
2491 views  Technical Discussions   Ed Ginzel R & D,  Materials Research Institute, Canada, Joined Nov 1998, ^{1268}   05:59 Dec152008 k factor I have been asked how the values for "k" used in the beam divergence equations have been derived. My favourite references of Krautkramer and Ermolov touch on the subject and allude to the use of the Bessel J1(x) function. However, I cannot find the link to the k values for dB drop using this function described in either text. Does anyone have a more complete formulation of the equations to derive k?
 
   James Barshinger Engineering General Electric Global Research Center, USA, Joined Aug 2000, ^{8}   03:02 Dec152008 Re: k factor Ed,To derive the values for "k" in the beam divergence equation for circular oscillators, 1st start with the equation: R(g)=2*J1(x)/x where x=pi*D/l*sin(g)  These equations are in krautramer though I have used g instead of "gamma" and l instead of "lambda" To find a "k" for a certain dB drop, you start with the J1(x)/x term, equating that to the desired amplitude reduction. For example: J1(x)/x=.5 for a 6dB drop of the "free field", or for the "echo field", (J1(x)/x)^2=.5. You need to then use a numerical solver to obtain the x that satisfies the equation for the particular dB drop you are interested in. Now, using the second equation, x=pi*D/l*sin(g). You can rewrite this equation as: sin(g)=(x/pi)*(l/D). "k" is simply the quantity (x/pi), thus you get the equation in the Krautkramer book. For rectangular oscillators, the process is the same with the exception of using Sin(x)/x instead of J1(x)/x Jim  Start Original Message  : I have been asked how the values for "k" used in the beam divergence equations have been derived. My favourite references of Krautkramer and Ermolov touch on the subject and allude to the use of the Bessel J1(x) function. However, I cannot find the link to the k values for dB drop using this function described in either text. : Does anyone have a more complete formulation of the equations to derive k?  End Original Message 
 
   Neil Burleigh Sales Krautkramer Australia Pty Ltd, Australia, Joined Dec 2002, ^{158}   03:49 Dec152008 Re: k factor  Start Original Message  : Ed, : To derive the values for "k" in the beam divergence equation for circular oscillators, 1st start with the equation: : R(g)=2*J1(x)/x where x=pi*D/l*sin(g) :  These equations are in krautramer though I have used g instead of "gamma" and l instead of "lambda" : To find a "k" for a certain dB drop, you start with the J1(x)/x term, equating that to the desired amplitude reduction. For example: J1(x)/x=.5 for a 6dB drop of the "free field", or for the "echo field", (J1(x)/x)^2=.5. You need to then use a numerical solver to obtain the x that satisfies the equation for the particular dB drop you are interested in. : Now, using the second equation, x=pi*D/l*sin(g). You can rewrite this equation as: sin(g)=(x/pi)*(l/D). "k" is simply the quantity (x/pi), thus you get the equation in the Krautkramer book. : For rectangular oscillators, the process is the same with the exception of using Sin(x)/x instead of J1(x)/x : Jim : : I have been asked how the values for "k" used in the beam divergence equations have been derived. My favourite references of Krautkramer and Ermolov touch on the subject and allude to the use of the Bessel J1(x) function. However, I cannot find the link to the k values for dB drop using this function described in either text. : : Does anyone have a more complete formulation of the equations to derive k?  End Original Message Morning Ed, Some years ago I had a similar situation, we were using a K factor of 1.08 for the 20dB edge and the theoretical determination of the beam was always larger than the practical determination. The 2 K factors we were told to use (from the training and examination boards) were 1.22 for the infinite edge and 1.08 for the 20 dB edge. In the little pocket book, the "Krautkramer Blue Book", listed K factor for the 20dB edge for rectangular crystals as 0.87. When we used this constant the practical and the theoretical determination of the edge of the beam were very similar. I asked the author of the "Blue Book" Udo Schlengermann and he explained that originally that these constants came from astronomy and light transmission from celestial bodies. Which meant that the K factor of 1.08 is for through transmission whereas the K factor of 0.87 is for pulse echo. Hope this helps in the history. Regards Neil Burleigh
 
   Udo Schlengermann Consultant,  Standards Consulting, Germany, Joined Nov 1998, ^{177}   02:06 Dec162008 Re: k factor Reply:Hello Ed, Jim and Neil, the explanations for the derivation of the k factor of sound beam divergence are correct. The pulseecho technique has to take into account the characteristics of both the transmitting and the receiving transducer. With equal transducers and with the logarithmic decibelnotation it simply means half the dBdrop as for free radiation. For circular sources Bessels function J1(x)/x has to be used. For rectangular sources it is the function sin(x)/x for one direction and sin(y)/y for the perpendicular direction. Unfortunately neither Krautkramer's blue pocket book nor Krautkramer's red book on ultrasonic materials testing are available anymore. As everything has been said by my former collegues, I take the chance to wish everyboby a Merry Christmas and a Prosperous New Year. Best regards Udo Schlengermann Chairman ISO/TC135/SC3 (UT) Chairman CEN/TC138/WG2 (UT)  Start Original Message  : : Ed, : : To derive thevalues for "k" in the beam divergence equation for circular oscillators, 1st start with the equation: : : R(g)=2*J1(x)/x where x=pi*D/l*sin(g) : :  These equations are in krautramer though I have used g instead of "gamma" and l instead of "lambda" : : To find a "k" for a certain dB drop, you start with the J1(x)/x term, equating that to the desired amplitude reduction. For example: J1(x)/x=.5 for a 6dB drop of the "free field", or for the "echo field", (J1(x)/x)^2=.5. You need to then use a numerical solver to obtain the x that satisfies the equation for the particular dB drop you are interested in. : : Now, using the second equation, x=pi*D/l*sin(g). You can rewrite this equation as: sin(g)=(x/pi)*(l/D). "k" is simply the quantity (x/pi), thus you get the equation in the Krautkramer book. : : For rectangular oscillators, the process is the same with the exception of using Sin(x)/x instead of J1(x)/x : : Jim : : : I have been asked how the values for "k" used in the beam divergence equations have been derived. My favourite references of Krautkramer and Ermolov touch on the subject and allude to the use of the Bessel J1(x) function. However, I cannot find the link to the k values for dB drop using this function described in either text. : : : Does anyone have a more complete formulation of the equations to derive k? : Morning Ed, : Some years ago I had a similar situation, we were using a K factor of 1.08 for the 20dB edge and the theoretical determination of the beam was always larger than the practical determination. The 2 K factors we were told to use (from the training and examination boards) were 1.22 for the infinite edge and 1.08 for the 20 dB edge. : In the little pocket book, the "Krautkramer Blue Book", : listed K factor for the 20dB edge for rectangular crystals as 0.87. When we used this constant the practical and the theoretical determination of the edge of the beam were very similar. I asked the author of the "Blue Book" Udo Schlengermann and he explained that originally that these constants came from astronomy and light transmission from celestial bodies. Which meant that the K factor of 1.08 is for through transmission whereas the K factor of 0.87 is for pulse echo. : Hope this helps in the history. : Regards : Neil Burleigh  End Original Message 
 
   Joe Buckley Consultant, ASNT LIII, Honorary Secretary of BINDT Level X NDT, BINDT, United Kingdom, Joined Oct 1999, ^{522}  Joe Buckley Consultant, ASNT LIII, Honorary Secretary of BINDT Level X NDT, BINDT, United Kingdom, Joined Oct 1999 ^{522}
 00:29 Dec162008 Re: KK factor Udo,If GE are no longer circulating the Blue book, do you thuink there is any possibility of getting it uploaded to the internet? I have to say that it would be in my top 5 of 'most useful NDT documents' and I would be really upset if I ever lost mine. Joe  Start Original Message  : Reply: : Hello Ed, Jim and Neil, : the explanations for the derivation of the k factor of sound beam divergence are correct. : The pulseecho technique has to take into account the characteristics of both the transmitting and the receiving transducer. : With equal transducers and with the logarithmic decibelnotation it simply means half the dBdrop as for free radiation. : For circular sources Bessels function J1(x)/x has to be used. : For rectangular sources it is the function sin(x)/x for one direction and sin(y)/y for the perpendicular direction. : Unfortunately neither Krautkramer's blue pocket book nor Krautkramer's red book on ultrasonic materials testing are available anymore. : As everything has been said by my former collegues, I take the chance to wish everyboby : a Merry Christmas and a Prosperous New Year. : Best regards : Udo Schlengermann : Chairman ISO/TC135/SC3 (UT) : Chairman CEN/TC138/WG2 (UT) : : : : Ed, : : : To derive the values for "k" in the beam divergence equation for circular oscillators, 1st start with the equation: : : : R(g)=2*J1(x)/x where x=pi*D/l*sin(g) : : :  These equations are in krautramer though I have used g instead of "gamma" and l instead of "lambda" : : : To find a "k" for a certain dB drop, you start with the J1(x)/x term, equating that to the desired amplitude reduction. For example: J1(x)/x=.5 for a 6dB drop of the "free field", or for the "echo field", (J1(x)/x)^2=.5. You need to then use a numerical solver to obtain the x that satisfies the equation for the particular dB drop you are interested in. : : : Now, using the second equation, x=pi*D/l*sin(g). You can rewrite this equation as: sin(g)=(x/pi)*(l/D). "k" is simply the quantity (x/pi), thus you get the equation in the Krautkramer book. : : : For rectangular oscillators, the process is the same with the exception of using Sin(x)/x instead of J1(x)/x : : : Jim : : : : I have been asked how the values for "k" used in the beam divergence equations have been derived. My favourite references of Krautkramer and Ermolov touch on the subject and allude to the use of the Bessel J1(x) function. However, I cannot find the link to the k values for dB drop using this function described in either text. : : : : Does anyone have a more complete formulation of the equations to derive k? : : Morning Ed, : : Some years ago I had a similar situation, we were using a K factor of 1.08 for the 20dB edge and the theoretical determination of the beam was always larger than the practical determination. The 2 K factors we were told to use (from the training and examination boards) were 1.22 for the infinite edge and 1.08 for the 20 dB edge. : : In the little pocket book, the "Krautkramer Blue Book", : : listed K factor for the 20dB edge for rectangular crystals as 0.87. When we used this constant the practical and the theoretical determination of the edge of the beam were very similar. I asked the author of the "Blue Book" Udo Schlengermann and he explained that originally that these constants came from astronomy and light transmission from celestial bodies. Which meant that the K factor of 1.08 is for through transmission whereas the K factor of 0.87 is for pulse echo. : : Hope this helps in the history. : : Regards : : Neil Burleigh  End Original Message 
 
   Neil Burleigh Sales Krautkramer Australia Pty Ltd, Australia, Joined Dec 2002, ^{158}   03:44 Dec162008 Re: KK factor  Start Original Message  G'day Joe, I will check in the publicity department within GE to see if they have produced an electronic copy. Merry Christmas from Down underNeil Burleigh : Udo, : If GE are no longer circulating the Blue book, do you thuink there is any possibility of getting it uploaded to the internet? : I have to say that it would be in my top 5 of 'most useful NDT documents' and I would be really upset if I ever lost mine. : Joe : : Reply: : : Hello Ed, Jim and Neil, : : the explanations for the derivation of the k factor of sound beam divergence are correct. : : The pulseecho technique has to take into account the characteristics of both the transmitting and the receiving transducer. : : With equal transducers and with the logarithmic decibelnotation it simply means half the dBdrop as for free radiation. : : For circular sources Bessels function J1(x)/x has to be used. : : For rectangular sources it is the function sin(x)/xfor one direction and sin(y)/y for the perpendicular direction. : : Unfortunately neither Krautkramer's blue pocket book nor Krautkramer's red book on ultrasonic materials testing are available anymore. : : As everything has been said by my former collegues, I take the chance to wish everyboby : : a Merry Christmas and a Prosperous New Year. : : Best regards : : Udo Schlengermann : : Chairman ISO/TC135/SC3 (UT) : : Chairman CEN/TC138/WG2 (UT) : : : : : : Ed, : : : : To derive the values for "k" in the beam divergence equation for circular oscillators, 1st start with the equation: : : : : R(g)=2*J1(x)/x where x=pi*D/l*sin(g) : : : :  These equations are in krautramer though I have used g instead of "gamma" and l instead of "lambda" : : : : To find a "k" for a certain dB drop, you start with the J1(x)/x term, equating that to the desired amplitude reduction. For example: J1(x)/x=.5 for a 6dB drop of the "free field", or for the "echo field", (J1(x)/x)^2=.5. You need to then use a numerical solver to obtain the x that satisfies the equation for the particular dB drop you are interested in. : : : : Now, using the second equation, x=pi*D/l*sin(g). You can rewrite this equation as: sin(g)=(x/pi)*(l/D). "k" is simply the quantity (x/pi), thus you get the equation in the Krautkramer book. : : : : For rectangular oscillators, the process is the same with the exception of using Sin(x)/x instead of J1(x)/x : : : : Jim : : : : : I have been asked how the values for "k" used in the beam divergence equations have been derived. My favourite references of Krautkramer and Ermolov touch on the subject and allude to the use of the Bessel J1(x) function. However, I cannot find the link to the k values for dB drop using this function described in either text. : : : : : Does anyone have a more complete formulation of the equations to derive k? : : : Morning Ed, : : : Some years ago I had a similar situation, we were using a K factor of 1.08 for the 20dB edgeand the theoretical determination of the beam was always larger than the practical determination. The 2 K factors we were told to use (from the training and examination boards) were 1.22 for the infinite edge and 1.08 for the 20 dB edge. : : : In the little pocket book, the "Krautkramer Blue Book", : : : listed K factor for the 20dB edge for rectangular crystals as 0.87. When we used this constant the practical and the theoretical determination of the edge of the beam were very similar. I asked the author of the "Blue Book" Udo Schlengermann and he explained that originally that these constants came from astronomy and light transmission from celestial bodies. Which meant that the K factor of 1.08 is for through transmission whereas the K factor of 0.87 is for pulse echo. : : : Hope this helps in the history. : : : Regards : : : Neil Burleigh  End Original Message 
 
   S.V.Swamy Engineering,  Material Testing Inspection & Quality Control Retired from Nuclear Fuel Complex , India, Joined Feb 2001, ^{787}  S.V.Swamy Engineering,  Material Testing Inspection & Quality Control Retired from Nuclear Fuel Complex , India, Joined Feb 2001 ^{787}
 07:45 Dec172008 Re: k factor Sir,You wrote: As everything has been said by my former collegues, I take the chance to wish everyboby : a Merry Christmas and a Prosperous New Year. : Best regards : Udo Schlengermann : Chairman ISO/TC135/SC3 (UT) : Chairman CEN/TC138/WG2 (UT) I too take this opportunity to wish you a happy new year. I tried to mail you separately but the mail was rejected. With best wishes, Swamy Hyderabad, India ndtguru@gmail.com  Start Original Message  : Reply: : Hello Ed, Jim and Neil, : the explanations for the derivation of the k factor of sound beam divergence are correct. : The pulseecho technique has to take into account the characteristics of both the transmitting and the receiving transducer. : With equal transducers and with the logarithmic decibelnotation it simply means half the dBdrop as for free radiation. : For circular sources Bessels function J1(x)/x has to be used. : For rectangular sources it is the function sin(x)/x for one direction and sin(y)/y for the perpendicular direction. : Unfortunately neither Krautkramer's blue pocket book nor Krautkramer's red book on ultrasonic materials testing are available anymore. : As everything has been said by my former collegues, I take the chance to wish everyboby : a Merry Christmas and a Prosperous New Year. : Best regards : Udo Schlengermann : Chairman ISO/TC135/SC3 (UT) : Chairman CEN/TC138/WG2 (UT)
 
   Ed Ginzel R & D,  Materials Research Institute, Canada, Joined Nov 1998, ^{1268}   02:59 Dec172008 Re: k factor Thank you all for the explanations! The little blue book being discontinued is bad..but I am also saddened to read that the main text is also discontinued! Regards Ed Start Original Message  : Reply: : Hello Ed, Jim and Neil, : the explanations for the derivation of the k factor of sound beam divergence are correct. : The pulseecho technique has to take into account the characteristics of both the transmitting and the receiving transducer. : With equal transducers and with the logarithmic decibelnotation it simply means half the dBdrop as for free radiation. : For circular sources Bessels function J1(x)/x has to be used. : For rectangular sources it is the function sin(x)/x for one direction and sin(y)/y for the perpendicular direction. : Unfortunately neither Krautkramer's blue pocket book nor Krautkramer's red book on ultrasonic materials testing are available anymore. : As everything has been said by my former collegues, I take the chance to wish everyboby : a Merry Christmas and a Prosperous New Year. : Best regards : Udo Schlengermann : Chairman ISO/TC135/SC3 (UT) : Chairman CEN/TC138/WG2 (UT) : : : : Ed, : : : To derive the values for "k" in the beam divergence equation for circular oscillators, 1st start with the equation: : : : R(g)=2*J1(x)/x where x=pi*D/l*sin(g) : : :  These equations are in krautramer though I have used g instead of "gamma" and l instead of "lambda" : : : To find a "k" for a certain dB drop, you start with the J1(x)/x term, equating that to the desired amplitude reduction. For example: J1(x)/x=.5 for a 6dB drop of the "free field", or for the "echo field", (J1(x)/x)^2=.5. You need to then use a numerical solver to obtain the x that satisfies the equation for the particular dB drop you are interested in. : : : Now, using the second equation, x=pi*D/l*sin(g). You can rewrite this equation as: sin(g)=(x/pi)*(l/D). "k" is simply the quantity (x/pi), thus you get the equation inthe Krautkramer book. : : : For rectangular oscillators, the process is the same with the exception of using Sin(x)/x instead of J1(x)/x : : : Jim : : : : I have been asked how the values for "k" used in the beam divergence equations have been derived. My favourite references of Krautkramer and Ermolov touch on the subject and allude to the use of the Bessel J1(x) function. However, I cannot find the link to the k values for dB drop using this function described in either text. : : : : Does anyone have a more complete formulation of the equations to derive k? : : Morning Ed, : : Some years ago I had a similar situation, we were using a K factor of 1.08 for the 20dB edge and the theoretical determination of the beam was always larger than the practical determination. The 2 K factors we were told to use (from the training and examination boards) were 1.22 for the infinite edge and 1.08 for the 20 dB edge. : : In the little pocket book, the "Krautkramer Blue Book", : : listed K factor for the 20dB edge for rectangular crystals as 0.87. When we used this constant the practical and the theoretical determination of the edge of the beam were very similar. I asked the author of the "Blue Book" Udo Schlengermann and he explained that originally that these constants came from astronomy and light transmission from celestial bodies. Which meant that the K factor of 1.08 is for through transmission whereas the K factor of 0.87 is for pulse echo. : : Hope this helps in the history. : : Regards : : Neil Burleigh  End Original Message 
 
  
