

[0015] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0016] The present invention will be further described below with reference to the accompanying drawings and embodiments, wherein: Figure 1 This is a schematic diagram of the probe triggering process according to an embodiment of the present invention; Figure 2 This is a schematic diagram illustrating signal transmission delay calculation according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the mechanical probe structure and its stress according to an embodiment of the present invention; Figure 4 This is a schematic diagram illustrating the effect of the triggering force on the deflection direction of the measuring rod according to an embodiment of the present invention; Figure 5 A support rod winding according to one embodiment of the present invention Axis Schematic diagram of 1-axis rotation; Figure 6 This is a schematic diagram of a pre-travel 3D model according to an embodiment of the present invention; Figure 7 This is a schematic diagram of the kinematic chain of a machine tool for measuring a standard ball according to an embodiment of the present invention; Figure 8 This is a schematic diagram of the planned distribution of test points on a standard sphere according to an embodiment of the present invention; Figure 9 This is a schematic diagram of the interpolation calculation of the normal pre-stroke of the test point on the tooth surface of a face gear according to an embodiment of the present invention. Detailed Implementation

[0017] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0018] In the description of this invention, it should be understood that the orientation descriptions, such as up, down, etc., are based on the orientation or positional relationship shown in the drawings and are only for the convenience of describing this invention and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention.

[0019] In the description of this invention, "multiple" refers to two or more. The use of "first" and "second" is for distinguishing technical features only and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features or their sequential relationship.

[0020] In the description of this invention, unless otherwise explicitly defined, terms such as "set up," "install," and "connect" should be interpreted broadly, and those skilled in the art can reasonably determine the specific meaning of the above terms in this invention in conjunction with the specific content of the technical solution.

[0021] Reference Figures 1 to 9 As shown, an embodiment of the present invention provides a method for compensating for in-machine measurement errors of aircraft surface gears based on pre-stroke drive, comprising the following steps: Step 1: Calculate the error caused by data transmission delay at different measurement speeds of the probe; Step 2: Establish a model for the pre-stroke error caused by the probe's mechanical structure; Step 3: Referring to the probe pre-stroke error model, complete the measurement of the standard ball and the calibration of the probe, and calculate the probe pre-stroke along each measurement direction. The amount of motion of the probe from the moment it contacts the point to be measured until the probe triggers the machine tool to receive the interrupt signal and record the position of each axis is called the pre-stroke. The probe triggering process is as follows: Figure 1As shown, at point P0, the probe contacts the surface to be measured. This position is the ideal position for recording the measurement value. However, since the triggering force is zero at this point and there is no triggering signal, the probe will continue to move along the predetermined direction. During this process, the triggering force gradually increases until the triggering force at point P1 increases to trigger the internal mechanism of the probe, thereby generating a triggering signal. After the triggering signal is generated, the signal needs a certain amount of time to be transmitted to the machine tool signal receiver, recording the position of each axis of the machine tool at this moment, corresponding to point P2 in the figure. At the same time, the machine tool will issue a stop signal, controlling the axis of the measurement motion to stop moving. The machine tool axis completely stops at point P3. In summary, the pre-stroke mainly consists of two parts: P0P1 and P1P2. The P0P1 segment is caused by the structure of the probe; the P1P2 segment is caused by the signal transmission delay. The P2P3 segment has no effect on the measurement result. Therefore, this invention calculates the signal transmission delay and mechanical pre-stroke error separately, and improves the on-machine measurement accuracy to near the offline measurement level through a standard ball calibration process, providing technical support for high-precision closed-loop machining.

[0022] Reference Figure 2 As shown, it can be understood that step one specifically includes the following steps: controlling the probe to measure the same point to be measured along the same measurement direction at different speeds, recording different measurement data corresponding to different measurement speeds, and then calculating the error caused by data transmission delay at different measurement speeds. During the process from when the probe generates a trigger signal to when the machine tool receiver receives the trigger signal and records the position of each axis of the machine tool, the probe still moves in a uniform linear motion according to the set speed and direction, such as... Figure 2 As shown, by controlling the probe to measure the same point twice along the same measurement direction at different speeds, and recording the different measurement data corresponding to the different measurement speeds, the formula can be applied: Calculate the data transmission delay, and then use the formula The errors caused by data transmission delays at different measurement speeds are calculated. X 1 represents the position recorded during the first measurement. X 2 represents the location recorded during the second measurement. v 1 represents the speed during the first measurement. v 2 represents the speed during the second measurement. t e_r This represents the data transmission delay time. E e_r This error is caused by data transmission delay.

[0023] Understandably, step two specifically includes the following steps: Based on the symmetrical structure of the mechanical probe, analyze the motion mode of the support rod under different triggering force directions, and calculate the distribution law of pre-stroke variation with triggering force direction. By classifying and calculating different triggering force directions, the pre-stroke calculation becomes more accurate.

[0024] Reference Figure 3 As shown, it can be understood that the mechanical probe includes a probe rod, three support rods, and three support balls. Figure 3 This diagram illustrates the structure and force of a mechanical probe. The probe rod is vertically positioned, with a probe ball connected to its lower end. Three support rods are symmetrically connected to the upper end of the probe rod, each connected to a balance spring. The balance springs push the support rods into contact with the support balls. In the untriggered state, current flows through the probe, and the support rods and balls form a closed circuit. Under the triggering force, the probe rod shifts, causing the support rod to disengage from one of the support balls, interrupting the current inside the probe and generating a trigger signal. The Z-direction represents the supporting force exerted by all the support balls on the probe rod. F NZ It is equal to the preload of the balance spring. F s and the weight of the measuring rod itself G The sum of them satisfies the formula Using Hertz's point contact theory, the deformation of each supporting sphere can be calculated. , In the formula, k cb This represents the Hertzian contact stiffness coefficient. That is, under the action of a triggering force, the probe will trigger when the offset distance of a certain support rod exceeds δ. Due to the symmetry of the mechanical probe structure, such as... Figure 4 As shown, only calculation is needed. The triggering force and pre-stroke of the probe within the range can be calculated based on symmetry. The trigger force and pre-stroke of the probe. α The angle between the component of the triggering force in the xoy plane and the nearest support rod satisfies the formula in the xoy plane. , F Txy It is the component of the triggering force in the xoy plane. F fxy It is the frictional force between the probe and the surface being measured. F Rxy It is the component of the supporting force exerted on the support rod by the supporting ball in the xoy plane.

[0025] Reference Figure 4 and Figure 5As shown, it can be understood that analyzing the motion mode of the support rod under different triggering force directions specifically includes the following steps: Different triggering force directions are divided into three types. The first type involves the triggering force causing the support rod to rotate around a specific axis. The triggering force and pre-stroke are derived using the Hertzian contact deformation and the balance spring torque equation. The second type involves the triggering force causing the support rod to rotate around an axis perpendicular to the triggering force. The deformation of the balance spring is calculated by combining the support point displacement, and the triggering force is calculated from the spring deformation. The third type involves the triggering force causing the support rod to translate upwards. The triggering force is equal to the preload of the balance spring and gravity. The first type... α ∈(0°, 11°) and γ ∈(0°, 11°), γ For the support rod to wrap around Figure 4 In Axis Rotation along one axis, such as Figure 5 As shown, the offset distance of the right end of the support rod is δ, The deformation of the center balance spring of the measuring rod δ sp for ,in , d It is the side length of the equilateral triangle formed by the supporting rods. Then the force on the balance spring becomes... , F s It is the initial preload on the balance spring. k s It is the spring constant of the balancing spring, obtained from the torque balance at point P. , This represents the component of the trigger force in the zoy plane; the magnitude of the actual trigger force can be expressed as... , in .

[0026] The second type α ∈(11°, 60°) and γ ∈(0°, 11°), the support rod is around and F Txy Vertical Axis 2-axis rotation , In this case, when the probe is triggered A The displacement of the point is 0. C The displacement of the point is δ , B The displacement of the point is , D The displacement of the point is δ / 2 Therefore, the deformation of the balance spring in the middle of the support rod can be calculated as follows: .

[0027] At this moment, the force on the balance spring is .

[0028] The triggering force can be calculated based on the torque balance equation. .

[0029] The third type γ ∈(11°, 90°), the support rod moves upwards. At this time, the support rod moves a distance vertically. δ The vertical component of the triggering force is equal to the balancing spring force and the weight of the measuring rod, i.e. .

[0030] Reference Figure 6 As shown, it can be understood that calculating the distribution law of the pre-stroke variation with the direction of the triggering force specifically includes the following steps: Based on the obtained triggering force, calculate the bending effect of the triggering force on the probe, thereby obtaining the probe pre-stroke. The existence of the triggering force will cause the overall displacement of the probe, the bending of the probe, and the Hertzian deformation of the probe and the surface to be measured. Since the overall displacement of the probe and the Hertzian deformation of the probe and the surface to be measured are very small, the bending effect of the triggering force on the probe is mainly considered. According to the material mechanics formula, the bending effect of the triggering force on the probe can be expressed as: .

[0031] in, E It is the Young's modulus of the measuring rod material; J It is the moment of inertia. According to the formulas in mechanics of materials, the moment of inertia of a solid cylindrical rod can be expressed as: .

[0032] The probe pre-stroke calculation results are as follows Figure 6 As shown. In a two-dimensional plane (corresponding to γ (equal to a certain value), the probe's pre-travel roughly forms a triangle. When the direction of the triggering force is along the direction of a certain support rod (from the center of the probe rod to the edge of the support rod), the probe's pre-travel is small; when the direction of the triggering force is away from the direction of a certain support rod, the probe's pre-travel is large.

[0033] Understandably, step three specifically includes the following steps: calculating the center position of the standard sphere; based on the center position, planning multiple test points on the standard sphere; calculating the pre-travel of the probe along the normal direction of each test point on the standard sphere; determining the magnitude of the pre-travel of the probe along each measurement direction; and using bilinear interpolation to map the pre-travel data of discrete calibration points to arbitrary tooth surface measurement directions. Dynamic adaptive compensation under operating conditions is achieved through high-precision standard sphere measurement and interpolation. The bilinear interpolation method extends the discrete calibration data to arbitrary measurement points on the tooth surface.

[0034] Understandably, calculating the position of the standard ball's center relative to the machine tool's A-axis center involves the following steps: First, it is necessary to preliminarily determine the position of the standard ball's center relative to the center point of the machine tool's A-axis end face after installation, i.e. Figure 7 In d wx , d wy and d wz . d wx The center of the standard ball is at X Coordinates on the axis d wy The center of the standard ball is at Y Coordinates on the axis d wz The center of the standard ball is at Z Coordinates on the axis.

[0035] The transformation matrix from the machine tool coordinate system to the probe coordinate system is: .

[0036] Establish the transformation matrix from the machine tool coordinate system to the standard spherical coordinate system. .

[0037] Manually trigger the probe to contact multiple standard balls and record the position of each axis of the machine tool at that moment. , ( i =1,2,…, n , n >3). Through coordinate transformation, the coordinates in the standard spherical coordinate system S are calculated. B (x B ,y B ,z B The corresponding coordinates of ) .

[0038] P i A point is a point on a standard spherically equidistant surface that satisfies the equation of the sphere and contains unknown position parameters. d wx , d wy and d wz Therefore, the position of the center of the standard sphere relative to the center point of the machine tool's A-axis can be preliminarily calculated using optimization algorithms such as least squares. Establish an optimization model In the formula R b This represents the radius of a standard sphere.

[0039] Plan multiple points to be measured on a standard sphere, perform measurements, and substitute the measurement results into the formula. This yields the coordinates of the measured point containing unknown position parameters in the standard spherical coordinate system, for the formula... , Add further constraints .

[0040] Accurately calculate the position of the standard ball's center relative to the machine tool's A-axis center point after installation: d2 wx , d2 wy, d2 wz ).

[0041] It is understandable that planning multiple test points on a standard sphere involves the following steps: the angular interval between adjacent test points in the same cross section along the Z-axis is 60°.

[0042] Understandably, planning multiple test points on a standard sphere involves the following steps: to avoid interference during measurement due to inaccurate initial calculations of the standard sphere's center position, the planned test points are offset inwards by a certain distance along their normal vector direction. According to... Figure 6 The probe's pre-stroke distribution pattern is shown. To ensure the center of the standard sphere fitted based on the measurement results is not eccentric, adjacent test points within the same cross section along the Z-axis are spaced 60° apart. However, considering the small distribution range of the normal vector of the test points on the gear tooth surface, to facilitate subsequent interpolation calculations, this invention adds two more columns of test points outside this range, such as... Figure 8 As shown. Assume the coordinates of the planned measurement point are P in the standard spherical coordinate system. bi The normal vector corresponding to the point to be measured is n. bi Based on the three-axis linkage in-machine measurement method, when measuring a standard ball, the positions of each axis of the machine tool can be determined using the formula... To avoid interference during measurement due to inaccurate calculation of the sphere's center position in the first step, the planned measurement point still needs to be offset inward by a certain distance along its normal vector direction, which will not be elaborated here.

[0043] Based on the accurate location of the center point of the standard sphere, the measurement program is updated, and multiple test points are repeatedly planned on the standard sphere. The standard sphere is then measured, and the results are calculated according to the formula. Calculate the pre-travel of the probe along the normal direction of each point to be measured on the standard sphere. For example... Figure 9 As shown, assume the point to be measured on the tooth surface of the face gear. P m The parameters of the normal vector in spherical coordinates are ( θ m , φ m First, according to θ m Value judgment pointP m The area in which it is located, θ m Taking π as an example, it is located in P 2. P 3. P 4 and P Within the defined range of 5, first calculate the result using interpolation. P m point θ Points with the same parameters P 7 and P 8 pre-trip .

[0044] and parameters φ value .

[0045] Then calculate P m Point corresponding to the pre-trip .

[0046] The components in each direction can be represented as .

[0047] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for compensating for in-machine measurement errors of aircraft surface gears based on pre-stroke drive, characterized in that, Includes the following steps: Step 1: Calculate the error caused by data transmission delay at different measurement speeds of the probe; Step two: Establish a model for the pre-stroke error caused by the mechanical structure of the probe. Specifically, based on the symmetrical structure of the mechanical probe, analyze the motion mode of the support rod under different triggering force directions, and calculate the distribution law of the pre-stroke variation with the triggering force direction. The mechanical probe includes a probe rod, three support rods, and three support balls. The probe rod is vertically set, with a probe ball connected to the lower end of the probe rod, and three support rods symmetrically connected to the upper end of the probe rod. The support rods are connected to balance springs, which push the support rods to contact the support balls. When in the untriggered state, current flows inside the probe, and the support rods and support balls form a closed loop. Under the action of the triggering force, the probe rod deflects, and the pre-stroke error is calculated. The probe's support rod disengages from a support ball, interrupting the internal current and generating a trigger signal. The analysis of the support rod's motion mode under different trigger force directions specifically includes the following steps: different trigger force directions are divided into three types. The first type is where the trigger force causes the support rod to rotate around a specific axis. The trigger force and pre-stroke are derived using the Hertz contact deformation and the balance spring torque equation. The second type is where the trigger force causes the support rod to rotate around an axis perpendicular to the trigger force. The balance spring deformation is calculated by combining the support point displacement, and the trigger force is calculated from the spring deformation. The third type is where the trigger force causes the support rod to translate upwards. The trigger force is equal to the balance spring preload and gravity. Step 3: Referencing the probe pre-stroke error model, complete the measurement of the standard ball and the calibration of the probe, calculate the pre-stroke size of the probe along each measurement direction, and calculate the pre-stroke size corresponding to the test point on the gear tooth surface by interpolation.

2. The method for compensating for in-flight measurement errors of aircraft surface gears based on pre-stroke drive according to claim 1, characterized in that, Step one specifically includes the following steps: controlling the probe to measure the same point to be measured along the same measurement direction at different speeds, recording different measurement data corresponding to different measurement speeds, and then calculating the error caused by data transmission delay at different measurement speeds.

3. The method for compensating for in-flight measurement errors of aircraft surface gears based on pre-stroke drive according to claim 1, characterized in that, The calculation of the distribution law of the pre-stroke as a function of the triggering force includes the following steps: based on the obtained triggering force, calculate the bending effect of the triggering force on the probe, thereby obtaining the probe pre-stroke.

4. The method for compensating for in-machine measurement errors of aircraft surface gears based on pre-stroke drive according to claim 1, characterized in that: Step three specifically includes the following steps: calculating the center position of the standard sphere, planning multiple test points on the standard sphere based on the center position of the standard sphere, calculating the pre-travel of the probe along the normal of each test point on the standard sphere, determining the size of the pre-travel of the probe along each measurement direction, and using bilinear interpolation to map the pre-travel data of the discrete calibration points to any tooth surface measurement direction.

5. The method for compensating for in-machine measurement errors of aircraft surface gears based on pre-stroke drive according to claim 4, characterized in that, The specific steps for calculating the position of the standard ball's center relative to the machine tool's A-axis center are as follows: manually triggering the probe to contact multiple points on the standard ball, initially calculating the position of the standard ball's center through least squares optimization, establishing an optimization model, planning multiple test points on the standard ball, and accurately calculating the position of the standard ball's center.

6. The method for compensating for in-machine measurement errors of aircraft surface gears based on pre-stroke drive according to claim 5, characterized in that, The specific steps for planning multiple test points on a standard sphere include the following: the angular interval between adjacent test points in the same cross section along the Z-axis is 60°.

7. The method for compensating for in-flight measurement errors of aircraft surface gears based on pre-stroke drive according to claim 6, characterized in that, The specific steps for planning multiple test points on a standard sphere are as follows: In order to avoid interference during the measurement process due to inaccurate preliminary calculation of the center position of the standard sphere, the planned test points are offset inward by a certain distance along the direction of their normal vector.

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