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目次へ はすば歯車の計算[JGMA規格] |
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はすば歯車の計算[JGMA規格] |
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並歯 |
圧力角α0[deg] |
ﾓｼﾞｭｰﾙm |
歯数 Z |
回転数
n |
有効歯幅 B |
材料 |
歯面硬度 |
転位係数x |
ねじれ角β0[deg] |
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[rpm] |
[mm] |
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1 |
小歯車 |
20 |
4 |
20 |
1500 |
20 |
SCM415_浸炭 |
Hv500 |
0 |
20 |
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SCM415 |
2 |
8 |
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2 |
大歯車 |
40 |
750 |
SCM415_浸炭 |
Hv500 |
0 |
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SCM415 |
2 |
28 |
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●ピッチ円周上の周速 v (m/s) |
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v=π*d01*n1/(1000*60)=π*85.134*1500/(1000*60)=6.686[m/s] |
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●小歯車:曲げ強さによる接線力 |
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●トルク T [N-m] |
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F=σ0*m*B*KL*Kfx/(Yf*Yε*Yβ*Kv*K0*Sf) |
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T=F*D1/2000=13963*85.134/2000=594.36[N-m] |
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=416.5*4*20*1*1/(2.66*0.534*1*1.4*1*1.2)=13963[N] |
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Yf=歯形係数[30°接線法による]= |
2.66 |
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Yε=荷重分配係数=1/εa= |
0.534 |
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●スラスト Fx [N] |
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εa=正面かみ合い率= |
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1.872 |
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Fx=F*tan(β)=13963*tan(20)=5082.12[N] |
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Yβ=ねじれ角係数= |
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1 |
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KL=寿命係数= |
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1 |
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Kfx=歯元応力に対する寸法係数= |
1 |
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Kv=動荷重係数= |
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1.4 |
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K0=過負荷係数= |
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1 |
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Sf=歯元曲げ破損に対する安全率= |
1.2 |
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σ0=許容歯元曲げ応力= |
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416.5 |
[N/mm2] |
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●大歯車:曲げ強さによる接線力 |
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●トルク T [N-m] |
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F=σ0*m*B*KL*Kfx/(Yf*Yε*Yβ*Kv*K0*Sf) |
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T=F*D2/2000=15872*170.268/2000=1351.25[N-m] |
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=416.5*4*20*1*1/(2.34*0.534*1*1.4*1*1.2)=15872[N] |
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●スラスト Fx [N] |
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Yf=歯形係数[30°接線法による]= |
2.34 |
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Fx=F*tan(β)=15872*tan(20)=5776.94[N] |
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σ0=許容歯元曲げ応力= |
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416.5 |
[N/mm2] |
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●小歯車面圧強さによる接線力 |
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F=σh0^2*d01*B*[i/(i+1)]*[KHL*ZL*Zr*Zv*Zw*Khx/(Zh*Zm*Zε*Zβ)]^2/(Khβ*Kv*K0*Sh^2) |
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=1607^2*85.134*20*(2/(2+1))*(1*1*0.9*0.99*1*1/(2.36*189.8*1*1))^2/(1.025*1.4*1*1.15^2) |
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=6112[N] |
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σh0=許容ヘルツ応力= |
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1607 |
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d01=小歯車ピッチ円径= |
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85.134 |
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i=歯数比=Z2/Z1= |
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2 |
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Zh=領域係数= |
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2.36 |
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●トルク T [N-m] |
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Zm=材料定数係数= |
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189.8 |
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T=F*D1/2000=6112*85.134/2000=260.17[N-m] |
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Zε=かみあい率係数= |
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1 |
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Zβ=ねじれ角係数= |
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1 |
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●スラスト Fx [N] |
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KHL=寿命係数= |
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1 |
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Fx=F*tan(β)=6112*tan(20)=2224.59[N] |
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ZL=潤滑油係数 |
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1 |
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Zr=粗さ係数 |
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0.9 |
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Zv=潤滑速度係数 |
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0.99 |
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Zw=硬さ比係数 |
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1 |
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Khx=寸法係数 |
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1 |
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Khβ=荷重分布係数 |
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1.025 |
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Kv=動荷重係数 |
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1.4 |
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K0=過負荷係数 |
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1 |
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Sh=安全率 |
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1.15 |
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●大歯車面圧強さによる接線力 |
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F=σh0^2*d01*B*[i/(i+1)]*[KHL*ZL*Zr*Zv*Zw*Khx/(Zh*Zm*Zε*Zβ)]^2/(Khβ*Kv*K0*Sh^2) |
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=1607^2*85.134*20*(2/(2+1))*(1*1*0.9*0.99*1*1/(2.36*189.8*1*1))^2/(1.025*1.4*1*1.15^2) |
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=6112[N] |
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σh0=許容ヘルツ応力= |
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1607 |
[N/mm2] |
●トルク T [N-m] |
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d01=小歯車ピッチ円径= |
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T=F*D2/2000=6112*170.268/2000=520.34[N-m] |
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ZL=潤滑油係数= |
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1 |
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●スラスト Fx [N] |
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Fx=F*tan(β)=6112*tan(20)=2224.59[N] |
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●伝達動力 |
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P=F*v/1000=6112*6.686/1000=40.86[kW] |
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v=ピッチ円上の周速= |
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6.686 |
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F=ピッチ円上の許容円周力= |
6112 |
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