JP4288926B2 - Linear guide device and table device - Google Patents

Description

で計算される。
【００５０】
図４に示すように、クラウニング部２０が、直線状である場合、上記と同様にして、θ_C：接触角方向の断面内で見たクラウニング部の傾きとすると、クラウニング部有効長Ｌｃｅは、
【数２】

で計算される。
【００５１】
スライダ軌道面の全長Ｌ₁のうち、転動体１３が予圧を受ける部分の長さを、スライダ軌道面の有効長と呼ぶ。スライダ軌道面有効長Ｌｅｓは、次式で計算できる。
【数３】

ただし、上式で計算されるＬｅｓが、Ｌｅｓ＞Ｌ₁−２Ｃとなる場合、またはクラウニング部が無い場合には、次式でＬｅｓを計算する。ここで、Ｃは面取り部２１の長さである。面取り部が無い場合は、Ｃ＝０を代入する。
【数４】

【００５２】
Ｌｃｅは、オーバーサイズ量δ₀によって変化するから、［数３］のＬｅｓも、δ₀の値によって変化する。通常のリニアガイド装置では、用途毎に転動体１３のオーバーサイズ量を変更して用いている。例えば、工作機械等では、剛性を必要とするため、オーバーサイズ量は大きくなる。
また、高速な駆動が必要な測定器等で、摺動抵抗を小さくしたい場合には、オーバーサイズ量を小さくする。オーバーサイズ量が特定できる場合には、スライダ軌道面１９の有効長として、［数３］のＬｅｓを用いても良い。しかし、通常の場合は、スライダ軌道面の有効長として、上記のＬｅｓの代わりに、オーバーサイズ量に因らずに定められる次式のＬｅを用いるのが良い。
【数５】

このＬｅは、オーバーサイズを変化させた場合の、最大のＬｅｓ（＝Ｌ₁−２Ｃ）と、最小のＬｅｓ（＝Ｌ₁−２Ｌ_C）との平均値である。Ｌｅは、広い範囲のオーバーサイズに対する平均的なスライダ軌道面有効長を表す。上記式５は、クラウニング部２０，２０が同一形状である場合に用いる。
【００５３】
クラウニング部２０，２０の形状が異なる場合、Ｌｅは、次式で計算される。
【数６】

ここで、Ｌｃ₁，Ｌｃ₂：左右端部のクラウニング部長さ
Ｃ₁，Ｃ₂：左右端部の面取り部長さ
である。
【００５４】
次に、以降の計算に際して、以下を仮定する。
レール軌道面１５，１５の波打ちは、正弦波として表す。
転動体１３と軌道面１５，１５，１９，１９との接触部は、スライダ軌道面１９，１９に一様に、連続的に分布する線形ばねとする。
【００５５】
図５に示すように、直動方向にｘ軸をとり、レール軌道面１５，１５の位置ｘにおける上下方向の波打ち量ｙをとると、波打ち量ｙは、次式によって表される。このとき、Ａは定数であり、レール軌道面１５，１５の波打ちの片振幅である。
【数７】

【００５６】
そして、ｉ番目のスライダ軌道面が位置ｘにおいて受ける単位長さあたりの荷重ｆｉ（ｘ）は、次式で表される。
【数８】

ここで、
Ｘ_Ｓ：スライダ軌道面の中心座標
Δｚ：スライダの上方向への変位量
Δφ：スライダのピッチング方向への変位量
ｋi：ｉ番目のスライダ軌道面の転動体・軌道面接触部の単位長さあたりの上下方向ばね係数(転動体と軌道面の仕様、接触角によって決まる。)
である。
【００５７】
従って、スライダ１２が、４列の転動体列から受ける荷重の和Ｆは、スライド中心のｘ座標をＸ_Ｓとし、スライダ軌道面有効長をＬｅとして、次式となる。
【数９】

ここで、Ｋ＝ｋ₁＋ｋ₂＋ｋ₃＋ｋ₄
である。
【００５８】
スライダ１２に作用する上方向への外力をＦ₀とすると、力の釣り合いにより次式が成り立つ。
【数１０】

【００５９】
上式［数９］及び［数１０］により、スライダ１２の上下方向変位は次式となる。
【数１１】

【００６０】
案内レール１１の波打ちに起因するスライダ１２の上下方向変位の片振幅Δｖは、波打ちの片振幅Ａに対する比として、次式で表される。
【数１２】

ここで、ξ＝Ｌｅ／Ｐである。
【００６１】
図６は、ξとΔｖ／Ａの大きさの関係を表す図である。次式が成り立つ時に、Δｖが零（０）になる。
【数１３】

【００６２】
上式が厳密に成り立たなくても、ξが次式の範囲であれば、上下振幅Δｖを十分小さくできる。
【数１４】

ここで、ｍ：１以上の整数（ｍ＝１，２，３…）である。
【００６３】
一方、スライダ１２が４列の転動体列から受けるピッチング方向のモーメントの和Ｍは、次式により表される。
【数１５】

【００６４】
また、スライダ１２に作用するピッチング方向の外部モーメントをＭ₀とすると、力の釣り合いから、次式が成り立つ。
【数１６】

【００６５】
そして、上式［数１５］及び［数１６］より、スライダ１２のピッチング方向の変位は次式にて表される。
【数１７】

【００６６】
波打ちに起因するスライダ１２のピッチング方向の変位における片振幅Δｐは、波打ちの最大傾斜Θに対する比として、次式にて表される。ここで、Θ＝２πＡ／Ｐである。
【数１８】

ここで、ξ＝Ｌｅ／Ｐである。
【００６７】
続いて、図７は、ξとΔｐ／Θの大きさ関係を表している。次式が成り立つ時に、Δｐが零（０）になる。
【数１９】

【００６８】
上式を満たすξ＝ξ_Lは、数値計算によって次式のように求められる。
【数２０】

【００６９】
上式が厳密に成り立たなくても、ξが次式の範囲にあれば、ピッチング振幅Δｐを十分小さくできる。
【数２１】

【００７０】
第１実施形態のリニアガイド装置１０によれば、スライダ軌道面有効長Ｌｅと、レール軌道面波打ち波長Ｐとが、ｍ−0.1≦Ｌｅ／Ｐ≦ｍ＋0.1に設定される。したがって、スライダ１２がどの位置に移動した場合においても、スライダ１２の姿勢変化がほぼゼロになるように、スライダ軌道面１９の有効長さと波打ち波長との関係が定められる。これによって、レール軌道面１５に波打ちが生じていても、スライダ１２の姿勢変化を小さく保つことができ、ボルト締結等によって生じる軌道面の周期的な変形がスライダ１２の運動精度に及ぼす影響を小さくすることができる。
また、ξ_Lを方程式sinπξ_L−πξ_Lcosπξ_L＝0の解として、レール軌道面波打ち波長Ｐと、スライダ軌道面有効長Ｌｅとが、ξ_L−0.1≦Ｌｅ／Ｐ≦ξ_L＋0.1に設定されても、レール軌道面１５に波打ちが生じていても、スライダ１２の姿勢変化を小さく保つことができ、ボルト締結等によって生じる軌道面の周期的な変形がスライダ１２の運動精度に及ぼす影響を小さくすることができる。
【００７１】
次に、本発明に係る第１実施形態のテーブル装置について説明する。
図８に示すように、テーブル装置３０は、単一の案内レール３１と、案内レール３１上に配されて案内レール３１の軸方向に移動可能に組み付けられた２個のスライダ３２，３３と、スライダ３２，３３上に配された単一のテーブル３４と、を備えている。
案内レール３１の両側面に、レール軌道面が形成され、スライダ３２，３３にスライダ軌道面が形成され、レール軌道面とスライダ軌道面との間に転動体が転動自在に配されている。
【００７２】
図９に示すように、直動方向にｘ軸をとる。リニアガイド装置１０の場合と同様にして、以降の計算に際して、以下を仮定する。
レール軌道面のうねりは、［数７］の正弦波として表せることとする。
転動体と軌道面との接触部は、スライダ軌道面に一様に分布する線形ばねとする。
そして、以下の記号を用いる。
ｘ_T：テーブル位置（テーブル３４上のＰのｘ座標）
Ｓ：２個のスライダ３２，３３の中心間距離
Ｓ_A：テーブル３４上の点Ｐから、スライダ３２の軌道面の中心までの距離
Ｓ_B：テーブル３４上の点Ｐから、スライダ３３の軌道面の中心までの距離
Δｚ_T：テーブル３４の上方向への変位量
Δφ_T：ピッチング方向への変位量
ｋ_Ai：スライダ３２のｉ番目軌道面の転動体・軌道面接触部の単位長さあたりのばね係数
ｋ_Bi：スライダ３３のｉ番目軌道面の転動体・軌道面接触部の単位長さあたりのばね係数
Ｋ_A：スライダ３２の全ての軌道面についてのｋ_Aiの和
Ｋ_B：スライダ３３の全ての軌道面についてのｋ_Biの和
Δｚ_A：スライダ３２の上方向への変位量
Δφ_A：スライダ３２のピッチング方向への変位量
Δｚ_B：スライダ３３のテーブル３４の上方向への変位量
Δφ_B：スライダ３３のピッチング方向への変位量
これらを用い、テーブル３４上のＰ点は、次式のように定める。
【数２２】

【００７３】
また、幾何学的な関係から、次式が成り立つ。
【数２３】

【数２４】

【数２５】

【００７４】
そして、リニアガイド装置１０の場合と同様にして、スライダ３２，３３に作用する上下方向荷重Ｆ_A，Ｆ_Bは次式となる。
【数２６】

【数２７】

【００７５】
更に、テーブル３４に作用する上方向への外力をＦ_Tとすると、力の釣り合いから次式が成り立つ。
【数２８】

【００７６】
そして、上式［数２２］〜［数２８］により、テーブル３４の上下方向変位ΔｚＴは、次式となる。
【数２９】

【００７７】
そして、上式により、次式が成り立つ時に、テーブル位置ｘ_TによらずΔｚ_Tは常に一定となる。
【数３０】

ここで、ｍ_Aとｍ_Bは、ともに１以上の整数（ｍ_A＝１，２，３，…；ｍ_B＝１，２，３，…）である。
リニアガイド装置１０の場合と同様に、上式を厳密に満たさなくても、Ｌ_A／ＰとＬ_B／Ｐが下式の範囲であれば、Δｚ_Tの変化を十分小さくできる。
【数３１】

【００７８】
以下、２個のスライダ３２，３３の転動体寸法、スライダ軌道面有効長の全てが同じ場合について考える。この場合、Ｋ_A＝Ｋ_B＝Ｋ_T，Ｌ_A＝Ｌ_B＝Ｌ_T，Ｓ_A＝Ｓ_B＝Ｓ／２である。従って、［数２９］は次式となる。
【数３２】

【００７９】
上式より、次式が成り立つ時に、テーブル位置ｘ_TによらずΔｚ_Tは常に一定となる。
【数３３】

ここで、ｍ_Tとｎとは、ともに１以上の整数（ｍ_T＝１，２，３，…；ｎ＝１，２，３，…）である。
リニアガイド装置１０の場合と同様に、上式を厳密に満たさなくても、下式の範囲であれば、Δｚ_Tの変化を十分小さくできる。
【数３４】

【００８０】
一方、スライダ３２，３３が受けるピッチング方向モーメントＭ_A，Ｍ_Bは次式となる。
【数３５】

【数３６】

【００８１】
テーブル３４に外部から作用するピッチングモーメントをＭ_Tとすると、モーメントの釣り合いから次式が成り立つ。
【数３７】

【００８２】
そして、上式［数２２］〜［数２７］と上式［数３５］〜［数３７］より、スライダ３２，３３のピッチング方向変位は次式となる。
【数３８】

【００８３】
上式より、次式が成り立つ時に、テーブル位置ｘ_TによらずΔφ_Tは常に一定となる。
【数３９】

ここで、ξ_T及びη_Tは、次式の方程式の解である。
【数４０】

【００８４】
図１０に、上式を満たすξとηとの関係を示す。
線上に位置するξとηとの組であれば、［数４０］が満たされる。例えば、ξ＝1.5に対して、η＝0.89,1.95,2.97,3.97,4.98,5.98…であれば、［数４０］が満たされる。なお、寸法上の制限から、Ｌ_T≦Ｓであるから、ξ≦ηの必要がある。
【００８５】
リニアガイド装置１０の場合と同様に、上式を厳密に満たさなくても、下式の範囲であれば、Δφ_Tの変化を十分小さくできる。
【数４１】

【００８６】
更に、上式［数３３］及び［数３９］が満たされれば、テーブル位置によらず、テーブル３４の上下方向変位とピッチング変位の両方について、変化量を零（０）にすることができる。次式のようにＬ_TとＳとを選べば、［数３３］と［数３９］とが、ともに満たされる。
【数４２】

ここで、ｍ_Tとｎとは、ともに１以上の整数（ｍ_T＝１，２，３，…；ｎ＝１，２，３，…）である。
上式を厳密に満たさなくとも、Ｌ_T／ＰとＳ／Ｐとが下式の範囲であれば、上下方向の姿勢変化を同時に十分小さくできる。
【数４３】

【００８７】
第１実施形態のテーブル装置３０によれば、２個のスライダ軌道面有効長Ｌ_A，Ｌ_Bと、レール軌道面波打ち波長Ｐとが、ｍ_A−0.1≦Ｌ_A／Ｐ≦ｍ_A＋0.1で且つ、ｍ_B−0.1≦Ｌ_B／Ｐ≦ｍ_A＋0.1に設定される。
したがって、テーブル３４がどの位置に移動した場合においても、テーブル３４の姿勢変化がほぼゼロになるように、スライダ軌道面の有効長さと、波打ち波長との関係が定められる。これによって、レール軌道面に波打ちが生じていても、テーブル３４の姿勢変化を小さく保つことができ、ボルト締結等によって生じる軌道面の周期的な変形がテーブルの運動精度に及ぼす影響を小さくすることができる。
【００８８】
また、２個が同一である場合のスライダ軌道面有効長Ｌ_Tと、レール軌道面波打ち波長Ｐと、スライダ軌道面中心間距離Ｓとが、ｍ_T−0.1≦Ｌ_T／Ｐ≦ｍ_T＋0.1または、ｎ＋0.4≦Ｓ／Ｐ≦ｎ＋0.6に設定されても良い。そうすることにより、レール軌道面に波打ちが生じていても、テーブル３４の姿勢変化を小さく保つことができ、ボルト締結等によって生じる軌道面の周期的な変形がテーブル３４の運動精度に及ぼす影響を小さくすることができる。
【００８９】
そして、ξ_T，η_Tを方程式πη_Tsinπξ_Tsinπη_T＋{sinπξ_T−πξ_Tcosπξ_T}cosπη_T＝0の解として、２個が同一のスライダ軌道面有効長Ｌ_Tと、レール軌道面波打ち波長Ｐと、スライダ軌道面中心間距離Ｓとが、ξ_T−0.1≦Ｌ_T／Ｐ≦ξ_T＋0.1で且つ、η_T−0.１≦Ｓ／Ｐ≦η_T＋0.1に設定されても良い。そうすることにより、レール軌道面に波打ちが生じていても、テーブル３４の姿勢変化を小さく保つことができ、ボルト締結等によって生じる軌道面の周期的な変形がテーブル３４の運動精度に及ぼす影響を小さくすることができる。
【００９０】
更に、２個が同一のスライダ軌道面有効長Ｌ_Tと、レール軌道面波打ち波長Ｐと、スライダ軌道面中心間距離Ｓとが、ｍ_T−0.1≦Ｌ_T／Ｐ≦ｍ_T＋0.1で且つ、ｎ＋0.4≦Ｓ／Ｐ≦ｎ＋0.6に設定されても良い。これにより、レール軌道面に波打ちが生じていても、テーブル３４の姿勢変化を小さく保つことができ、ボルト締結等によって生じる軌道面の周期的な変形がテーブル３４の運動精度に及ぼす影響を小さくすることができる。
また更に、複数個のテーブル装置を組み合わせて一つに構成したり、レール軌道面波打ち波長Ｐを案内レールの取付けボルトピッチに置き換えたり、レール軌道面波打ち波長Ｐを横押し板の取付け間隔に置き換えたりしても良い。これらの場合にも、レール軌道面に波打ちが生じていても、テーブル３４の姿勢変化を小さく保つことができ、ボルト締結等によって生じる軌道面の周期的な変形がテーブル３４の運動精度に及ぼす影響を小さくすることができる。
【００９１】
次に、図１１を用いて本発明に係る第２実施形態のリニアガイド装置について説明する。
第２実施形態のリニアガイド装置４０は、案内レール１１の両側面に、ボールである転動体１３を摺動させるための一対のレール軌道面１５がスライダ軌道面１９に対向して形成されており、２列の転動体１３を配している。
そして、第２実施形態のリニアガイド装置４０は、第１実施形態と同様にして、レール軌道面の波打ち波長をＰとし、ｍを１以上の整数として、スライダ軌道面有効長Ｌｅと、レール軌道面波打ち波長Ｐとが、ｍ−0.1≦Ｌｅ／Ｐ≦ｍ＋0.1に設定されている。
また、ξ_Lを方程式sinπξ_L−πξ_Lcosπξ_L＝0の解として、レール軌道面波打ち波長Ｐと、スライダ軌道面有効長Ｌｅとが、ξ_L−0.1≦Ｌｅ／Ｐ≦ξ_L＋0.1に設定されている。
【００９２】
次に、図１２を用いて本発明に係る第３実施形態のリニアガイド装置について説明する。
第３実施形態のリニアガイド装置５０は、案内レール１１の両側面に、ボールである転動体１３を摺動させるための三対のレール軌道面(上溝，中溝，下溝)１５，１５，１５がスライダ軌道面１９，１９，１９に対向して形成されており、３列の転動体１３を配している。
そして、第３実施形態のリニアガイド装置５０は、第１実施形態と同様にして、レール軌道面の波打ち波長をＰとし、ｍを１以上の整数として、スライダ軌道面有効長Ｌｅと、レール軌道面波打ち波長Ｐとが、ｍ−0.1≦Ｌｅ／Ｐ≦ｍ＋0.1に設定されている。
また、ξ_Lを方程式sinπξ_L−πξ_Lcosπξ_L＝0の解として、レール軌道面波打ち波長Ｐと、スライダ軌道面有効長Ｌｅとが、ξ_L−0.1≦Ｌｅ／Ｐ≦ξ_L＋0.1に設定されている。
【００９３】
続いて、図１３を用いて本発明に係る第４実施形態のリニアガイド装置について説明する。
第４実施形態のリニアガイド装置６０は、案内レール１１の両側面に、円筒ころである転動体１３を摺動させるための二対のレール軌道面(上溝，下溝)１５，１５がスライダ軌道面１９，１９に対向して形成されており、２列の転動体１３を配している。
そして、第４実施形態のリニアガイド装置６０は、第１実施形態と同様にして、レール軌道面の波打ち波長をＰとし、ｍを１以上の整数として、スライダ軌道面有効長Ｌｅと、レール軌道面波打ち波長Ｐとが、ｍ−0.1≦Ｌｅ／Ｐ≦ｍ＋0.1に設定されている。
また、ξ_Lを方程式sinπξ_L−πξ_Lcosπξ_L＝0の解として、レール軌道面波打ち波長Ｐと、スライダ軌道面有効長Ｌｅとが、ξ_L−0.1≦Ｌｅ／Ｐ≦ξ_L＋0.1に設定されている。
【００９４】
【実施例】
上述した各実施形態のリニアガイド装置及びテーブル装置に関して、実施例及び比較例を以下のように行った。
【００９５】
＜実施例１＞
実施例１に用いられるリニアガイド装置は、図１に示したリニアガイド装置１０と同等の構成をもつ。
ここで、実施例１に用いたリニアガイド装置は以下の詳細な数値を有する。
溝数 ：４溝
転動体接触角 ：α＝50°
転動体直径 ：Ｄａ＝4.7625mm
軌道面の半径 ：ｒ＝2.4765mm（転動体直径の52％）
オーバーサイズ量 ：δ₀＝0.0022mm
クラウニング部 ：形状＝円弧、長さＬｃ＝11mm、半径Ｒｃ＝4980mm、クラウニング部有効長Ｌｃｅ＝4.68mm
【００９６】
なお、クラウニング部は、加工時は溝底方向に半径Ｒｃ´＝3200mmで加工、接触方向に換算した半径Ｒｃは、Ｒｃ＝Ｒｃ´／cosα＝4980mmとなる。
面取り部面取り量 ：Ｃ＝0.2mm
案内レールのボルトピッチ：Ｐ＝80mm
スライダ軌道面有効長は、［数１４］及び［数２１］より、以下が望ましい。
上下変位を低減：72≦Ｌｅ≦88（ｍ＝1）
152≦Ｌｅ≦168（ｍ＝2）
ピッチング変位を低減：106.4≦Ｌｅ≦122.4（ξ_L＝1.43）
188.0≦Ｌｅ≦204.0（ξ_L＝2.45）
［数５］より、Ｌ₁＝Ｌｅ−（Ｌｃ＋Ｃ）であるので、スライダ本体長Ｌ₁の範囲は以下となる。
上下変位を低減：83.2≦Ｌ₁≦99.2（ｍ＝1）
163.2≦Ｌ₁≦179.2（ｍ＝2）
ピッチング変位を低減：117.6≦Ｌ₁≦133.6（ξ_L＝1.43）
199.2≦Ｌ₁≦215.2（ξ_L＝2.45）
そして、本発明による実施例１ａ，１ｂと比較例１ｃ，１ｄとして、以下を選択した。
【００９７】
＜実施例１ａ＞ Ｌ₁＝172mm 上下変位を低減するための条件式［数１４］を満たす。
【００９８】
＜実施例１ｂ＞ Ｌ₁＝127mm ピッチング変位を低減するための条件式［数２１］を満たす。
【００９９】
＜比較例１ｃ＞ Ｌ₁＝108mm
【０１００】
＜比較例１ｄ＞ Ｌ₁＝147mm
上記の実施例と比較例について、レール軌道面にボルトピッチの波打ちがある場合の、スライダの運動精度を調べた。案内レールの波打ちは、ほぼ正弦波とみなすことができ、片振幅は、Ａ＝0.0005mmである。
【０１０１】
図１４に、上下変位を低減する実施例１ａと、比較例１ｃ、１ｄについて、スライダの移動に伴う、上下方向の変位を調べた結果を示す。
実施例１ａは、比較例１ｃ、１ｄに比べて、上下方向の変位が小さいことがわかる。
【０１０２】
図１５に、ピッチング変位を低減する実施例１ｂと、比較例１ｃ、１ｄについて、スライダの移動に伴う、ピッチング方向の変位を調べた結果を示す。
実施例１ｂは、比較例１ｃ、１ｄに比べて、ピッチング方向の変位が小さいことがわかる。
＜実施例１の変形例＞
本変形例に用いられるリニアガイド装置は、図１２に示したリニアガイド装置５０と同等の構成をもつ。
ここで、本変形例に用いたリニアガイド装置は以下の詳細な数値を有する。
溝数 ：６溝
転動体接触角 ：α＝45°
転動体直径 ：Ｄａ＝4.7625mm
軌道面の半径 ：上下溝 ｒ₁＝2.428mm（転動体直径の51％）
中溝 ｒ₂＝2.571mm（転動体直径の54％）
オーバーサイズ量 ：上下溝 δ₀₁＝0.0075mm
中溝 δ₀₂＝0.0046mm
クラウニング部 ：形状＝円弧、長さＬｃ＝11mm、半径Ｒｃ＝4530mm
【０１０３】
なお、クラウニング部は、加工時は溝底方向に半径Ｒｃ´＝3200mmで加工、接触方向に換算した半径Ｒｃは、Ｒｃ＝Ｒｃ´／cosα＝4530mmとなる。
面取り部面取り量 ：Ｃ＝0.2mm
案内レールのボルトピッチ：Ｐ＝40mm 実施例１に比べて小さいので、スライダ全長を短くできる。
実施例１と同様にして、スライダ全長は、以下の範囲が望ましい。
上下変位を低減：47.2≦Ｌ₁≦55.2（ｍ＝1）
87.2≦Ｌ₁≦95.2（ｍ＝2）
127.2≦Ｌ₁≦135.2（ｍ＝３）
167.2≦Ｌ₁≦175.2（ｍ＝４）
ピッチング変位を低減：64.4≦Ｌ₁≦72.4（ξ_L＝1.43）
105.2≦Ｌ₁≦113.2（ξ_L＝2.45）
146.0≦Ｌ₁≦154.0（ξ_L＝3.47）
186.4≦Ｌ₁≦194.4（ξ_L＝4.48）
そして、本発明による実施例１ｅ，１ｆと比較例１ｇとして、以下を選択した。
【０１０４】
＜実施例１ｅ＞ Ｌ₁＝130mm 上下変位を低減するための条件式［数１４］を満たす。
【０１０５】
＜実施例１ｆ＞ Ｌ₁＝150mm ピッチング変位を低減するための条件式［数２１］を満たす。
【０１０６】
＜比較例１ｇ＞ Ｌ₁＝140mm
上記の実施例と比較例について、レール軌道面にボルトピッチの波打ちがある場合の、スライダの運動精度を調べた。案内レールの波打ちは、ほぼ正弦波とみなすことができ、片振幅は、Ａ＝0. 0005mmである。
【０１０７】
図１６に、上下変位を低減する実施例１ｅと、比較例１ｇについて、スライダの移動に伴う、上下方向の変位を調べた結果を示す。
実施例１ｅは、比較例１ｇに比べて、上下方向の変位が小さいことがわかる。
【０１０８】
図１７に、ピッチング変位を低減する実施例１ｆと、比較例１ｇについて、スライダの移動に伴う、ピッチング方向の変位を調べた結果を示す。
実施例１ｆは、比較例１ｇに比べて、ピッチング方向の変位が小さいことがわかる。
上述したように、案内レールの軌道面の波打ちによるスライダの姿勢変化を低減することができる。
【０１０９】
＜実施例２＞
図１８（ａ），（ｂ），（ｃ），（ｄ）に示すように、実施例２に用いられるテーブル装置は、図８に示したリニアガイド装置３０と同等の構成をもつ。
ここで、実施例２に用いたテーブル装置は以下の詳細な数値を有する。
案内レールのボルトピッチ：Ｐ＝80mm
オーバーサイズ量 ：δ₀＝0.0068mm （両スライダとも同一である）
クラウニング部 ：形状＝円弧、長さＬｃ＝6.45mm、半径Ｒｃ＝1710mm （両スライダとも同一である）
面取り部面取り量 ：Ｃ＝0.2mm
そして、本発明による実施例と、本発明によらない比較例として、以下を選択した。
【０１１０】
＜実施例２ａ＞ 図１８（ａ）に示す。上下変位を低減するための条件式［数３１］を満たす。
スライダ３２ ：軌道面有効長Ｌ_A＝156.35mm、全長Ｌ_1A＝163mm
スライダ３３ ：軌道面有効長Ｌ_B＝76.35mm、全長Ｌ_1B＝83mm
スライダ中心間距離：Ｓ＝180mm
ここで、Ｌ_A／Ｐ＝1.95，Ｌ_B／Ｐ＝0.954なので、［数３１］を満たす（ｍ_A＝2，ｍ_B＝1に対して）。
【０１１１】
＜実施例２ｂ＞ 図１８（ｂ）に示す。上下変位を低減するための条件式［数３４］を満たす。
スライダ３２，３３：軌道面有効長Ｌ_T＝63.35mm、全長Ｌ_1T＝70mm （両スライダとも同一である）
スライダ中心間距離：Ｓ＝120mm
ここで、Ｓ／Ｐ＝1.5なので、［数３４］を満たす（ｎ＝1に対して）。
【０１１２】
＜実施例２ｃ＞ 図１８（ｃ）に示す。ピッチング変位を低減するための条件式［数４１］を満たす。
スライダ３２，３３：軌道面有効長Ｌ_T＝140.35mm、全長Ｌ_1T＝147mm （両スライダとも同一である）
スライダ中心間距離：Ｓ＝220mm
ここで、Ｌ_T／Ｐ＝1.75，Ｓ／Ｐ＝2.75なので、［数４１］を満たす（ξ_T＝1.8，η_T＝2.75に対して）。
【０１１３】
＜実施例２ｄ＞ 図１８（ｄ）に示す。上下変位及びピッチング変位を同時に低減するための条件式［数４３］を満たす。
スライダ３２，３３：軌道面有効長Ｌ_T＝156.35mm、全長Ｌ_1T＝163mm （両スライダとも同一である）
スライダ中心間距離：Ｓ＝200mm
ここで、Ｌ_T／Ｐ＝1.95，Ｓ／Ｐ＝2.5なので、［数４３］を満たす（ｍ_T＝2，ｎ＝2に対して）。
【０１１４】
＜比較例２ｅ＞ 本発明によらない。
スライダ ：軌道面有効長Ｌ_T＝63.35mm、全長Ｌ_1T＝70mm （両スライダとも同一である）
スライダ中心間距離：Ｓ＝160mm
【０１１５】
＜比較例２ｆ＞ 本発明によらない。
スライダ ：軌道面有効長Ｌ_T＝140.35mm、全長Ｌ_1T＝147mm （両スライダとも同一である）
スライダ中心間距離：Ｓ＝250mm
上記各実施例と比較例について、レール軌道面にボルトピッチの波打ちがある場合の、スライダの運動精度を調べた。ここで、案内レールの波打ち片振幅は、Ａ＝0.0005mmである。
【０１１６】
図１９，２０，２１，２２に、上下変位を低減する実施例２ａ，２ｂ，２ｄと、比較例２ｅ，２ｆについて、スライダの移動に伴う上下方向の変位を調べた結果を示す。
いずれの実施例においても、比較例に比べて上下方向の変位が小さいことがわかる。
【０１１７】
図２３，２４，２５に、ピッチング変位を低減する実施例２ｃ，２ｄと、比較例２ｅ，２ｆについて、スライダの移動に伴うピッチング方向の変位を調べた結果を示す。
いずれの実施例においても、比較例に比べてピッチング方向の変位が小さいことがわかる。
上述したように、案内レールの軌道面の波打ちによるスライダの姿勢変化を低減できる。
【０１１８】
＜実施例３＞
図２６（ａ），（ｂ）に示すように、実施例３に用いられるテーブル装置は、単一のスライダ３２に、２個のスライダ軌道面３２ａ，３２ｂを有し、端部にクラウニング部３２ｃ，３２ｃが形成されている。スライダ軌道面３２ａ，３２ｂの中央部には、転動体が荷重を受けない無負荷部３２ｄが形成されている。
ここで、実施例３に用いたテーブル装置は以下の詳細な数値を有する。
各軌道面の有効長 ：Ｌ_T＝78mm
軌道面の中心間距離：Ｓ＝120mm
なお、無負荷部３２ｄは、逃げ量＝19μmであり、クラウニング部３２ｃ，３２ｃを含む軌道面と同時にＮＣ研削加工によって加工される。このテーブル装置では、スライダ３２が単一であるため、組み立てを簡単に行うことができる。
【０１１９】
＜実施例４＞
図２７（ａ），（ｂ），（ｃ）に示すように、実施例４に用いられるテーブル装置は、４個のスライダ３２，３２，３２，３２を用いた場合について、上下方向及びピッチング方向の両方の姿勢変化を低減するように構成されている。実施例４では、いずれも、上下変位及びピッチング変位を同時に低減する条件式［数４３］を満たす、単一の案内レール３１と２個のスライダ３２，３２との組合せを２組配置して、１個のテーブル装置を構成した。
【０１２０】
＜実施例４ａ＞ 図２７（ａ）に示す。条件式［数４３］を満たす、単一の案内レールと２個のスライダとの組を並べて配置した。
案内レールのボルトピッチ ：Ｐ＝80mm
図中左側２個のスライダの組：各スライダの軌道面有効長＝80mm
スライダ中心間距離＝120mm
図中右側２個のスライダの組：各スライダの軌道面有効長＝160mm
スライダ中心間距離＝200mm
【０１２１】
＜実施例４ｂ＞ 図２７（ｂ）に示す。条件式［数４３］を満たす、単一の案内レールと２個のスライダとの組を入れ子式に配置した。
案内レールのボルトピッチ ：Ｐ＝80mm
図中内側２個のスライダの組：各スライダの軌道面有効長＝80mm
スライダ中心間距離＝120mm
図中外側２個のスライダの組：各スライダの軌道面有効長＝160mm
スライダ中心間距離＝440mm
【０１２２】
＜実施例４ｃ＞ 図２７（ｃ）に示す。条件式［数４３］を満たす、単一の案内レールと２個のスライダとの組を交差して配置した。
案内レールのボルトピッチ ：Ｐ＝80mm
図中左端と右から２番目のスライダの組：各スライダの軌道面有効長＝80mm
スライダ中心間距離＝200mm
図中右端と左から２番目のスライダの組：各スライダの軌道面有効長＝80mm
スライダ中心間距離＝200mm
ここで、実施例４ａ〜４ｃと同様にして、６個以上の偶数個のスライダを用いてテーブル装置を構成することもできる。
また、実施例４ａ〜４ｃにおいて、隣接するスライダを一体化してスライダの個数を減らしても、同様の効果を得ることができる。スライダを一体化する方法としては、複数個のスライダを連結部材等で連結しても良いし、初めから一体構造のスライダを作製しても良い。
【０１２３】
＜実施例４ｄ＞ 図２８（ａ）に示す。実施例４ａにおいての隣接するスライダ（内側の２個）を隣接させて、単一部材で構成した。
スライダの軌道面有効長：左＝80mm、中央＝240mm、右＝160mm
スライダの中心間距離 ：左〜中央＝200mm、中央〜右＝240mm
【０１２４】
＜実施例４ｅ＞ 図２８（ｂ）に示す。実施例４ｂにおいての隣接するスライダ（左側の２個）を隣接させて、単一部材で構成した。
スライダの軌道面有効長：左＝240mm、中央＝80mm、右＝160mm
スライダの中心間距離 ：左〜中央＝200mm、中央〜右＝200mm
【０１２５】
＜実施例４ｄ＞ 図２８（ｃ）に示す。実施例４ｃにおいての隣接するスライダ（内側の２個）を隣接させて、単一部材で構成した。
スライダの軌道面有効長：左＝80mm、中央＝160mm、右＝80mm
スライダの中心間距離 ：左〜中央＝160mm、中央〜右＝160mm
【０１２６】
実施例４においても、上下方向の変位及びピッチング方向の変位が小さい。そのため、案内レールの軌道面の波打ちによるスライダの姿勢変化を低減することができる。
【０１２７】
＜実施例５＞
図２９，３０に示すように、実施例５に用いられるテーブル装置は、実施例２〜４で述べた単一の案内レールとスライダとの組からなるテーブル装置を平行に配置して、１個のテーブル装置を構成した。ここでは、案内レールのボルトピッチは、案内レール毎に同じであっても、異なっていても良い。
【０１２８】
＜実施例５ａ＞ 図２９に示す。実施例２ｄのテーブル装置を２個平行に並べて構成した。
【０１２９】
＜実施例５ｂ＞ 図３０に示す。実施例４ａと実施例４ｅのテーブル装置を平行に並べて構成した。
【０１３０】
実施例５においても、上下方向の変位及びピッチング方向の変位が小さい。そのため、案内レールの軌道面の波打ちによるスライダの姿勢変化を低減することができる。
【０１３１】
なお、本発明は前述した実施形態に限定されるものではなく、適宜な変形、改良等が可能である。
例えば、ボールや円筒ころである転動体の列は２列、４列、６列に限らず、それ以上の複数対配されたリニアガイド装置及びテーブル装置に本発明を用いても良い。
【０１３２】
【発明の効果】
以上説明したように、本発明のリニアガイド装置によれば、スライダ軌道面有効長Ｌｅと、レール軌道面波打ち波長Ｐとが、ｍ−0.1≦Ｌｅ／Ｐ≦ｍ＋0.1に設定される。
したがって、スライダがどの位置に移動した場合においても、スライダの姿勢変化がゼロになるように、スライダ軌道面の有効長さと波打ち波長との関係が定められる。よって、レール軌道面に波打ちが生じていても、スライダの姿勢変化を小さく保つことができ、ボルト締結等によって生じる軌道面の周期的な変形がスライダの運動精度に及ぼす影響を小さくすることができる。
【０１３３】
また、ξ_Lを方程式sinπξ_L−πξ_Lcosπξ_L＝0の解として、レール軌道面波打ち波長Ｐと、スライダ軌道面有効長Ｌｅとが、ξ_L−0.1≦Ｌｅ／Ｐ≦ξ_L＋0.1に設定されることによって、レール軌道面に波打ちが生じていても、スライダの姿勢変化を小さく保つことができ、ボルト締結によって生じる軌道面の周期的な変形がスライダの運動精度に及ぼす影響を小さくすることができる。
【０１３４】
また、本発明のテーブル装置によれば、２個のスライダ軌道面有効長Ｌ_A，Ｌ_Bと、レール軌道面波打ち波長Ｐとが、ｍ_A−0.1≦Ｌ_A／Ｐ≦ｍ_A＋0.1で且つ、ｍ_B−0.1≦Ｌ_B／Ｐ≦ｍ_A＋0.1に設定される。
したがって、テーブルがどの位置に移動した場合においても、テーブルの姿勢変化がほぼゼロになるように、スライダ軌道面の有効長さと、波打ち波長との関係が定められる。よって、レール軌道面に波打ちが生じていても、テーブルの姿勢変化を小さく保つことができ、ボルト締結等によって生じる軌道面の周期的な変形がテーブルの運動精度に及ぼす影響を小さくすることができる。
【０１３５】
また、２個が同一である場合のスライダ軌道面有効長Ｌ_Tと、レール軌道面波打ち波長Ｐと、スライダ軌道面中心間距離Ｓとが、ｍ_T−0.1≦Ｌ_T／Ｐ≦ｍ_T＋0.1または、ｎ＋0.4≦Ｓ／Ｐ≦ｎ＋0.6に設定されることによって、レール軌道面に波打ちが生じていても、テーブルの姿勢変化を小さく保つことができ、ボルト締結等によって生じる軌道面の周期的な変形がテーブルの運動精度に及ぼす影響を小さくすることができる。
【０１３６】
そして、ξ_T，η_Tを方程式πη_Tsinπξ_Tsinπη_T＋{sinπξ_T−πξ_Tcosπξ_T}cosπη_T＝0の解として、２個が同一のスライダ軌道面有効長Ｌ_Tと、レール軌道面波打ち波長Ｐと、スライダ軌道面中心間距離Ｓとが、ξ_T−0.1≦Ｌ_T／Ｐ≦ξ_T＋0.1で且つ、η_T−0.１≦Ｓ／Ｐ≦η_T＋0.1に設定されることによって、レール軌道面に波打ちが生じていても、テーブルの姿勢変化を小さく保つことができ、ボルト締結等によって生じる軌道面の周期的な変形がテーブルの運動精度に及ぼす影響を小さくすることができる。
【０１３７】
更に、２個が同一のスライダ軌道面有効長Ｌ_Tと、レール軌道面波打ち波長Ｐと、スライダ軌道面中心間距離Ｓとが、ｍ_T−0.1≦Ｌ_T／Ｐ≦ｍ_T＋0.1で且つ、ｎ＋0.4≦Ｓ／Ｐ≦ｎ＋0.6に設定されることによって、レール軌道面に波打ちが生じていても、テーブルの姿勢変化を小さく保つことができ、ボルト締結等によって生じる軌道面の周期的な変形がテーブルの運動精度に及ぼす影響を小さくすることができる。
【０１３８】
また更に、複数個のテーブル装置を組み合わせて一つに構成したり、レール軌道面波打ち波長Ｐを案内レールの取付けボルトピッチに置き換えたり、レール軌道面波打ち波長Ｐを横押し板の取付け間隔に置き換えたりすることによって、これらの場合にも、レール軌道面に波打ちが生じていても、テーブルの姿勢変化を小さく保つことができ、ボルト締結等によって生じる軌道面の周期的な変形がテーブルの運動精度に及ぼす影響を小さくすることができる。
以上によって、ボルト締結等によって生じるレール軌道面の周期的な変形がスライダの運動精度に及ぼす影響を小さくすることができるリニアガイド装置及びテーブル装置を提供することができる。
【図面の簡単な説明】
【図１】本発明に係る第１実施形態のリニアガイド装置の外観斜視図である。
【図２】（ａ）は図１に示したリニアガイド装置の断面図、（ｂ）は（ａ）の（ａ−ａ）線断面図である。
【図３】図１に示したリニアガイド装置におけるスライダの拡大断面図である。
【図４】図１に示したリニアガイド装置におけるスライダの拡大断面図である。
【図５】図１に示したリニアガイド装置におけるレール軌道面の波打ちの説明図である。
【図６】図１に示すリニアガイド装置におけるスライダの上下方向変位の片振幅の特性図である。
【図７】図１に示すリニアガイド装置におけるスライダのピッチング方向変位の片振幅の特性図である。
【図８】本発明に係る第１実施形態のテーブル装置の外観斜視図である。
【図９】図８に示すテーブル装置におけるレール軌道面の波打ちの説明図である。
【図１０】図８に示すテーブル装置におけるテーブルのピッチング方向の姿勢変化をゼロにする条件の説明図である。
【図１１】本発明に係る第２実施形態のリニアガイド装置の外観斜視図である。
【図１２】本発明に係る第３実施形態のリニアガイド装置の断面図である。
【図１３】本発明に係る第４実施形態のリニアガイド装置の断面図である。
【図１４】リニアガイド装置の実施例におけるスライダの移動に伴う上下方向の変位を調べたグラフである。
【図１５】リニアガイド装置の実施例におけるスライダの移動に伴うピッチング方向の変位を調べたグラフである。
【図１６】リニアガイド装置の実施例におけるスライダの移動に伴う上下方向の変位を調べたグラフである。
【図１７】リニアガイド装置の実施例におけるスライダの移動に伴うピッチング方向の変位を調べたグラフである。
【図１８】（ａ）はテーブル装置の実施例の正面図、（ｂ）はテーブル装置の実施例の正面図、（ｃ）はテーブル装置の実施例の正面図、（ｄ）はテーブル装置の実施例の正面図である。
【図１９】テーブル装置の実施例におけるスライダの移動に伴う上下方向の変位を調べたグラフである。
【図２０】テーブル装置の実施例におけるスライダの移動に伴う上下方向の変位を調べたグラフである。
【図２１】テーブル装置の実施例におけるスライダの移動に伴う上下方向の変位を調べたグラフである。
【図２２】テーブル装置の実施例におけるスライダの移動に伴う上下方向の変位を調べたグラフである。
【図２３】テーブル装置の実施例におけるスライダの移動に伴うピッチング方向の変位を調べたグラフである。
【図２４】テーブル装置の実施例におけるスライダの移動に伴うピッチング方向の変位を調べたグラフである。
【図２５】テーブル装置の実施例におけるスライダの移動に伴うピッチング方向の変位を調べたグラフである。
【図２６】（ａ）はテーブル装置の実施例の正面図、（ｂ）は（ａ）のスライダの部分断面図である。
【図２７】（ａ）はテーブル装置の実施例の正面図、（ｂ）はテーブル装置の実施例の正面図、（ｃ）はテーブル装置の実施例の正面図である。
【図２８】（ａ）はテーブル装置の実施例の正面図、（ｂ）はテーブル装置の実施例の正面図、（ｃ）はテーブル装置の実施例の正面図である。
【図２９】テーブル装置の実施例の外観斜視図である。
【図３０】テーブル装置の実施例の外観斜視図である。
【図３１】従来のテーブル装置の外観斜視図である。
【図３２】従来のテーブル装置を用いた測定装置の正面図である。
【図３３】図３２とは異なる構造の測定装置の正面図である。
【図３４】従来のリニアガイド装置の正面図である。
【図３５】図３４とは異なる構造のリニアガイド装置の正面図である。
【図３６】（ａ），（ｂ）は図３５とは異なる構造のリニアガイド装置の正面図である。
【図３７】（ａ），（ｂ），（ｃ）はリニアガイド装置における波打ちの説明図である。
【符号の説明】
１０，４０，５０，６０ リニアガイド装置
１１ 案内レール
１２ スライダ
１３ 転動体
１５ レール軌道面
１９ スライダ軌道面
２０ クラウニング部
２１ 面取り部
３０ テーブル装置
３１ 案内レール
３２，３３ スライダ
３４ テーブル
１２１ 横押し板[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a linear guide device used in various machines such as a semiconductor manufacturing device, a precision processing machine, and a precision measuring instrument, and a table device configured by using a plurality of the linear guide devices.
[0002]
[Prior art]
The linear guide device used to guide the guided object linearly includes a guide rail extending in the axial direction, a slider disposed on the guide rail and assembled to be movable in the axial direction of the guide rail, and a ball What is provided with the rolling element which is is known.
[0003]
Rail raceways for sliding the rolling elements are formed on both side surfaces of the guide rail, and the slider raceway surface for sliding the rolling elements in the rolling element circulation path that holds the rolling elements while circulating them. Is formed.
[0004]
In the rail surface of the guide rail, a plurality of bolt holes penetrating vertically are formed along the axial direction. The guide rail is fixed to the processing table by screwing a plurality of bolts into the machine base through the bolt holes.
[0005]
The slider has a sliding surface on the bottom surface of the guide rail, and the moving body of various machines such as semiconductor manufacturing equipment, precision processing machines, and precision measuring instruments is fixed by bolt fastening. When moving, the rolling elements circulate in the rolling element circulation path of the slider while rolling between the rail raceway surface of the guide rail and the slider raceway surface of the slider, thereby moving the guide rail in the axial direction. To support smoothly.
[0006]
Since the linear guide device is used in various machines such as a semiconductor manufacturing device, a precision processing machine, and a precision measuring instrument, the motion accuracy of the linear guide device directly affects the processing accuracy and measurement accuracy of these various machines.
[0007]
Such a linear guide device may be used alone, or may be used as a table device in which a plurality of linear guide devices are combined.
[0008]
As shown in FIG. 31, the motion accuracy of the table device (linear guide device) 70 by the combination of the guide rail 71 and the slider 72 includes motion accuracy in the translational direction and motion accuracy in the tilt direction.
Among these, the motion accuracy in the translational direction includes the motion accuracy in the vertical direction and the horizontal direction. As the motion accuracy in the tilt direction, there are motion accuracy in the pitching direction p, the yawing direction y, and the rolling direction r, and the motion accuracy in which direction is important depends on the application in which the linear guide device or the table device is used.
[0009]
FIG. 32 shows a table device 80 in the case of constituting a part measuring apparatus in which the vertical movement accuracy is important. In the table device 80, a table 83 is disposed on a slider 82 assembled to a guide rail 81, and a measuring element 84 on the table 83 contacts a component 85. In such a table device 80, the vertical displacement of the table 83 directly changes the relative distance between the measuring element 84 and the component 85. Therefore, it is necessary to keep the vertical displacement as small as possible. On the other hand, even if the table 83 is slightly displaced in the pitching direction, the relative distance between the component 85 (measurement target) and the measuring element 84 hardly changes. This is because the probe 84 is located almost directly above the center of rotation of the table 83. Therefore, the importance of the movement accuracy in the pitching direction is low.
[0010]
FIG. 33 shows a table device 90 in the case of constituting a part measuring device in which the motion accuracy in the pitching direction is important. In the table device 90, a table 93 is arranged on a slider 92 assembled to the guide rail 91, and the measuring element 94 on the table 93 contacts the component 95.
In such a table device 90, the measurement point is greatly overhanging from the center of the table, and even if the pitching displacement of the table 93 is slight, it appears as a large vertical displacement at the measurement point. In such a table device 90, the motion accuracy in the pitching direction is more important than the motion accuracy in the vertical direction of the table 93.
[0011]
As described above, depending on the application of the linear guide device or the table device, it depends on whether the motion accuracy in the translation direction or the tilt direction is important. Of course, in applications that require extremely high accuracy, it is needless to say that the motion accuracy in both the translation direction and the tilt direction is important.
[0012]
In the normal linear guide apparatus 100 shown in FIG. 34, the guide rail 101 is fixed to the machine base by fastening the bolt by passing the bolt 102 through the bolt hole 101a from above the guide rail 101. When the bolt is fastened, the space between the bottom surface of the bolt 102 and the bottom surface of the guide rail 101 is compressed by the axial force of the bolt 102, and as a result, the guide rail 101 is elastically deformed.
At this time, since the rail track surface formed on the guide rail 101 also sinks due to the elastic deformation of the surroundings, undulations at the bolt pitch appear on the rail track surface. Such waviness of the rail track surface directly affects the motion accuracy of the slider 103 traveling on the guide rail 101.
[0013]
As a method for preventing the wavy phenomenon of the rail raceway surface in the guide rail, when machining the rail raceway surface, a method is known in which the guide rail is bolted to the machining table with a prescribed fastening torque. And also at the time of use of a linear guide apparatus, a guide rail is bolt-fastened with the same fastening torque as the time of a process. In this way, if the rate of elastic deformation of the guide rail at the time of processing is the same as that at the time of use, the waviness of the rail track surface at the time of use can be reduced.
However, in reality, there are variations in axial force at the time of bolt fastening, and differences in the dimensions and materials of the mounting base between processing and use. For this reason, it is difficult to make the amount of change in the rail raceway perfectly match during processing and use. Therefore, it is difficult to completely prevent the rail track surface from corrugating.
[0014]
With respect to these problems, the present applicant has defined the counterbore depth of the bolt holes provided in the guide rail so that the waviness of the rail surface can be reduced (see, for example, Patent Document 1). This makes it possible to reduce the deformation of the rail track surface even if there is some variation in the axial force at the time of bolt fastening.
[0015]
[Patent Document 1]
Japanese Patent Laid-Open No. 8-303459 (page 3, FIG. 1)
[0016]
[Problems to be solved by the invention]
However, recently, to reduce the weight of machinery and equipment, the mounting base has been made thinner and light metal using aluminum alloy, etc., and the dimensions and material of the mounting base during processing and use are always the same. It has become difficult to make them identical. Therefore, a difference is easily generated in the deformation amount of the rail raceway surface between processing and use.
Moreover, even if the counterbore depth of the bolt hole is defined, the reduction of the wavy phenomenon on the rail raceway surface may be insufficient.
[0017]
Moreover, it takes a considerable amount of time and labor to fasten the bolts during processing. From the viewpoint of productivity, a quick fixing method such as a magnet chuck is desired.
As shown in FIG. 35, in the linear guide device 110 that is fixed to the work table by screwing a bolt into the screw hole 113 provided in the bottom surface 112 arranged on the lower surface of the guide rail 111, the fixing at the time of processing is performed. A magnet chuck is effective to perform the process quickly.
However, with the fixing method using the magnet chuck, it is difficult to prevent the rail raceway surface from being waved in the state of use, that is, after the bolt is tightened.
[0018]
Further, the rail raceway surface may be processed without fixing the guide rail to the processing table. This is the case when performing processing by rolling. Also in this case, it is difficult to prevent the wavy phenomenon on the rail raceway surface in the state after the bolt is fastened.
[0019]
In addition, as shown in FIGS. 36A and 36B, the guide rail 124 may be fixed to the machine base 125 by pressing against the lateral reference plane 123 using the lateral pushing plate 121 and the bolt 122. is there. Also in this case, the horizontal pushing plate 121 causes the rail raceway surface to undulate in the left-right direction at the mounting cycle of the horizontal pushing plate 121, and it is difficult to prevent this waving.
[0020]
As described above, it is very difficult to prevent the rail raceway surface from wavy. For this reason, the deterioration of the slider movement accuracy due to the wave of the rail track surface often becomes a problem.
[0021]
Here, for example, as shown in FIGS. 37 (a), (b), and (c), when the rail track surface 132 of the guide rail 131 is wavy in the vertical direction, the linear guide device used for precise applications. Then, since a preload is applied to the rolling elements to prevent the slider 133 from rattling, it is necessary to balance the preload in the slider 133 when no external force is applied to the slider 133.
For this reason, when the slider 133 is in the position A, the slider 133 is tilted counterclockwise. Subsequently, when the slider 133 moves to the position B, the slider 133 is tilted clockwise. As described above, when the rail raceway surface 132 is wavy, the slider 133 changes its posture along with the movement.
The slider 133 causes the posture variation in the vertical direction in the same manner as the posture variation in the pitching direction. Further, when the rail raceway surface 132 is undulated in the left-right direction, the slider 133 changes its posture in the left-right direction as well as the yawing direction.
[0022]
The present invention has been made in view of the above circumstances, and provides a linear guide device and a table device that can reduce the influence of periodic deformation of a rail raceway surface caused by bolt fastening on the motion accuracy of a slider. That is the purpose.
[0023]
[Means for Solving the Problems]
  The said subject which concerns on this invention can be solved by following (1)-(11).
(1) A guide rail having a rail track surface, a slider having a slider track surface disposed opposite to the rail track surface and moving along the rail track surface, and the rail track surface and the slider track surface. A linear guide device including a rolling element that is freely rollable between the slider raceway surfaces, wherein the wavy wavelength of the rail raceway surface is P and m is an integer of 1 or more.ofEffective length Le and the rail track surfaceofThe linear guide device characterized in that the waving wavelength P is set to m−0.1 ≦ Le / P ≦ m + 0.1.
[0024]
(2) a guide rail having a rail track surface, a slider having a slider track surface disposed opposite to the rail track surface and moving along the rail track surface, and the rail track surface and the slider track surface. A linear guide device provided with rolling elements arranged in a freely rotatable manner between them, ξ_LThe equation sinπξ_L−πξ_Lcosπξ_L= 0, the rail raceway surfaceofRippling wavelength P and the slider track surfaceofEffective length Le is ξ_L−0.1 ≦ Le / P ≦ ξ_LIt is set to +0.1, The linear guide apparatus as described in said (1) characterized by the above-mentioned.
[0025]
  (3) A single guide rail having a rail track surface, a slider having a slider track surface disposed opposite to the rail track surface and moving along the rail track surface, the rail track surface and the slider track A rolling element that is freely rollable between the surface and the slide.DaA table device provided on the table, wherein the slider track surface has an effective length L_A, L_BThe wavy wavelength of the rail raceway surface is P, m_A, M_BWhere each slider track surface is an integer of 1 or more.ofEffective length L_A, L_BAnd the rail track surfaceofThe wavy wavelength P is m_A-0.1 ≦ L_A/ P ≦ m_A+0.1 and m_B-0.1 ≦ L_B/ P ≦ m_BA table device characterized by being set to +0.1.
[0026]
(4) A single guide rail having a rail track surface, a slider having a slider track surface disposed opposite to the rail track surface and moving along the rail track surface, the rail track surface and the slider track A table device comprising a rolling element that is freely rollable between a surface and a table that is arranged on the slider, wherein the slider raceway surface has the same effective length L_TThe rail raceway surfaceofThe waved wavelength is P, m_T, N is an integer equal to or greater than 1, and S is the distance between the centers of the two slider raceway surfaces.ofEffective length L_TAnd the rail track surfaceofRippling wavelength P and the slider track surfaceofThe center-to-center distance S is m_T-0.1 ≦ L_T/ P ≦ m_T+0.1 or n + 0.4 ≦ S / P ≦ n + 0.6 is set.
[0027]
(5) A single guide rail having a rail track surface, a slider having a slider track surface disposed opposite to the rail track surface and moving along the rail track surface, the rail track surface and the slider track A table device comprising: a rolling element that is movably arranged between the surface and a table arranged on the slider, wherein the slider raceway surface has the same effective length L_TThe rail track surface wavy wavelength is P, the center distance between the two slider track surfaces is S, and ξ_T, Η_TThe equation πη_Tsinπξ_Tsinπη_T+ {Sinπξ_T−πξ_Tcosπξ_T} cosπη_T= 0, the slider raceway surfaceofEffective length L_TThe wavy wavelength P of the rail track surface, and the slider track surfaceofThe center-to-center distance S is ξ_T-0.1 ≦ L_T/ P ≦ ξ_T+0.1 and η_T−0.1 ≦ S / P ≦ η_TA table device characterized by being set to +0.1.
[0028]
(6) A single guide rail having a rail track surface, a slider having a slider track surface disposed opposite to the rail track surface and moving along the rail track surface, the rail track surface and the slider track A table device comprising a rolling element that is freely rollable between a surface and a table that is arranged on the slider, wherein the slider track surface has the same effective length L_TAnd the wavy wavelength of the rail raceway surface is P, m_T, N is an integer equal to or greater than 1, and S is the distance between the centers of the two slider raceway surfaces.ofEffective length L_TAnd the rail track surfaceofRippling wavelength P and the slider track surfaceofThe center-to-center distance S is m_T-0.1 ≦ L_T/ P ≦ m_T+0.1 and n + 0.4 ≦ S / P ≦ n + 0.6 is set.
[0029]
(7) A table device comprising a plurality of the table devices according to (6) combined into one.
[0030]
(8) Rail rail surfaceofThe linear guide device or the table device according to any one of (1) to (7), wherein the wavy wavelength P is set to a guide rail mounting bolt pitch.
[0031]
(9) The rail track surfaceofThe linear guide device or the table device according to any one of (1) to (7), wherein the wavy wavelength P is set as the mounting interval of the laterally pushing plates.
[0032]
(10) A chamfered portion is formed at an end of the slider raceway surface, and the total length of the slider raceway surface is L₁The length of the chamfered portion is C, and the slider raceway surfaceofAs an effective length Le, Le = L₁-2C is used, The linear guide apparatus or table apparatus in any one of said (1)-(9) characterized by the above-mentioned.
[0033]
(11) A crowning portion is formed near an end portion of the slider raceway surface, and a chamfered portion is formed at an end portion of the crowning portion.₁And the length of the crowning portion is L_CThe length of the chamfered portion is C, and the slider raceway surfaceofAs an effective length Le, Le = L₁-(L_C+ C) is used, The linear guide device or the table device according to any one of (1) to (9) above.
[0034]
According to the linear guide device having the above-described configuration, the slider raceway surface effective length Le and the rail track surface corrugation wavelength P are set to m−0.1 ≦ Le / P ≦ m + 0.1.
Therefore, the relationship between the effective length of the slider track surface and the wavy wavelength is determined so that the change in the attitude of the slider becomes almost zero regardless of the position of the slider. As a result, even if the rail track surface is wavy, the change in the posture of the slider can be kept small, and the influence of periodic deformation of the track surface caused by bolt fastening etc. on the slider motion accuracy can be reduced. it can.
[0035]
And ξ_LThe equation sinπξ_L−πξ_Lcosπξ_L= 0, the rail track surface wavy wavelength P and the slider track surface effective length Le are ξ_L−0.1 ≦ Le / P ≦ ξ_LEven if it is set to +0.1, even if the rail raceway surface is wavy, the change in the posture of the slider can be kept small. The influence can be reduced.
According to the table device having the above configuration, the two slider track surface effective lengths L_A, L_BAnd the rail track surface wavy wavelength P is m_A-0.1 ≦ L_A/ P ≦ m_A+0.1 and m_B-0.1 ≦ L_B/ P ≦ m_ASet to +0.1.
Accordingly, the relationship between the effective length of the slider track surface and the waved wavelength is determined so that the position change of the table becomes almost zero regardless of the position of the table. As a result, even if the rail track surface is wavy, the change in the posture of the table can be kept small, and the influence of periodic deformation of the track surface caused by bolt fastening etc. on the motion accuracy of the table can be reduced. it can.
[0036]
Also, the effective length L of the slider track surface when the two are the same_TAnd the rail track surface wavy wavelength P and the slider track surface center distance S are m_T-0.1 ≦ L_T/ P ≦ m_T+0.1 or n + 0.4 ≦ S / P ≦ n + 0.6 may be set. By doing so, even if the rail track surface is wavy, the change in the posture of the table can be kept small, and the influence of periodic deformation of the track surface caused by bolt fastening etc. on the motion accuracy of the table is reduced. be able to.
[0037]
And ξ_T, Η_TThe equation πη_Tsinπξ_Tsinπη_T+ {Sinπξ_T−πξ_Tcosπξ_T} cosπη_T= 0 as the solution of two, the same slider track surface effective length L_TAnd the rail track surface wavy wavelength P and the slider track surface center distance S are ξ_T-0.1 ≦ L_T/ P ≦ ξ_T+0.1 and η_T−0.1 ≦ S / P ≦ η_TIt may be set to +0.1. By doing so, even if the rail track surface is wavy, the change in the posture of the table can be kept small, and the influence of periodic deformation of the track surface caused by bolt fastening etc. on the motion accuracy of the table is reduced. be able to.
[0038]
In addition, two slider track surface effective length L is the same_TAnd the rail track surface wavy wavelength P and the slider track surface center distance S are m_T-0.1 ≦ L_T/ P ≦ m_T+0.1 and n + 0.4 ≦ S / P ≦ n + 0.6 may be set. By doing so, even if the rail track surface is wavy, the change in the posture of the table can be kept small, and the influence of periodic deformation of the track surface caused by bolt fastening etc. on the motion accuracy of the table is reduced. be able to.
[0039]
Furthermore, a plurality of table devices are combined into one, or the rail track surface wavy wavelength P is replaced with the guide rail mounting bolt pitch, or the rail track surface wavy wavelength P is replaced with the mounting distance of the laterally pushing plate. In these cases, even if the rail track surface is wavy, the change in the posture of the table can be kept small, and periodic deformation of the track surface caused by bolt fastening or the like causes the table motion. The influence on accuracy can be reduced.
[0040]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.
1 is an external perspective view of the linear guide device according to the first embodiment of the present invention, FIG. 2A is a cross-sectional view of the linear guide device shown in FIG. 1, and FIG. FIG. 3 is an enlarged sectional view of the slider in the linear guide device shown in FIG. 1, FIG. 4 is an enlarged sectional view of the slider in the linear guide device shown in FIG. 1, and FIG. FIG. 6 is a characteristic diagram of the half amplitude of the vertical displacement of the slider in the linear guide device shown in FIG. 1, and FIG. 7 is the pitching direction of the slider in the linear guide device shown in FIG. It is a characteristic figure of the half amplitude of displacement.
[0041]
FIG. 8 is an external perspective view of the table device of the first embodiment according to the present invention, FIG. 9 is an explanatory view of the wavy rail track surface in the table device shown in FIG. 8, and FIG. 10 is a table of the table device in the table device shown in FIG. FIG. 11 is an external perspective view of the linear guide device according to the second embodiment of the present invention, and FIG. 12 is an illustration of the linear guide device of the third embodiment according to the present invention. FIG. 13 is a cross-sectional view of a linear guide device according to a fourth embodiment of the present invention, FIG. 14 is a graph in which the vertical displacement associated with the movement of the slider in the example of the linear guide device is examined, and FIG. FIG. 16 is a graph showing the displacement in the pitching direction accompanying the movement of the slider in the embodiment of the guide device. FIG. 16 shows the vertical displacement accompanying the movement of the slider in the embodiment of the linear guide device. Graph examined, FIG. 17 is a graph examining the pitching direction of the displacement caused by the movement of the slider in the embodiment of the linear guide device.
[0042]
18A is a front view of an embodiment of the table device, FIG. 18B is a front view of the embodiment of the table device, FIG. 18C is a front view of the embodiment of the table device, and FIG. Is a front view of the embodiment of the table device, FIG. 19 is a graph in which the displacement in the vertical direction accompanying the movement of the slider in the embodiment of the table device is examined, FIG. 20 is a graph of the vertical direction accompanying the movement of the slider in the embodiment of the table device FIG. 21 is a graph in which the displacement in the vertical direction accompanying the movement of the slider in the embodiment of the table device is examined. FIG. 22 is a graph in which the displacement in the vertical direction according to the movement of the slider in the embodiment of the table device is examined. 23 is a graph in which the displacement in the pitching direction accompanying the movement of the slider in the embodiment of the table device is examined. FIG. 24 is a graph showing the displacement of the slider in the embodiment of the table device. Graph was examined pitching direction of the displacement, FIG. 25 is a graph examining the pitching direction of the displacement caused by the movement of the slider in the embodiment of the table device.
[0043]
26A is a front view of the embodiment of the table device, FIG. 26B is a partial sectional view of the slider of FIG. 26A, FIG. 27A is a front view of the embodiment of the table device, and FIG. (B) is a front view of the embodiment of the table device, FIG. 27 (c) is a front view of the embodiment of the table device, FIG. 28 (a) is a front view of the embodiment of the table device, and FIG. FIG. 28C is a front view of the embodiment of the table device, FIG. 29 is an external perspective view of the embodiment of the table device, and FIG. 30 is an external perspective view of the embodiment of the table device. .
In each of the following embodiments of the linear guide device, the members having the same configuration / action as those already described are given the same reference numerals in the drawing to simplify the description or Omitted.
[0044]
As shown in FIG. 1, a linear guide device 10 according to a first embodiment of the present invention includes a guide rail 11 and a slider 12 that is disposed on the guide rail 11 and is movably assembled in the axial direction of the guide rail 11. And a plurality of rolling elements 13 which are balls.
[0045]
A rail surface 14 is formed on the upper surface of the guide rail 11, and rail track surfaces 15, 15 for sliding the rolling elements 13 are formed on the upper and lower sides of the guide rail 11. A plurality of bolt holes 17 penetrating vertically are formed in the rail surface 14 along the axial direction. The guide rail 11 is fixed to the processing table by bolts being screwed into the processing table via the bolt holes 17.
[0046]
In the slider 12, slider raceway surfaces (upper grooves, lower grooves) 19 and 19 for sliding the rolling elements 13 are formed in rolling element circulation paths 18 that hold the rolling elements 13 while circulating them.
[0047]
As shown in FIG. 2A, the rail track surfaces 15 and 15 of the guide rail 11 are arranged in pairs on both sides via the rail surface 14, and the rolling elements 13 are arranged in four rows.
[0048]
As shown in FIG. 2B, near the both end portions of the slider raceway surface 19 of the slider 12, there are formed gently inclined surface-like arcuate or linear crowning portions 20, 20. Chamfered portions 21 and 21 are formed at the ends of the portions 20 and 20. In the crowning portion 20, the rolling elements 13 do not receive a load in the vicinity of the end portion of the slider raceway surface 19.
[0049]
As shown in FIG. 3, when the crowning portion 20 has an arc shape, the length of the portion of the total length Lc of the crowning portion 20 where the rolling element 13 receives a load is referred to as a crowning portion effective length Lce.
Where δ₀: Oversize amount of rolling element 13, R_C: When the radius of the crowning portion 20 is seen in the cross section in the contact angle direction, the crowning portion effective length Lce is:
[Expression 1]

Calculated by
[0050]
As shown in FIG. 4, when the crowning portion 20 is linear, θ_C: When the inclination of the crowning portion as seen in the cross section in the contact angle direction is taken, the crowning portion effective length Lce is
[Expression 2]

Calculated by
[0051]
Total length L of slider raceway₁Of these, the length of the portion where the rolling element 13 receives the preload is referred to as the effective length of the slider raceway surface. The slider raceway surface effective length Les can be calculated by the following equation.
[Equation 3]

However, Les calculated by the above formula is Les> L₁In the case of −2C, or when there is no crowning part, Les is calculated by the following equation. Here, C is the length of the chamfered portion 21. When there is no chamfered portion, C = 0 is substituted.
[Expression 4]

[0052]
Lce is the oversize amount δ₀Therefore, Les in [Equation 3] is also δ₀Varies depending on the value of. In a normal linear guide device, the oversize amount of the rolling element 13 is changed for each application. For example, since a machine tool or the like requires rigidity, the oversize amount becomes large.
In addition, when it is desired to reduce the sliding resistance in a measuring instrument that requires high-speed driving, the oversize amount is reduced. In the case where the oversize amount can be specified, Les in [Equation 3] may be used as the effective length of the slider raceway surface 19. However, in a normal case, it is preferable to use the following expression Le that is determined regardless of the oversize amount, instead of the above-mentioned Les as the effective length of the slider raceway surface.
[Equation 5]

This Le is the maximum Les (= L when the oversize is changed.₁-2C) and the minimum Les (= L₁-2L_C) And the average value. Le represents an average slider track surface effective length for a wide range of oversizes. The above formula 5 is used when the crowning portions 20, 20 have the same shape.
[0053]
When the shapes of the crowning portions 20, 20 are different, Le is calculated by the following equation.
[Formula 6]

Where Lc₁, Lc₂: Length of crowning part at left and right ends
C₁, C₂: Chamfer length at left and right ends
It is.
[0054]
Next, in the following calculation, the following is assumed.
The waviness of the rail track surfaces 15, 15 is expressed as a sine wave.
The contact portion between the rolling element 13 and the raceway surfaces 15, 15, 19, and 19 is a linear spring that is uniformly and continuously distributed on the slider raceway surfaces 19 and 19.
[0055]
As shown in FIG. 5, when the x-axis is taken in the linear motion direction and the wavy amount y in the vertical direction at the position x of the rail track surfaces 15 and 15 is taken, the wavy amount y is expressed by the following equation. At this time, A is a constant, and is the half amplitude of the wave of the rail track surfaces 15 and 15.
[Expression 7]

[0056]
  The load per unit length that the i-th slider raceway surface receives at the position xfi (x)Is expressed by the following equation.
[Equation 8]

  here,
  X_S: Center coordinates of slider track surface
  Δz: Slider upward displacement
  Δφ: Slider displacement in the pitching direction
  ki: Vertical spring coefficient per unit length of the rolling element / tracking surface contact portion of the i-th slider raceway surface (determined by the specifications of the rolling element and the raceway surface and the contact angle).
It is.
[0057]
  Therefore, the sum F of the loads received by the slider 12 from the four rolling element rows is expressed by the x coordinate of the slide center as X._SAnd the effective length of the slider raceway surface is Le, and the following equation is obtained.
[Equation 9]

  Where K = k₁+ K₂+ K_Three+ K_Four
It is.
[0058]
The upward external force acting on the slider 12 is F₀Then, the following equation holds according to the balance of forces.
[Expression 10]

[0059]
From the above equations [Equation 9] and [Equation 10], the vertical displacement of the slider 12 is expressed by the following equation.
## EQU11 ##

[0060]
The piece amplitude Δv of the displacement in the vertical direction of the slider 12 caused by the wave of the guide rail 11 is expressed by the following equation as a ratio to the piece amplitude A of the wave.
[Expression 12]

Here, ξ = Le / P.
[0061]
FIG. 6 is a diagram illustrating the relationship between ξ and Δv / A. When the following equation holds, Δv becomes zero (0).
[Formula 13]

[0062]
Even if the above equation does not hold strictly, the vertical amplitude Δv can be made sufficiently small if ξ is in the range of the following equation.
[Expression 14]

Here, m is an integer of 1 or more (m = 1, 2, 3,...).
[0063]
  On the other hand, the sum M of the moments in the pitching direction received by the slider 12 from the four rows of rolling elements is expressed by the following equation.
[Expression 15]

[0064]
Further, the external moment in the pitching direction acting on the slider 12 is expressed as M.₀Then, from the balance of force, the following equation holds.
[Expression 16]

[0065]
  From the above equations [Equation 15] and [Equation 16], the displacement of the slider 12 in the pitching direction is expressed by the following equation.
[Expression 17]

[0066]
  The piece amplitude Δp in the displacement in the pitching direction of the slider 12 caused by the undulation is expressed by the following equation as a ratio to the maximum inclination Θ of the undulation. Where Θ = 2πA /PIt is.
[Formula 18]

  Here, ξ = Le / P.
[0067]
Next, FIG. 7 shows the magnitude relationship between ξ and Δp / Θ. When the following equation holds, Δp becomes zero (0).
[Equation 19]

[0068]
Ξ = ξ satisfying the above equation_LIs obtained by numerical calculation as follows.
[Expression 20]

[0069]
Even if the above equation does not hold strictly, the pitching amplitude Δp can be made sufficiently small if ξ is in the range of the following equation.
[Expression 21]

[0070]
According to the linear guide device 10 of the first embodiment, the slider track surface effective length Le and the rail track surface wavy wavelength P are set to m−0.1 ≦ Le / P ≦ m + 0.1. Accordingly, the relationship between the effective length of the slider raceway surface 19 and the waving wavelength is determined so that the change in the posture of the slider 12 becomes almost zero regardless of the position of the slider 12. Thereby, even if the rail raceway surface 15 is wavy, the change in the posture of the slider 12 can be kept small, and the influence of periodic deformation of the raceway surface caused by bolt fastening or the like on the motion accuracy of the slider 12 can be reduced. can do.
And ξ_LThe equation sinπξ_L−πξ_Lcosπξ_L= 0, the rail track surface wavy wavelength P and the slider track surface effective length Le are ξ_L−0.1 ≦ Le / P ≦ ξ_LEven if it is set to +0.1, even if the rail raceway surface 15 is wavy, the change in posture of the slider 12 can be kept small, and the periodic deformation of the raceway surface caused by bolt fastening or the like causes the movement of the slider 12. The influence on accuracy can be reduced.
[0071]
Next, the table device according to the first embodiment of the present invention will be described.
As shown in FIG. 8, the table device 30 includes a single guide rail 31, two sliders 32 and 33 that are arranged on the guide rail 31 so as to be movable in the axial direction of the guide rail 31, And a single table 34 disposed on the sliders 32 and 33.
Rail track surfaces are formed on both side surfaces of the guide rail 31, slider track surfaces are formed on the sliders 32 and 33, and rolling elements are disposed between the rail track surface and the slider track surface so as to be freely rollable.
[0072]
As shown in FIG. 9, the x axis is taken in the linear motion direction. As in the case of the linear guide device 10, the following is assumed in the subsequent calculations.
The waviness of the rail track surface can be expressed as a sine wave of [Equation 7].
The contact portion between the rolling element and the raceway surface is a linear spring that is uniformly distributed on the slider raceway surface.
The following symbols are used.
x_T: Table position (x coordinate of P on table 34)
S: Distance between the centers of the two sliders 32 and 33
S_A: Distance from the point P on the table 34 to the center of the track surface of the slider 32
S_B: Distance from the point P on the table 34 to the center of the track surface of the slider 33
Δz_T: Upward displacement of table 34
Δφ_T: Displacement in the pitching direction
k_Ai: Spring coefficient per unit length of the rolling element / track surface contact portion of the i-th track surface of the slider 32
k_Bi: Spring coefficient per unit length of the rolling element / track surface contact portion of the i-th track surface of the slider 33
K_A: K for all raceway surfaces of the slider 32_AiSum of
K_B: K for all raceway surfaces of the slider 33_BiSum of
Δz_A: Displacement in the upward direction of the slider 32
Δφ_A: Displacement amount of the slider 32 in the pitching direction
Δz_B: Displacement of the slider 33 in the upward direction of the table 34
Δφ_B: Displacement amount of the slider 33 in the pitching direction
Using these, the point P on the table 34 is determined as follows.
[Expression 22]

[0073]
Further, the following equation holds from the geometric relationship.
[Expression 23]

[Expression 24]

[Expression 25]

[0074]
Then, in the same manner as in the case of the linear guide device 10, the vertical load F acting on the sliders 32 and 33._A, F_BIs as follows.
[Equation 26]

[Expression 27]

[0075]
Further, the upward external force acting on the table 34 is F._TThen, the following equation holds from the balance of forces.
[Expression 28]

[0076]
Then, the vertical displacement ΔzT of the table 34 is expressed by the following equation using the above equations [Equation 22] to [Equation 28].
[Expression 29]

[0077]
Then, according to the above equation, when the following equation holds, the table position x_TRegardless of Δz_TIs always constant.
[30]

Where m_AAnd m_BAre both integers greater than or equal to 1 (m_A= 1, 2, 3, ...; m_B= 1, 2, 3, ...).
As in the case of the linear guide device 10, even if the above equation is not strictly satisfied, L_A/ P and L_BIf / P is in the range_TCan be made sufficiently small.
[31]

[0078]
Hereinafter, a case where the rolling element dimensions of the two sliders 32 and 33 and the slider track surface effective length are all the same is considered. In this case, K_A= K_B= K_T, L_A= L_B= L_T, S_A= S_B= S / 2. Therefore, [Equation 29] is as follows.
[Expression 32]

[0079]
From the above equation, when the following equation holds, the table position x_TRegardless of Δz_TIs always constant.
[Expression 33]

Where m_TAnd n are both integers greater than or equal to 1 (m_T= 1, 2, 3,...; N = 1, 2, 3,.
As in the case of the linear guide device 10, even if the above equation is not strictly satisfied, Δz_TCan be made sufficiently small.
[Expression 34]

[0080]
On the other hand, the moment M in the pitching direction received by the sliders 32 and 33_A, M_BIs as follows.
[Expression 35]

[Expression 36]

[0081]
The pitching moment acting on the table 34 from the outside is represented by M._TThen, the following equation holds from the balance of moments.
[Expression 37]

[0082]
From the above equations [Expression 22] to [Expression 27] and the above expressions [Expression 35] to [Expression 37], the displacement in the pitching direction of the sliders 32 and 33 is expressed by the following expression.
[Formula 38]

[0083]
From the above equation, when the following equation holds, the table position x_TRegardless of Δφ_TIs always constant.
[39]

Where ξ_TAnd η_TIs the solution of the equation:
[Formula 40]

[0084]
FIG. 10 shows the relationship between ξ and η that satisfy the above equation.
For a pair of ξ and η located on the line, [Equation 40] is satisfied. For example, with respect to ξ = 1.5, if η = 0.89, 1.95, 2.97, 3.97, 4.98, 5.98, etc., [Formula 40] is satisfied. Note that due to dimensional limitations, L_TSince ≦ S, ξ ≦ η needs to be satisfied.
[0085]
As in the case of the linear guide device 10, even if the above equation is not strictly satisfied, Δφ is within the range of the following equation._TCan be made sufficiently small.
[Expression 41]

[0086]
Furthermore, if the above equations [Equation 33] and [Equation 39] are satisfied, the amount of change can be made zero (0) for both the vertical displacement and the pitching displacement of the table 34 regardless of the table position. L as_TAnd S are satisfied, both [Equation 33] and [Equation 39] are satisfied.
[Expression 42]

Where m_TAnd n are both integers greater than or equal to 1 (m_T= 1, 2, 3,...; N = 1, 2, 3,.
Even if the above equation is not strictly satisfied, L_TIf / P and S / P are in the range of the following formula, the change in posture in the vertical direction can be made sufficiently small at the same time.
[Expression 43]

[0087]
According to the table device 30 of the first embodiment, two slider track surface effective lengths L_A, L_BAnd the rail track surface wavy wavelength P is m_A-0.1 ≦ L_A/ P ≦ m_A+0.1 and m_B-0.1 ≦ L_B/ P ≦ m_ASet to +0.1.
Therefore, the relationship between the effective length of the slider track surface and the waving wavelength is determined so that the position change of the table 34 becomes almost zero regardless of the position where the table 34 moves. As a result, even if the rail track surface is wavy, the change in the posture of the table 34 can be kept small, and the influence of periodic deformation of the track surface caused by bolt fastening or the like on the motion accuracy of the table can be reduced. Can do.
[0088]
Also, the effective length L of the slider track surface when the two are the same_TAnd the rail track surface wavy wavelength P and the slider track surface center distance S are m_T-0.1 ≦ L_T/ P ≦ m_T+0.1 or n + 0.4 ≦ S / P ≦ n + 0.6 may be set. By doing so, even if the rail track surface is wavy, the change in the posture of the table 34 can be kept small, and the periodic deformation of the track surface caused by bolt fastening or the like has an effect on the motion accuracy of the table 34. Can be small.
[0089]
And ξ_T, Η_TThe equation πη_Tsinπξ_Tsinπη_T+ {Sinπξ_T−πξ_Tcosπξ_T} cosπη_T= 0 as the solution of two, the same slider track surface effective length L_TAnd the rail track surface wavy wavelength P and the slider track surface center distance S are ξ_T-0.1 ≦ L_T/ P ≦ ξ_T+0.1 and η_T−0.1 ≦ S / P ≦ η_TIt may be set to +0.1. By doing so, even if the rail track surface is wavy, the change in the posture of the table 34 can be kept small, and the periodic deformation of the track surface caused by bolt fastening or the like has an effect on the motion accuracy of the table 34. Can be small.
[0090]
In addition, two slider track surface effective length L is the same_TAnd the rail track surface wavy wavelength P and the slider track surface center distance S are m_T-0.1 ≦ L_T/ P ≦ m_T+0.1 and n + 0.4 ≦ S / P ≦ n + 0.6 may be set. Thereby, even if the rail track surface is wavy, the change in posture of the table 34 can be kept small, and the influence of periodic deformation of the track surface caused by bolt fastening or the like on the motion accuracy of the table 34 is reduced. be able to.
Furthermore, a plurality of table devices are combined into one, or the rail track surface wavy wavelength P is replaced with the guide rail mounting bolt pitch, or the rail track surface wavy wavelength P is replaced with the mounting distance of the laterally pushing plate. You may do it. Also in these cases, even if the rail raceway surface is wavy, the change in the posture of the table 34 can be kept small, and the influence of periodic deformation of the raceway surface caused by bolt fastening or the like on the motion accuracy of the table 34. Can be reduced.
[0091]
Next, a linear guide device according to a second embodiment of the present invention will be described with reference to FIG.
In the linear guide device 40 of the second embodiment, a pair of rail raceway surfaces 15 for sliding the rolling elements 13 as balls are formed on both side surfaces of the guide rail 11 so as to face the slider raceway surface 19. Two rows of rolling elements 13 are arranged.
The linear guide device 40 according to the second embodiment is similar to the first embodiment in that the wavy wavelength of the rail track surface is P, m is an integer of 1 or more, the slider track surface effective length Le, the rail track The surface wave wavelength P is set to m−0.1 ≦ Le / P ≦ m + 0.1.
And ξ_LThe equation sinπξ_L−πξ_Lcosπξ_L= 0, the rail track surface wavy wavelength P and the slider track surface effective length Le are ξ_L−0.1 ≦ Le / P ≦ ξ_LIt is set to +0.1.
[0092]
Next, a linear guide device according to a third embodiment of the present invention will be described with reference to FIG.
The linear guide device 50 according to the third embodiment has three pairs of rail track surfaces (upper grooves, middle grooves, lower grooves) 15, 15, 15 for sliding the rolling elements 13, which are balls, on both side surfaces of the guide rail 11. The slider raceway surfaces 19, 19, 19 are formed to face each other, and three rows of rolling elements 13 are arranged.
The linear guide device 50 according to the third embodiment is similar to the first embodiment in that the wavy wavelength of the rail raceway surface is P, m is an integer of 1 or more, the slider raceway surface effective length Le, and the rail track The surface wave wavelength P is set to m−0.1 ≦ Le / P ≦ m + 0.1.
And ξ_LThe equation sinπξ_L−πξ_Lcosπξ_L= 0, the rail track surface wavy wavelength P and the slider track surface effective length Le are ξ_L−0.1 ≦ Le / P ≦ ξ_LIt is set to +0.1.
[0093]
Then, the linear guide apparatus of 4th Embodiment which concerns on this invention is demonstrated using FIG.
In the linear guide device 60 according to the fourth embodiment, two pairs of rail raceway surfaces (upper grooves and lower grooves) 15 and 15 for sliding the rolling elements 13 that are cylindrical rollers are provided on both sides of the guide rail 11. 19 and 19, and two rows of rolling elements 13 are arranged.
The linear guide device 60 of the fourth embodiment is similar to the first embodiment in that the wavy wavelength of the rail track surface is P, m is an integer of 1 or more, the slider track surface effective length Le, the rail track The surface wave wavelength P is set to m−0.1 ≦ Le / P ≦ m + 0.1.
And ξ_LThe equation sinπξ_L−πξ_Lcosπξ_L= 0, the rail track surface wavy wavelength P and the slider track surface effective length Le are ξ_L−0.1 ≦ Le / P ≦ ξ_LIt is set to +0.1.
[0094]
【Example】
With respect to the linear guide device and the table device of each embodiment described above, examples and comparative examples were performed as follows.
[0095]
<Example 1>
The linear guide device used in Embodiment 1 has the same configuration as the linear guide device 10 shown in FIG.
Here, the linear guide device used in Example 1 has the following detailed numerical values.
Number of grooves: 4 grooves
Rolling element contact angle: α = 50 °
Rolling element diameter: Da = 4.7625mm
Raceway radius: r = 2.4765mm (52% of rolling element diameter)
Oversize amount: δ₀= 0.0022mm
Crowning part: Shape = arc, length Lc = 11 mm, radius Rc = 4980 mm, crowning part effective length Lce = 4.68 mm
[0096]
The crowning portion is processed with a radius Rc ′ = 3200 mm in the groove bottom direction during processing, and the radius Rc converted to the contact direction is Rc = Rc ′ / cosα = 4980 mm.
Chamfering amount of chamfered part: C = 0.2mm
Guide rail bolt pitch: P = 80mm
From [Equation 14] and [Equation 21], it is desirable that the slider raceway surface effective length is
Reduce vertical displacement: 72 ≦ Le ≦ 88 (m = 1)
152 ≦ Le ≦ 168 (m = 2)
Reduce pitching displacement: 106.4 ≤ Le ≤ 122.4 (ξ_L= 1.43)
188.0 ≦ Le ≦ 204.0 (ξ_L= 2.45)
From [Equation 5], L₁= Le- (Lc + C), so the slider body length L₁The range is as follows.
Reduce vertical displacement: 83.2 ≦ L₁≤99.2 (m = 1)
163.2 ≦ L₁≦ 179.2 (m = 2)
Reduce pitching displacement: 117.6 ≦ L₁≤133.6 (ξ_L= 1.43)
199.2 ≦ L₁≤215.2 (ξ_L= 2.45)
The following were selected as Examples 1a and 1b and Comparative Examples 1c and 1d according to the present invention.
[0097]
<Example 1a> L₁= 172 mm Conditional expression [Formula 14] for reducing vertical displacement is satisfied.
[0098]
<Example 1b> L₁= 127 mm The conditional expression [Equation 21] for reducing the pitching displacement is satisfied.
[0099]
<Comparative Example 1c> L₁= 108mm
[0100]
<Comparative Example 1d> L₁= 147mm
Regarding the above examples and comparative examples, the motion accuracy of the slider when the rail raceway surface has a undulating bolt pitch was investigated. The waviness of the guide rail can be regarded as almost a sine wave, and the half amplitude is A = 0.0005 mm.
[0101]
FIG. 14 shows the results of examining the displacement in the vertical direction accompanying the movement of the slider in Example 1a for reducing the vertical displacement and Comparative Examples 1c and 1d.
It can be seen that the displacement in the vertical direction is smaller in Example 1a than in Comparative Examples 1c and 1d.
[0102]
FIG. 15 shows the results of examining the displacement in the pitching direction accompanying the movement of the slider in Example 1b for reducing the pitching displacement and Comparative Examples 1c and 1d.
It can be seen that Example 1b has a smaller displacement in the pitching direction than Comparative Examples 1c and 1d.
<Modification of Example 1>
The linear guide device used in this modification has the same configuration as the linear guide device 50 shown in FIG.
Here, the linear guide device used in this modification has the following detailed numerical values.
Number of grooves: 6 grooves
Rolling element contact angle: α = 45 °
Rolling element diameter: Da = 4.7625mm
Radius of raceway: Vertical groove r₁= 2.428mm (51% of rolling element diameter)
Middle groove r₂= 2.571mm (54% of rolling element diameter)
Oversize amount: Vertical groove δ₀₁= 0.0075mm
Middle groove δ₀₂= 0.0046mm
Crowning part: Shape = arc, length Lc = 11mm, radius Rc = 4530mm
[0103]
The crowning portion is processed with a radius Rc ′ = 3200 mm in the groove bottom direction during processing, and the radius Rc converted into the contact direction is Rc = Rc ′ / cosα = 4530 mm.
Chamfering amount of chamfered part: C = 0.2mm
Guide rail bolt pitch: P = 40 mm Since it is smaller than that of the first embodiment, the slider overall length can be shortened.
Similar to the first embodiment, the total length of the slider is preferably in the following range.
Reduce vertical displacement: 47.2 ≦ L₁≦ 55.2 (m = 1)
87.2 ≦ L₁≤95.2 (m = 2)
127.2 ≦ L₁≦ 135.2 (m = 3)
167.2 ≦ L₁≦ 175.2 (m = 4)
Reduce pitching displacement: 64.4 ≦ L₁≤72.4 (ξ_L= 1.43)
105.2 ≦ L₁≤113.2 (ξ_L= 2.45)
146.0 ≦ L₁≤154.0 (ξ_L= 3.47)
186.4 ≦ L₁≤194.4 (ξ_L= 4.48)
The following were selected as Examples 1e and 1f and Comparative Example 1g according to the present invention.
[0104]
<Example 1e> L₁= 130 mm Conditional expression [Formula 14] for reducing the vertical displacement is satisfied.
[0105]
<Example 1f> L₁= 150 mm Satisfying conditional expression [Equation 21] for reducing the pitching displacement.
[0106]
<Comparative Example 1g> L₁= 140mm
Regarding the above examples and comparative examples, the motion accuracy of the slider when the rail raceway surface has a undulating bolt pitch was examined. The waviness of the guide rail can be regarded as almost a sine wave, and the half amplitude is A = 0.0005 mm.
[0107]
FIG. 16 shows the result of examining the displacement in the vertical direction accompanying the movement of the slider in Example 1e for reducing the vertical displacement and Comparative Example 1g.
It turns out that the displacement of Example 1e is small compared with the comparative example 1g.
[0108]
FIG. 17 shows the results of examining the displacement in the pitching direction accompanying the movement of the slider in Example 1f for reducing the pitching displacement and Comparative Example 1g.
It can be seen that Example 1f has a smaller displacement in the pitching direction than that of Comparative Example 1g.
As described above, it is possible to reduce the change in the posture of the slider due to the undulation of the track surface of the guide rail.
[0109]
<Example 2>
As shown in FIGS. 18A, 18B, 18C, and 18D, the table device used in the second embodiment has the same configuration as the linear guide device 30 shown in FIG.
Here, the table device used in Example 2 has the following detailed numerical values.
Guide rail bolt pitch: P = 80mm
Oversize amount: δ₀= 0.0068mm (Both sliders are the same)
Crowning part: shape = arc, length Lc = 6.45 mm, radius Rc = 1710 mm (both sliders are the same)
Chamfering amount of chamfered part: C = 0.2mm
The following was selected as an example according to the present invention and a comparative example not according to the present invention.
[0110]
<Example 2a> As shown in FIG. The conditional expression [Equation 31] for reducing the vertical displacement is satisfied.
Slider 32: Effective length L of raceway surface_A= 156.35mm, total length L_1A= 163mm
Slider 33: Track surface effective length L_B= 76.35mm, total length L_1B= 83mm
Distance between slider centers: S = 180mm
Where L_A/P=1.95, L_BSince / P = 0.954, [Equation 31] is satisfied (m_A= 2, m_B= 1).
[0111]
Example 2b Shown in FIG. The conditional expression [Formula 34] for reducing the vertical displacement is satisfied.
Slider 32, 33: Effective length L of raceway surface_T= 63.35mm, total length L_1T= 70mm (Both sliders are the same)
Distance between slider centers: S = 120mm
Here, since S / P = 1.5, [Equation 34] is satisfied (for n = 1).
[0112]
Example 2c As shown in FIG. The conditional expression [Equation 41] for reducing the pitching displacement is satisfied.
Slider 32, 33: Effective length L of raceway surface_T= 140.35mm, total length L_1T= 147mm (Both sliders are the same)
Distance between slider centers: S = 220mm
Where L_TSince /P=1.75 and S / P = 2.75, [Equation 41] is satisfied (ξ_T= 1.8, η_T= Against 2.75).
[0113]
<Example 2d> As shown in FIG. Conditional expression [Formula 43] for simultaneously reducing the vertical displacement and the pitching displacement is satisfied.
Slider 32, 33: Effective length L of raceway surface_T= 156.35mm, total length L_1T= 163mm (Both sliders are the same)
Distance between slider centers: S = 200mm
Where L_TSince /P=1.95 and S / P = 2.5, [Equation 43] is satisfied (m_T= 2, n = 2).
[0114]
<Comparative Example 2e> Not according to the present invention.
Slider: Track surface effective length L_T= 63.35mm, total length L_1T= 70mm (Both sliders are the same)
Distance between slider centers: S = 160mm
[0115]
<Comparative Example 2f> Not according to the present invention.
Slider: Track surface effective length L_T= 140.35mm, total length L_1T= 147mm (Both sliders are the same)
Distance between slider centers: S = 250mm
For each of the above examples and the comparative example, the motion accuracy of the slider when the rail raceway surface has a undulating bolt pitch was examined. Here, the wavy piece amplitude of the guide rail is A = 0.0005 mm.
[0116]
19, 20, 21, and 22 show the results of examining the vertical displacement associated with the movement of the sliders in Examples 2a, 2b, and 2d for reducing vertical displacement and Comparative Examples 2e and 2f.
In any of the examples, it can be seen that the displacement in the vertical direction is smaller than that of the comparative example.
[0117]
23, 24, and 25 show the results of examining the displacement in the pitching direction accompanying the movement of the slider in Examples 2c and 2d for reducing the pitching displacement and Comparative Examples 2e and 2f.
In any of the examples, it can be seen that the displacement in the pitching direction is smaller than in the comparative example.
As described above, it is possible to reduce the change in the posture of the slider due to the undulation of the track surface of the guide rail.
[0118]
<Example 3>
As shown in FIGS. 26 (a) and 26 (b), the table device used in the third embodiment has a single slider 32 having two slider raceway surfaces 32a and 32b, and a crowning portion 32c at the end. , 32c are formed. An unloaded portion 32d where the rolling elements do not receive a load is formed at the center of the slider raceway surfaces 32a and 32b.
Here, the table device used in Example 3 has the following detailed numerical values.
Effective length of each raceway: L_T= 78mm
Distance between center of raceway surface: S = 120mm
The unloaded portion 32d has a clearance of 19 μm and is processed by NC grinding simultaneously with the raceway surface including the crowning portions 32c and 32c. In this table apparatus, since the slider 32 is single, the assembly can be easily performed.
[0119]
<Example 4>
As shown in FIGS. 27A, 27B, and 27C, the table device used in the fourth embodiment has a vertical direction and a pitching direction when four sliders 32, 32, 32, and 32 are used. Both are configured to reduce the posture change. In Example 4, two combinations of the single guide rail 31 and the two sliders 32 and 32 satisfying the conditional expression [Equation 43] for simultaneously reducing the vertical displacement and the pitching displacement are arranged. One table device was constructed.
[0120]
<Example 4a> As shown in FIG. A set of a single guide rail and two sliders satisfying the conditional expression [Equation 43] was arranged side by side.
Guide rail bolt pitch: P = 80mm
Set of two sliders on the left side in the figure: Effective length of each slider raceway surface = 80mm
Distance between slider centers = 120 mm
Set of two sliders on the right side of the figure: Effective length of each slider's raceway surface = 160 mm
Distance between slider centers = 200 mm
[0121]
Example 4b Shown in FIG. A set of a single guide rail and two sliders satisfying the conditional expression [Equation 43] was arranged in a nested manner.
Guide rail bolt pitch: P = 80mm
Set of two sliders on the inside in the figure: Effective length of each slider's raceway surface = 80 mm
Distance between slider centers = 120 mm
Set of two sliders on the outside in the figure: Effective length of each slider's raceway surface = 160 mm
Distance between slider centers = 440mm
[0122]
Example 4c Shown in FIG. A set of a single guide rail and two sliders satisfying the conditional expression [Equation 43] was arranged to intersect.
Guide rail bolt pitch: P = 80mm
The left slider in the figure and the second slider from the right: Effective length of each slider's raceway surface = 80 mm
Distance between slider centers = 200 mm
In the figure, the rightmost slider and the second slider from the left: Effective length of each slider's raceway surface = 80 mm
Distance between slider centers = 200 mm
Here, in the same manner as in Examples 4a to 4c, a table device can be configured using an even number of six or more sliders.
In Examples 4a to 4c, the same effect can be obtained even if adjacent sliders are integrated to reduce the number of sliders. As a method for integrating the sliders, a plurality of sliders may be connected by a connecting member or the like, or a slider having an integral structure may be manufactured from the beginning.
[0123]
<Example 4d> As shown in FIG. Adjacent sliders (inner two) in Example 4a were made adjacent to each other and constituted by a single member.
Effective length of slider raceway surface: left = 80mm, center = 240mm, right = 160mm
Distance between slider centers: Left to center = 200 mm, center to right = 240 mm
[0124]
Example 4e As shown in FIG. Adjacent sliders (two on the left side) in Example 4b were made adjacent to each other to form a single member.
Effective length of slider raceway surface: Left = 240mm, Center = 80mm, Right = 160mm
Distance between slider centers: Left to center = 200 mm, center to right = 200 mm
[0125]
<Example 4d> As shown in FIG. Adjacent sliders (inner two) in Example 4c were made adjacent to each other to form a single member.
Effective length of slider raceway surface: left = 80mm, center = 160mm, right = 80mm
Distance between slider centers: Left to center = 160 mm, center to right = 160 mm
[0126]
Also in Example 4, the displacement in the vertical direction and the displacement in the pitching direction are small. Therefore, it is possible to reduce the change in the posture of the slider due to the waviness of the track surface of the guide rail.
[0127]
<Example 5>
As shown in FIGS. 29 and 30, the table device used in the fifth embodiment includes one table device composed of a set of a single guide rail and a slider described in the second to fourth embodiments in parallel. The table device was configured. Here, the bolt pitch of the guide rail may be the same or different for each guide rail.
[0128]
Example 5a Shown in FIG. Two table devices of Example 2d were arranged in parallel.
[0129]
<Example 5b> FIG. The table devices of Example 4a and Example 4e were arranged in parallel.
[0130]
Also in Example 5, the displacement in the vertical direction and the displacement in the pitching direction are small. Therefore, it is possible to reduce the change in the posture of the slider due to the waviness of the track surface of the guide rail.
[0131]
In addition, this invention is not limited to embodiment mentioned above, A suitable deformation | transformation, improvement, etc. are possible.
For example, the rows of rolling elements such as balls and cylindrical rollers are not limited to two rows, four rows, and six rows, and the present invention may be applied to a plurality of linear guide devices and table devices arranged in pairs.
[0132]
【The invention's effect】
As described above, according to the linear guide device of the present invention, the slider raceway surface effective length Le and the rail track surface corrugation wavelength P are set to m−0.1 ≦ Le / P ≦ m + 0.1.
Therefore, the relationship between the effective length of the slider raceway surface and the wavy wavelength is determined so that the change in the position of the slider becomes zero regardless of the position of the slider. Therefore, even if the rail track surface is wavy, the change in the posture of the slider can be kept small, and the influence of periodic deformation of the track surface caused by bolt fastening or the like on the motion accuracy of the slider can be reduced. .
[0133]
And ξ_LThe equation sinπξ_L−πξ_Lcosπξ_L= 0, the rail track surface wavy wavelength P and the slider track surface effective length Le are ξ_L−0.1 ≦ Le / P ≦ ξ_LBy setting it to +0.1, even if the rail track surface is wavy, the change in the posture of the slider can be kept small, and the periodic deformation of the track surface caused by bolt fastening affects the slider's motion accuracy. The influence can be reduced.
[0134]
Further, according to the table device of the present invention, the two slider track surface effective lengths L_A, L_BAnd the rail track surface wavy wavelength P is m_A-0.1 ≦ L_A/ P ≦ m_A+0.1 and m_B-0.1 ≦ L_B/ P ≦ m_ASet to +0.1.
Accordingly, the relationship between the effective length of the slider track surface and the waved wavelength is determined so that the position change of the table becomes almost zero regardless of the position of the table. Therefore, even if the rail track surface is wavy, the change in the posture of the table can be kept small, and the influence of periodic deformation of the track surface caused by bolt fastening etc. on the motion accuracy of the table can be reduced. .
[0135]
Also, the effective length L of the slider track surface when the two are the same_TAnd the rail track surface wavy wavelength P and the slider track surface center distance S are m_T-0.1 ≦ L_T/ P ≦ m_TBy setting to +0.1 or n + 0.4 ≦ S / P ≦ n + 0.6, even if the rail track surface is wavy, the change in the posture of the table can be kept small, which is caused by bolt fastening or the like. The influence of periodic deformation of the raceway on the motion accuracy of the table can be reduced.
[0136]
And ξ_T, Η_TThe equation πη_Tsinπξ_Tsinπη_T+ {Sinπξ_T−πξ_Tcosπξ_T} cosπη_T= 0 as the solution of two, the same slider track surface effective length L_TAnd the rail track surface wavy wavelength P and the slider track surface center distance S are ξ_T-0.1 ≦ L_T/ P ≦ ξ_T+0.1 and η_T−0.1 ≦ S / P ≦ η_TBy setting it to +0.1, even if the rail track surface is wavy, the change in the posture of the table can be kept small, and the periodic deformation of the track surface caused by bolt fastening or the like will improve the motion accuracy of the table. The influence exerted can be reduced.
[0137]
In addition, two slider track surface effective length L is the same_TAnd the rail track surface wavy wavelength P and the slider track surface center distance S are m_T-0.1 ≦ L_T/ P ≦ m_TBy setting +0.1 and n + 0.4 ≦ S / P ≦ n + 0.6, even if the rail track surface is wavy, the change in the posture of the table can be kept small. The influence of the periodic deformation of the generated track surface on the motion accuracy of the table can be reduced.
[0138]
Furthermore, a plurality of table devices can be combined into one, or the rail track surface wavy wavelength P can be replaced with the guide rail mounting bolt pitch, or the rail track surface wavy wavelength P can be replaced with the mounting distance of the lateral push plate. Even in these cases, even if the rail track surface is wavy, the change in the posture of the table can be kept small. Can be reduced.
As described above, it is possible to provide a linear guide device and a table device that can reduce the influence of periodic deformation of the rail raceway surface caused by bolt fastening or the like on the motion accuracy of the slider.
[Brief description of the drawings]
FIG. 1 is an external perspective view of a linear guide device according to a first embodiment of the present invention.
2A is a cross-sectional view of the linear guide device shown in FIG. 1, and FIG. 2B is a cross-sectional view taken along line (a-a) of FIG.
FIG. 3 is an enlarged sectional view of a slider in the linear guide device shown in FIG.
4 is an enlarged sectional view of a slider in the linear guide device shown in FIG.
FIG. 5 is an explanatory diagram of undulations on the rail track surface in the linear guide device shown in FIG. 1;
6 is a characteristic diagram of a half amplitude of a vertical displacement of a slider in the linear guide device shown in FIG.
7 is a characteristic diagram of a half amplitude of displacement in the pitching direction of the slider in the linear guide device shown in FIG.
FIG. 8 is an external perspective view of the table device according to the first embodiment of the present invention.
FIG. 9 is an explanatory diagram of corrugation of the rail track surface in the table device shown in FIG.
FIG. 10 is an explanatory diagram of conditions for setting the posture change in the pitching direction of the table to zero in the table apparatus shown in FIG.
FIG. 11 is an external perspective view of a linear guide device according to a second embodiment of the present invention.
FIG. 12 is a sectional view of a linear guide device according to a third embodiment of the present invention.
FIG. 13 is a sectional view of a linear guide device according to a fourth embodiment of the present invention.
FIG. 14 is a graph obtained by examining the vertical displacement accompanying the movement of the slider in the example of the linear guide device.
FIG. 15 is a graph in which the displacement in the pitching direction accompanying the movement of the slider in the embodiment of the linear guide device is examined.
FIG. 16 is a graph obtained by examining the vertical displacement accompanying the movement of the slider in the example of the linear guide device.
FIG. 17 is a graph in which a displacement in the pitching direction accompanying the movement of the slider in the example of the linear guide device is examined.
18A is a front view of an embodiment of the table device, FIG. 18B is a front view of the embodiment of the table device, FIG. 18C is a front view of the embodiment of the table device, and FIG. It is a front view of an Example.
FIG. 19 is a graph obtained by examining the vertical displacement accompanying the movement of the slider in the example of the table device.
FIG. 20 is a graph obtained by examining the vertical displacement accompanying the movement of the slider in the example of the table device.
FIG. 21 is a graph obtained by examining the vertical displacement accompanying the movement of the slider in the example of the table device.
FIG. 22 is a graph obtained by examining the vertical displacement associated with the movement of the slider in the example of the table device.
FIG. 23 is a graph showing the displacement in the pitching direction accompanying the movement of the slider in the example of the table device.
FIG. 24 is a graph showing the displacement in the pitching direction accompanying the movement of the slider in the example of the table device.
FIG. 25 is a graph showing the displacement in the pitching direction accompanying the movement of the slider in the example of the table device.
FIG. 26A is a front view of an embodiment of the table device, and FIG. 26B is a partial cross-sectional view of the slider of FIG.
27A is a front view of an embodiment of the table device, FIG. 27B is a front view of the embodiment of the table device, and FIG. 27C is a front view of the embodiment of the table device.
28A is a front view of an embodiment of the table device, FIG. 28B is a front view of the embodiment of the table device, and FIG. 28C is a front view of the embodiment of the table device.
FIG. 29 is an external perspective view of an embodiment of a table device.
FIG. 30 is an external perspective view of an embodiment of a table device.
FIG. 31 is an external perspective view of a conventional table device.
FIG. 32 is a front view of a measuring apparatus using a conventional table device.
33 is a front view of a measuring apparatus having a structure different from that of FIG. 32. FIG.
FIG. 34 is a front view of a conventional linear guide device.
35 is a front view of a linear guide device having a structure different from that of FIG. 34. FIG.
36 (a) and 36 (b) are front views of a linear guide device having a structure different from that shown in FIG.
37 (a), (b), and (c) are explanatory views of undulations in the linear guide device.
[Explanation of symbols]
10, 40, 50, 60 Linear guide device
11 Guide rail
12 Slider
13 Rolling elements
15 Rail track surface
19 Slider raceway surface
20 Crowning Club
21 Chamfer
30 Table device
31 guide rail
32, 33 slider
34 tables
121 Side push plate

Claims (11)

A guide rail having a rail track surface, a slider having a slider track surface disposed opposite to the rail track surface and moving along the rail track surface, and a rail between the rail track surface and the slider track surface. A linear guide device comprising rolling elements arranged freely,
When the wavy wavelength of the rail track surface is P and m is an integer of 1 or more, the effective length Le of the slider track surface and the wavy wavelength P of the rail track surface are:
m−0.1 ≦ Le / P ≦ m + 0.1
A linear guide device characterized in that it is set to. A guide rail having a rail track surface, a slider having a slider track surface disposed opposite to the rail track surface and moving along the rail track surface, and a rail between the rail track surface and the slider track surface. A linear guide device comprising rolling elements arranged freely,
Assuming that ξ _L is a solution of the equation sinπξ _L −πξ _L cosπξ _L = 0, the wavy wavelength P of the rail raceway surface and the effective length Le of the slider raceway surface are:
ξ _L −0.1 ≦ Le / P ≦ ξ _L +0.1
A linear guide device characterized in that it is set to. A single guide rail having a rail track surface, a slider having a slider track surface disposed opposite to the rail track surface and moving along the rail track surface, and the rail track surface and the slider track surface. a table device comprising a rollably disposed the rolling elements, and a table disposed on said slider between,
The slider raceway surface consists of two effective lengths L _A and L _B , where the wavy wavelength of the rail raceway surface is P, and m _A and m _B are integers of 1 or more,
The effective lengths L _A and L _B of the slider raceway surfaces and the corrugated wavelength P of the rail raceway surface are:
_A table device, wherein m _A −0.1 ≦ L _A / P ≦ m _A +0.1 and m _B −0.1 ≦ L _B / P ≦ m _B +0.1. A single guide rail having a rail track surface, a slider having a slider track surface disposed opposite to the rail track surface and moving along the rail track surface, and the rail track surface and the slider track surface. A table device comprising a rolling element arranged to be freely rollable between, and a table arranged on the slider,
The slider raceway surface is composed of two pieces having the same effective length L _T , the wavy wavelength of the rail raceway surface is P, m _T and n are integers of 1 or more, and the distance between the centers of the two slider raceway surfaces is Let S be the distance
The effective length L _T of the slider raceway surface, the wavelength P undulation of the rail raceway surfaces, the center-to-center distance S of the slider raceway surfaces,
m _T −0.1 ≦ L _T / P ≦ m _T +0.1 or n + 0.4 ≦ S / P ≦ n + 0.6
A table device characterized by being set to. A single guide rail having a rail track surface, a slider having a slider track surface disposed opposite to the rail track surface and moving along the rail track surface, and the rail track surface and the slider track surface. A table device comprising a rolling element arranged to be freely rollable between, and a table arranged on the slider,
It consists of two of said slider raceway surfaces have the same effective length L _T, the wavelength waviness of the rail track surface is P, a distance between the centers of the two sliders raceways and S, ξ _T, the eta _T As a solution to the equation πη _T sinπξ _T sinπη _T + {sinπξ _T −πξ _T cosπξ _T } cosπη _T = 0,
The effective length L _T of the slider raceway surface, the wavelength P undulation of the rail raceway surfaces, the center-to-center distance S of the slider raceway surfaces,
A table apparatus, wherein ξ _T −0.1 ≦ L _T / P ≦ ξ _T +0.1 and η _T −0.1 ≦ S / P ≦ η _T +0.1. A single guide rail having a rail track surface, a slider having a slider track surface disposed opposite to the rail track surface and moving along the rail track surface, and the rail track surface and the slider track surface. A table device comprising a rolling element arranged to be freely rollable between, and a table arranged on the slider,
It consists of two of said slider raceway surfaces have the same effective length L _T, the wavelength waviness of the rail raceway surface and P, m _T, n was an integer equal to or larger than 1, the center of the two sliders raceways Let S be the distance between
The effective length L _T of the slider raceway surface, the wavelength P undulation of the rail raceway surfaces, the center-to-center distance S of the slider raceway surfaces,
m _T −0.1 ≦ L _T / P ≦ m _T +0.1 and n + 0.4 ≦ S / P ≦ n + 0.6
A table device characterized by being set to.   A table device comprising a plurality of the table devices according to claim 6 combined into one. The linear guide device or table device according to any one of claims 1 to 7, characterized in that the wavy wavelength P of the rail track surface is set as a guide rail mounting bolt pitch. The linear guide device or the table device according to any one of claims 1 to 7, wherein a wavy wavelength P of the rail raceway surface is set as a mounting interval of the lateral pushing plate. Chamfered portion is formed on an end portion of the slider raceway surface, the entire length of the slider raceway surface and L _1, the length of the chamfered portion is C, as the effective length Le of the slider raceway surfaces,
Le = L ₁ -2C
The linear guide device or the table device according to claim 1, wherein the linear guide device or the table device is used. A crowning portion is formed near the end of the slider raceway surface, and a chamfered portion is formed at the end of the crowning portion,
The total length of the slider raceway surface and L _1, the length of the crowning portion and L _C, the length of the chamfered portion is C, as the effective length Le of the slider raceway surfaces,
Le = L ₁ − (L _C + C)
The linear guide device or the table device according to claim 1, wherein the linear guide device or the table device is used.

Images