1 COMSOL Multiphysics Dynamic Electromagnetic Analysis of Guitar Pickup aided by COMSOL Multiphysics Tatsuya FURUKAWA, Hideaki TANAKA, Hideaki ITOH, H
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1 1 COMSOL Multiphysics Dynamic Electromagnetic Analysis of Guitar Pickup aided by COMSOL Multiphysics Tatsuya FURUKAWA, Hideaki TANAKA, Hideaki ITOH, Hisao FUKUMOTO and Masashi OHCHI Graduate School, Saga University, Toyota Technical Development Co., Chiba Institute of Technology Abstract The electric guitar is widely used by many musicians. However, the relation between the string vibrations of a guitar and the electric signals that it produces is not fully investigated. The pickup devices, which transduce the string vibrations to the electric signals, are therefore not easy to design. Currently, designing the pickups requires knowledge and intuition of trained experts. If the simulation of the pickup process becomes possible, it will become easy for a musician to design his or her own pickups that produce the sound that he/she likes, without knowledge and intuition of trained experts. However, in transient analyses of electromagnetic fields with moving media, it is difficult to grasp the phenomena theoretically in the same manner of the convective heat diffusion since the treatment on the coupled problem with the field and dynamics is necessary. In this paper, we illustrate the dynamic magnetic flux patterns around the electric guitar pickup, where the string will move over the permanent magnet surrounded by the pickup coil, using COMSOL Multiphysics. Keywords: Finite Element Analysis, Electromagnetic Analysis, Guitar Pickup, Moving Medium, Weak Coupled Problem 1 Rickenbacker George Beauchamp 1931 *1 [1] * Les Paul *1 Frying Pan *2 () Leo Fender [2] 80 [3, 4, 5, 6] [3, 4, 5]
2 3 [7, 8, 9, 10] [6] 2 [7, 8, 9, 10] COMSOL Multiphysics 3 2 *3 1 () mm ( ) Permanent Magnet 1 N S Steel String Windings *3 kω () M B = µh + M (1) 1 (B M) = H (2) µ B A 1/µ ν ν( A M) = J 0 (3) ν ν A J 0 ν M = 0 (4) (4) 3 B H M B M J 0 (4) 3 A R 0 R I (R 0 + R)I + dφ dt = 0 (5) (5) Φ, A, n c, S c 2
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![50[s] の間で弦の進行 方向を等速度で変化させており 弦の移動によって出力 される信号の値が変化していることがわかる また 図 13 に示す出力信号の実測値と比較すると 同図の中央あ たりに見られる特徴的な波形を再現できているようであ るが 加速度を伴う弦の振動を考慮できていないので 実測値とは かけ離れた時間的な変化となっており 透 磁率の変化で弦の運動を模擬しようとする本方法の限界](/docs-images/96/128955994/images/4-1.jpg "が見えた したがって ピックアップの特性を理論的に 把握するためには 実際の弦振動を考慮する よりリア リスティックなモデルでの電磁界解析を展開する必要が ある プランジャ駆動装置 TC4069 Vdd 12[V] R1 Rp C S1 R2 S2 0.00015 図 10 プランジャ駆動回路 0.")
![0001 5e-05 佐賀大学大学院 古川達也他 Voltage[V] コイルの巻数を 184 回とする また 節点数は 30,358 辺要素数は 194,473 である 3.](/docs-images/96/128955994/images/4-2.jpg "5 実験装置 実験の再現性を図るために 図 8 に示す撥弦装置を製 作した 図 8 に示したプランジャは 図 9 で示すプラン ジャ駆動回路部のスイッチ S1 と S2 を押下することで プランジャ軸の先に取り付けられたピックで弦を弾くこ とができる 図 10 は 具体的な駆動回路図である 図 10 の IC TC4069 は 図中の S1 と S2 を同時でオンにす ることで")
4 ギターピックアップの動的電磁界解析 すべて向いていることがわかる また 弦部分には比透 磁率 600 を与えているため 磁束密度が高くなり 矢印 が大きくなっていることがわかる 周辺の空気領域では 矢印が磁石領域の上部から下部に向かっていることもわ かる 図8 製作した撥弦装置 図 11 磁束密度分布 図9 弦の振動と発生する電気信号の関係を解析した結果 を図 12 に示す この図では 0.17[s] と 0.18[s] の間 0.33[s] と 0.34[s] の間 0.49[s] と 0.50[s] の間で弦の進行 方向を等速度で変化させており 弦の移動によって出力 される信号の値が変化していることがわかる また 図 13 に示す出力信号の実測値と比較すると 同図の中央あ たりに見られる特徴的な波形を再現できているようであ るが 加速度を伴う弦の振動を考慮できていないので 実測値とは かけ離れた時間的な変化となっており 透 磁率の変化で弦の運動を模擬しようとする本方法の限界 が見えた したがって ピックアップの特性を理論的に 把握するためには 実際の弦振動を考慮する よりリア リスティックなモデルでの電磁界解析を展開する必要が ある プランジャ駆動装置 TC4069 Vdd 12[V] R1 Rp C S1 R2 S 図 10 プランジャ駆動回路 e-05 佐賀大学大学院 古川達也他 Voltage[V] コイルの巻数を 184 回とする また 節点数は 30,358 辺要素数は 194,473 である 3.5 実験装置 実験の再現性を図るために 図 8 に示す撥弦装置を製 作した 図 8 に示したプランジャは 図 9 で示すプラン ジャ駆動回路部のスイッチ S1 と S2 を押下することで プランジャ軸の先に取り付けられたピックで弦を弾くこ とができる 図 10 は 具体的な駆動回路図である 図 10 の IC TC4069 は 図中の S1 と S2 を同時でオンにす ることで 振動式プランジャを駆動するために使用する 発振回路であり R2 の可変抵抗によって振動数を変え ることも可能であるが 今回使用した図 8 に示したプラ ンジャでは 1 発だけの撥弦のため S1 だけを使用した 3.6 モデルギターの解析値と数値計算結果の比較 図 11 に第 3.4 節で示した解析モデルに対して辺要素 有限要素法電磁界解析を実施した場合の結果を示す 図 中の矢印は 磁束密度をベクトルで表したものである 永久磁石の部分に磁化を y 方向にだけ与えているため 図 11 のように中心の永久磁石の部分は矢印が y 方向に 0-5e Time[s] 図 12 透磁率の変化で弦振動を模擬した 3 次元辺要素 有限要素解析でのピックアップ出力結果 4 COMSOL Multiphysics による解析 第 3.6 節の最後で述べたように 従前の透磁率の変 化で弦の運動を模擬するには かなりの無理があり 弦 の位置による磁束変化を考慮できるが実際の弦の運動 を考慮することができなかった 本節では COMSOL 4
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![23-29, 1989 01 [5] A, 104(379), pp.25 30, 2004 10 [6] http://www.moore.org.au/pick001.htm [7] 22 GS5 5 CD ROM 2010 9 [8], MAG 10 192, pp.1 5 2010 12 [9] 23 64,12 2A 01, pp.](/docs-images/96/128955994/images/9-1.jpg "419(cd ROM) 2011 9 [10],,,,, IEEE IM S11 09, pp 12, 2011 11 [11] :, 1982 [12] http://store.gibson.com/p-90-single-coilwith-soapbar-cover/ [13] http://en.wikipedia.")
9 35 34 Gibson P 90 Gibson P 90 COMSOL Multiphysics COMSOL Multiphysics [1] pan %28guitar%29 [2] vol [3] 44 3 pp [4] Masahiro Harazono, Electromangetic pickup responce excitede by a string vibration, Journal of the Acoustical Society of Japan (E), vol. 10, no. 1, pp , [5] A, 104(379), pp.25 30, [6] [7] 22 GS5 5 CD ROM [8], MAG , pp [9] 23 64,12 2A 01, pp.419(cd ROM) [10],,,,, IEEE IM S11 09, pp 12, [11] :, 1982 [12] [13] [14] COMSOL Multiphysics Ver.4.2 (chosoku guide vol1.pdf) [15] 20Innovating%20High%20Sensitivity%20Guitar %20Pickups.pdf, COMSOL Multiphysics 1 1 9
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