This application claims priority to Taiwan Application Serial Number 104140229, filed Dec. 1, 2015, which is herein incorporated by reference.
Technical Field
The present disclosure relates to double ball-bars in measurement apparatuses and in particular to the compensation of geometric and thermal errors of double ball-bars in hexapod measurement apparatuses or machines.
Description of Related Art
A double ball-bar has precision ball and socket joints at its two ends. It is used to measure the absolute bar length or the change of bar length between the two precision balls. Its applications can be found in both machine tools and hexapod coordinate measurement machines. The displacement sensor for a double ball-bar includes linear variable differential transformer (LVDT), laser interferometer, linear magnetic encoder and linear optical encoder, and the measurement principle can be either incremental or absolute.
In the present disclosure, the distance between the centers of the two connected ball and socket joints is defined as the center distance. Like any other precision machines, the double ball-bar also has geometric and thermal errors. One example of the geometric errors is the misalignment between the sensor measuring direction and the center line connecting the two ball centers. Another geometric error is the deflection of the double ball-bar due to the gravitational force. When a double ball-bar has stiffness problem and becomes curved due to its own weight, the difference between bar length and center distance is not ignorable. For a highly accurate double ball-bar, the displacement sensor is meant to measure the center distance, not the bar length. Further, the accuracy of a double ball-bar is sensitive to ambient temperature. The measurement apparatus or machine may be used in a workshop without temperature control. A change in ambient temperature will cause the double ball-bar to expand or contract between the two ball and socket joints, which results in thermal errors in the measured center distance.
Investigations have shown that the readhead of an optical linear encoder or a magnetic linear encoder is also a heat source and may cause thermal error in the double ball-bar. Although the power of the electrical circuit in the readhead is low, the generated heat may raise the temperature of the readhead and the neighboring elements notably as their mass is small.
Because of the geometric and thermal errors, the relationship between the center distance and the measured displacement amount is non-linear and time-variant. For highly accurate applications like hexapod measurement apparatuses or machines, it is important to identify these errors and to compensate them.
The disclosed double ball-bar measuring system overcomes the above mentioned problems compared to prior art and provides highly accurate double ball-bars for measurement apparatuses, in particular hexapod measurement apparatuses or machines. According to one embodiment of the present disclosure, the double ball-bar system includes a calibration unit, at least two double ball-bars and a measuring module. Among the double ball-bars, at least one double ball-bar is a measuring double ball-bar and at least one double ball-bar is a reference double ball-bar. The calibration unit includes at least three supporting members and provides at least two reference center distances. The measuring double ball-bar is installed on a measurement apparatus to measure or to calibrate a target machine. The reference double ball-bar is disposed on two of the at least three supporting members of the calibration unit.
When the target machine is driven for measurement or calibration, the measuring double ball-bar measures a displacement amount and the reference double ball-bar measures a thermal error amount. The measuring module processes the displacement amount and the thermal error amount, compensates the geometric and thermal errors of the measuring double ball-bar and performs measurement data processing.
According to another embodiment of the present disclosure, an errors compensation method of the double ball-bar measuring system includes the following steps. A calibration unit is provided which comprises at least three supporting members and provides at least two reference center distances. At least two double ball-bar are provided, wherein at least one double ball-bar is a measuring double ball-bar and at least one double ball-bar is a reference double ball-bar. The measuring double ball-bar is disposed on the calibration unit to measure at least two calibration points. A center distance function of the measuring double ball-bar is established in accordance with the calibration points. The measuring double ball-bar is installed on a measurement apparatus to measure or to calibrate a target machine. The reference double ball-bar is disposed on the calibration unit. The target machine is driven for a measurement or a calibration. The measuring double ball-bar measures a displacement amount and the reference double ball-bar measures a thermal error amount. A center distance of the measuring double ball-bar is determined in accordance with the center distance function and the displacement amount. The center distance is compensated in accordance with the thermal error amount. The compensated center distance is used for further measurement data processing.
Embodiments of the disclosure will now be described in more detail, with reference to the accompanying drawings in which:
Among the parallel connecting bars of one assembly, at least two are guiding bars fitting with linear bearings on the other assembly. In the embodiment of
The readhead assembly 292 includes a ball base 205, a guiding base 206, a readhead 208 and three connecting bars 231, 232 and 233. The ball base 205 carries a measuring ball 202. The connecting bars 231 and 232 are guiding bars and the connecting bar 233 is a tension bar. The guiding base 204 has two linear bearings 210 and 211 and a hole 224, wherein the two guiding bars 231 and 232 pass through the linear bearings 210 and 211, respectively, and the tension bar 233 passes through the hole 224. The tension bar 233 and the guiding base 204 are separated by a gap between the hole 224 and the tension bar 233. The guiding base 206 includes two linear bearings 212 and 213 and a hole 234 for being passed through by the two guiding bars 221 and 222 and the tension bar 223, respectively. The tension bar 223 and the guiding base 206 are separated by a gap between the tension bar 223 and the hole 234.
As a whole, four parallel guiding bars 221, 222, 231, 232 are arranged between the two guiding bases 204 and 206. The center line of the double ball-bar, which is the line between the centers of the two measuring balls 201 and 202, is on the upper surface of the optical scale 207 to avoid Abbe error. Besides, the structure of the scale assembly 291 and the readhead assembly 292 keeps weight low and has high area moment of inertia and high bending stiffness to avoid geometric error resulting from the ball-bar deflection. Other advantages of the arrangement regarding the thermal behavior of the double ball-bar 200 will be described in more detail below with reference to
The center distance Dc of the double ball-bar 200 is the distance between the centers of the two measuring balls 201 and 202. To reduce the thermal error, the elements effecting the center distance, such as the guiding bars 221, 222, 231, 232, the tension bars 223, 233 and the scale, are made of materials of low or near-zero coefficient of thermal expansions, for example INVAR®, Super INVAR®, ZERODUR® or quartz glass. In contrast, the ball bases 203, 205 and the guiding bases 204, 206 may be made of aluminum alloy to reduce weight. The measuring balls 201, 202 are made of magnetic stainless steel so that they can be attracted to ball sockets. At room temperature, the coefficient of thermal expansion of INVAR® is around 1.5-2.0 ppm/° C., Super INVAR® around 0.63 ppm/° C., quartz glass 0.5 ppm/° C. and ZERODUR® 0-0.1 ppm/° C.
The relative position and orientation between the first structure 710 and the second structure 810 are to measure by the hexapod measurement apparatus 900. The measuring double ball-bars 500 of the hexapod measurement apparatus 900 are tilt at an angle, and their mean tilt angle can be found by analyzing the kinematics of the hexapod. It is advantageous that the calibration unit 300 is on a tilted plane with a tilt angle equal to the mean tilt angle of the measuring double ball-bars 500. Further, it is preferable that the center distance function of each measuring double ball-bar is established at this mean tilt angle.
In one embodiment of the present disclosure, the initialization of double ball-bars is performed near the machine tool under room temperature. The initialization begins by disposing a double ball-bar on two supporting members 301 of the calibration unit 300, whereby a reference displacement amount is measured. The center distance Dc of the double ball-bar is set equal to the reference center distance Dr defined by the two supporting members 301. The reference center distance Dr and the corresponding reference displacement amount n define a calibration point P=(Dr, n). Based on at least two calibration points, a center distance function can be established for the double ball-bar, which describes the relationship between the measured displacement amount and the center distance. The center distance function can be a data table, which provides data for the compensation of error in center distance. The center distance function can also be a parametric function, or any function which outputs a center distance from an input of displacement amount. Besides, the tilt angle A of the double ball-bar can also be an input parameter of the center distance function.
In one embodiment of the present disclosure, the center distance function is a polynomial function of degree two (order three). The center distance function can be represented as follows.
D(n)=a(nk)2+b(nk)+c (1)
Wherein k is the resolution of the displacement sensor 207, and n is the displacement amount. If three reference center distances are available, the three unknown coefficients a, b and c can be solved explicitly. In case that the reference center distance Dr is the minimal center distance, the corresponding reference displacement amount can be set to zero (n=0). The coefficient c is then equal to the minimal distance Dmin. The polynomial function D(n) can also be obtained by other algorithms such as curve fitting algorithm. In this case the number of the calibration points is larger than the order (degree+1) of the polynomial function D(n).
The double ball-bar 200 in
In
δDmin=δImin=δIL+δIS+δIR (2)
In
δDmax=δImax=δDmin+δIM (3)
In
The thermal error of a double ball-bar can be obtained by building a thermal error model, which describes the relationship between the thermal error and the actual ambient temperature. In the present disclosure, at least one reference double ball-bar is used to measure the thermal error. The basic theory of the reference double ball-bar is described as follows. Assume that the equivalent coefficient of thermal expansion of the double ball-bar having the minimal center distance Dmin, is α. Assume that the coefficient of thermal expansion of the optical linear scale 207 is β. Considering the thermal error model of the double ball-bar as a first order dynamic system, and assume the ambient temperature raises in stepwise ΔT° C. Assume the time constant of the thermal error model is TR for the double ball-bar having the minimal center distance Dmin, and TS for the optical linear scale 207. The thermal errors of the double ball-bars in
When the time approaches infinity, the exponential parts of the equations are as follows:
The stationary thermal errors of the double ball-bars having minimal, maximal and intermediate center distances are as follows:
δDmin=αIminΔT (9)
δDmax=αIminΔT+βIMΔT (10)
δDp=αIminΔT+βIpΔT (11)
Equations (4)-(6) and (9)-(11) show that the thermal error δDp of a double ball-bar having any center distance Dp is the sum of the common thermal error δDmin=αIminΔT and the thermal error of the linear scale. In one embodiment of the present disclosure, the common thermal error δDmin is measured by a reference double ball-bar having a minimal center distance Dmin. The measured common thermal error is called thermal error amount and is used to compensate thermal errors of the measuring double ball-bars. Besides, from equation (9) the stationary temperature ΔT can be calculated from the measured common thermal error δDmin as follow:
ΔT=δDmin/(αImin)=δDmin/(αDmin) (12)
To ensure that the common thermal error δDmin is optimal for the thermal error compensation, experiments can be conducted to find out thermal errors of double ball-bars in accordance with an ambient temperature change. The double ball-bar having the thermal error closest to the mean thermal error of all double ball-bars is used as reference double ball-bar. The difference between the thermal error of the reference double ball-bar and the thermal error of each of the measuring double ball-bars can be reduced to within a given tolerance, for example 1 micrometer.
In case that the optical linear scale 207 is made of ZERODUR®, the coefficient of thermal expansion β is almost zero, β≈0, so that the thermal error of the optical linear scale is ignorable, βIpΔT=0. Therefore, the thermal error δDp of a double ball-bar having any center distance Dp is equal to common thermal error δDmin, δDp=δDmin. The measured thermal error amount δDmin of a reference double ball-bar is the thermal error of all measuring double ball-bars.
In another case, the optical linear scale 207 is not made of ZERODUR, β≠0. The overall thermal error consists of two components, one is the common thermal error δDmin and the other is the thermal error of the optical linear scale βIpΔT. The thermal error resulting from the change of resolution is ignorable. The minimal center distance Imin=Dmin, the scale length Ip and the coefficients α and β determine an error ratio ε=βIp/αDmin. In one embodiment of the present disclosure, to fully compensate the thermal error of a measuring double ball-bar having a center distance Dp, the error ratio ε is calculated firstly, then the thermal error of the optical linear scale is calculated as ε·δDmin. In this case, one reference double ball-bar of minimal center distance Dmin is also enough to compensate thermal error of a measuring double ball-bar of any center distance. Similarly, if the reference double ball-bar has a center distance other than the minimal center distance Dmin, the thermal error of the optical linear scale of a measuring double ball-bar can also be calculated and compensated. The above described method is valid for double ball-bars having a linear scale, for example optical or magnetic linear scale.
In another embodiment of the present disclosure in
δDp=δDmin+(δDmax−δDmin)*((Dp−Dmin)/(Dmax−Dmin)). (13)
This equation shows the thermal error δDp of a measuring double ball-bar of any center distance Dp can be obtained from the measured thermal error amounts δDmin and δDmax.
In
The double ball-bar can be initialized either in a metrology laboratory at a specified temperature or in workshop near the target machine at room temperature. The temperature by the initialization of a double ball-bar is the base temperature for a zero thermal error. The initialized center distance function is valid only for the base temperature. In one embodiment of the present disclosure, the initialization of double ball-bars is performed in a metrology laboratory and the base temperature for a zero thermal error is 20° C. By disposing a double ball-bar 400 or 500 under the room temperature on the calibration unit, the double ball-bar measures an initial thermal error amount. This initial thermal error amount is caused by the temperature change from the base temperature to the room temperature and can be used to calculate the temperature gap, see equation (12).
The disclosed method for the thermal error compensation can apply to double ball-bar having either absolute or incremental encoder. If the double ball-bar is an incremental one, it is preferable that the encoder provides a zero reference signal. The zero reference signal can be used to preset the reference displacement amount. For example, the reference displacement amount nmin can be set equal to quotient of the following division: nmin=Dmin/k, whereby k is the resolution of the displacement sensor.
Further, according to another embodiment in
Further, according to yet another embodiment in
According to the foregoing embodiments, the advantages of the present disclosure are summarized as follows: 1. The parallel connecting bars and the linear bearings of the double ball-bar provide accurate linear guide and optimal stiffness. The thermal errors of the double ball-bar is reduced by using material of low or near-zero coefficient of thermal expansion. 2. The center distance function describes the relationship between the displacement amount and the center distance, thereby compensates all geometric errors. 3. Although the thermal behaviors of measuring double ball-bars are complicated, their thermal errors can be obtained and accurately compensated by using one or two reference double ball-bars.
The present disclosure can efficiently compensate geometric and thermal errors of double ball-bars in a measurement apparatus or machine. The center distance function and the reference double ball-bar can apply to double ball-bars having other structure or using other displacement sensor. It will be apparent to those skilled in the art that various modifications and variations can be made to the present disclosure without departing from the scope or principle of the present disclosure. For example, a magnetic linear scale or LVDT can be used instead of the optical linear scale. The double ball-bar can have the structure of a telescopic cylinder. In view of the foregoing, it is intended that the present disclosure cover modifications and variations of this disclosure provided they fall within the scope of the following claims.
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