Abstract:
The present invention relates to measurement of cross-inertia-moment in a limited angular rotatory axis, and more specifically, to a measuring device and method of cross-inertia-moment in a limited angular rotatory axis. The measuring device includes a base plate; a pair of first supporters, each end portion being secured on the base plate through a load cell, for supporting a first rotatory axis; a second supporter installed inbetween the pair of first supporters to be able to rotate round the first rotatory axis, for supporting a second rotatory axis that is orthogonal to the first rotatory axis; and a roller installed at the inside of the second supporter, being rotatable round the second rotatory axis. Therefore, the present invention enables to measure and amend the cross-inertia-moment of multiple axis LOS (line of sight) stabilizer as well as low speed rotatory machinery. The present invention is also effective for minimizing the interference of the cross-inertia-moment due to the inertia in a precision stabilizer like the multiple axis LOS stabilizer, consequently improving the precision of the multiple axis LOS stabilizer

Description:
CLAIM OF PRIORITY 
     This application makes reference to and claims all benefits accruing under 35 U.S.C. Section 119 from an application entitled, “Measuring device and method of cross-inertia-moment in limited angular rotary axis”, filed in the Korean Industrial Property Office on May 20, 2002 and there duly assigned Serial No. 2002-27855. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates generally to measurement of cross-inertia-device, and in particular, to a method and device for measuring cross-inertia-moment in a multiple axis LOS (line of sight) stabilizer applications. 
     2. Description of the Related Art 
     In general, cross-inertia-moment of a rotary body, such as an automobile&#39;s wheel balancer or textile machine&#39;s wheel balancer, is measured and calibrated to maintain high speed rotation. Such measurement of cross-inertia-moment in a high speed rotary machine is measured by using changes in the reaction force generated in a bearing that supports the angular rotary axis as the object to be measured is continuously rotated. Hence, by measuring the changes in the reaction force generated in the bearing and expecting the cross-inertia-moment of a high-speed machine or static unbalance amount of the rotatory body, or the object to be measured based on the change, the rotatory axis is finally calibrated. 
     Unfortunately however, the cross-inertia-moment measurement described above is not applicable to the angular rotatory axis, particularly to multiple axis LOS stabilizer using multiple axis gimbals. That is, although the conventional measurement is applicable to a high-speed, unlimited rotatory machinery, it cannot measure the cross-inertia-moment in a limited rotatory machinery and does not work for low-speed rotary machinery, either. 
     SUMMARY OF THE INVENTION 
     The present invention is directed to a method and device for measuring cross-inertia-moment in a limited angular rotary axis, particularly, multiple axis gimbals. 
     Accordingly, there is provided the measuring device of cross-inertia-moment in a limited angular rotary axis, including: a base plate; a pair of first supporters, each end portion being secured on the base plate through a load cell, for supporting a first rotatory axis; a second supporter installed inbetween the first supporters to be able to rotate round the first rotatory axis, for supporting a second rotatory axis that is orthogonal to the first rotatory axis; and a roller installed inside of the second supporter, being rotatable round the second rotatory axis. 
     Another aspect of the present invention provides a measuring method of the cross-inertia-moment in a limited angular rotatory axis, the method including: (a) a first measuring procedure, including the substeps of: securing a first rotatory axis in a roller, wherein the roller includes the first rotatory axis that is supported by four load cells, a second rotatory axis that is orthogonal to the first rotatory axis and is rotatable round the first rotatory axis, and a third rotatory axis that is orthogonal to the first rotatory axis and the second rotatory axis, respectively, and is rotatable; applying sine wave vibration to the second rotatory axis; detecting signals outputted from each load cell by the applied vibration to the second rotatory axis; and calculating, based on the outputted signals from each load cell, moment and cross-inertia-moment for the first rotatory axis; (b) a second measuring procedure, including the substeps of: disposing, at the roller, the third rotatory axis to face the same direction with the first rotatory axis, and securing the first rotatory axis; applying sine wave vibration to the second rotatory axis; detecting signals outputted from each load cell by the applied vibration to the second rotatory axis; and calculating, based on the outputted signals from each load cell, moment and cross-inertia-moment for the third rotatory axis; (c) a third measuring procedure, including the substeps of: securing the second rotatory axis at the roller; applying sine wave vibration to the first rotatory axis; detecting signals outputted from each load cell by the applied vibration to the first rotatory axis; and calculating, based on the outputted signals from each load cell, moment and cross-inertia-moment for the second rotatory axis; (d) a fourth procedure, including the substeps of: disposing, at the roller, the third rotatory axis to face the same direction with the initial direction of the second rotatory axis, and securing the second rotatory axis; applying sine wave vibration to the first rotatory axis; detecting signals outputted from each load cell by the applied vibration to the first rotatory axis; and, calculating, based on the outputted signals from each load cell, moment and cross-inertia-moment for the third rotatory axis. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The above features and advantages of the present invention will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings in which: 
     FIG. 1 is a diagram illustrating a measuring device of cross-inertia-moment in a limited angular rotatory axis in accordance with a preferred embodiment of the present invention; and 
     FIGS. 2 a  through  2   d  are flow charts illustrating a measuring method of cross-inertia-moment in a limited angular rotatory axis in accordance with the preferred embodiment of the present invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     In the following description, for purposes of explanation rather than limitation, specific details are set forth such as the particular architecture, interfaces, techniques, etc., in order to provide a thorough understanding of the present invention. However, it will be apparent to those skilled in the art that the present invention may be practiced in other embodiments, which depart from these specific details. For purposes of simplicity and clarity, detailed descriptions of well-known devices, circuits, and methods are omitted so as not to obscure the description of the present invention with unnecessary detail. 
     FIG. 1 is a diagram illustrating a measuring device  100  of cross-inertia-moment in a limited angular rotatory axis in accordance with a preferred embodiment of the present invention. As shown in FIG. 1, the measuring device  100  of cross-inertia-moment in a limited angular rotatory axis in accordance with a preferred embodiment of the present invention includes a base plate  101 , load cells  103   a  through  103   d , a pair of first supporters  105   a  and  105   b , a second supporter  107 , and a roller  109 , and calculates the cross-inertia-moment through a designated data processor  160 . 
     The pair of first supporters  105   a  and  105   b  are disposed to face each other, each being supported by four load cells  103   a  through  103   d  that are secured at the base plate  101 , and support the first rotatory axis  120   a.    
     The load cells  103   a - 103   d  detect the reaction forces generated by the rotation of the second supporter  107  or the roller  109 . Furthermore, the load cells  103   a - 103   d  are able to detect the reaction forces generated by a vibration applied to the first supporters  105   a  and  105   b.    
     As shown in FIG. 1, the second supporter  107  is a hollow shaped frame disposed between the first supporters  105   a  and  105   b  and rotates round the first rotatory axis  120   a . And the second supporter  107  supports the second rotatory axis  120   b . Herein, the second support  107  rotates with respect to the first rotatory axis  120   a . In addition, the second rotatory axis  120   b  is orthogonal to the first rotatory axis  120   a . The roller  109  is disposed inside the second supporter and rotates round the second rotatory axis  120   b . The third rotatory axis  120   c  is disposed on the top surface of the roller  109  to be orthogonal to the first and the second rotatory axis  120   a  and  120   b , respectively. 
     As such, the third rotatory axis  120   c  is rotatable round the second rotatory axis  120   b , as well as the first rotatory axis  120   a  as the second supporter  107  rotates round the first rotatory axis  120   a . That is, the roller  109  is disposed in such manner that it can rotate biaxially 
     The third rotatory axis  120   c  is vertically extended from the surface of the roller  109 . The roller  109  is rotatable with respect to the second rotatory axis  120   b . Therefore, the third rotatory axis  120   c  is rotatable with respect to the second rotatory axis  120   b.    
     The second rotatory axis  120   b  supported by the second supporter  107  rotates with the second supporter  107  as the second supporter  107  rotates with respect to the first rotatory axis  120   a . If the roller  109  is fixed to the second supporter  107  temporarily and the second supporter  107  rotates with respect to the first rotatory axis  120   a , the third rotatory axis  120   c  is also rotatable with the second supporter  107  with respect to the first rotatory axis  120   a.    
     Finally speaking, the third rotatory axis  120   c  is rotatable with respect to the first rotatory axis  120   a  as well as the second rotatory axis  120   b.    
     During operation, when load is added onto the measuring device  100  of cross-inertia-moment in a limited angular rotatory axis, the load is transferred to the load cells  103   a  through  103   d , and the load cells  103   a  through  103   d  outputs electric signals of electric resistance change that correspond to the load, and using the data processor  160 , the measuring device  100  calculates the load added and the cross-inertia-moment. Herein, it is noted that a limited angular rotatory axis is a rotatory axis that the rotation angle is limited by mechanical stopper (not shown) to obtain the operational limited angle of the rotatory axis and safety, for example a rotatory axis of a steering wheel on an automobile. 
     Now, the measuring method using the cross-inertia-moment measuring device  10  described above is explained hereinafter with reference to FIGS. 2 a  through  2   d.    
     FIG. 2 a  illustrates the first measuring procedure (a) for measuring the cross-inertia-moment against the first rotatory axis  120   a , when vibration is applied to the second rotatory axis  120   b.    
     According to the first measuring procedure, the first rotatory axis  120   a  is secured  201  (S 201 ) so that the second and the third axis  120   b  and  120   c  do not move freely. At this time, the third rotatory axis  120   c  is at the initial stage, that is, orthogonal to the first and the second rotatory axis  120   a  and  120   b . Once the first rotatory axis  120   a  is secured, i.e., not moving, sine wave vibration is applied to the second rotatory axis  120   b  (S 203 ). By the vibration applied to the second rotatory axis  120   b , the load cells  103   a  through  103   d  are loaded, and the load cells  103   a  through  103   d  detect this load as electric signals (S 205 ). The electric signals detected from the load cells  103   a  through  103   d  are inputted to the data processor  160 , where the cross-inertia-moment is calculated (S 207 ). 
     Here, the frequency of the sine wave vibration that was applied to the second rotatory axis  120   b  is designated as 7 Hz, the angular acceleration is designated as 1 rad/sec 2 . The angular velocity of the sine wave vibration in such condition is 0.0227 rad/sec. 
     Under the conditions, the moment value is obtained using the following formula: 
     [Mathematical Formula 1] 
     
       
           M   1   =−I   21   ×a   2   +I   32 ×ω 2   2    
       
     
     Here, M 1  is the moment against the first rotatory axis  120   a ; I 21  is the cross-inertia-moment against the first rotatory axis  120   a , ω 2  is the angular velocity of the sine wave vibration applied to the second rotatory axis  120   b ; I 32  is the cross-inertia-moment against the second rotatory axis  120   b ; and a 2  is the angular acceleration of the sine wave vibration applied to the second rotatory axis  120   b . Among the aforementioned conditions for the sine wave vibration, the angular velocity ω 2  can be disregarded because it is smaller than 1, and its square is also small enough to be neglected. 
     Therefore, the [Mathematical Formula 1] can be summarized as follows: 
     [Mathematical Formula 2] 
     
       
         
           I 
           21 
           ≈M 
           1 
           /a 
           2  
         
       
     
     On the other hand, the moment M 1  can be calculated by using the output values from the load cells  103   a  through  103   d  as follows: 
     [Mathematical Formula 3] 
     
       
           M   1 =[( lc   3   +lc   4 )−( lc   1   +lc   2 )]× l   23    
       
     
     Here, Ic 1  through Ic 4  indicate the output values from the load cells  103   a  through  103   d  by the load added onto each load cell  103   a  through  103   d . The I 23  indicates the distance between two load cells, particularly, the load cells  103   b  and  103   c  among those four load cells  103   a  through  103   b . The distance is actually the same with the distance between the load cell  103   a  and the load cell  103   d.    
     Based on the output values from the load cells  103   a  through  103   d , the moment M 1  is obtained using the above formula, and the M 1  is substituted in [Mathematical Formula 2], where the M 1  is divided by the angular acceleration a 2  applied to the second rotatory axis  120   b . In this manner, the cross-inertia-moment, I 21 , is obtained. 
     Next, FIG. 2 b  illustrates the second measuring procedure (b) for measuring the cross-inertia-moment against the third rotatory axis  120   c , which is generated by the vibration applied to the second rotatory axis  120   b.    
     According to the second measuring procedure (b), the third rotatory axis  120   c  is first adjusted to face the direction of the first rotatory axis  120   a . Then, the first rotatory axis  120   a  is secured (S 211 ) so that the second and the third rotatory axis  120   b  and  120   c  do not move freely round the first rotatory axis  120   a . When the first rotatory axis  120   a  is secured, sine wave vibration is applied to the second rotatory axis  120   b . By the vibration applied to the second rotatory axis  120   b , the load cells  103   a  through  103   d  are loaded, and the load cells  103   a  through  103   d  detect this load as electric signals (S 215 ). The electric signals detected from the load cells  103   a  through  103   d  are inputted to the data processor  160 , where the cross-inertia-moment is calculated (S 217 ). 
     Similar to before, the frequency of the sine wave vibration that was applied to the second rotatory axis  120   b  is designated as 7 Hz, the angular acceleration is designated as 1 rad/sec 2 . The angular velocity of the sine wave vibration in such condition is 0.0227 rad/sec. 
     Under the condition, the moment value is obtained using the following formula: 
     [Mathematical Formula 4] 
     
       
         
           M 
           3 
           =−I 
           21 
           ×ω 
           2 
           2 
           −I 
           32 
           ×a 
           2  
         
       
     
     The definition on each symbol is not provided here because the same definitions explained in the first measuring procedure (a) are applied to each symbol. Again, among the conditions, the angular velocity ω 2  is disregarded because it is smaller than 1, and its square is also small enough to be neglected. 
     Therefore, the above formula can be summarized as follows: 
     [Mathematical Formula 5] 
     
       
         
           I 
           32 
           ≈M 
           3 
           /a 
           2  
         
       
     
     In the meantime, the moment M 3  can be calculated by using the output values from the load cells  103   a  through  103   d  as follows: 
     [Mathematical Formula 6] 
     
       
           M   3 [( lc   3   +lc   4 )−( lc   1   +lc   2 )]× l   23    
       
     
     The definition on each symbol is not provided here because the same definitions explained in the first measuring procedure (a) are applied to each symbol. 
     Based on the output values from the load cells  103   a  through  103   d , the moment M 1  is obtained using the above formula, and the M 1  is substituted in [Mathematical Formula 5], where the M 3  is divided by the angular acceleration a 2  applied to the second rotatory axis  120   b . In this manner, the cross-inertia-moment, I 32 , is obtained. 
     FIG. 2 c  illustrates the third measuring procedure (c) for measuring the cross-inertia-moment against the second rotatory axis  120   b , which is generated by the vibration applied to the first rotatory axis  120   a.    
     According to the third measuring procedure (c), the second rotatory axis  120   b  is secured (S 221 ) so that the third rotatory axis  120   b  does not move freely round the second rotatory axis  120   b . Preferably, the third rotatory axis  120   c  is disposed to face the direction of the first rotatory axis  120   a . Once the second rotatory axis  120   b  is secured, sine wave vibration is applied to the first rotatory axis  120   a  (S 223 ). By the vibration applied to the first rotatory axis  120   a , the load cells  103   a  through  103   d  are loaded, and the load cells  103   a  through  103   d  detect this load as electric signals (S 225 ). The electric signals detected from the load cells  103   a  through  103   d  are inputted to the data processor  160 , where the cross-inertia-moment is calculated (S 227 ). 
     Again, the frequency of the sine wave vibration that was applied to the second rotatory axis  120   b  is designated as 7 Hz, the angular acceleration is designated as 1 rad/sec 2 . The angular velocity of the sine wave vibration in such condition is 0.0227 rad/sec. 
     Under the conditions, the moment value is obtained using the following formula: 
     [Mathematical Formula 7] 
     
       
           M   2   =−I   21   ×a   1   −I   13 ×ω 1   2    
       
     
     The definition on each symbol is not provided here because the same definitions explained in the first measuring procedure (a) are applied to each symbol. Again, among the conditions, the angular velocity ω 1  is disregarded because it is smaller than 1, and its square is also small enough to be neglected. 
     Therefore, the above formula can be summarized as follows: 
     [Mathematical Formula 8] 
     
       
         I 21   ≈−M   2   /a   1    
       
     
     Meanwhile, the moment M 2  can be calculated by using the output values from the load cells  103   a  through  103   d  as follows: 
     [Mathematical Formula 9] 
     
       
           M   2 =[( lc   2   +lc   3 )−( lc   1   +lc   4 )]× l   12    
       
     
     The definition on each symbol is not provided here because the same definitions explained in the first measuring procedure (a) are applied to each symbol. 
     Based on the output values from the load cells  103   a  through  103   d , the moment M 1  is obtained using the above formula, and the M 1  is substituted in [Mathematical Formula 8], where the M 1  is divided by the angular acceleration a 2  applied to the first rotatory axis  120   a . In this manner, the cross-inertia-moment, I 21 , is obtained. 
     Lastly, FIG. 2 d  illustrates the fourth measuring procedure (d) for measuring the cross-inertia-moment against the third rotatory axis  120   c , which is generated by the vibration applied to the first rotatory axis  120   a.    
     According to the fourth measuring procedure (d), the third rotatory axis  120   c  is first adjusted to face the same direction of the second rotatory axis  120   b . In this way, the second rotatory axis  120   b  is orthogonal to the plane including the first supporters  105   a  and  105   b . When the third rotatory axis  120   c  is adjusted, the second rotatory axis  120   b  is secured (S 231 ) so that the third rotatory axis  120   b  does not move freely round the second rotatory axis  120   b . Preferably, the third rotatory axis  120   c  is disposed to face the direction of the first rotatory axis  120   a . Once the second rotatory axis  120   b  is secured, sine wave vibration is applied to the first rotatory axis  120   a  (S 233 ). By the vibration applied to the first rotatory axis  120   a , the load cells  103   a  through  103   d  are loaded, and the load cells  103   a  through  103   d  detect this load as electric signals (S 235 ). The electric signals detected from the load cells  103   a  through  103   d  are inputted to the data processor  160 , where the cross-inertia-moment is calculated (S 237 ). 
     Again, the frequency of the sine wave vibration that was applied to the second rotatory axis  120   b  is designated as 7 Hz, the angular acceleration is designated as 1 rad/sec 2 . The angular velocity of the sine wave vibration in such condition is 0.0227 rad/sec. 
     Under the conditions, the moment value is obtained using the following formula: 
     [Mathematical Formula 10] 
     
       
         
           M 
           3 
           =I 
           21×ω 
           1 
           2 
           −I 
           13 
           ×a 
           1  
         
       
     
     The definition on each symbol is not provided here because the same definitions explained in the first measuring procedure (a) are applied to each symbol. Again, among the conditions, the angular velocity ω 1  is disregarded because it is smaller than 1, and its square is also small enough to be neglected. 
     Therefore, the above formula can be summarized as follows: 
     [Mathematical Formula 11] 
     
       
         
           I 
           13 
           ≈−M 
           3 
           /a 
           1  
         
       
     
     On the other hand, the moment M 3  can be calculated by using the output values from the load cells as follows: 
     [Mathematical Formula 12] 
     
       
           M   3 =[( lc   2   +lc   3 )−( lc   1   +lc   4 )]× l   12    
       
     
     The definition on each symbol is not provided here because the same definitions explained in the first measuring procedure (a) are applied to each symbol. 
     Based on the output values from the load cells  103   a  through  103   d , the moment M 3  is obtained using the above formula, and the M 1  is substituted in [Mathematical Formula 11], where the M 3  is divided by the angular acceleration a 2  applied to the first rotatory axis  120   a . In this manner, the cross-inertia-moment, I 13 , is obtained. 
     Since the first through the fourth measuring procedures (a through d) are carried out independently, the order of procedures does not have to be the same with the embodiment of the present invention. In addition, the sine wave vibration that is applied to the first rotatory axis  120   a  and to the second rotatory axis  120   b  is preferably within range of from 6 to 10 Hz. The measurement is made under the experiment conditions of limited rotation and low speed rotation. 
     In conclusion, the present invention provides the measuring device and method of cross-inertia-moment in a limited angular rotatory axis, through which the cross-inertia-moment of multiple axis LOS stabilizer can be successfully measured or amended. Further, the present invention is also applicable to low speed rotatory machinery. Therefore, it is now possible to minimize the interference of the cross-inertia-moment due to the inertia in a precision stabilizer like the multiple axis LOS stabilizer, consequently improving the precision of the multiple axis LOS stabilizer. 
     While the preferred embodiments of the present invention have been illustrated and described, it will be understood by those skilled in the art that various changes and modifications may be made, and equivalents may be substituted for elements thereof without departing from the true scope of the present invention. In addition, many modifications may be made to adapt to a particular situation and the teaching of the present invention without departing from the central scope. Therefore, it is intended that the present invention not be limited to the particular embodiment disclosed as the best mode contemplated for carrying out the present invention, but that the present invention include all embodiments falling within the scope of the appended claims.